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Maximise the impact of new approaches and practices.

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Updated Metacognition and Self-Regulated Learning Guidance Report

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Updated Metacognition and Self-Regulated Learning Guidance Report

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7.  Frontiers in Psychology; Kluger, A. N., & DeNisi, A. (1996). The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychological Bulletin, 119(2), 254–284 

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7.  Frontiers in Psychology; Kluger, A. N., & DeNisi, A. (1996). The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychological Bulletin, 119(2), 254–284 

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6. Shute, V. (2007), Focus on Formative Feedback, Education Teaching Service, p.1. See also, Shute, V (2008), Focus on Formative Feedback, Review of Educational Research 78(1), 153–189. 

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6. Shute, V. (2007), Focus on Formative Feedback, Education Teaching Service, p.1. See also, Shute, V (2008), Focus on Formative Feedback, Review of Educational Research 78(1), 153–189. 

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www.researchgate.net needs to review the security of your connection before proceeding.

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5. Wiliam, D (2018), Feedback, At the Heart of—But Definitely Not All of—Formative Assessment, in Lipnevich, A and Smith, J, (2018) The Cambridge Handbook of Instructional Feedback, Cambridge University Press, p.15 

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5. Wiliam, D (2018), Feedback, At the Heart of—But Definitely Not All of—Formative Assessment, in Lipnevich, A and Smith, J, (2018) The Cambridge Handbook of Instructional Feedback, Cambridge University Press, p.15 

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4b. Newman, M et al (2021, in press), A Systematic Review of Feedback Approaches in the Classroom, EEF; EEF Teaching and Learning Toolkit; 

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4b. Newman, M et al (2021, in press), A Systematic Review of Feedback Approaches in the Classroom, EEF; EEF Teaching and Learning Toolkit; 

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4a. Wisniewski B, Zierer K, Hattie J (2020). The Power of Feedback Revisited: A Meta-Analysis of Educational Feedback Research. Frontiers in Psychology. 

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4a. Wisniewski B, Zierer K, Hattie J (2020). The Power of Feedback Revisited: A Meta-Analysis of Educational Feedback Research. Frontiers in Psychology. 

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The Power of Feedback Revisited: A Meta-Analysis of Educational Feedback Research

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A meta-analysis (435 studies, k = 994, N > 61,000) of empirical research on the effects of feedback on student learning was conducted with the purpose of replicating and expanding the Visible Learning research (Hattie and Timperley, 2007; Hattie, 2009; Hattie and Zierer, 2019) from meta-synthesis. Overall results based on a random-effects model indicate a medium effect (d = 0.48) of feedback on student learning, but the significant heterogeneity in the data shows that feedback cannot be understood as a single consistent form of treatment. A moderator analysis revealed that the impact is substantially influenced by the information content conveyed. Furthermore, feedback has higher impact on cognitive and motor skills outcomes than on motivational and behavioral outcomes. We discuss these findings in the light of the assumptions made in The power of feedback (Hattie and Timperley, 2007). In general, the results suggest that feedback has rightly become a focus of teaching research and practice. However, they also point toward the necessity of interpreting different forms of feedback as independent measures.

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3. Dann, R (2018), Developing Feedback for Pupil Learning, Teaching, Learning and Assessment in Schools, Routledge. p.45. 

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3. Dann, R (2018), Developing Feedback for Pupil Learning, Teaching, Learning and Assessment in Schools, Routledge. p.45. 

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2. Stiggins, R. J., Arter, J. A., Chappuis, J. and Chappuis, J. (2004) Classroom Assessment for Student Learning, Assessment Training Institute, p.17. 

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2. Stiggins, R. J., Arter, J. A., Chappuis, J. and Chappuis, J. (2004) Classroom Assessment for Student Learning, Assessment Training Institute, p.17. 

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1. Kulhavy, R. W. (1977) Feedback in Written Instruction, Review of Educational Research, 47 (2, 211–232) p.211. 

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1. Kulhavy, R. W. (1977) Feedback in Written Instruction, Review of Educational Research, 47 (2, 211–232) p.211. 

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all school leaders understand the importance of providing meaningful feedback. done well

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and thereby closing the gap between where a pupil is and where the teacher wants them to be.  however

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not all feedback has positive effects. done badly

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feedback can even harm progress. nor is feedback ‘free’. large amounts of time are spent providing pupils with feedback

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perhaps not always productively.  historically

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much consideration has been given to the methods by which feedback is delivered. specifically

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or should it be verbal? this guidance report aims to move beyond this and focus on what really matters: the principles of good feedback rather than the written or verbal methods of feedback delivery.  the guidance report is based on the best available international evidence

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in addition to a review of current practice

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and refined through consultation with teachers and other experts.

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Teacher Feedback to Improve Pupil Learning

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Six recommendations for using teacher feedback to improve pupil learning

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49.  . Siraj-Blatchford, I. (2005) ‘Quality Interactions in the Early Years’. Presented at: TACTYC Annual Conference, Cardiff

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49.  . Siraj-Blatchford, I. (2005) ‘Quality Interactions in the Early Years’. Presented at: TACTYC Annual Conference, Cardiff

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48. Gelman, R. and Gallistel, C. (1978) The Child’s Understanding of Number, Cambridge,MA: Harvard University Press

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48. Gelman, R. and Gallistel, C. (1978) The Child’s Understanding of Number, Cambridge,MA: Harvard University Press

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47. Outhwaite, L. A. et al. (2018) ‘Raising Early Achievement in Math with Interactive Apps: A Randomized Control Trial.’ Journal of Educational Psychology (advance online publication)

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47. Outhwaite, L. A. et al. (2018) ‘Raising Early Achievement in Math with Interactive Apps: A Randomized Control Trial.’ Journal of Educational Psychology (advance online publication)

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46. . Nunes, T., Malmberg, L. E., Evans, D., Sanders-Ellis,D., Baker, S., Barros, R., Bryant, P. and Evangelou, M.(2019) ‘One billion: Evaluation Report’, London: EEF

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46. . Nunes, T., Malmberg, L. E., Evans, D., Sanders-Ellis,D., Baker, S., Barros, R., Bryant, P. and Evangelou, M.(2019) ‘One billion: Evaluation Report’, London: EEF

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45. Nunes, T., Barros, R., Evangelou, M., Strand, S.,Mathers, S. and Sanders-Ellis, D. (2018) ‘1stClass@Number: Evaluation report’, London: EEF.

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45. Nunes, T., Barros, R., Evangelou, M., Strand, S.,Mathers, S. and Sanders-Ellis, D. (2018) ‘1stClass@Number: Evaluation report’, London: EEF.

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44.  . Institute for Effective Education (2018) ‘Evidence 4Impact’. 

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44.  . Institute for Effective Education (2018) ‘Evidence 4Impact’. 

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What is Evidence 4 Impact?

Evidence 4 Impact (E4I) is an independent service that provides teachers and school leaders with accessible information on which educational interventions have been shown to be effective.

E4I supports educators in using evidence-based practice in order to improve outcomes for children.

See how it works View all interventions

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Effective educational intervention database - Evidence 4 Impact

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E4I is a service that provides teachers and schools with accessible information on which educational interventions have been shown to be effective.

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The EEF is an independent charity dedicated to breaking the link between family income and educational achievement.

# data[].attributes.headline
42. EEF (2019) ‘Using Digital Technology to Improve Learning’.

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42. EEF (2019) ‘Using Digital Technology to Improve Learning’.

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41. EEF (2015) ‘Making Best Use of Teaching Assistants’. 

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41. EEF (2015) ‘Making Best Use of Teaching Assistants’. 

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40. Pellegrini, M., Inns, A. and Slavin, R. (2018, March)‘Effective Programs in Elementary Mathematics: A Best Evidence Synthesis’, paper presented at the annual meeting of the Society for Research on Educational Effectiveness, Washington, DC.

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40. Pellegrini, M., Inns, A. and Slavin, R. (2018, March)‘Effective Programs in Elementary Mathematics: A Best Evidence Synthesis’, paper presented at the annual meeting of the Society for Research on Educational Effectiveness, Washington, DC.

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39. Dietrichson, J., Bøg, M., Filges, T. and Klint Jørgensen,A.-M. (2017) ‘Academic Interventions for Elementary and Middle School Students with Low Socioeconomic Status: A Systematic Review and Meta-Analysis’, Review of Educational Research, 87 (2), pp. 243–282.

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39. Dietrichson, J., Bøg, M., Filges, T. and Klint Jørgensen,A.-M. (2017) ‘Academic Interventions for Elementary and Middle School Students with Low Socioeconomic Status: A Systematic Review and Meta-Analysis’, Review of Educational Research, 87 (2), pp. 243–282.

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38. Gelman, R. and Meck, E. (1983) ‘Preschoolers’Counting: Principles Before Skill’, Cognition, 13, pp.343–359.

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38. Gelman, R. and Meck, E. (1983) ‘Preschoolers’Counting: Principles Before Skill’, Cognition, 13, pp.343–359.

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37.Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T.,Jordan, A., Klusman, U., Krauss, S., Neubrand, S. and Tsai, Y-M. (2010) ‘Teachers’ Mathematical Knowledge,Cognitive Activation in the Classroom, and Student Progress’, American Educational Research Journal, 47(1) pp. 133–180. d

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37.Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T.,Jordan, A., Klusman, U., Krauss, S., Neubrand, S. and Tsai, Y-M. (2010) ‘Teachers’ Mathematical Knowledge,Cognitive Activation in the Classroom, and Student Progress’, American Educational Research Journal, 47(1) pp. 133–180. d

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36. Thomas, N. D., Mulligan, J. T. and Goldin, G. A.(2002) ‘Children’s Representation and Structural Development of the Counting Sequence 1–100’, Journal of Mathematical Behavior, 21, pp. 117–133

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36. Thomas, N. D., Mulligan, J. T. and Goldin, G. A.(2002) ‘Children’s Representation and Structural Development of the Counting Sequence 1–100’, Journal of Mathematical Behavior, 21, pp. 117–133

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35. Sung, W., Ahn, J. and Black, J. B. (2017) ‘Introducing Computational Thinking to Young Learners: Practicing Computational Perspectives through Embodiment in Mathematics Education’, Technology, Knowledge and Learning, 22 (3), pp. 443–463.

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35. Sung, W., Ahn, J. and Black, J. B. (2017) ‘Introducing Computational Thinking to Young Learners: Practicing Computational Perspectives through Embodiment in Mathematics Education’, Technology, Knowledge and Learning, 22 (3), pp. 443–463.

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34. Carbonneau, K. J., Marley, S. and Selig, J. P. (2013) ‘A Meta-Analysis of the Efficacy of Teaching Mathematics with Concrete Manipulatives’, Journal of Educational Psychology, 105 (2), pp. 380–400

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34. Carbonneau, K. J., Marley, S. and Selig, J. P. (2013) ‘A Meta-Analysis of the Efficacy of Teaching Mathematics with Concrete Manipulatives’, Journal of Educational Psychology, 105 (2), pp. 380–400

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33. Griffiths, R., Back, J. and Gifford, S. (2016) Making Numbers: Using Manipulatives to Teach Arithmetic,Oxford: Oxford University Press.

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33. Griffiths, R., Back, J. and Gifford, S. (2016) Making Numbers: Using Manipulatives to Teach Arithmetic,Oxford: Oxford University Press.

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Manipulatives are objects that can be handled and moved. These range from everyday items such as buttons and shells, to resources like abacuses, Cuisenaire rods, and Dienes blocks.

Research in teaching arithmetic to young children suggests that manipulatives can support mathematical development. However, the most effective ways to use manipulatives are not clearly understood by teachers, and so they are often under-used.

This study explored the learning and teaching of basic arithmetic for children aged 3 to 9, focusing on the effective use of manipulatives. The researchers reviewed current and historical research and practice. They then developed detailed exemplars of good practice together with teachers and children. The culmination of this work is an excellent handbook for teachers that is based upon the latest evidence from research.

Making Numbers shares examples of good practice in the use of manipulatives to help children develop mastery of counting, place value and calculation. The book is supported by a series of innovative animations and a short booklet that illustrate approaches to exploring numbers in a creative way.

These resources seek to support teachers as reflective practitioners, while also being of practical value to teachers and enhancing learning opportunities for pupils.

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Using manipulatives in the foundations of arithmetic - Nuffield Foundation

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Manipulatives are objects that can be handled and moved. These range from everyday items...

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32 National Centre for Excellence in the Teaching of Mathematics (2014). ‘Curriculum Glossary’.  

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32 National Centre for Excellence in the Teaching of Mathematics (2014). ‘Curriculum Glossary’.  

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31. Robinson-Smith, L., Fairhurst, C., Stone, G., Bell, K.,Elliott, L., Gascoine, L., Hallett, S., Hewitt, C., Hugill, J.,Torgerson, C., Torgerson, D., Menzies, V. and Ainsworth,H. (2018) ‘Maths Champions: Evaluation Report’,London: EEF 

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31. Robinson-Smith, L., Fairhurst, C., Stone, G., Bell, K.,Elliott, L., Gascoine, L., Hallett, S., Hewitt, C., Hugill, J.,Torgerson, C., Torgerson, D., Menzies, V. and Ainsworth,H. (2018) ‘Maths Champions: Evaluation Report’,London: EEF 

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30. McCray, S., Chen, J., Eisenband-Sorkin, J. (2018)Growing Mathematical Minds: Conversations Between Developmental Psychologists and Early Childhood Teachers, New York: Routledge.

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30. McCray, S., Chen, J., Eisenband-Sorkin, J. (2018)Growing Mathematical Minds: Conversations Between Developmental Psychologists and Early Childhood Teachers, New York: Routledge.

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Growing Mathematical Minds is the documentation of an innovative, bi-directional process of connecting research and practice in early childhood mathematics. The book translates research on early mathematics from developmental psychology into terms that are meaningful to teachers and readily applicable in early childhood classrooms. It documents teacher responses, and conveys their thoughts and questions back to representative researchers, who reply in turn.

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29. Deans for Impact (2019) ‘The Science of Early Learning:How Young Children Develop Agency, Numeracy,and Literacy’, Austin, TX: Deans for Impact 

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29. Deans for Impact (2019) ‘The Science of Early Learning:How Young Children Develop Agency, Numeracy,and Literacy’, Austin, TX: Deans for Impact 

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28.  Siraj-Blatchford, I., Taggart, B., Sylva, K., Sammons, P.and Melhuish, E. (2008) ‘Towards the Transformation of Practice in Early Childhood Education: The Effective Provision of Pre‐School Education (EPPE) Project’,Cambridge Journal of Education, 38 (1), pp. 23–36. 

