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Learning Disabilities and Accommodations for Success

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Learning Disabilities and Accommodations for Success

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Lots of good info, but start on page 10 to find;
1. Description of each cognitive
domain / process that affect students with LD.
2. Student actions in math that align with each doman/process.
3. Suggested accommodations which could help the student be successful in math.

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Math Continuums and Long Range Plan - Grades 5-8

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Math Continuums and Long Range Plan - Grades 5-8

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Look at the connections between curriculums. Does a student need to be modified, or can they access grade level with accommodations?

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Math Continuums and Long Range Plan - Grades K-4

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Math Continuums and Long Range Plan - Grades K-4

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If a student does need curriculum that is modified, what are the connections between grades that keep the student in the class learning with his/her peers?

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In addition to specific strategies for students with accommodations, an/or modifications in math, it is important to look at the whole math environment. What is good for one is often good for all. How do the environment, and belief systems of students impact success? What else can be examined in the IEP process?

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This document provides teachers with an opportunity to assess and determine students strengths and needs in the areas of Knowledge and Understanding, Thinking Communication and Application

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Accommodations, and UDL for learning provide ways to adapt programs without modifying grade level.

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Adapting Mathematics Instruction in the General Education Classroom for Students with Mathematics Disabilities | LD Topics | LD OnLine

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LD OnLine is the leading website on learning disabilities, learning disorders and differences. Parents and teachers of learning disabled children will find authoritative guidance on attention deficit disorder, ADD, ADHD, dyslexia, dysgraphia, dyscalculia, dysnomia, reading difficulties, speech and related disorders.

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By Hanna A. Kubas and James B. Hale
Mathematics. Some love it, some loathe it, but there are many myths about math achievement and math learning disabilities (LDs). The old belief - boys are naturally better at math than girls - may be more a consequence of teacher differences or societal expectations than individual differences in math skill (Lindberg, Hyde, Petersen, & Linn, 2010).

Similarly, the old belief that reading is a left brain task, and math is a right brain task, is not a useful dichotomy as clearly multiple shared and distinct brain regions explain these academic domains (e.g., Ashkenazi, Black, Abrams, Hoeft, & Menon, 2013).

Math is a language with symbols that represent quantity facts instead of language facts (i.e., vocabulary), so rules (syntax) are important for both (Maruyama, Pallier, Jobert, Sigman, & Dehaene, 2012). You might be surprised to learn that approximately 7% of school-aged children have a LD in mathematics (Geary, Hoard, Nugent, & Bailey 2012).

Let's first explore the fundamental skills needed for math achievement.

Number Sense / Numerical Knowledge

Children develop knowledge of quantity even before math instruction in schools, and kindergarten number sense is predictive of math computation and problem solving skills in elementary school (Jordan et al., 2010). These basic math skills include understanding of number magnitudes, relations, and operations (e.g., adding). Children link basic number sense to symbolic representations of quantity (numbers); the math "language". Poor early number sense predicts math LDs in later grades (Mazzocco & Thompson, 2005).

Math Computation vs. Math Fluency

Children often rely on various strategies when solving simple calculation problems, but math computation requires caring out a sequence of steps on paper or in your mind (working memory) to arrive at an answer. Math fluency refers to how quickly and accurately students can answer simple math problems without having to compute an answer (i.e., from memory 6 x 6 = 36), with no "steps", calculation, or number sense needed.

Children with fluency deficits often use immature counting strategies and often do not shift from computation to storing and retrieving math facts from memory, taking more time to provide an answer. Difficulty with retrieval of math facts is a weakness/deficit associated with math LDs (Geary et al., 2007; Gersten, Jordan, & Flojo, 2005). Without math fact automaticity, working memory may be taxed when doing computation, and the child "loses his place" in the problem while computing each part to arrive at a final answer.

Developmental Sequence of Math Skills

1. Finger Counting Strategies: Students first display both addends/numbers with their fingers; this is the most immature strategy.

2. Verbal Counting Strategies: Next, students begin to develop basic adding skills and typically go through three phases.

Sum: counting both addends/numbers starting from 1, this is a beginning math counting skill;

Max:counting from the smaller number; and finally

Min:counting from the larger number (most efficient strategy).