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28.  Siraj-Blatchford, I., Taggart, B., Sylva, K., Sammons, P.and Melhuish, E. (2008) ‘Towards the Transformation of Practice in Early Childhood Education: The Effective Provision of Pre‐School Education (EPPE) Project’,Cambridge Journal of Education, 38 (1), pp. 23–36. 

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27. . Department for Children, Schools and Families (2009)Learning, Playing and Interacting – Good Practice in the Early Years Foundation Stage. h

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27. . Department for Children, Schools and Families (2009)Learning, Playing and Interacting – Good Practice in the Early Years Foundation Stage. h

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26.  Worth, J., Sizmur, J., Ager, R. and Styles, B. (2015)‘Improving Numeracy and Literacy: Evaluation report’,London: EEF

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26.  Worth, J., Sizmur, J., Ager, R. and Styles, B. (2015)‘Improving Numeracy and Literacy: Evaluation report’,London: EEF

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25.  Stokes, L., Hudson-Sharp, N., Dorsett, R. et al. (2018)‘Mathematical Reasoning: Evaluation report’, London: EEF

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25.  Stokes, L., Hudson-Sharp, N., Dorsett, R. et al. (2018)‘Mathematical Reasoning: Evaluation report’, London: EEF

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24. Ramani, G. B. and Siegler, R. S. (2011) ‘Reducing the Gap in Numerical Knowledge Between Low- and Middle-Income Preschoolers’, Journal of Applied Developmental Psychology, 32 (3), pp. 146–159

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24. Ramani, G. B. and Siegler, R. S. (2011) ‘Reducing the Gap in Numerical Knowledge Between Low- and Middle-Income Preschoolers’, Journal of Applied Developmental Psychology, 32 (3), pp. 146–159

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23. Purpura, D. J., Napoli, A. R., Wehrspann, E. A. and Gold, Z. S. (2017) ‘Causal Connections Between Mathematical Language and Mathematical Knowledge:A Dialogic Reading Intervention’, Journal of Research on Educational Effectiveness, 10 (1), pp. 116–137.

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23. Purpura, D. J., Napoli, A. R., Wehrspann, E. A. and Gold, Z. S. (2017) ‘Causal Connections Between Mathematical Language and Mathematical Knowledge:A Dialogic Reading Intervention’, Journal of Research on Educational Effectiveness, 10 (1), pp. 116–137.

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22. Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M.,Jordan, N. C. and McDowell, J. (2013) Teaching Mathto Young Children: A Practice Guide (NCEE 2014-4005), Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. 

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22. Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M.,Jordan, N. C. and McDowell, J. (2013) Teaching Mathto Young Children: A Practice Guide (NCEE 2014-4005), Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. 

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21. Cross, C. T., Woods , T. A. and Schweingruber, H.(2009) Mathematics Learning in Early Childhood:Paths Towards Excellence and Equity, Washington DC: National Academies Press

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21. Cross, C. T., Woods , T. A. and Schweingruber, H.(2009) Mathematics Learning in Early Childhood:Paths Towards Excellence and Equity, Washington DC: National Academies Press

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# data[].attributes.attachment_link.authors[].name
Division of Behavioral and Social Sciences and Education

# data[].attributes.attachment_link.title
Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity

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Read online, download a free PDF, or order a copy in print or as an eBook.

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20. National Centre for Excellence in the Teaching of Mathematics (2019) ‘Early Years’

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20. National Centre for Excellence in the Teaching of Mathematics (2019) ‘Early Years’

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Early Years materials designed to support Reception teachers (those working with 4-5 year olds)

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19. Clements, Douglas H. and Sarama, Julie (2014) Learning and Teaching Early Math: The Learning Trajectories Approach (2nd edn), Studies in Mathematical Thinking and Learning Series, London: Routledge. Also see

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19. Clements, Douglas H. and Sarama, Julie (2014) Learning and Teaching Early Math: The Learning Trajectories Approach (2nd edn), Studies in Mathematical Thinking and Learning Series, London: Routledge. Also see

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18. Pirie, S. E. B. and Kieren, T. E. (1994) ‘Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It? Educational Studies in Mathematics, 26, pp. 165–190.

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18. Pirie, S. E. B. and Kieren, T. E. (1994) ‘Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It? Educational Studies in Mathematics, 26, pp. 165–190.

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Abstract

There has been a variety of approaches to the study of mathematical understanding, and some of these are reviewed before outlining the background to the model we are proposing for the growth of such understanding. The model is explained in detail and illustrated with reference to the concept of fractions. Key features of the model include 'don't need' boundaries, 'folding back', and the complementarities of 'acting' and 'expressing' that occur at each level of understanding. The theory is illustrated by examples of pupils' work from a variety of topics and stages. Finally one of the practical applications of the theory, mapping, is explained in some detail.

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References

Kieren, T. E. and Pirie, S. E. B.: 1992, 'Rational and fractional numbers: From quotient fields to recursive understanding', in T. P. Carpenter and E. Fennema (eds.), Learning, Teaching, andAsessing Rational Number Concepts: Multiple Research Perspectives, Lawrence Erlbaum Associates, Hillsdale, N.J., pp. 49-82.

Google Scholar

Kieren, T. E. and Pirie, S. E. B.: 1991, 'Recursion and the mathematical experience', in L. Steife (ed.), The Epistemology of Mathematical Experience, Springer Verlag Psychology Series, New York, pp. 78-101.

CrossRef Google Scholar

Pirie, S. E. B. and Newman, C. F.: 1990, 'Watching understanding grow', paper presented at the Midlands Mathematics Education Seminar, University of Birmingham.

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Pine, S. E. B. and Kieren, T. E.: 1990, 'A recursive theory for mathematical understanding - some elements and implications', paper presented at AERA annual meeting, Boston.

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Tomm, K.: 1989, 'Consciousness and Intentionality in the Work of Humberto Maturana', apresentation for the Faculty of Education, University of Alberta.

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Author information

Authors and Affiliations

1. Mathematics Education Research Centre, University of Oxford, Oxford, Great Britain, OX2 6PY

Susan Pirie

2. University of Alberta, Edmonton, Alberta, Canada, T6G 2G5

Thomas Kieren

Editor information

Editors and Affiliations

Peabody College, Vanderbilt University, 37203, Nashville, Tennessee, USA

Paul Cobb

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© 1994 Springer Science+Business Media Dordrecht

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Pirie, S., Kieren, T. (1994). Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It?. In: Cobb, P. (eds) Learning Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2057-1_3

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# data[].attributes.attachment_link.title
Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It?

# data[].attributes.attachment_link.description
There has been a variety of approaches to the study of mathematical understanding, and some of these are reviewed before outlining the background to the model we are proposing for the growth of such understanding. The model is explained in detail and illustrated with...

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17. EEF (2018) ‘Metacognition and self-regulated learning’

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17. EEF (2018) ‘Metacognition and self-regulated learning’

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16. Rittle-Johnson, B., Saylor, M. and Swygert, K. E. (2008)‘Learning from Explaining: Does it Matter if Mom is Listening?’, Journal of Experimental Child Psychology,100, pp. 215–224

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16. Rittle-Johnson, B., Saylor, M. and Swygert, K. E. (2008)‘Learning from Explaining: Does it Matter if Mom is Listening?’, Journal of Experimental Child Psychology,100, pp. 215–224

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15. Higgins, S. et al. (2017) Early Years Toolkit |Self regulation strategies, London: EEF

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15. Higgins, S. et al. (2017) Early Years Toolkit |Self regulation strategies, London: EEF

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14. . Dowker, A., Cheriton, O., Horton, R. and Mark, W. (2019)‘Relationships Between Attitudes and Performance in Children’s Mathematics’, Educational Studies in Mathematics, 100, p. 211

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14. . Dowker, A., Cheriton, O., Horton, R. and Mark, W. (2019)‘Relationships Between Attitudes and Performance in Children’s Mathematics’, Educational Studies in Mathematics, 100, p. 211

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Relationships between attitudes and performance in young children's mathematics

Abstract

Most studies of children's attitudes to mathematics have dealt with children in second grade or later, and have suggested that attitudes deteriorate, and anxiety increases with age. The present study investigated attitudes to mathematics in 67 English and 49 Chinese children at the end of their first year of school. The participants were given Thomas and Dowker's ( 2000) Mathematics Attitude Questionnaire, which uses pictorial rating scales to assess primary school children's mathematics anxiety, liking for mathematics, unhappiness at poor performance in mathematics, and self-rating in mathematics. They were also given the British Abilities Scales Basic Number Skills test. Attitudes were generally positive, though not more so than previously found for older primary school children. The Chinese children performed better in the arithmetic test and also rated themselves higher than the English children, but did not differ in other attitudes. Self-rating in mathematics and lack of unhappiness at poor performance were associated with better performance in the English group. There were no significant relationships between attitudes and performance in the Chinese group. Implications of the findings are discussed.

1 Introduction: theoretical and empirical background

There has been much recent interest in attitudes to arithmetic, and especially in mathematics anxiety (Carey, Hill, Devine, & Szucs, 2016; Dowker, Sarkar, & Looi, 2016). This research has shown that mathematical ability is dependent not only on cognitive abilities such as IQ and working memory but also on emotional factors and attitudes toward mathematics. Thus, exploring the development of attitudes and emotions with respect to mathematics is an especially important area of research. In particular, it is important to study the relations between attitudes and performance, which attitudes are particularly important to performance, and when these relations may emerge.

Mathematics anxiety is the attitude that has received most attention in previous research. It has been defined as a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems (Richardson & Suinn, 1972). It could be argued that this should not be classified as an attitude, as anxiety is predominantly emotional rather than evaluative. While acknowledging possible controversy on this issue, we here follow some previous researchers, such as Ma and Kishor ( 1997) in treating mathematics anxiety as an attitude. Many theories of attitudes incorporate affective components: e.g. Breckler's ( 1984) ABC model; and mathematics anxiety is thought to include both cognitive and affective components. Wigfield and Meece ( 1988) distinguish between a predominantly cognitive "worry" component, involving mathematics performance anxiety and a predominantly affective component, involving negative emotions in the presence of mathematical stimuli. The present paper deals predominantly with the cognitive "worry" component.

One reason why mathematics anxiety has received so much attention is because of its negative association with mathematical performance. Higher levels of mathematical anxiety have been linked to lower performance in high school tests, lower enjoyment of mathematics, and decreased motivation to take advanced mathematics courses (Hembree, 1990; Ma & Kishor, 1997).

Several different explanations have been proposed for the relation between mathematics anxiety and mathematical performance. One explanation for the negative relation is that high mathematical anxiety leads to avoidance of mathematics-related activities, affording less opportunity for practice (Ashcraft, 2002). Another theory is that higher levels of mathematical anxiety lead to greater mental rumination and preoccupying thoughts, and that this consumes working memory resources (Eysenck, 1992).

The relation between mathematics anxiety and performance seems to be bidirectional. In addition to mathematics anxiety having a negative impact on mathematics performance, poor performance in mathematics is also likely to increase anxiety (Ganley & Lubienski, 2016; Maloney & Beilock, 2012; Maloney, Ansari, & Fugelsang, 2011). Longitudinal studies provide evidence for both types of relation. For example, Ma and Xu ( 2004) found evidence of stronger correlations between performance and mathematical anxiety than between anxiety and performance across time. On the other hand, Cargnelutti, Tomasetto, and Passolunghi ( 2017), in a longitudinal study of progression from second to third grade, found a stronger predictive relation of mathematics anxiety to performance than the other way around. Thus, there is evidence that mathematical anxiety both influences and is influenced by performance. Jansen et al. ( 2013) argue that this leads to a vicious cycle where higher anxiety can lead to suboptimal strategy use or avoidance behaviour, which might then negatively impact performance and increase anxiety.

Most studies of attitudes to mathematics and mathematics anxiety have been done in secondary school children and adults. This leaves a significant gap in knowledge regarding when and how positive and negative feelings toward mathematics develop. Understanding this could potentially help to encourage the development of positive attitudes toward mathematics, and to prevent or reduce mathematics anxiety. Fortunately, in recent years, several scales have been developed to assess primary school children's attitudes to mathematics (Adelson & McCoach, 2011; Dowker, Bennett, & Smith, 2012; Ganley & McGraw, 2016; Harari, Vukovic, & Bailey, 2013; Jameson, 2013; Ramirez, Gunderson, Levine, & Beilock, 2013; Wu, Barth, Amin, Malcarne, & Menon, 2012).

On the whole, studies suggest that primary school children's attitudes to mathematics tend to be positive, but that they deteriorate with age during childhood and adolescence (Gierl & Bisanz, 1995; Krinzinger, Kaufmann, & Willmes, 2009; Ma & Kishor, 1997; Wigfield & Meece, 1988). However, some studies (e.g. Jameson, 2013, 2014) have elicited evidence of early-developing mathematics anxiety. In some studies, even first-graders have been shown to report and demonstrate mathematics anxiety (Jameson, 2014; Ma & Kishor, 1997; Ramirez et al., 2013; Vukovic, Kieffer, Bailey, & Harari, 2013). Petronzi ( 2016) reported significant mathematics anxiety in children as young as five. In contrast with the general findings showing deterioration in attitudes with age, Sorvo et al. ( 2017) found that Finnish children in Year 2 showed greater anxiety in Year 2 than children in later elementary grades.

Although mathematics anxiety dominates studies of attitudes of mathematics, other attitudes are also potentially important and are investigated in the present study. For example, there is evidence that experiences of failure and resulting discouragement are contributory factors to the development of mathematics anxiety (Maloney et al., 2011). Thus, it is important to study the extent to which children experience unhappiness in response to episodes of failure in, or inability to perform, a mathematical task. Though likely to be associated with mathematics anxiety, it is not identical with it, since it refers to unhappiness in response to failure rather than anxiety in anticipation of failure. For example, a child may generally anticipate success in mathematics, and not experience much anxiety, but be distressed on those occasions when they do experience failure. We wished to investigate whether mathematics anxiety and unhappiness at failure might have different associations with mathematical performance.

Most studies have focused on the more negative attitudes to mathematics, especially anxiety. However, positive attitudes such as enjoyment of mathematics and self-confidence in mathematics are also important topics to study, and cannot be reduced to the simple absence of anxiety.

Confidence in one's own mathematical ability is usually found to be positively related to performance (Abed & Alkhateeb, 2000; Pinxten, Marsh, DeFraine, Van den Noortgate, & Van Damme, 2014). Indeed, some studies suggest that in primary school children, mathematical performance may correlate more with self-rating than with anxiety (Dowker et al., 2012; Krinzinger et al., 2009; Wood et al., 2012) and that at all ages it may have a significant mediating role for the relations between mathematical performance and anxiety and other attitudes (Pinxten et al., 2014; Van der Beek, Van der Ven, Kroesbergen, & Leseman, 2017). Most studies show a decline in self-rating with age (House, 2006; Upadyaya & Eccles, 2015).

Enjoyment of mathematics is an important construct in itself, and also because it may influence the extent to which children are willing to practice mathematical activities, which may enable them to improve in the subject. Most studies indicate that younger children report high levels of enjoyment of mathematics, though there are some exceptions (Markovits & Forgasz, 2017). However, the same studies mostly suggest that enjoyment deteriorates with age (Adelson & McCoach, 2011; Blatchford, 1996; Gierl & Bisanz, 1995; Gottfried, Marcoulides, Gottfried, Oliver, & Guerin, 2007; House, 2006; Upadyaya & Eccles, 2014; Wigfield & Meece, 1988). Van der Beek et al. ( 2017) found that mathematics achievement correlated positively with mathematics enjoyment and negatively with mathematics anxiety in a Dutch adolescent sample. Pinxten et al. ( 2014) carried out a longitudinal study of Belgian upper primary school children, and mathematics enjoyment was a mild positive predictor of later mathematics achievement and later perceived effort in mathematics. There has been comparatively little research on the factors that cause children to like or dislike mathematics, but Upadyaya and Eccles ( 2014) found that teachers' ratings of primary pupils' effort and ability in mathematics predict not only their subsequent achievement and self-rating in mathematics, but their subsequent enjoyment of it.

The studies which have been done on relations between attitudes and performance in younger primary school children have shown mixed results as regards both the extent to which attitudes predict performance, and the attitudes that are the strongest predictors of performance. On the one hand, some studies do not show a relationship between mathematics anxiety and achievement (Dowker et al., 2012; Krinzinger et al., 2009). Dowker et al. ( 2012) obtained results which suggested that performance is related to self-rating rather than to mathematics anxiety, and that this relationship develops over time, and is not present in younger primary school children. On the other hand, studies by Wu et al. ( 2012) and Vukovic et al. ( 2013) found that mathematical anxiety correlated with performance even in the early years of elementary school.

The present study aimed to examine attitudes to mathematics and any relationships to performance in children at the end of Year 1 in primary school. It was expected that children of this age would show relatively positive attitudes, with high levels of liking for mathematics and self-rating for mathematics, and low anxiety. It was not predicted that there would be any relationship between attitudes and performance, as other studies using similar methodology have suggested that this only emerges somewhat later.

It also aimed to investigate whether there are gender differences in very young children's attitudes. Most studies suggest that adolescent and adult females are more anxious than males about mathematics, and have generally less positive attitudes to the subject (Devine, Fawcett, Szucs, & Dowker, 2012; Else-Quest, Hyde, & Linn, 2010; Hembree, 1990; Kyttala & Bjorn, 2010), though in most recent studies they do not in fact perform worse than males. Some studies suggest that the relations between mathematics anxiety and performance may indeed differ between males and females, though findings have been conflicting, with some studies reporting a greater relationship between anxiety and performance in boys (Hembree, 1990; Ma & Xu, 2004) and some in girls (Devine et al., 2012).

Gender differences in mathematics anxiety seem, however, to be mostly restricted to secondary school pupils and adults. In most studies, younger children do not show gender differences in mathematics anxiety (Dowker et al., 2012; Erturan & Jansen, 2015; Harari et al., 2013; Wu, Willcutt, Escovar, & Menon, 2014). This may, however, depend to some degree on how mathematics anxiety is defined and measured. Sorvo et al. ( 2017) found that Finnish primary school girls showed more negative emotional reactions to mathematics than boys, though they did not express greater anxiety about performance.

Studies of attitudes other than anxiety have shown gender differences in attitudes even at primary school level. By far the most consistent gender difference found regarding primary school children's attitudes has been found for self-rating. For example, Dowker et al. ( 2012) found that primary school boys rated themselves higher in mathematics than girls, despite showing no significant differences in other attitudes or in actual performance. Similarly, Ganley and Lubienski ( 2016) found that primary school children showed few gender differences in their liking for and interest in mathematics, but that boys were more confident. Herbert and Stipek ( 2005), Kyttala & Bjorn ( 2010), Markovits & Forgasz ( 2017), Skaalvik and Skaalvik ( 2004), and Upadyaya and Eccles ( 2015) also found that primary school boys showed more confidence than girls in their own mathematical ability. In the present study, it was predicted that, as in the study by Dowker et al. ( 2012), there would be no gender differences in either anxiety or in actual performance, but that boys would rate themselves higher.

Finally, we wished to investigate possible cross-cultural differences in attitudes and in the relation between attitudes and performance. Specifically, we wished to compare first-grade children in England and Hong Kong, as this might elucidate some seemingly conflicting findings about within- and between-country associations between mathematics attitudes and performance. International comparisons consistently show better mathematics performance by Chinese children, and those in other Pacific Rim countries, than in most other countries. One might therefore expect that Chinese children would have more positive attitudes to mathematics than those in most other countries. Within Chinese samples, there is indeed a significant negative relationship between mathematics anxiety and performance, as in virtually all other countries (Dulaney, Herts, Borgonovi, & Beilock, 2017). House ( 2006) found similar results with regard to another Pacific Rim country with regard to other attitudes. Although Japanese 9-year-olds performed much better in mathematics than American 9-year-olds, both groups showed positive relationships between mathematical performance and both enjoyment of mathematics and finding it "easy".

However, several studies have indicated that, in contrast to children from high-performing West European countries, children from China and other East Asian countries show greater mathematics anxiety and less confidence and enjoyment than those in most lower-attaining countries, including England (Dulaney et al., 2017; Mullis, Martin, & Loveless, 2016a). The TIMSS international comparisons have shown that Hong Kong pupils, and those elsewhere in the Pacific Rim, report less enjoyment and confidence in mathematics than those in most other countries, including England, both at younger (4th grade) and older (8th grade) ages.

This seems at first sight to be paradoxical. If negative attitudes are associated with poor performance in mathematics, why would pupils in high attaining countries show relatively negative attitudes? Possible explanations include the likelihood that they are comparing themselves with other high achieving peers rather than with the world in general; possible cultural pressures toward modesty (though this could only explain reduced confidence and not reduced enjoyment); and/or a high-pressure training regime which results both in high achievement and high anxiety. The question arises as to when the relatively negative attitudes begin. It is known that Chinese children already perform better on numerical tasks than Western children even at the time when they start school, but there is even less knowledge about very young Chinese children's attitudes to mathematics than about very young Western children's attitudes to mathematics.

Similarly, Ching ( 2017) found that Chinese children's mathematics anxiety negatively predicted their mathematics performance longitudinally from second to third grade, but only in the case of children who had relatively high working memory scores, suggesting that the effect of mathematics anxiety is most noticeable in children who do not have additional cognitive explanations for reduced attainment. This finding is not specific to Chinese children, but is similar to Ramirez et al.'s ( 2013) findings with American children. It has also been found that, as with children in other countries, Chinese children's attitudes to mathematics are closely linked to their parents' and teachers' attitudes (Stevenson et al. 2000). There has, however, been little research on the attitudes of Chinese children below second grade.

Our predictions were that (1) children in this age-range would have positive attitudes to mathematics; (2) that most attitudes would not correlate with arithmetical performance; (3) that self-rating would correlate with arithmetical performance in the Chinese and possibly in the English group; (4) that the Chinese children might already begin to show a negative within-group correlation between mathematics anxiety and mathematics performance; (5) that Chinese children would perform better than English children at arithmetic; (6) that Chinese children would show greater mathematics anxiety than English children; (7) that English children would show higher self-rating than Chinese children; (8) that English children would express more liking for mathematics than Chinese children; (9) that there would be no gender difference in arithmetical performance; and (10) that boys would rate themselves higher in mathematics than girls.

2 Methods

2.1 Participants

Sixty-seven English participants were recruited from two non-fee-paying neighbourhood primary schools one in Carlisle, Cumbria, and one in Oxford. Forty-nine Chinese participants were recruited from two primary schools in Hong Kong. These were the same children whose performance on various numerical tasks was described by Mark and Dowker ( 2015). All children were tested in their native language.

The English children included 40 boys and 27 girls. Their mean age was 6 years 3 months (standard deviation 7.2 months). Unfortunately, due to confidentiality rules in the Hong Kong schools, we were not able to obtain detailed information as to the gender and exact ages of individuals. However, it is known that the mean age of the group was 6 years 10 months. None of the children in the study had known disabilities or special educational needs. Consent was obtained from the schools, and individual informed consent was obtained from the parents of all participants. The study received ethical approval from Oxford University's Central University Research Ethics Committee.

2.2 Materials and procedure

The participants completed two different assessments: a mathematics attitude questionnaire and an arithmetic calculation test.

2.2.1 Mathematics attitude questionnaire

Attitudes to mathematics were assessed using Thomas and Dowker's ( 2000) 28-item questionnaire (also see Dowker et al., 2012; Krinzinger et al., 2007). The questionnaire contains four scales, each including attitudes to seven aspects of mathematics: mathematics in general, written sums, mental sums, easy mathematics, difficult mathematics, mathematics tests, and understanding of the teacher talking about mathematics. For each item, children were asked about their Self-rating (how good they thought they were at it), Liking (how much they liked it), Anxiety (how anxious they would feel if they could not do it), and Unhappiness (how unhappy they would feel if they were unable to do it). The possible rating scores for each item ranged from 1 to 5, where 1 was the most negative score and 5 was the most positive score. As there were seven items on each rating scale, the possible score on each rating scale ranged from 7 to 35. For all scales, the scores were computed so that the more positive attitudes gave the higher score; so higher scores on the Anxiety and Unhappiness measures reflected low anxiety and low unhappiness. These measures are therefore termed in this article (Non)-Anxiety and (Non)-Unhappiness to clarify their direction.

For each set of items, the children were given four different five-point pictorial rating scales and asked to point to the picture that most represented their answers. Before starting the questionnaire, the children were given two sets of practice questions, on topics unrelated to mathematics, to familiarize them with the format of the rating scales. Self-rating was measured using "crosses and ticks" (2 crosses (very bad), 1 cross, blank space, 1 tick or 2 ticks (very good)). Liking was measured using "sweets and wasps" (2 wasps (hate very much), 1 wasp, blank space, 1 sweet, or 2 sweets (like very much)). Anxiety was measured using a Mr. Men scale (Mr Worry (very worried) to Mr. Happy (very relaxed)). Unhappiness at failure was measured with "emotive faces" (very frowny (very unhappy), frowny, flat mouthed face, smiley, or very smiley (very happy)). These scales were controlled for lateral preference by alternating the order.

In a study of 450 German children in their first 3 years of primary school, Krinzinger et al. ( 2007) had found that scale had good internal validity, with Cronbach's alpha for the four scales ranging from 0.83 to 0.91, as well as good concurrent validity shown by high correlations with the TEDU-Math test.

2.2.2 Arithmetical calculation test

The children also completed a standardized arithmetic test: the Basic Number Skills subset of the British Ability Scales (BAS), 2nd edition (Blatchford, 1996). This edition of the British Ability Scales was standardized with 1659 children in the UK. The Basic Number Skills subtest is a test for pupils of 6 to 16, consisting of written arithmetic problems. There are 48 items in all, divided into six blocks of increasing difficulty The test is discontinued after a child gets fewer than 5 items correct within a block of 8. The measure used in the analyses was Raw Score rather than Standard (scaled) Score, because the test was not standardized in Hong Kong, making Raw Score a more appropriate measure, and because the inability to obtain exact ages from individual Hong Kong pupils would have made it impossible to obtain standard scores.

2.3 Procedure

Each child was tested individually by a researcher in a quiet area near to their classroom. The children were informed that the purpose of the study was to find out what they thought about mathematics, and that they would be given a couple of tests. Verbal consent was then obtained from the child before continuing. None of the children refused to take part in any of the tasks.

3 Results

Table 1 shows the scores obtained by the English and Chinese groups on the British Abilities Scales Basic Number Skills test (raw score), and on the four attitude measures. Basic Number Skills test standard scores were only available for the English children, who obtained a mean standard score of 117.3 (s.d. 13.43). The lack of precise age information for individual Chinese children made it impossible to calculate individual standard scores for that group, but the mean age of 6 years 10 months combined with a mean raw score of 17.47 leads to an estimated mean standard score of approximately 130.

Table 1 Means and standard deviations of scores on arithmetic and attitude measures in English and Chinese children and results of independent sample t tests comparing nationalities (standard deviation in brackets)

3.1 Reliability of attitude measures

Due to the relatively small samples, and the fact that the attitude questionnaire had not previously been used with Chinese children, it was important to check the reliability of the attitude measures. These were satisfactory in both groups. In the English group, Cronbach's alpha was 0.75 for Self-Rating; 0.82 for Liking for Mathematics; 0.85 for Anxiety; and 0.9 for Unhappiness at Failure. In the Chinese group, Cronbach's alpha was 0.83 for Self-Rating; 0.75 for Liking for Mathematics; 0.84 for Anxiety; and 0.85 for Unhappiness at Failure.

Table 2 shows the correlations between all the scores in the group as a whole.

As Table 2 shows, the only significant correlate of Basic Number Skills in the group as a whole was Self-Rating. Significant correlations between the attitudes include correlations between Liking for Mathematics and Self-Rating; Liking for Mathematics; and (Non)-Unhappiness at Failure; and Self-Rating and (Non)-Anxiety.

Table 3 indicates that in the English group on its own, the only significant correlate of Basic Number Skills was (Non)-Unhappiness at Failure, though the correlation with Self-Rating almost reached significance (Table 3). Significant correlations between the attitudes include correlations between Liking for Mathematics and (Non)-Unhappiness at Failure; and (Non)-Anxiety and (Non)-Unhappiness at Failure.

Table 4 indicates that the only significant correlate of Basic Number Skills in the Chinese group was Self-Rating. Self-rating correlated significantly with all the other attitude variables: Liking for Mathematics; (Non)-Anxiety and (Non)-Unhappiness at Failure. (Non)-Anxiety correlated with (Non)-Unhappiness at Failure (Table 4).

3.2 Multiple regressions

An entry-type linear multiple regression was carried out for the whole group with British Abilities Basic Number Skills Raw Score as the dependent variable and Liking for Mathematics, Self-Rating, (Non)-Anxiety, and (Non)-Unhappiness at Failure as the predictors. The regression overall was significant (F(4, 112) = 10.983; p < 0.001). R ² = 0.284; R ² adjusted = 0.248). The predictor variables explained 24.8% of the variance in Basic Number Skills Raw Score. The regression table is shown in Table 6.

As Table 5 shows, the only significant independent predictor of Basic Number Skills Raw Score in the whole group was Self-Rating, though (Non)-Unhappiness at Failure approached significance.