3. Decomposition (Splitting) Strategies: Students learn that a whole can be decomposed into parts in different ways, a good problem solving strategy for unknown math facts

4. Automatic Retrieval from Long-Term Memory: Students become faster and more efficient at pairing problems they see with correct answers stored in long-term memory (as is the case with sight word reading), no computation is required

The Role of Visual-Spatial Skills

Basic arithmetic skills are factual, detailed "left hemisphere" functions (similar to basic reading), but Byron Rourke (2001) discovered many students with nonverbal or "right hemisphere" LDs had math calculation problems, suggesting left was verbal and right nonverbal.

Students need "right hemisphere" visual/spatial skills to align numbers when setting up multistep math problems, they need to need to be able to understand and spatially represent relationships and magnitude between numbers, and they need to be able to interpret spatially represented information (Geary, 2013).

Neuropsychology has also taught us that children with visual/spatial problems may neglect the left side of stimuli (the left visual field is contralateral to the right hemisphere) (Hale & Fiorello, 2004; Rourke, 2000).

Math Reasoning and Problem-Solving

Word problems require both receptive and expressive language skills, unlike simple calculation, so students with language-based LDs may struggle even if math skills are good. Students must translate math problem sentences/words into numbers and equations, so they must identify what the sentences are asking them to do in terms of calculation, and then perform the calculation

Students with LDs are typically poor strategic learners and problem solvers, and often manifest strategy deficits that hinder performance, particularly on tasks that require higher level processing (Montague, 2008). So there is a strong relationship between fluid reasoning, executive functioning, and quantitative reasoning (Hale et al., 2008). Students with LDs often benefit from explicit instruction in selecting, applying, monitoring, evaluating use of appropriate strategies to solve word problems.

The Brain, Math, and LDs

Click here to access a printable PDF version of LD@school's diagram of brain areas and math skills.

Strategies for Promoting Math Computation and Fluency

Note : Your understanding of foundational mathematical concepts and skills is critical for targeted interventions that are developed, implemented, monitored, evaluated, and modified until treatment efficacy is obtained!
Remember: early identification and intervention are key!
Click here to access a printable PDF version of the Strategies for Promoting Math Computation and Fluency explained below.

Strategic Number Counting
Fuchs et al. 2009
Goal: Improve counting strategies (e.g., MIN; decomposition) to efficiently pair problem stems and answers

Skills Targeted: Explicitly teach math counting strategies when number sense or algorithm adherence is limited

Target Age Group: Elementary students struggling with basic computation and quantity-number association
Description:

Direct instruction of efficient counting (g., MIN for addition), followed by guided practice.

For two-number addition, students start with larger number and count for smaller number/addend.

For two-number subtraction, students start at 'minus number' and count up to 'starting number,' tallying numbers

Flashcards used to math fact encoding, storage, and/or retrieval deficits. Optional number line can enhance method.

Fuchs et al. (2009) found strategic counting led to better math fact fluency compared to control groups, even better if combined with intensive drill and practice

Strategic counting with and without deliberate practice better math fluency, with deliberate practice better than controls (Fuchs et al., 2010)

Additional Resources:
Drill and Practice
Fuchs et al. 2008
Goal: Drill and practice interventions help children quickly and accurately recall simple math facts

Skills Targeted: Practice and repetition of math fact calculations

Target Age Group: Students struggling with basic math facts, especially with limited automaticity
Description:

May be paper-and-pencil and/or computerized drill and practice in either a game or drill format, typically includes modeling, practice, frequent administration, and brief, timed practice, self-management, and reinforcement

Drill and practice with math problem solving strategies may be more effective

Software to ensure correct student response; math facts appear for 1-3 seconds, and students reproduce the whole equation and answer from short-term memory

Students visually encode both the number question and answer for long-term memory storage

Connection between math fact rehearsal and increased fact retention and generalization (Burns, 2005; Codding et al., 2010; Duhon et al., 2012)

Promotes efficient paring of problems and the correct answers (Fuchs et al., 2008)

Computer versions improve math fact retrieval fluency (Burns et al., 2010; Slavin & Lake, 2008)

Additional Resources:
Cover-Copy-Compare
Skinner et al. 1997
Goal: Improve accuracy and speed in basic math facts

Skills Targeted: Students taught self-management through modeling, guided practice, and corrective feedback

Target Age Group: Students learning basic math facts, those with executive, sequential, or integration problems
Description:

Students learn 5-step strategy to solve simple math equations and self-evaluating correct responses

Students look at math problem, cover it, copy it, and evaluate response to compare to original

For errors, brief error correction procedure undertaken before next item introduced

Strategy requires little teaching time or student training

CCC procedures enhance math accuracy and fluency across general education (Codding et al., 2009; Grafman & Cates, 2010) and special education (Poncy et al., 2007; Skinner et al., 1997)

Meta-analysis of many studies shows CCC improves math performance, especially when coupled with other evidence-based methods (e.g., token economies, goal setting, correct digits, increased response opportunity; Joseph et al., 2012)

Additional Resources:
Detect-Practice-Repair
Poncy, Skinner & O'Mara, 2006
Goal: Promote efficient basic math fact practice targeting problems not completed accurately and/or fluently

Skills Targeted: Encoding and retrieval of math facts from long-term memory

Target Age Group: Students developing basic math facts, may be useful for executive memory difficulties
Description:

DPR is a 3-phase test-teach-test procedure for individualizing math fact instruction for basic fact groups (e.g., addition)

(1) Detect phase - metronome determined rate to determine automatic (< 2 seconds) vs. slow (>2 second) math fact responding

(2) Practice phase using Cover-Copy-Compare (CCC; see description above)

(3) Repair phase using 1-minute math sprint with items requiring practice embedded in automatic ones

DPR validated across grades, skills, and research designs (Poncy et al., 2013)

Improves subtraction, multiplication, and division fluency (Axtell et al., 2009; Poncy et al., 2006; 2010; Parkhurst et al., 2010)

Differentiation possible because DPR targets specific difficulties (Poncy et al., 2013)

Reciprocal Peer Tutoring
Fuchs et al., 2008
Goal: Peer tutoring procedure includes explicit timing, immediate response feedback, and overcorrection

Skills Targeted: Basic math fact retrieval and automaticity through constant engagement in dyads

Target Age Group: All students, but especially useful for students with poor attention or persistence
Description:

Students are paired up and take turns serving as the "tutor"

Flashcards with problem on one side (e.g., 2 x 3 = ___) and answer on other side (e.g., 6)

Student tutors shows flashcard, tutee responds verbally

Tutor states either "correct," (and puts in correct stack) or "incorrect" (and puts in incorrect stack)

If incorrect, tutee writes problem and correct answer 3 times on paper

Roles change after 2 minutes; then students complete 1 minute math probes and grade each other

Multicomponent approach + other evidence-based efforts improve math fact rates (Rhymer et al., 2000)

Improves math achievement, engagement, and prosocial interactions (Rohrbeck et al., 2003)

Improves achievement, self-concept, and attitudes (Bowman-Perrot et al., 2013; Tsuei, 2012)

Strategies for Promoting Math Problem-Solving

Click here to access a printable PDF version of the Strategies for Promoting Math Problem-Solving explained below.

Schema Theory Instruction
Jitendra et al. 2002
Goal: Teaches mathematical problem structures, strategies to solve, and transfer to solve novel problems

Skills Targeted: Expanding student math problem solving schemas

Target Age Group: Students in any grade learning math problem solving skills, helps conceptual "gestalt"
Description:

Encourages math problem solving schemas for word problems, identifying new, unfamiliar, or unnecessary information, and grouping novel problem features into broad schema for strategy use

Explicit instruction in recognizing, understanding, and solving problems based on mathematical structures; can be used with schema-broadening instruction for generalization (e.g., Fuchs et al., 2008)

Randomized controlled trials show improved math word problem solving (Fuchs et al., 2008, 2009)

Schema-based approach generalizes into better math word problem solving (Jitendra et al., 2002; 2007; Xin, Jitendra, & Deatline-Buchman, 2005)

Fast Draw
Mercer & Miller, 1992
Goal: Self-regulated strategy instruction method for increasing math problem solving skills

Skills Targeted: Targets self-teaching, self-monitoring, and self-support strategies for identifying salient math words in sentences, determining and completing operation, and checking accuracy

Target Age Group: Students struggling with executive monitoring and evaluation skills
Description:

Teaches 8-step math word problems strategy and self-regulation

The mnemonic FAST DRAW cues students, can use as checklist

Increases math achievement and improves math attitude (Tok & Keskin, 2012)

Increases math achievement in math LD (Miller & Mercer, 1997; Cassel & Reid, 1996)

Click here to access LD@school's template for the FAST DRAW mnemonic.