A similar regression analysis was carried out for the English children only. The regression overall was significant (F(4, 63) = 4.014, p = 0.006; R ² = 0.206; R ² adjusted = 0.154). The regression table is shown in Table 6.

Table 6 indicates that the only significant predictors of Basic Number Skills Raw Score in the English group were Self-Rating and Unhappiness at Failure.

A similar regression analysis was carried out for the Chinese children only. The regression was non-significant overall (F(4, 45) = 1.244; p = 0.306; R ² = 0.102; R ² = 0.02). The regression table is shown in Table 8.

Not surprisingly, Table 7 indicates that no predictor was independently significant in the Chinese group, though there was a trend for Self-Rating to predict Raw Score.

3.3 Collinearity checks

Multicollinearity was checked for all the attitude measures included in the multiple regression on Raw Score, within each nationality group and within the whole group. It was found not to be at a problematic level for any measure. The Variance Inflation Factor ranged from 1.01 (Self-rating) to 1.502 (Unhappiness at Failure) within the English group and from 1.75 (Liking for Mathematics) to 2.27 (Anxiety) within the Chinese group. Within the group as a whole, the Variance Inflation Factor ranged from 1.29 (Self-Rating) to 1.58 (Unhappiness at Failure). Since even the most conservative criteria treat a Variance Inflation Factor of less than 2.5 as unlikely to be problematic, we may assume that multicollinearity was not a major issue in the present study,

3.4 Gender differences (English group only)

Gender information about individuals was only available for the English group (Table 8).

Analyses of variance were carried out with Gender (Male versus Female) as the grouping factor, and British Abilities Scales Basic Number Skills raw score and all the attitude scores as the dependent variables. As can be seen, there were no significant gender differences in arithmetic score, Liking for mathematics, or Self-rating; but girls showed significantly less Anxiety about mathematics or Unhappiness at failure than did boys.

Individual exact age information was also only available for the English group. Within that group, Pearson correlation coefficients were computed between Age in months, and the Arithmetic and Attitude scores. No correlation between any score and Age was significant.

4 Discussion

The results indicate that in the English group attitudes to mathematics did show significant relationships to arithmetical performance, even at this early age. In particular, both self-rating and (non)-unhappiness at failure was associated with performance. In the Chinese group, there was a correlation between self-rating and performance, but it ceased to reach significance after controlling for other attitudes. The Chinese children performed better in arithmetic than the English children, and also gave themselves higher self-ratings. They did not differ in other attitudes.

These results will now be discussed in greater detail. We will first discuss the attitudes themselves, and then the relationship between attitudes and performance. We will then discuss similarities and differences between the English and Chinese children. We will then discuss relationships between the different attitudes. The discussion will then turn to gender differences within the English group, where boys and girls performed equally well but girls seemed to have lower mathematics anxiety. Finally, we will discuss some limitations of the study, and implications for further research and for education.

4.1 Relatively positive attitudes to mathematics

As predicted by the first hypothesis, the children in this study demonstrated relatively positive attitudes to mathematics, with a mean score for Liking for Mathematics of 27.25 out of 35, and also fairly high scores for Self-rating and on Freedom from Anxiety and Unhappiness at Failure. This is consistent with other findings that show that, though primary school children are not immune to negative attitudes about mathematics (Petronzi, 2016), most express positive attitudes to it (Blatchford, 1996; Dowker et al., 2012; Gierl & Bisanz, 1995; Upadyaya & Eccles, 2014; Wigfield & Meece, 1988). Most of these previous studies had not looked at children as early as the first year of primary school. It is interesting that such young children show similar results to the somewhat older primary school children in previous studies.

4.2 Relations between attitudes and performance

The second prediction that there would be relatively little relationship between attitudes and performance was partially but not completely confirmed, while the third prediction that there would be a specific relationship between self-rating and performance in the Chinese group was supported to some extent, but much less than in the English group, which had not been expected to show such a relationship at this age. There was more association between attitudes on performance than is sometimes found with young children (e.g. Dowker et al., 2012), with attitudes accounting for approximately 26% of the variance in arithmetical performance in the group as a whole. But Self-rating was the only individual attitude variable that correlated significantly with performance, and it remained significant as an independent predictor in a multiple regression after controlling for other variables.

It is interesting that attitudes were far more strongly related to performance in the English group specifically than had been predicted for children of such a young age. Self-rating was a strong independent predictor of performance in the English group, and (Non)-unhappiness at poor performance was also a predictor. Such relationships have in previous studies only been found in rather older primary school children (Dowker et al., 2012; Ho et al., 2000; Krinzinger et al., 2007; Sorvo et al., 2017). It may be that the increasing emphasis on early assessment in UK primary schools (e.g. the Early Years Foundation Stage Profile) is making children more aware of, and perhaps more concerned about, their performance at an early stage.

The findings of the present study are in line with findings that in somewhat older primary school children, self-rating is a particularly strong correlate of mathematics performance: stronger than, for example, mathematics anxiety (Dowker et al., 2012; Krinzinger et al., 2007; Wood et al., 2012). There are several possible reasons for this relationship. It may be that the causal direction is from performance to self-rating: i.e. children are relatively accurate in their self-ratings, and are aware of how well or badly they are performing in class. It may also be that high self-esteem in mathematics contributes to children's willingness to practice the subject, and to persist in the face of difficulties. Longitudinal studies suggest that there are relationships in both directions (e.g. Aunola, Leskinen, & Nurmi, 2006). It is also found that teachers' ratings of children's mathematical ability influence both children's later self-ratings and actual performance (Upadyaya & Eccles, 2015). The same is true for parent ratings, though this relationship appears more noticeable in the later primary years than earlier (Herbert & Stipek, 2005).

It is interesting that unhappiness at failure-but not anxiety itself-was found to be a predictor of performance. This is in contrast with the studies that show a strong relationship between anxiety and performance in older children and adults. It is also in contrast with findings that indicate relatively little relationship between attitudes and performance in very young children, though not many studies have looked directly at unhappiness at failure. The findings could suggest that in the earliest stages of development, response to failure itself has a stronger influence on performance than response to anticipation of failure. Perhaps excessive distress at failure reduces the ability to learn from mistakes and thus to improve. The direction of causation could also be in the other direction: unhappiness at failure may be greater in those who have experienced more failures.

Within-group analyses showed that, contrary to the fourth prediction, attitudes were more predictive of performance in the English than the Chinese group. Both self-rating and (non)-unhappiness at failure predicted performance in the English group. Only self-rating correlated with arithmetical performance in the Chinese group, and it did not remain as a significant predictor after controlling for other variables in a multiple regression (though there was still a trend toward significance). Indeed attitude variables accounted for very little-only about 2%-of the variance in arithmetical performance in the Chinese group. This did not reflect any lack of variance in the attitude variables in that group, nor any worrying degree of collinearity of the variables. We may conclude that, at least in this particular Chinese group at this young age, self-reported attitudes had relatively little relationship to performance.

4.3 Comparisons between English and Chinese children

In accordance with the fifth prediction, the Chinese pupils performed much better than English pupils on the arithmetic test, despite the fact that the English pupils also obtained above-average scores. This may be in part because they were somewhat older; but their standard scores also appeared to be much higher. This supports many findings that show better performance by Chinese pupils than those in Western countries (Leung, Graf, & Lopez-Real, 2006; Mark & Dowker, 2015; Mullis et al., 2016a; Mullis, Martin, Foy, & Hooper, 2016b).

The sixth, seventh, and eighth predictions, which suggested that Chinese children would show more negative attitudes to mathematics than English children, were not supported. The groups did not differ on most of the attitude variables, and the Chinese pupils indeed gave much higher self-ratings of their own mathematical ability than did the English children. This finding is consistent with the fact that the Chinese children actually did perform better than the English children. However, it was not consistent with the earlier findings that suggest that Chinese children and others from Pacific Rim countries are actually more anxious and less confident than many from Western countries, perhaps due to the amount of academic pressure placed on them (Askew, Hodgen, Hossain, & Bretscher, 2010; Dulaney et al., 2017). It may be that the higher Chinese self-ratings found in the present study are a function of the children's younger age in comparison with those of the previous studies. It may be that they become more anxious and less confident as a result of increased academic pressure and testing over the years. Further research should study Chinese children of different ages, starting with first-grade children, to investigate whether there are indeed changes with age in Chinese children's attitudes, and whether they coincide with any changes in teaching methods as children grow older.

4.4 Relations between the different attitudes

Examinations of correlations between variables in the group overall and in the separate national groups showed that Self-Rating was correlated with (Non)-Anxiety and with Liking for mathematics. Liking for mathematics was correlated with (Non)-Unhappiness at failure, but not with (Non)-Anxiety. Surprisingly, (Non)-Anxiety was not significantly correlated with (Non) Unhappiness at failure in the group as a whole, or among the English children specifically though there was a significant correlation between the two variables in the Chinese group on its own. The importance of Self-rating in predicting both performance and other attitudes is consistent with the findings of Dowker et al. ( 2012) for somewhat older primary school children, and with Jameson's ( 2014) finding that mathematical self-concept was the strongest negative predictor of anxiety in second-grade pupils. It had not, however, been predicted for such young children.

It would be of interest to compare children of different ages, or ideally to follow-up the same children longitudinally, to see whether the relationships between different attitudes change with age. Ganley and McGraw ( 2016) found that the relationships between different attitudes increased with age. For example, they found that interest in mathematics, but not mathematical self-confidence, predicted mathematics anxiety in a sample of American first-grade children, while both, together with regarding mathematics as important, predicted mathematics anxiety in third grade pupils. In the present study, liking for mathematics did not show a significant relationship to anxiety, while self-rating did.

4.5 Gender, attitudes, and performance

Unfortunately, gender information was only available for individual children in the English group, so the gender analyses could only be carried out for that group. Within that group, the ninth prediction that there would be no gender differences in performance was confirmed. The tenth, that boys would show higher self-rating than girls, was not supported. There were gender differences in other attitudes, but not in the direction that might have been expected on the basis of studies of older children. Although studies of older children, adolescents, and adults usually show higher levels of mathematics anxiety in females than males (Devine et al., 2012), most studies had not shown any gender differences in anxiety in very young children (Dowker et al., 2012; Erturan & Jansen, 2015; Harari et al., 2013; Wu et al., 2014). However, the present study showed some gender differences in the English sample, but in the unexpected direction of greater anxiety and unhappiness over failure in boys. This result would need replication in similar age-groups, before any strong interpretation could be made. If it is replicated, it might reflect the generally more negative attitudes that boys have to schoolwork in primary school, which have been suggested to be possibly related to their lower verbal and social maturity at school entrance in a school system where children begin formal instruction very early (e.g., Lever-Chain, 2002). It would also be desirable to investigate gender differences in other national cultural groups, and to investigate the possibility of interactions between culture and gender regarding attitudes, performance, and relationships between them.

4.6 Limitations of the study and implications for further research

Some caution is needed in drawing strong conclusions, as the sample sizes were relatively small, and in particular the Chinese children were only from one part-Hong Kong-of a huge country. Future studies should include larger samples from a wider variety of regions and, if possible, countries. It is also desirable to incorporate more study of the contexts in which the children are learning, which are likely to vary in multiple ways, so that cultural or national differences can rarely be reduced to a single factor. Moreover, the English participants may have been somewhat unrepresentative, in that they had above-average British Abilities Scales standard scores. In this respect, however, they did not differ greatly from those some other studies of children, e.g. the study by Dowker et al. ( 2012); or from most studies of adults, which commonly use university students as participants. One important limitation to be noted is that the study was cross-sectional rather than longitudinal. It would be desirable to carry out more longitudinal studies starting from an early stage of schooling.

It would also be of interest to study other attitudes to mathematics, e.g. children's views of how interesting and engaging their school mathematics lessons are. The TIMSS studies have shown fourth-graders' attitudes to this issue to be extremely positive in a wide range of countries: more positive than their liking for mathematics as such (Mullis et al., 2016a, 2016b). Future studies could also assess children's self-efficacy; how easy or difficult they consider mathematics to be; and how useful they consider it to be. It would also be desirable to look at both performance and attitudes with regard to a wider range of mathematical tasks. Both the questionnaire and the standardized test used in the study focused mainly on computation; and one should investigate whether similar results would be obtained for other aspects including applications of arithmetic, number representation (e.g. on number lines), measurement, and shape and space. Finally, this study used questionnaire measures and focused on cognitive aspects of attitudes to mathematics. Future studies could include measures of emotional aspects of mathematics anxiety, which earlier studies suggest might be more closely related to performance even in young children than the cognitive aspects are, and could incorporate direct physiological measures of emotions related to mathematics, e.g. heart rate and skin conductance.

4.7 Implications for education

The study suggests that attitudes to mathematics are associated with arithmetical performance even in children in the first year at school, with self-rating and unhappiness at failure being much more important than anxiety, or for that matter liking for mathematics, in predicting mathematical performance. Though it is not at present possible to determine direction of causation, results suggest that it may be desirable to focus in these early years on reducing distress at failure, and on preserving confidence in ability to solve mathematical problems.

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Authors and Affiliations

1. Department of Experimental Psychology, Oxford University, 15 Parks Road, Oxford, OX1 3PG, UK

Ann Dowker

2. Magdalen College, Oxford, UK

Olivia Cheriton

3. St Anne's College, Oxford, UK

Rachel Horton

4. Hong Kong University, Hong Kong, China

Winifred Mark

Corresponding author

Correspondence to Ann Dowker.

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Appendices

APPENDIX 1: Questionnaire items from the Mathematics Attitude and Anxiety Questionnaire (Thomas & Dowker, 2000)

1.1 PRACTICE ITEMS

Show me on this how good you think you are at schoolwork.

Show me on this how much you like or hate schoolwork.

Show me on this how happy or unhappy you would feel if you did badly at something in schoolwork.

Show me on this how worried or relaxed you would feel if you couldn't do something in schoolwork.

Show me on this how good you think you are at written work.

Show me on this how much you like or hate written work.

Show me on this how happy or unhappy you would feel if you did badly at something in written work.

Show me on this how worried or relaxed you would feel if you couldn't do something in written work.

1.2 MAIN ITEMS

Supposing you are having a maths lesson:

Show me on this how good you think you are at maths in general.

Show me on this how much you like or hate maths in general.

Show me on this how happy or unhappy you would feel if you did badly at something in maths.

Show me on this how worried or relaxed you would feel if you couldn't do something in maths.

Show me on this how good you think you are at written sums.

Show me on this how much you like or hate written sums.

Show me on this how happy or unhappy you would feel if you did badly at a written sum.

Show me on this how worried or relaxed you would feel if you couldn't do a written sum.

(The same questions were asked about mental sums; easy maths; difficult maths; taking tests in maths; and listening to the teacher talking about maths).

Show me on this how good you think you are at easy maths.

Show me on this how much you like or hate easy maths.

Show me on this how happy or unhappy you would feel if you did badly at something in easy maths.

Show me on this how worried or relaxed you would feel if you couldn't do something in easy maths.

Show me on this how good you think you are at difficult maths.

Show me on this how much you like or hate difficult maths.

Show me on this how happy or unhappy you would feel if you did badly at something in difficult maths.

Show me on this how worried or relaxed you would feel if you couldn't do something in difficult maths.

Show me on this how good you think you are at maths tests.

Show me on this how much you like or hate maths tests.

Show me on this how happy or unhappy you would feel if you did badly at a maths test.

Show me on this how worried or relaxed you would feel if you couldn't do a maths test.

Show me on this how good you think you are at understanding the teacher when she talks about maths.

Show me on this how much you like or hate trying to understand what the teacher says about maths.

Show me on this how happy or unhappy you would feel if you did badly at understanding the teacher when she talks about maths.

Show me on this how worried or relaxed you would feel if you couldn't understand the teacher when she talks about maths.

APPENDIX 2

Pictorial rating scale from the Mathematics Attitude and Anxiety Questionnaire (Thomas & Dowker, 2000) (see attached)

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Dowker, A., Cheriton, O., Horton, R. et al. Relationships between attitudes and performance in young children's mathematics. Educ Stud Math 100, 211-230 (2019). https://doi.org/10.1007/s10649-019-9880-5
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Abstract

Self-explanation is a process by which learners generate inferences about causal connections or conceptual relationships. A meta-analysis was conducted on research that investigated learning outcomes for participants who received self-explanation prompts while studying or solving problems. Our systematic search of relevant bibliographic databases identified 69 effect sizes (from 64 research reports) which met certain inclusion criteria. The overall weighted mean effect size using a random effects model was g  = .55. We coded and analyzed 20 moderator variables including type of learning task (e.g., solving problems, studying worked problems, and studying text), subject area, level of education, type of inducement, and treatment duration. We found that self-explanation prompts are a potentially powerful intervention across a range of instructional conditions. Due to the limitations of relying on instructor-scripted prompts, we recommend that future research explore computer-generation of self-explanation prompts.

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This study was funded by Social Sciences and Humanities Research Council of Canada (grant number 435-2012-0723).

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Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

Kiran Bisra, Qing Liu, John C. Nesbit, Farimah Salimi & Philip H. Winne

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Correspondence to Kiran Bisra.

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Bisra, K., Liu, Q., Nesbit, J.C. et al. Inducing Self-Explanation: a Meta-Analysis. Educ Psychol Rev 30, 703-725 (2018). https://doi.org/10.1007/s10648-018-9434-x
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# data[].attributes.attachment_link.title
Inducing Self-Explanation: a Meta-Analysis - Educational Psychology Review

# data[].attributes.attachment_link.description
Self-explanation is a process by which learners generate inferences about causal connections or conceptual relationships. A meta-analysis was conducted on research that investigated learning outcomes for participants who received self-explanation prompts while studying or solving problems. Our systematic search of relevant bibliographic databases identified 69 effect sizes (from 64 research reports) which met certain inclusion criteria.

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56. Education Endowment Foundation: Teaching and Learning Toolkit (Oral Language Interventions)

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Oral language interventions (also known as oracy or speaking and listening interventions) refer to approaches that emphasise the importance of spoken language and verbal interaction in the classroom. They include dialogic activities.

Oral language interventions are based on the idea that comprehension and reading skills benefit from explicit discussion of either content or processes of learning, or both, oral language interventions aim to support learners' use of vocabulary, articulation of ideas and spoken expression.

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targeted reading aloud and book discussion with young children;

explicitly extending pupils' spoken vocabulary;

the use of structured questioning to develop reading comprehension; and

the use of purposeful, curriculum-focused, dialogue and interaction.

Oral language interventions have some similarity to approaches based on Metacognition (which make talk about learning explicit in classrooms), and to Collaborative learning approaches which promote pupils' interaction in groups.

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Approaches that emphasise the importance of spoken language and verbal interaction in the classroom.

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53. Hebert, M., Kearns, D., Hayes, J., Bazis, P. and Cooper, S.(2018). Why Children With Dyslexia Struggle With Writing and How to Help Them. Language, Speech, and Hearing Services in Schools, 49(4), pp.843-863.

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53. Hebert, M., Kearns, D., Hayes, J., Bazis, P. and Cooper, S.(2018). Why Children With Dyslexia Struggle With Writing and How to Help Them. Language, Speech, and Hearing Services in Schools, 49(4), pp.843-863.

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Lang Speech Hear Serv Sch. 2018 Oct; 49(4): 843-863.

Abstract

Purpose

Children with dyslexia often have related writing difficulties. In the simple view of writing model, high-quality writing depends on good transcription skills, working memory, and executive function-all of which can be difficult for children with dyslexia and result in poor spelling and low overall writing quality. In this article, we describe the challenges of children with dyslexia in terms of the simple view of writing and instructional strategies to increase spelling and overall writing quality in children with dyslexia.

Method

For spelling strategies, we conducted systematic searches across 2 databases for studies examining the effectiveness of spelling interventions for students with dyslexia as well as including studies from 2 meta-analyses. To locate other instructional practices to increase writing quality (e.g., handwriting and executive function), we examined recent meta-analyses of writing and supplemented that by conducting forward searches.

Results

Through the search, we found evidence of effective remedial and compensatory intervention strategies in spelling, transcription, executive function, and working memory. Some strategies included spelling using sound-spellings and morphemes and overall quality using text structure, sentence combining, and self-regulated strategy development.

Conclusions

Many students with dyslexia experience writing difficulty in multiple areas. However, their writing (and even reading) skills can improve with the instructional strategies identified in this article. We describe instructional procedures and provide links to resources throughout the article.

Students with dyslexia often also have writing difficulties. This is not surprising, as reading is theorized to be a central component of writing in some cognitive models of writing development (e.g., Graham, 2018; Hayes, 1996). The writing difficulties of students with dyslexia can be partially attributed to their reading difficulties and can manifest in many ways in their writing, such as poor spelling, poor legibility, lack of diverse vocabulary, poor idea development, and/or lack of organization.

Dyslexia and writing difficulties co-occur for two overarching reasons. First, reading and writing rely on related underlying processes ( Graham & Hebert, 2010, 2011). For example, dyslexia involves difficulties related to processing phonological information needed for decoding words, whereas writing requires encoding phonological information when writing words. Because the disability impacts the underlying process for both the reading and writing systems, the prevalence of writing difficulties for students with dyslexia is not unexpected. Second, reading is a subskill required throughout the writing process. Writers often need to read source materials before writing their own text and also need to read and reread their own writing to diagnose text problems, such as spelling errors, grammar errors, and disorganization ( Hayes, 1996). The presence of reading difficulties complicates this task, especially if students have poor handwriting skills that make it even more difficult for them to read their own writing.

The focus of this article is to address the various types of writing issues children with dyslexia may have and to provide information about research-based practices that can work toward remediation of these difficulties. First, we use the simple writing model to provide an overview of the skills needed for writing. To illustrate some of the writing difficulties students with dyslexia have, we then provide a case study of a student with dyslexia (Jordan) and discuss how some of his writing errors indicate difficulties related to reading challenges. Next, we provide theory for why students with dyslexia may struggle with writing by presenting research and theory about some of the links among their reading and writing difficulties. Finally, we identify instructional strategies shown to be effective for improving writing skills (and related reading skills) of students with reading and writing disabilities.

Conceptual Framework: Simple View of Writing

One way to characterize the skills involved in writing is to use the simple view of writing ( Berninger & Amtmann, 2003). This theoretical model includes the subskills that are essential for the writing task and provides a framework for showing how those skills are interrelated. The model includes skills in four overarching categories: transcription, executive functions, working memory, and text generation (see Figure 1 ). We use the model as a heuristic, meaning that it is useful as a basic framework for understanding the components of writing, but we do not use it as a comprehensive description of how writing occurs. Researchers have proposed more comprehensive cognitive models of writing development (e.g., Graham, 2018; Hayes, 1996; Hayes & Flower, 1980; Scardamalia & Bereiter, 1986), but we decided to use the simple view of writing because it focuses on important aspects of writing skills that are relevant for teaching students with dyslexia. As we discuss various reasons students with dyslexia may have difficulty with writing, we will reference the simple view of writing to help explain how these difficulties may impact their writing. We will then link suggested interventions with the model as well in order to illustrate why the interventions are likely to be effective.

The simple view of writing is represented by a triangle, with each of the vertices linked to a specific writing skill or outcome. The two vertices at the base of the triangle represent (a) transcription skills (e.g., spelling, handwriting) and (b) executive function skills (e.g., self-regulation, planning, organization). Berninger, Abbott, Abbott, Graham, and Richards (2002) provide evidence that these skills enable (c) text generation, which is represented by the top vertex of the triangle. Because of the complexity of writing, the center of the triangle is used to illustrate that all of these skills are constrained by (d) working memory. 1

When more working memory resources are needed for any individual component of the process, fewer resources are available to manage other components of writing tasks. For example, a writer with poor spelling skills may need to rely more on his or her working memory when spelling words, which leaves fewer working memory resources available for generating ideas for his or her writing or holding them in memory throughout the writing process. All too familiar is the anecdote of the student who stops to ask a teacher how to spell a word, only to return to his or her writing and state, "I forgot what I was going to say."

Because all of the writing components operate in working memory and require considerable resources and attention, it is postulated that, when transcription skills are sufficiently automatic, more working memory space and resources are available for self-regulation strategies such as goal setting, planning, monitoring, and revising, allowing writers to generate text more similar to that of skilled adult writers ( Berninger et al., 2002).

Writings Difficulties of Students With Dyslexia in the Simple View of Writing

As we discussed previously, many students with dyslexia also have related writing difficulties. These difficulties can occur in many areas of writing related to the simple view of writing model and can manifest in many different ways. For example, the writing of students with dyslexia may suffer from one or more of the following issues: a high percentage of misspelled words, difficult-to-read handwriting, poor organization, a lack of fully developed ideas, and/or a lack of diverse vocabulary.

It is important to note that the causes of some of these writing difficulties may not be obvious. For example, it might be assumed that the cause of poor handwriting is poor motor control. Although this may be true, it could also be that the true causes of handwriting difficulties are more complicated than it first appears. Some researchers (e.g., Berninger, Nielsen, Abbott, Wijsman, & Raskind, 2008) have demonstrated that poor handwriting skills may actually be the result of poor spelling skills. These researchers hypothesize that students with poor spelling skills hesitate more often when writing words, leading to less fluent letter writing ( Berninger et al., 2008). When writing a single word, this may not make much difference to a writer's overall handwriting skills, but consistent hesitation and dysfluent word writing may not allow students to improve their handwriting skills. Similar to how spelling may contribute to poor handwriting, poor handwriting may sometimes contribute to poor organization in the writing of these students. We will explore some of the research behind these issues in more detail later in the article, but first, we illustrate some of the writing challenges a student with dyslexia might experience using a writing sample from Jordan, a fourth grader with reading disability.

Jordan: A Writing Case Study for a Student With Dyslexia

Jordan (a pseudonym) is a 10-year-old fourth grader. He participated in a research study led by the first author, and his scores indicate a level of difficulty that would qualify him for special education services based on a diagnosis of dyslexia. His scores on the word reading subtests of a standardized test, the Woodcock Reading Mastery Test-Third Edition, indicate a level of reading difficulty-below the 17th percentile-that is often used as an evidence of dyslexia (see the scores in Table 1 ).

Table 1.

Test

Standard score

Percentile

Jordan also shows difficulty with writing. He was given the Essay Composition Subtest of the Wechsler Individualized Achievement Test-Fourth Edition. For this test, children have 10 min to write about a favorite game and three reasons they like it. Jordan's essay writing places his performance at the 25th percentile compared with other fourth graders. Jordan's writing sample (see Figure 2 ) illustrates some of the writing difficulties of children with dyslexia.

His difficulties map onto the dimensions of the simple view of writing. First, Jordan has some difficulty with transcription skills. In terms of handwriting, Jordan appears to form letters in unconventional ways. For example, he appears to start and end the lowercase o on the bottom of the line. His handwriting also impairs the reader's ability to follow because he omits spaces between words and extends letters below the line, such as the L in battelships* and the A in play on Line 2. For spelling, he appears not to have memorized the spellings of frequent but irregular words such as friends (written frinds*) and has an incomplete understanding of the "drop the E" convention that results in plaing* for playing (he overgeneralizes and drops the final Y).

These difficulties appear to strain his working memory, as the simple view predicts. Jordan spells because in two different ways-one of them correct. So, he knows the correct spelling of because. His handwriting also appears to degrade as he writes (the third line has many more letters below the line than the first). These transcription difficulties indicate difficulty balancing transcription accuracy with the expression of ideas that requires strong executive function. Overall, he may be struggling with transcription simply because transcription is hard and also because the need to focus on other aspects of writing taxes his executive control. He has difficulty remembering the spoken word he intends to write (suggesting challenges retaining information in the phonological loop) or has difficulty retaining his visual representations of the letters (perhaps difficulty within the visuospatial sketchpad) in the face of other demands.

Turning to the other base of the simple view, the content of Jordan's paragraph suggests difficulty with executive function. The content of the paragraph is quite limited: He repeats his primary reason for enjoying Battleship ("I get to play with friends," and "Playing with friends are fun to play with them"). Perhaps, these ideas are subtly different (first, the game is an excuse to spend time with friends, and second, he enjoys the gameplay), or he may simply have repeated himself. Either way, this confusion suggests he probably wrote his ideas as he thought of them, rather than creating an organizer first. In addition, the sentence "Playing with friends are fun to play with them" also has a circular logic that suggests he did not monitor his writing as he went.

On the basis of the simple view of writing model, it is likely that Jordan's difficulties with transcription skills and executive function skills are linked, due to constraints of working memory. Because Jordan has difficulty with transcription skills, more working memory resources are allocated to those tasks when he is transcribing his sentences. This decreases the available working memory capacity for holding ideas and organizational plans in memory while writing (even at the sentence level), leading to incoherence. Conversely, Jordan's lack of executive function skills for goal setting and planning (e.g., making a list of ideas before writing) places a burden on working memory resources, leaving fewer resources available for monitoring spelling and conventions.

In addition to the interrelationships among the difficulties with writing skills, Jordan's difficulties can also be shown to be related to his reading disability (i.e., dyslexia). We will explore these connections later, but we first provide theory and research evidence for why dyslexia and writing difficulties co-occur. Then, we will return to Jordan's case study based on the research evidence.