Cognitive Strategy Instruction
Montague & Dietz, 2009
Goal: Teach multiple cognitive strategies to enhance math problem solving skills

Skills Targeted: Focuses on cognitive processes, including executive functions (self-regulation/metacognition)

Target Age Group: Useful for differentiating instruction based on processing weaknesses
Description:

Teaches 7-step cognitive strategy for solving math word problems, with 3-step metacognitive self-coaching routine for each step

Direct instruction includes structured lesson plans, cognitive modeling, guided practice cues and prompts, distributed practice, frequent teacher-student interaction, immediate corrective feedback, positive reinforcement, overlearning, and mastery

7-step process includes:

1. Read the problem for understanding

2. Paraphrase the problem in your own words

3. Visualize a picture or a diagram to accompany the written problem

4. Hypothesize a plan to solve the problem

5. Estimate/predict the answer

6. Compute the answer

7. Check your answer to make sure everything is right Say, Ask, Check metacognitive routine in each of the 7-step cognitive processes

Say requires self-talk to identify and direct self when solving problem

Ask requires self-questioning, promoting self-talk internal dialogue

Check requires self-monitoring strategy for checking understanding and accuracy

Self-regulation strategies foster math problem solving in meta-analyses (Kroesbergen & van Luit, 2003)

Cognitive strategy instruction increases math problem solving skills in general education (Mercer & Miller, 1992, Montague et al. 2011) and ADHD and LD (Iseman & Naglieri, 2011)

Additional Resources:
Related Resources on the LD@school Website

Click here to access the article Math Heuristics.

Click here to access the article Helping Students with LDs Learn to Diagram Math Problems.

Click here to access the answer to the question: There is a lot of information about identifying learning disabilities in mathematics. However, information about strategies and ideas for working with these disabilities is limited. What strategies work?.

Click here to access the video Using Collaborative Teacher Inquiry to Support Students with LDs in Math.

Click here to access the recording of the webinar Understanding Developmental Dyscalculia: A Math Learning Disability.

References

Ashkenazi, S., Black, J. M., Abrams, D. A., Hoeft, F., & Menon, V. (2013). Neurobiological underpinnings of math and reading learning disabilities. Journal of learning disabilities, 46(6), 549-569.

Axtell, P. K., McCallum, R. S., Mee Bell, S., & Poncy, B. (2009). Developing math automaticity using a classwide fluency building procedure for middle school students: A preliminary study. Psychology in the Schools, 46(6), 526-538.

Bowman-Perrott, L., Davis, H., Vannest, K., Williams, L., Greenwood, C., & Parker, R. (2013). Academic benefits of peer tutoring: A meta-analytic review of single-case research. School Psychology Review, 42(1), 39-55.

Burns, M. K. (2005). Using incremental rehearsal to increase fluency of single-digit multiplication facts with children identified as learning disabled in mathematics computation. Education and Treatment of Children, 237-249.

Cassel, J., & Reid, R. (1996). Use of a self-regulated strategy intervention to improve word problem-solving skills of students with mild disabilities. Journal of Behavioral Education, 6(2), 153-172.

Codding, R. S., Archer, J., & Connell, J. (2010). A systematic replication and extension of using incremental rehearsal to improve multiplication skills: An investigation of generalization. Journal of Behavioral Education, 19(1), 93-105.

Codding, R. S., Chan-Iannetta, L., Palmer, M., & Lukito, G. (2009). Examining a classwide application of cover-copy-compare with and without goal setting to enhance mathematics fluency. School Psychology Quarterly, 24(3), 173.

Duhon, G. J., House, S. H., & Stinnett, T. A. (2012). Evaluating the generalization of math fact fluency gains across paper and computer performance modalities. Journal of school psychology, 50(3), 335-345.

Fuchs, L. S., & Fuchs, D. (2006). A framework for building capacity for responsiveness to intervention. School Psychology Review, 35(4), 621.

Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D., & Hamlett, C. L. (2010). The effects of strategic counting instruction, with and without deliberate practice, on number combination skill among students with mathematics difficulties. Learning and individual differences, 20(2), 89-100.

Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D., ... & Zumeta, R. O. (2009). Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology, 101(3), 561.

Fuchs, L. S., Seethaler, P. M., Powell, S. R., Fuchs, D., Hamlett, C. L., & Fletcher, J. M. (2008). Effects of preventative tutoring on the mathematical problem solving of third-grade students with math and reading difficulties. Exceptional Children, 74(2), 155-173.

Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22(1), 23-27.

Geary, D. C., Hoard, M. K., Byrd‐Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child development, 78(4), 1343-1359.

Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104(1), 206-217.

Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of learning disabilities, 38(4), 293-304.

Grafman, J. M., & Cates, G. L. (2010). The differential effects of two self‐managed math instruction procedures: Cover, Copy, and Compare versus Copy, Cover, and Compare. Psychology in the Schools, 47(2), 153-165.

Hale, J. B., & Fiorello, C. A. (2004). School neuropsychology: A practitioner's handbook. New York, NY: Guilford Press.

Hale, J. B., Fiorello, C. A., Dumont, R., Willis, J. O., Rackley, C., & Elliott, C. (2008). Differential Ability Scales-Second Edition (neuro)psychological Predictors of Math Performance for Typical Children and Children with Math Disabilities. Psychology in the Schools, 45, 838-858.

Iseman, J. S., & Naglieri, J. A. (2011). A cognitive strategy instruction to improve math calculation for children with ADHD and LD: A randomized controlled study. Journal of Learning Disabilities, 44(2), 184-195.

Jitendra, A. (2002). Teaching students math problem-solving through graphic representations. Teaching Exceptional Children, 34(4), 34-38.

Jitendra, A. K., DuPaul, G. J., Volpe, R. J., Tresco, K. E., Junod, R. E. V., Lutz, J. G., ... & Mannella, M. C. (2007). Consultation-based academic intervention for children with attention deficit hyperactivity disorder: School functioning outcomes. School Psychology Review, 36(2), 217.

Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and individual differences, 20(2), 82-88.

Joseph, L. M., Konrad, M., Cates, G., Vajcner, T., Eveleigh, E., & Fishley, K. M. (2012). A meta‐analytic review of the cover‐copy‐compare and variations of this self‐management procedure. Psychology in the Schools, 49(2), 122-136.

Kroesbergen, E. H., & Van Luit, J. E. (2003). Mathematics interventions for children with special educational needs a meta-analysis. Remedial and Special Education, 24(2), 97-114.

Lindberg, S. M., Hyde, J. S., Petersen, J. L., & Linn, M. C. (2010). New trends in gender and mathematics performance: a meta-analysis. Psychological bulletin, 136(6), 1123.

Maruyama, M., Pallier, C., Jobert, A., Sigman, M., & Dehaene, S. (2012). The cortical representation of simple mathematical expressions. NeuroImage, 61(4), 1444-1460.

Mayes, S. D., & Calhoun, S. L. (2006). Frequency of reading, math, and writing disabilities in children with clinical disorders. Learning and individual Differences, 16(2), 145-157.

Mazzocco, M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research & Practice, 20(3), 142-155.

Mercer, C. D., & Miller, S. P. (1992). Teaching students with learning problems in math to acquire, understand, and apply basic math facts. Remedial and Special Education, 13(3), 19-35.

Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Learning Disability Quarterly, 31(1), 37-44.

Montague, M., & Dietz, S. (2009). Evaluating the evidence base for cognitive strategy instruction and mathematical problem solving. Exceptional Children, 75(3), 285-302.

Montague, M., Enders, C., & Dietz, S. (2011). Effects of cognitive strategy instruction on math problem solving of middle school students with learning disabilities. Learning Disability Quarterly, 34(4), 262-272.

Parkhurst, J., Skinner, C. H., Yaw, J., Poncy, B., Adcock, W., & Luna, E. (2010). Efficient class-wide remediation: Using technology to identify idiosyncratic math facts for additional automaticity drills. International Journal of Behavioral Consultation and Therapy, 6(2), 111.

Poncy, B. C., Fontenelle IV, S. F., & Skinner, C. H. (2013). Using detect, practice, and repair (DPR) to differentiate and individualize math fact instruction in a class-wide setting. Journal of Behavioral Education, 22(3), 211-228.

Poncy, B. C., Skinner, C. H., & Jaspers, K. E. (2007). Evaluating and comparing interventions designed to enhance math fact accuracy and fluency: Cover, copy, and compare versus taped problems. Journal of Behavioral Education, 16(1), 27-37.

Poncy, B. C., Skinner, C. H., & O'Mara, T. (2006). Detect, Practice, and Repair: The Effects of a Classwide Intervention on Elementary Students' Math-Fact Fluency. Journal of Evidence-Based Practices for Schools.

Rhymer, K. N., Dittmer, K. I., Skinner, C. H., & Jackson, B. (2000). Effectiveness of a multi-component treatment for improving mathematics fluency. School Psychology Quarterly, 15(1), 40.