Theory and Research Evidence Linking Dyslexia and Poor Writing Skills

Data indicate that there is a strong relationship between dyslexia and writing difficulty, and we explore these data within the simple view. First, we focus on transcription, particularly spelling and handwriting. We then follow this up with a discussion of relationships between dyslexia and writing in both executive function and working memory skills.

Spelling Skills and Dyslexia

Spelling and reading involve reciprocal parts of one task-connecting letters and sounds. As a result, people with dyslexia often exhibit similar levels of spelling difficulty ( Scarborough, 1998), and children with dyslexia often show spelling difficulty into adolescence ( Ehri, 1997). The source of difficulty is in phonological processing ( Ramus & Szenkovits, 2009). People with dyslexia show impairment in the ability to encode, retain, and access phonological information. This makes it difficult to read unknown words (decode them): Readers must produce a grapheme for each phoneme, retain each in memory, combine them into a single pronunciation, and connect this pronunciation with a word in memory ( Kearns, Rogers, Koriakin, & Al Ghanem, 2016). Spelling unknown words (encoding) requires a complementary process, listening to an unknown spoken word, breaking it into phonemes, selecting the appropriate grapheme for the phoneme, repeating this process for each phoneme, and then checking the result to make sure it looks like a real word (see Figure 3 for an example of the reciprocal processes). For this reason, children's spelling abilities predict their later reading abilities ( Ouellette & Sénéchal, 2017)

Because reading and spelling skills both require phonological skills, spelling and phonological skills are strongly linked ( Furnes & Samuelsson, 2010). People with dyslexia are likely to make spelling errors that indicate some sounds were not adequately processed ( Bruck, 1993; Cassar, Treiman, Moats, Pollo, & Kessler, 2005; Pennington et al., 1986). For example, a child with dyslexia might spell jump as jup* or blind as blid* ( Bourassa, Treiman, & Kessler, 2006)-suggesting that the child did not distinguish the two bilabial sounds (/m/ and /p/) in jump or the alveolar ones (/n/ and /d/) in blind. It also appears that people with dyslexia use different sources of information to spell words than their peers with typical achievement. College students with dyslexia appear to rely on words' meaningful parts (morphemes) to support their spelling ( Bourassa et al., 2006)-more so than their typical peers ( Bruck, 1993; Frith, 1978). It is also noteworthy that spelling difficulty continues to be associated with word reading difficulty into the upper elementary and middle school grades. Studies generally suggest that the link between word reading skills and reading comprehension declines as children age, but the association with spelling remains very strong ( Badian, 1999).

People do not always spell using encoding. Eventually, they develop a representation of the word in which the letters, sounds, and meanings are very tightly connected ( Ehri, 2005). When that happens, spelling a word does not really involve encoding. The person simply remembers which letters to use and writes them. In many cases, people may use encoding and memory together. For example, Jordan's misspelling of because-after spelling it correctly earlier in the writing sample-probably suggests that he has much of the word memorized. The ause part is pronounced /ʌz/ so the correct pronunciation of that must be from memory. Missing the C probably indicates he failed to use encoding for that part.

Part of the challenge for children like Jordan is that English has a remarkably complex orthographic (letter) system. English has just 26 letters but about 40 phonemes, so some sounds must be spelled with multiple letters (e.g., /ʧ/ spelled with CH). In addition, sounds sometimes have multiple spellings (e.g., /ʧ/ spelled with TCH as in batch). However, the system has many "exemplary regularities" ( Perfetti, 1992, p. 18) and helpful spelling conventions (a selection is given in Table 2 ). Jordan's writing suggests that he does not have a firm grasp on these. For example, battelship* should have LE instead of EL at the end of battle, a convention for spelling /əl/ or /l̩/ at the end of words, one used in more than 4,000 English words readers might encounter in first through eighth grades (analysis based on data from Fitt, 2001, and Zeno, Ivens, Millard, & Duvvuri, 1995). He used plaing* for playing (but spelled play correct), potentially indicating that he has partial understanding of the convention to drop the E at the end of a word before adding a suffix beginning with a vowel (e.g., place to placing). The good news is that children like Jordan can improve their spelling and reading by learning about English spelling conventions (also sometimes called patterns or [perhaps inaccurately] rules). 2

Table 2.

Name

Description

Example

FLSZ

F, L, S, and Z are doubled when they follow a short vowel.

buff vs. beef
bill vs. boil
bass vs. base
buzz vs. booze

TCH/CH
DGE/GE

TCH and DGE are used after a short vowel; GE and CH otherwise.

batch vs. beach
badge vs. cage

WA

/ɑ/ is spelled with A when /w/ precedes it.

watch vs. botch

V

V never ends a word.

have
weave

AI/AY
AU/AW
EA/(E)Y
OA/OW
OI/OY

The first of these is used in the middle of a word; the second, at the end.

mail, may
launch, law
veal, valley
boat, bow
boil, boy

C/G

These make different sounds if followed by A, O, or U than if followed by E, I, or Y.

cat, cot, cut; cede, cite, cyan
gap, got, gut; gent, gin, gym

Learning to spell can also improve the quality of written compositions ( Berninger & Richards, 2010; Sanders, Berninger, & Abbott, 2017). Put differently, this means that learning to spell better results in children writing better overall. In short, the value of teaching spelling to children with dyslexia extends beyond reading into written composition.

In summary, people with dyslexia have difficulty with spelling because reading and spelling are related abilities. The errors people with dyslexia make when spelling are similar to the errors they make when reading. In addition, English spelling makes the task somewhat challenging anyway-although this does not mean children with dyslexia should be taught that English is a mess or totally confusing. There are many ways in which the system works well, and children with dyslexia can be taught to use it to improve their spelling.

Handwriting. Handwriting problems are often associated with dyslexia, although researchers and practitioners do not always consider them together (cf. Pagliarini et al., 2015). 3 However, children with dyslexia show persistent difficulty with handwriting ( Sumner, Connelly, & Barnett, 2016). As a result, it is important to consider handwriting on its own within the transcription dimension of the simple view.

Data appear to be clear that children with dyslexia experience handwriting difficulty, often showing difficulty writing quickly with correct letter formation. It is easy to conclude that these difficulties are the result of poor motor function, but studies have indicated that this may not be the case. Across all types of children-that is, when you consider a wide range of learners including those without dyslexia-there is a relationship between motor function and writing composition quality. However, this is not the case for children with dyslexia ( Graham, Berninger, Abbott, Abbott, & Whitaker, 1997). For example, Stanley and Watson (1980) examined the performance of children with and without dyslexia on a composition and figure drawing task. Both groups of children drew figures with similar speed and accuracy, whereas the students with dyslexia wrote more slowly and with more spelling errors. If handwriting difficulty was the result of motor problems, differences would occur in drawing and writing. This is not what the authors observed, suggesting that handwriting problems are related to spelling-not graphomotor-difficulty.

There is support for the connection between handwriting and spelling. Research on composition has found that some of the best early predictors of success have been the speed shown when writing the alphabet and coding orthographic material in spelling ( Berninger, 2004; Montgomery, 2008). To examine this further, Berninger et al. (2008) evaluated the role of non-handwriting graphomotor planning in dyslexia and showed that it did not have a significant relationship with the quality of written compositions. However, handwriting and spelling are themselves strongly linked ( Tarnopol & Feldman, 1987). Although the reason for this connection is not clearly established, poor letter formation may result from the working memory demand of retaining the correct phonological information in memory while producing the correct letter form. If children are focused primarily on spelling, they may struggle to simultaneously coordinate the handwriting task.

That does not mean that poor motor control should be ruled out of handwriting difficulties but instead suggests that the poor motor control exhibited by students may be the result of hesitations and lack of rhythmic movements due to uncertainty in spelling. In one study examining handwriting movements, Pagliarini et al. (2015) found that handwriting is controlled by two principles of organization: (a) isochrony, or the speed or timing of the movement in relation to the trajectory length, and (b) homothety, or the relative duration of the movement. The researchers also found that handwriting difficulties have a direct association to dyslexia and these difficulties can be characterized in terms of compliance with the rhythmic principles of writing. The dyslexic group was found to be slower in average writing speed and wrote less fluently than the typically developing group. Children who wrote less fluently turned out to read more slowly, make more errors, and have poorer receptive vocabulary. Overall, the study showed the individuals with dyslexia displayed rhythmic motor difficulties in handwriting.

To summarize, the data on handwriting suggest that handwriting difficulties may result from difficulty with spelling in children with dyslexia. Even those data indicating motor difficulties still suggest that this may result from spelling uncertainty. As a result, children with dyslexia have poor handwriting. It is possible that improved spelling will lead to improvements in handwriting, but the reverse is also true. On this basis, recent interventions for students with dyslexia have included both types of support (e.g., Berninger, Richards, & Abbott, 2015), and the very good news is that handwriting can be improved as the result of structured teaching focused on handwriting specifically ( Christensen, 2005).

Reversals. People with dyslexia appear to show a tendency to reverse letters and words when spelling ( b and d or saw and was). This is one reason people have a fundamental misunderstanding that dyslexia is a visual processing problem ( Orton, 1925). It cannot be overstated: Dyslexia is not a visual processing problem. Reversals in spelling do not indicate that it is.

However, this topic is somewhat complex, and there are confusing nuances about apparent cases of reversals. Here is a brief summary of data on this point:

1. Most children sometimes transpose similar letters such as b and d, and the percentage of reversals is similar between children with and without dyslexia. The reversals stand out in children with dyslexia because there are more reversals in their writing overall (although not in relative terms) and because they confirm our own biases ( Fischer, Liberman, & Shankweiler, 1978; Moats, 1983).

2. When children with dyslexia perform visual tasks that do not involve letters, they perform as well as children with typical achievement. When visuals are paired with sounds, children with dyslexia mix them up ( Vellutino, Pruzek, Steger, & Meshoulam, 1973).

3. When they reverse letters, children write the left-facing version ( b) more often than the right-facing one ( d). Right-facing letters are more common in English, so they may be using the more common pattern ( Treiman, Gordon, Boada, Peterson, & Pennington, 2014). What is important to understand is that reversals do not occur in both directions with equal frequency, so reversals are not arbitrary-as we would expect if it is a visual problem.

4. Almost all people with dyslexia have phonological difficulties, but a very small minority also may have visual deficits. Some people with dyslexia do have problems with visual attention, that is, how much visual information they can process ( Goswami et al., 2002; Valdois, Bosse, & Tainturier, 2004). However, studies do not show that reversals specifically occur more in people with dyslexia.

Taken together, these data validate the idea that dyslexia is a phonological deficit, and reversals are not part of what is a visual processing deficit in some people. As a result, spelling instruction should not focus on reversals, although strategies to help children associate the correct letter with the correct sound are almost certainly important (see Intervention section).

Overall, data suggest that children with dyslexia have spelling difficulty that is strongly related to their reading difficulty. The data also indicate that the spelling problem originates in difficulty processing sound information, similar to the problem with reading. Children with dyslexia also appear to use morphemes to support their spelling. These data provide some clues about how we can provide effective spelling instruction for children with dyslexia.

Executive Function

As discussed in a recent Institute of Education Sciences report, research findings have suggested that children with dyslexia have difficulty with executive function skills, such as inhibition control and switching attention ( Zelazo et al., 2016). For example, Altemeier, Abbott, and Berninger (2008) found that students with dyslexia have difficulty inhibiting prepotent responses. When reading an unknown word, they often overrely on their first instinct and guess at the word before sounding out all of the letters, not inhibiting their response before confirming it is accurate. Similarly, Brooks, Berninger, and Abbott (2011) found evidence that difficulty switching attention may impact learning to read, due to momentary breakdowns in efficiency of cross-code integration of phonological and orthographic information.

According to the simple view of writing model, executive functioning in writing involves the ability to plan, organize, set goals, self-regulate, and self-monitor. Inhibition control and other executive functions are correlated with writing tasks in normally developing populations ( Hooper, Swartz, Wakely, De Kruif, & Montgomery, 2002), influence handwriting ( Berninger et al., 2006) and overall written output ( Hooper et al., 2002), and add unique variance to models of integrated reading-writing tasks such as notetaking and report writing ( Altemeier et al., 2008). Individual differences in executive function for self-regulation of the writing process may affect high-level composing and lower level transcription processes (spelling and handwriting). For example, handwriting automaticity depends on executive control to integrate the multiple processes (e.g., motor planning, orthography). Thus, for students with dyslexia, some handwriting issues may be related to poor executive function skills that contribute to poor coordination in time of phonological codes with serial finger movements in letter formation and production ( Berninger, 2009). Although more research needs to be conducted in the examination of the relationships among the reading, writing, and executive function skills of students with dyslexia, this work demonstrates that deficits in executive function can impact both reading and writing skills for these students.

The attention required for handwriting and other transcription skills may also detract from students' ability to plan and organize text at higher levels of language. Deficiencies in these areas could be addressed by providing students with strategy instruction aimed at improving planning and organization before writing. When students plan and rehearse their ideas before writing, it mitigates the impacts transcription difficulties might have on the quality of ideas and organization of a student's text. In other words, taking notes to plan and organize ideas before writing can act as an external memory, reducing the cognitive load during the writing task ( Graham, 2018) and allowing students to switch their attention between writing functions more readily.

Working Memory

Some researchers include working memory within the constellation of executive functioning skills. However, in the simple view of writing, working memory is separate from executive function and is represented as a constraint for the writing task. Working memory is made of three components: central executive, phonological loop, and the visuospatial sketchpad. Each of these components is linked to specific reading and writing skills, and deficits in any working memory are likely to lead to related deficits in both. Kellogg (1996) explored the heavy demands placed on working memory by writing tasks and how each of the components is used to support different components of the writing task.

Because dyslexia is primarily a phonological awareness deficit, the phonological loop is the most obvious aspect of working memory that might impact both reading and writing. The phonological loop helps students hold acoustic and verbal information in memory while manipulating it, a skill that is needed for reading. Information held in phonological memory decays over time but can be refreshed through rehearsal. However, if students have difficulty representing phonological information accurately, due to a phonological awareness deficit (such as those exhibited by students with dyslexia), they may also have difficulty holding the information in memory or rehearsing it correctly. Deficits in phonological memory compound this problem, because students with poor working memory skills may not be able to hold as much phonological information in their short-term memory. This can lead to difficulties in decoding longer words when reading, or spelling longer words and writing longer sentences in writing.