Rohrbeck, C. A., Ginsburg-Block, M. D., Fantuzzo, J. W., & Miller, T. R. (2003). Peer-assisted learning interventions with elementary school students: A meta-analytic review. Journal of Educational Psychology, 95(2), 240.

Rourke, B. P. (2000). Neuropsychological and psychosocial subtyping: A review of investigations within the University of Windsor laboratory. Canadian Psychology/Psychologie Canadienne, 41(1), 34.

Skinner, C. H., McLaughlin, T. F., & Logan, P. (1997). Cover, copy, and compare: A self-managed academic intervention effective across skills, students, and settings. Journal of Behavioral Education, 7(3), 295-306.

Slavin, R. E., & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78(3), 427-515.

Tok, Ş., & Keskin, A. (2012). The Effect of Fast Draw Learning Strategy on the Academic Achievement and Attitudes Towards Mathematics. International Journal of Innovation in Science and Mathematics Education (formerly CAL-laborate International), 20(4).

Tsuei, M. (2012). Using synchronous peer tutoring system to promote elementary students' learning in mathematics. Computers & Education, 58(4), 1171-1182.

Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word Problem-Solving instruction on middle school students with learning problems. The Journal of Special Education, 39(3), 181-192.

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LDs in Mathematics: Evidence-Based Interventions, Strategies, and Resources

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By Hanna A. Kubas and James B. Hale Mathematics. Some love it, some loathe it, but there are many myths about math achievement and math learning disabilities (LDs). The old belief - boys are naturally better at math than girls -

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LD at School - Developing Effective IEP's

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LD at School - Developing Effective IEP's

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Continuum of Support, LD and UDL

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Answered by Erlene M. Shea
In order to answer this question, educators first need to consider the goal of IEP development.

For a student with a learning disability, the goal of an IEP is to maximize the student's ability to access the curriculum.

Now, what do we know about students with a learning disability? We know they are smart; that they have average to above average intellectual abilities. We also know they will have needs in their ability to learn and that these needs will require accommodations to facilitate success.

Educators' Beliefs about Math

Sutton & Krueger indicated in their publication, What We Know about Mathematics Teaching and Learning, 2002, p. 1, 'All students can learn mathematics, and they deserve the opportunity to do so.' This is a critical belief for teachers of math and translates into creating an equitable environment for all, with a variety of instructional strategies employed. The Ontario Curriculum, Grades 1-8, Mathematics indicates the need for students to acquire a positive attitude toward math, as a necessary condition to learning math in a way that will serve them well throughout their lives. Carol Dweck's book, 'Mindset' and Mary Cay Ricci's 'Mindsets in the Classroom' provide teachers with insight and strategies to build a growth mindset in the classroom.

The big idea in creating an effective IEP to support math learning for a student with LDs is that m ost students can access mathematical concepts at grade level in some capacity. Therefore, in order to provide opportunities for all students to participate in an engaging math-learning environment, we will want to develop IEPs that are more closely aligned with grade level expectations. This process involves differentiated instruction and assessment of expectations tailored to the student's strengths and needs.
In making a long-range plan (an IEP) for a balanced mathematics program, teachers need to consider where to start:

Be familiar with the knowledge and skills that students are expected to acquire at their current grade level, and the knowledge and skills they were expected to acquire in the previous grade.

(The Guide to Effective Instruction in Mathematics, K-6, Vol. 1, p.48)

Though teachers should not go beyond the expectations for their grade, it is important to have an awareness of how the expectation will be dealt with in subsequent grades.

Focus Instruction on Key Concepts
The Literacy and Numeracy Secretariat, Capacity Building Series, Differentiating Mathematics Instruction, September 2008

To differentiate instruction meaningfully for any mathematics concept, procedure and/or strategy, teachers need to recognize the key concepts.

Overall curriculum expectations provide a starting point for what the key concepts are, but probably do not help a teacher easily plan to differentiate instruction.

One approach: cluster specific curriculum expectations and use them as learning goals over a series of lessons. It is by clustering specific expectations, in conjunction with looking at the curriculum for other grade levels, that the key concepts become evident.

Example: Focusing Instruction on Key Concepts Gr. 6 lesson; Number Sense and Numeration, Multiplying whole numbers by decimals

Goal: performing a computation like 3 x 1.5
Key Concepts:

Multiplication has many meanings (e.g. repeated addition, counting of equal groups).

Multiplication has those same meanings regardless of the values being multiplied.

Multiplication can be accomplished in parts (distributive property).

In the Grade 6 multiplication example, the key concepts relate more to what multiplication means, when it is used and its fundamental principles about the operation than the details about what kinds of numbers students can multiply. This allows for multiple entry points, which can address students at different levels of mathematical sophistication.
Good Questions, Great Ways to Differentiate Mathematics Instruction, Marian Small The following chart provides considerations for instructional and assessment accommodations:

Know the student's strengths and leverage these strengths in instruction.

For example, a kinaesthetic learner will benefit from engaging in mathematically rich tasks, heterogeneous grouping and adequate resources coupled with explicit instruction

(e.g. manipulatives, calculators, digital tools), as will all students (UDL, Learning for All, 2013, p. 13).

Know the student's needs and accommodate for them in instruction.

Examples:

a student with visual-spatial needs will benefit from having visual representations paired with verbal explanations and instructions; a think-aloud strategy

a student with memory challenges will benefit from a formula chart for assignments and tests

Consider the student's strengths and needs in assessment as well. Typically, the best assessments for and of learning for students with a learning disability will be paper and pencil tasks.

Though such assessment will need to be practised at times, make a point of recording and documenting thinking in other ways; e.g. observations, conversations, products.

A Continuum of Support
When developing the IEP, work from an understanding of a continuum of support, with accommodations only as the first consideration, then modification to the number and complexity of expectations at grade level and finally, if necessary, modifications to a lower grade level.

It is advisable to consider each mathematics strand independently. For example, a student may have modified expectations for geometry and spatial sense from the current grade level and modified expectations for number sense and numeration from a lower grade level.

Identification of and Program Planning for Students with Learning Disabilities, PPM 8, 2014
← The continuum can be fluid; it can move both ways. → Click here to access the webinar recording, "IEP Development and Implementation: Considering the Student, the Environment and the Academic Domain". Click here to access the Ask the Experts answer to "What Strategies are Most Effective for Students with LDs in Math?" Click here to access the article, "Mathematics and LDs". Click here to access the learning module, "Concrete - Representational - Abstract: An Instructional Strategy for Math". Click here to access the webinar recording, "Understanding Developmental Dyscalculia: A Math Learning Disability".
Thus, considering the goal of IEP development, the student profile and our beliefs about math, one can create an effective IEP, which will result in continued growth in the learning of mathematics.

Related Resources on the LD@school Website

References

Ontario Ministry of Education. (2006). The Guide to Effective Instruction in Mathematics, K - 6, Vol.1. Queen's Printer for Ontario.

Ontario Ministry of Education. (2014). Policy/Program Memorandum No. 8, Identification of and Program Planning for Students with Learning Disabilities.

Ministère de l'Éducation de l'Ontario. (2013). Learning for All: A Guide for Effective Assessment and Instruction for All Students, Kindergarten to Grade 12. Queen's Printer for Ontario.
Erlene Shea has been an educator with the Peel District School Board for over 30 years. She has experience in all divisions, with special education being the focus for the bulk of her career. Erlene has also worked at Trillium, one of the province's Demonstration schools, in support of students with severe learning disabilities.
Small, Marian. (2014). Good Questions, Great Ways to Differentiate Mathematics Instruction. Modulo.

Sutton, J., & Kruefer, A. (2002). What We Know about Mathematics Teaching and Learning. McRel.

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How do I Develop an Effective IEP to support Math Learning for a Student with a Learning Disability?

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Answered by Erlene M. Shea In order to answer this question, educators first need to consider the goal of IEP development. For a student with a learning disability, the goal of an IEP is to maximize the student's ability to access the curriculum. Now, what do we know about students with a learning disability?

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Diagnostic Assessment
Diagnostic assessments for every topic clearly pinpoints significant gaps in student understanding.
Differentiated Instruction
Strategic intervention tools enable teachers to build on what students understand and close critical gaps in understanding.