Comparable with how the phonological loop is used to hold and manipulate auditory information, the visuospatial sketchpad is used to hold and manipulate visual information, such as shapes of letters, but is also important for conceptualizing organizational diagrams, visual plans, and relationships among ideas. As we have already discussed, dyslexia is primarily a phonological processing problem, not a visual processing problem. There is some evidence that students with dyslexia have difficulty remembering orthographic patterns and that this difficulty is caused by an inability to process the phonological information and link it with the visual components of the orthography (i.e., letter order). This may also be related to deficits in visuospatial memory, as students who cannot hold a sequence of letters in their visual memory may have difficulty when writing those letters during spelling and writing tasks. In addition, it may be that, due to fewer reading and writing experiences, students with dyslexia also have difficulties visualizing organizational patterns for ideas.

The central executive is a system that regulates and controls information in working memory, including how information is used in the phonological loop and visuospatial sketchpad. The central executive helps in retrieving information from long-term memory, task switching, and determining how to allocate and switch attention resources. Students with deficits in working memory may have difficulty regulating their attentional resources, such as determining how much attention to allocate for phonological loop resources when manipulating sounds and words when reading and writing, or visuospatial sketchpad resources when planning and organizing ideas for writing or reading comprehension tasks. Research shows a relationship between dyslexia and deficits in central executive. For example, Montgomery (2008) found that handwriting difficulties were frequently comorbid with attention disorders such as those found in students with attention-deficit/hyperactivity disorder.

Revisiting Jordan's Writing Difficulties Through the Dyslexia Lens

Earlier in the article, we examined Jordan's writing in relation to the simple view of writing model and showed the potential relationships among his writing skills. After exploring how writing skills and dyslexia co-occur, it is clear that some of Jordan's writing difficulties stem from his reading disability in several ways. First, Jordan is having some difficulty with transcription skills, including spelling and handwriting (refer back to Figure 2 ). The research is clear that spelling difficulties co-occur with decoding difficulties for students with dyslexia, and it may be that his handwriting difficulties are partially related to those spelling and decoding difficulties as well. Second, we illustrated that students with dyslexia often have difficulties with working memory (including the phonological loop and visuospatial sketchpad), which may be exacerbating Jordan's transcription difficulties. Because he has incomplete phonological representations for words, for example, Jordan must devote a considerable amount of working memory resources to the writing task, and any potential deficit in working memory will leave even fewer resources available for executive function tasks. Third, we illustrated that students with dyslexia often have difficulties with executive function skills, such as goal-directed behavior, planning, and organization. Jordan's difficulty with sentence level grammar and clarity show that he either (a) did not have working memory resources available to reread his writing and identify errors, (b) had difficulty rereading his own writing due to transcription difficulties and his reading disability, or (c) both. It is also probable that Jordan did not set goals or develop a plan for his writing, which may show deficits in executive function related to his dyslexia. Despite the difficulties Jordan faces in writing, there are effective interventions available to help him, and knowing the relationship between his reading and writing problems can help teachers develop an appropriate instructional plan.

Interventions to Improve the Writing Skills of Children With Dyslexia

The co-occurrence of dyslexia and writing skills leads to questions about how to approach writing for these students. As we illustrated by examining Jordan's writing, the writing difficulties faced by students with dyslexia can vary, and the difficulties in one area may be related to difficulties in other areas. In other words, stress on one part of the complex writing system can impact a student's ability to use another part of the system, impacting text generation and writing quality. Because of that, a multifaceted approach to instruction, with multiple interventions, is likely to be more effective than a single intervention.

In this section, we provide an overview of instructional strategies, organized according to components of the simple view of writing model that are addressed by the intervention (transcription or executive function). Next, we discuss the interventions in terms of whether they are aimed at (a) remediation of a skill or (b) compensation for a skill deficit. Remediation involves directly addressing a student's skill deficit in an attempt to improve the skill, whereas compensation involves providing students with strategies to reduce the cognitive demands of writing and make the writing task more manageable. The decision to focus on remediation or compensation in a particular lesson may depend on the purpose of the writing task, and teachers may sometimes include both compensation and remediation strategies within a single intervention. Table 3 classifies strategies into remediation or compensation categories.

Table 3.

Strategy type

Skill area

Transcription

Executive function

Working memory (WM)

Spelling

Handwriting

Compensation

* Using knowledge of morphemes
* Spell-check

* Learning keyboarding
* Using speech-to-text systems
* Dictating

* Structures Writing provides content for writing to compensate for planning difficulties

* Self-regulated strategy development (SRSD) reduces WM load by providing steps
* Structures Writing Program reduces WM load by providing ideas, vocabulary, and spelling
* Sentence combining reduced WM by providing content and spelling

Remediation

* Improving phonics skills
* Learning letter-sound relationships and rules
* Improving orthographic memory and analysis

* Improving letter formation
* Using modeling and self-verbalization
* Using visual cues
* Multicomponent interventions

* SRSD to improve
○ Planning
○ Organization
○ Goal setting
○ Self-monitoring
* Structures Writing to improve organization
* Sentence combining to improve sentence level planning and organization

To identify strategies, we conducted systematic searches (see Appendix), examined meta-analyses for studies used with students with reading and writing disabilities, and conducted forward searches to identify studies of additional strategies. When identifying and recommending strategies, we include strategies that have been shown to be effective for students with both reading and writing difficulties, who struggle with writing for a variety of reasons.

Interventions to Address Poor Transcription Skills

There are a variety of remediation and compensation strategies for transcription skills. For some skills, there are both remediation and compensation strategies that teachers can use flexibly to meet students' needs.

Strategies That Support Spelling Development

The nature of English itself gives us some hints about the kinds of instruction that may be effective for improving spelling. We located 19 studies that (a) used experimental designs that support causal inference (randomization or single-case methods) and (b) had positive effects on spelling achievement. We examined the instructional components of all the interventions and counted how often each of these components was used in those studies. Four instructional components were present in at least four studies, data that we think suggest these components may be useful parts of a spelling program for students with dyslexia. We describe each of these here (see Table 4 for a number of studies supporting each strategy).

Table 4.

Element

Studies

Multicomponent phonics program

8

Letter-sound analysis

7

Morphological analysis

5

Orthographic analysis or memory

3

Word meaning

2

Syllabic analysis

2

Vocabulary and reading comprehension program

2

Phonics. Phonics instruction was by far the most frequent of the instructional components related to spelling achievement, the focus in eight of the 19 studies. These studies included multicomponent phonics interventions and involved teaching students to (a) recognize and pronounce grapheme-phoneme correspondences (e.g., T = /t/, also called sound-spellings) and phonograms (the spellings of rhyming parts of words like OAT = /oʊt/), (b) decode words using sound-spellings and phonograms, (c) practice pronouncing and spelling high-frequency words, and (d) practice encoding using sound-spellings and phonograms (see Figure 4 for examples of these activities). Most programs also include reading words in sentences and texts with words chosen to focus on new and review skills. In our review, there were eight studies that used these types of phonics programs and found that they positively affected spelling outcomes: Guyer, Banks, and Guyer (1993); Lim and Oei (2015); Morris et al. (2012); O'Shaughnessy and Swanson (2000); Savage, Carless, and Stuart (2003); Schlesinger and Gray (2017); Schneider, Roth, and Ennemoser (2000); and Vaughn et al. (2010). Phonics instruction has been very effective in improving the reading achievement of children with dyslexia, so it is no surprise that it has a similar effect on spelling in children with dyslexia ( National Institute of Child Health and Human Development, 2000). Phonics instruction helps children solidify the relationships between letters and sounds and helps them to identify each sound in a word. For example, reading jump would involve providing a sound for each letter, so this would reinforce the connection between /mp/ and mp. After extensive phonics practice, readers will be unlikely to make the jump- jup* error anymore. This knowledge will almost certainly translate to spelling because spelling unknown words involves encoding the sounds to write letters, just as reading unknown words involves decoding the letters to produce sounds. Moreover, many of these phonics programs deliberately include encoding practice. There are many programs available that include most or all of these skills. Databases that provide information about programs with evidence of effectiveness come from the What Works Clearinghouse, the National Center for Intensive Intervention, and the Best Evidence Encyclopedia, among others.

Learning sound-spellings and phonograms. In effective spelling-focused programs, one important feature was instruction on sound-spellings ( Berninger, Lee, Abbott, & Breznitz, 2013; Darch, Kim, Johnson, & James, 2000; Hart, Berninger, & Abbott, 1997; Santoro, Coyne, & Simmons, 2006; Shippen, Reilly, & Dunn, 2008; Vadasy, Sanders, & Peyton, 2006). Obviously, learning sound-spellings is part of phonics instruction, but it can also support spelling even if they are not taught as part of a phonics program. Conrad (2008) even showed that practicing spelling words benefits word reading-even more than reading benefits spelling.

In addition, children with dyslexia may benefit from learning how to select spellings when there are multiple possible options. For example, /ʧ/ can be spelled with CH or TCH, if a reader would be able to read a word either way. However, they might have less luck spelling unfamiliar /ʧ/ sounds because either spelling could be correct: For example, cach* and catch both say catch. However, there is a pattern children can learn: The TCH spelling is used after a short vowel (a lax vowel sound, usually spelled with a single A, E, I, O, or U; refer back to Table 2 for examples of this and other short-vowel patterns). The point is that some spelling patterns support spelling accuracy but would have little additional impact on reading ( Caravolas, Hulme, & Snowling, 2001). Learning such spelling patterns still has value because they support transcription accuracy and therefore text generation.

One way to reinforce spelling patterns is to have students complete a dictation activity. In dictation, teachers have students examine words in sound-spelling or phonogram units. Students spell the word one unit at a time. See Figure 5 for an example.

Analysis of the morphemes in words. The phonological challenges children with dyslexia experience can make it difficult for them to use phonological information. In some cases, even the best phonics instruction may not result in adequate word reading improvement. One way to circumvent this problem is to teach children to recognize a different kind of unit, a morpheme. Morphemes are meaningful units in words, including affixes and base words. Replacement has the prefix re-, the base word place, and the suffix -ment. The problem with morphemes is that they are less efficient than sound-spellings because fewer words can be spelled correctly using morpheme information than using sound-spellings alone. English has many more morphemes than sound-spellings. For example, there are only 70 affixes with at least 100 occurrences in English words, versus 224 for sound-spellings. However, many words have more than one morpheme ( Nagy & Anderson, 1984), and readers at all ability levels appear to use morphological information ( Kearns, 2015). In short, there are good reasons for teaching students to spell using morphemes. To that end, five studies with positive spelling effects included instruction on using morphemes to spell words ( Darch et al., 2000; Kirk & Gillon, 2009; Shippen et al., 2008; Vadasy et al., 2006; Vaughn et al., 2010). These programs usually involved teaching both the spelling and meaning of affixes, with a greater emphasis on their spelling and pronunciation. Another valuable activity involves teaching base-word families, emphasizing how a base word changes when one or more affixes are attached to it (e.g., happy, happier, unhappy; Archer, Gleason, & Vachon, 2003; O'Connor, Beach, Sanchez, Bocain, & Flynn, 2015).

Orthographic analysis and word memory. Three studies indicate that children's spelling improves when they are taught strategies to remember the exact spellings of words ( Berninger et al., 2013; Fulk, 1996; Hart et al., 1997). For example, Berninger et al. (2013) taught students two strategies to remember the written forms of words, the Photographic Leprechaun and the Proofreader's Trick. The strategies both involved visualizing a word and answering questions about its spelling. For example, in the former, a reader like Jordan would look at a word, close his eyes, and answer questions such as "What is the second to last letter?" Then, he would open his eyes to check the answer. The latter was the same except that the children spelled the word backward with their eyes closed.

It is important to note that only three studies included this kind of instruction. In addition, two of these were in studies by the same research group, and the instruction in both included other components. However, the results were positive overall, so we included this study.

Spell-check. Spell-check has been available for quite some time, although evidence of effectiveness is limited ( Morphy & Graham, 2012) and (similar to the caveat for keyboarding skills) the effectiveness of spell-check will likely depend on students' ability to use it. Use of spell-check is also limited to computer-based writing and assumes that students can approach a reasonable approximation for the words they want to spell and identify the correct spelling for the word when options are provided.

Strategies to Help Students Improve Handwriting

Although there are ways to compose texts that do not require handwriting, it is still one of the most prevalent forms of writing in school, and some research shows that teaching handwriting can help improve reading outcomes for students with dyslexia. In a recent meta-analysis, Santangelo and Graham (2016) found that teaching handwriting instruction can improve legibility and fluency of students' writing and lead to improvements in writing quality and length of students' writing. Many studies involved students with significant handwriting difficulties, which we have demonstrated is a common attribute of students with dyslexia. It is important to note that Santangelo and Graham found that studies involving motor instruction did not produce better handwriting skills. However, individualizing handwriting instruction and using technology were effective. We identified some of the individual handwriting strategies from studies that included students with significant reading and writing difficulties.

Multicomponent interventions. By far, the most common and effective approach to teaching handwriting to students with handwriting difficulties has been the use of individualized approaches involving multiple components (e.g., Berninger et al., 1997; Christensen, 2005; Denton, Cope, & Moser, 2006; Graham, Harris, & Fink, 2000; Jones & Christensen, 1999; Peterson & Nelson, 2003; Sovik, Arntzen, & Thygesen, 1986; Veena, Romate, & Bhogle, 2002; Weintraub, Yinon, Hirsch, & Parush, 2009; Zwicker & Hadwin, 2009). Every study identified in Santangelo and Graham's (2016) meta-analysis as using a multicomponent intervention for handwriting instruction was found to be effective. Such interventions often group letters by shared characteristics (e.g., Christensen, 2005; Graham et al., 2000) and include some combination of teacher modeling (e.g., Jones & Christensen, 1999), assistance to correct specific errors, use of models or tracing letters' tracks (e.g., Weintraub et al., 2009), specific feedback (e.g., Denton et al., 2006), self-feedback (e.g., circle your best letter; Graham et al., 2000), and practice and repetition (e.g., Peterson & Nelson, 2003). See Figure 6 for an example of several tasks from a multicomponent intervention developed by the Center on Accelerated Student Learning; we have provided the URL in the reference list ( Graham & Harris, n.d.).

Use of models to teach handwriting. A few studies with students with disabilities suggested that the use of models is effective. Specific strategies include copying letters from models ( Berninger et al., 1997; Walser, 1981), matching letters to models ( Walser, 1981), or use of visual cues ( Berninger, 1987). Some of these strategies were shown in the multicomponent interventions but were also shown to be effective on their own.

Technology for developing handwriting skills. Using technology was also found to be effective in two studies involving students with handwriting problems ( Carrieres & Plamondon, 1994; Sovik et al., 1986). In both studies, the researchers used a digitizing tablet, and students traced letters. This approach seems promising, as technology can provide instant feedback, providing the teacher more flexibility in how practice is applied. However, we suggest incorporating the use of technology into a multicomponent intervention.

Keyboarding. There is some literature that shows the impact of using keyboarding to compensate for poor handwriting skills, but this should be approached cautiously. In a meta-analysis, Graham and Perin (2007) examined studies comparing students' writing when they were allowed to use a word processor with when they used paper and pencil. They found an effect size of 0.50, indicating that students wrote higher quality texts when typing. However, a more nuanced examination by Graham, Harris, and Hebert (2011) indicated that this is only effective for students who have experience using a word processor/keyboard and that it can underestimate the writing skills of some students if they do not have experience in typing. In these cases, teachers would want to provide instruction in keyboarding before expecting it to be an effective way to compensate for poor handwriting skills. This presents the teacher with a choice to (a) teach keyboarding skills to help students circumvent handwriting difficulties, (b) remediate handwriting skills, or (c) both.

Technology Strategies to Help Students Compensate for Both Handwriting and Spelling Difficulties

Technological developments continue to provide new ways to compensate for writing difficulties and reduce the complexity of writing. The number of these technology solutions and the pace at which they improve and change make it difficult to evaluate the efficacy of their use. Therefore, we limit our recommendations to three approaches with some research behind them that are also recommended by dyslexia experts (see Table 5 ).

Table 5.

Program

Description/features

Research

Where to find it

Co-writer, NEO2

A word processor with text predict, provides suggestions based on orthography and phonology of attempted words; the program offers a read-aloud option that will read the word options aloud as well as the final writing product.

Cullen et al. (2008)

http://donjohnston.com/cowriter/

Dragon Naturally Speaking

A speech recognition program that can be used to dictate a variety of writing tasks for students. Students use commands such as "Cap that" or "period" to include proper conventions. The text is shown on the screen as they dictate, which allows students to reread to make revisions or edits.

Higgins & Raskind (1999)

https://www.nuance.com/dragon.html

Livescribe

An assistive technology that can help dysfluent writers keep up with notetaking. The Livescribe technology is a smart pen that has a camera and a recording device. It can be used to take notes, while also listening to a presentation.

Belson et al. (2013)

http://www.livescribe.com/en-us/

Interventions to Address Poor Executive Function Skills

We present three interventions for improving poor executive function skills in writing: sentence combining, text structure instruction, and self-regulated strategy instruction. These interventions reduce the cognitive load for executive function tasks by breaking down complex skills into more manageable components for the beginning writers and/or incorporating compensatory strategies that help students focus on higher level skills.

Importantly, these skills also address language-related components of writing, including grammar, syntax, discourse structure, and organizational features of text. The use of these strategies compensates for the primary difficulties students with dyslexia face (e.g., spelling difficulties), allowing them to focus on higher order language skills related to text construction. Practitioners are encouraged to employ these strategies with a focus on the intersection of oral language and written expression, to emphasize language components of writing and executive function skills simultaneously.

Sentence Combining

Sentence combining has been shown through meta-analysis to be effective for improving writing skills of adolescents ( Graham & Perin, 2007) and elementary grade students ( Graham, McKeown, Kiuhara, & Harris, 2012) and has also been demonstrated to improve reading fluency skills ( Graham & Hebert, 2011). We include sentence combining under executive function rather than transcription skills, because the goal of instruction is to help students plan and organize ideas at the sentence level. Sentence combining is a general intervention that involves providing students with two or more simple sentences (called kernel sentences) and teaching them to combine those kernel sentences into a single, more complex sentence, while keeping the original ideas intact. The following example illustrates how sentence combining exercise works:

Kernel Sentence 1: Jellyfish have hoods and tentacles.

Kernel Sentence 2: Their tentacles are numerous.

Kernel Sentence 3: Their hoods are gelatinous.

Combined sentence: Jellyfish have gelatinous hoods and numerous tentacles.

As shown in the example, providing the kernel sentences for students reduces the cognitive load during sentence writing instruction by (a) eliminating the need for students to generate ideas for the sentences, (b) providing content and vocabulary for students, and (c) providing students with the spelling of complex (and not so complex) words. This allows the students to think about how the ideas are related and develop plans and goals for writing better sentences, improving executive function skills, text generation, and writing quality.

Moreover, sentence combining exercises can be utilized in a myriad of ways to focus on particular language skills and make connections between oral language and writing. The focus of the previous example was adjective use, but sentence combining exercises can be used to teach a variety of grammatical structures, including compound sentences with connectors, compound subjects, compound predicate phrases, prepositional phrases, dependent clauses with because, and adverb clauses, to name a few. A nonexhaustive set of example exercises are included in Figure 7 .

As students gain more experience and facility with sentence combining exercises composed of two or three kernel sentences, practitioners can use more complex exercises to help children develop more complex language skills related to writing. Exercises with five or more kernel sentences can be used to facilitate the use of complex elements that can be combined in multiple ways. Several sentence combining exercises might be grouped to help students connect ideas across sentences or in paragraphs. Practitioners can also develop de-combining exercises that require children to break more complex sentences into simpler ideas units. These kinds of exercises can help students develop flexibility in their language use when writing. See Figure 8 for examples of more complex sentence combining activities.

For Jordan and other students with dyslexia, these exercises are critical for improving writing skills. Jordan's writing included attempts at combining multiple ideas within a single sentence but included sentence level grammar errors that show a lack of sophistication in using dependent clauses. It may be that students with dyslexia either lack skills for complex sentence writing or have difficulty utilizing these skills when they write. Either way, this deficit is likely due to difficulties with transcription skills associated with demands on working memory during writing. Sentence combining instruction is an effective approach for remediating sentence construction of students with dyslexia because it reduces the demands transcription skills have on working memory. In turn, as students with dyslexia improve their sentence construction skills, it frees up cognitive resources that can be devoted to other executive functions and transcription.

Teachers can implement sentence combining intervention at a low cost, as they can create their own sentences using content and skills from class. A valuable resource for teachers looking who would like to learn to more about sentence combining is the Teacher's Guide to Effective Sentence Writing (What Works for Special Needs Learners), written by Bruce Saddler (2012).

Teach Children to Self-Regulate

One of the most effective approaches to improving the writing skills of students with writing difficulties is self-regulated strategy development (SRSD). The effectiveness of SRSD has been demonstrated in meta-analyses of group-design experimental research ( Graham & Harris, 2003; Graham, McKeown, et al., 2012; Graham & Perin, 2007) as well as single-subject-design research ( Rogers & Graham, 2008). It has been shown to be effective for students with reading and writing disabilities across the full range of grade levels. Students who have dyslexia may especially benefit from SRSD, as they often have fewer opportunities to learn how to use executive functions targeted by the intervention, including self-regulation skills, goal setting, self-speech, and self-monitoring. Students are taught to use these self-regulation skills through self-instruction involving defining the problem, focusing on attention and planning, engaging in writing, error correction, coping, and self-reinforcement, for example, when students might be taught to say things such as "My goals for this persuasive essay are to include three reasons," or when self-evaluating, they might be taught to say, "Am I following my plan?" The teacher models specific self-speech, acting as an external voice for the student, and then the student practices using the self-speech until he or she internalizes it and come up with some of his or her own self-instructions.

These self-regulation strategies are often paired with planning, organization, and revision strategies specific to writing and are taught in six stages: (a) develop background knowledge, (b) discuss it, (c) model it, (d) memorize it, (e) support it, and (f) independent performance. Some features of SRSD help to simultaneously improve and reduce the demands of executive function skills, by sequencing them in a way that chunks the writing task and makes it manageable for the writer. This allows the writer to dedicate more working memory resources to text production. For example, many SRSD strategies include a mnemonic that helps remind students of important steps for completing the writing task (see Figure 9 for examples of SRSD mnemonics). A useful web resource for educator training in SRSD is https://iris.peabody.vanderbilt.edu/module/srs/.

Teach Children Text Structures

Text structure instruction has been identified as an effective strategy for improving the expository reading and writing skills of students, especially those with learning disabilities ( Duke & Pearson, 2002; Gersten, Fuchs, Williams, & Baker, 2001; Roehling, Hebert, Nelson, & Bohaty, 2017). Hebert, Bohaty, Nelson, and Brown (2016) found that these strategies were particularly effective when writing was involved and also found larger effect sizes for students with learning disabilities. For teaching students with dyslexia writing skills, text structure instruction may be particularly beneficial because it can simplify the writing organizational choices for students, based on the structure needed for their purpose. There are five basic text structures: description, compare/contrast, sequence, cause/effect, and problem/solution.

A promising approach to teaching these text structures is the Structures Writing program, which has been shown to be specifically effective for improving the informational writing skills of students with reading and writing disabilities ( Hebert, Bohaty, Nelson, & Lambert, 2018; Hebert, Bohaty, Nelson, & Roehling, 2018). In this approach, students are provided information to write about, which reduces the cognitive load of the students by providing them with ideas, vocabulary, and spelling within an information frame (see Figure 10 for an example). This approach is designed to improve executive function skills in writing by reducing cognitive demands of transcription skills and idea generation, focusing students' attention on learning a step-by-step approach to organizing and writing information according to the text structure chosen. More information and resources for Structures Writing can be obtained by contacting the first author of the current article.

Summary

Students with dyslexia suffer from reading difficulties that co-occur with writing difficulties for a variety of reasons. We presented one writing sample of a student with dyslexia (Jordan) to help illustrate the writing difficulties these students face as well as research on the underlying relationships. We then presented several interventions for remediating writing difficulties and/or helping students compensate for skill deficits. Although we attempted to provide a set of recommended strategies that target skills that students with dyslexia may struggle with, this list of interventions is far from complete. Meta-analytic efforts over the past 15 years have revealed a compendium of effective strategies for improving students' writing skills. These include effective strategies for teaching writing skills to adolescent writers ( Graham & Perin, 2007) and elementary writers ( Graham, McKeown, et al., 2012); strategies for using writing to improve learning outcomes ( Bangert-Drowns, Hurley, & Wilkinson, 2004); strategies for using writing to impact reading ( Graham & Hebert, 2011); strategies illustrating the impacts of writing assessment on writing outcomes ( Graham et al., 2011); strategies targeting specific skills, such as handwriting ( Santangelo & Graham, 2016), spelling ( Graham & Santangelo, 2014), and SRSD ( Graham & Harris, 2003); and strategies that have specifically been effective for students with learning disabilities ( Gillespie & Graham, 2014). In addition to these meta-analyses, we point the reader to two additional useful resources developed by the Institute of Education Sciences: (a) a practice guide for teaching elementary school students to be effective writers ( Graham, Bollinger, et al., 2012) and (b) a practice guide for teaching secondary students to write effectively ( Graham et al., 2016).

We also encourage educators to use a combination of interventions to address the specific writing needs of their students with dyslexia. To illustrate how a teacher might approach this, we look one more time at the writing of our case study student, Jordan. We noted that Jordan had some difficulty with transcription skills, specifically some minor handwriting and spelling issues. Jordan's handwriting difficulties would not rise to the level of referral to an occupational therapist. Therefore, we would suggest targeted handwriting instruction for specific letters, such as circular letters like o and a, along with regular distributed practice. The spelling issues might be best addressed with a combination of phonics instruction and dictated spelling instruction targeting high-frequency words, in addition to regular classroom spelling instruction. Finally, Jordan has difficulty constructing sentences and holding onto ideas. To address these issues, we might recommend incorporating sentence combining instruction to improve sentence-level writing skills as well as teaching Jordan a planning strategy to compensate for working memory challenges; SRSD instruction would be a good choice for this. In this way, Jordan's complex writing challenges are addressed using a combination of interventions targeting an array of writing skills.

Finally, use of the instructional strategies we described can improve the writing skills of students with dyslexia, making it easier for those students to express their ideas. However, instruction should not stop with improvements in basic skills alone. Practitioners must help children use their improved skills to tell stories, teach others interesting information, and share their opinions and make arguments to address issues they care about ( Graham et al., 2017). In this way, targeted writing (and reading) interventions will help children with dyslexia exercise the immense power of communication by the written word.

Acknowledgments

Support for this research was provided by the National Institutes of Health Grant 1R37HD090153-01A1 (awarded to Haskins Laboratory). The content herein does not represent the views of the agency.

Appendix

Search Procedure

To locate articles on intervention to support spelling, we searched ERIC and PsycINFO using four keyword categories, namely, that the studies involved (a) children or adolescents, (b) dyslexia in the title or abstract, (c) spelling in the title or abstract, and (d) instruction or intervention. We initially identified 196 studies that contained the required target words. We read them to make sure that they involved instruction for people with dyslexia and related difficulties, had research designs that would allow us to state confidently that the instruction is likely to be effective, measured spelling skill, and concerned reading in English. We decided to eliminate studies of other languages because of the unique characteristics of English orthography. We also examined meta-analyses by Galuschka, Ise, Krick, and Schulte-Körne (2014), Goodwin and Ahn (2013), Scammacca et al. (2007), Wanzek et al. (2013), and Williams, Walker, Vaughn, and Wanzek (2017). We read each article to ensure they met inclusion criteria. We then removed studies where the authors did not observe significant improvement in spelling. The result was a set of 19 articles, those reported in this article.

Funding Statement

Support for this research was provided by the National Institutes of Health Grant 1R37HD090153-01A1 (awarded to Haskins Laboratory).

Footnotes

¹It should be noted that the simple view of writing separates working memory from executive function, although it is more often included under the umbrella of executive function skills, along with cognitive flexibility and inhibitory control (see Zelazo, Blair, & Willoughby, 2016). For the purposes of this article, we also discuss working memory and executive function skills as separate, in order to situate our discussion within the simple view of writing, which provides a straightforward framework for considering the links between dyslexia and writing.

²Some studies (e.g., Moll & Landerl, 2009) have shown a dissociation between reading and spelling skills because reading is more strongly associated with rapid naming than spelling. That is, good spelling does not require the processing speed required for good reading. However, it is likely that this is a greater concern in more transparent orthographies than English. Moll and Landerl's study was conducted in German, and other studies have shown that English readers process words differently from their peers in more transparent orthographies (e.g., Rau, Moll, Snowling, & Landerl, 2015; Torppa, Georgiou, Niemi, Lerkkanen, & Poikkeus, 2017). As a result, we focus on the strong association between reading and spelling but acknowledge that there may be a dissociation between reading speed and spelling as English-speaking children with dyslexia become more accurate and better able to spell.

³Difficulty with handwriting, particularly in the absence of word recognition or language comprehension difficulty, is sometimes called dysgraphia ( Berninger et al., 2015; Thompson et al., 2018). However, researchers have not agreed on common measures for identifying this difficulty, and it is not clear whether dysgraphia includes cases where children have fine motor problems beyond handwriting. Moreover, handwriting difficulties are frequently associated with other academic difficulties, so it is difficult to separate a specific dysgraphic profile. As a result, we do not use that term here, but we acknowledge that others do.

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