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Leaps and Bounds Mathematics Intervention for Grades 1,2,3,4,5,6,7,8

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Teacher's Resource

Diagnostic assessment tools for every strand identify gaps in student understanding

Diagnostic tool reveals background information on why students struggle and the misconceptions

2-5 pathways provide open-ended intervention and guided intervention for every topic

Teaching Notes support differentiated instruction and include good questions

Student Resource Digital Teacher's Resource with Interactive Whiteboard activities

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Teacher's Resource Diagnostic assessment tools for every strand identify gaps in student understanding Diagnostic tool reveals background information on why students struggle and the misconceptions 2-5 pathways provide open-ended intervention and guided intervention for every topic Teaching Notes support differentiated instruction and include good questions Student Resource Digital Teacher's Resource with Interactive Whiteboard activities

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Other Resources to assist teachers in developing differentiated tasks

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Other Resources to assist teachers in developing differentiated tasks

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Learning Tools - OAME
Mathies Home

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

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What Does Math Feel Like for a Student with a Learning Disability? 

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What Does Math Feel Like for a Student with a Learning Disability? 

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Try the activity! Share your thoughts in the comments below.

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Understood | For Learning and Attention Issues

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Help your child thrive. Chat with experts, connect with parents and get tips on parenting kids with reading, writing, math, organization, attention issues and more.

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The following article provides an overview of accommodations, modifications and alternative skill areas, and discusses where students with learning disabilities (LDs) fit in.

Accommodations

Accommodations are the special teaching and assessment strategies, supports and/or individualized equipment (including technology) that are required to enable a student to learn and demonstrate learning. Accommodations do not alter the provincial learning expectations for the grade level.

For subjects that are accommodated only, there should be a list of Instructional Accommodations (different ways of teaching or presenting materials) Environmental Accommodations (e.g. seating, cueing, hallway routines) and Assessment Accommodations (including use of technology). These accommodations may be common to all subjects or may vary from subject to subject, in which case the subjects should be listed separately.

Accommodated only (AC) is the term used on the IEP form to identify subjects or courses from the Ontario curriculum in which the student requires accommodations alone in order to work towards achieving the regular grade expectations.

AC subjects or courses should not have the IEP box checked off on the provincial report card. Marks for Accommodated only subjects/courses are based on grade level curriculum, rather than on modified expectations. The IEP box on the provincial report card is only for courses where the curriculum expectations are modified or alternative, and the marks are not based on the same criteria as the other students.

Modifications

Modifications refer to the changes made to the age-appropriate grade level expectations for a subject or course in order to meet the needs of the student.

Modified (MOD) is the term used on the IEP form to identify subjects or courses from the Ontario curriculum in which the student requires modified expectations - expectations that differ in some way from the regular grade expectations.

Modifications may involve either raising or lowering grade level expectations. For the core subjects, such as Math and Language, the expectations may be taken from a different grade level (higher or lower). For content subjects, such as Social Studies or History, the modifications may include significant changes to the number and/or complexity of learning expectations in the regular grade level curriculum.

For each subject that is modified, even partially, a Program page of the IEP gets filled out with Current Level of Achievement, an annual program goal, and Learning Expectations for each reporting period (report card term).

At the secondary level, a student might be working in a subject on almost all the course curriculum expectations, but the complexity or number of expectations might be modified in a few areas. In this case the IEP would indicate "the student will do all the curriculum expectations except ...". The school principal would decide how much modification could be allowed in order for the student to get credit for the course.

Alternative skill areas

Alternative skill areas (ALT) are based on expectations developed to help students acquire knowledge and skills that are not represented in the Ontario curriculum. Alternative skill areas are listed on the Program page of the IEP, and have the current level of achievement, an annual program goal, learning expectations, teaching strategies and assessment methods. Alternative programs are provided in both the elementary and the secondary school panels.

Examples of alternative programs include: speech remediation, social skills, orientation/mobility training, and personal care programs. For the vast majority of students, these programs would be given in addition to modified or regular grade-level expectations from the Ontario curriculum. They must be directly taught by a designated person.

Alternative courses, at the secondary school level, are non-credit courses. The course expectations in an alternative course are individualized for the student and generally focus on preparing the student for daily living. School boards must use the "K" course codes and titles found in the ministry's Common Course Code listings ( click here to access the page) to identify alternative courses. Examples of alternative courses include Transit Training and Community Exploration (KCC), Culinary Skills (KHI), and Money Management and Personal Banking (KBB).

Where do students with LDs fit in?

Students with LDs in primary and junior grades, who are working on basic academic skills in reading, spelling and math, may be working toward modified curriculum expectations, from a lower grade level, on some parts of their subjects. Only those parts of the subject would be evaluated according to modified expectations, and therefore have the IEP box checked off on the provincial report card.

Many students with LDs in intermediate and secondary grades would have most of their content subjects (e.g. social studies, science) accommodated only. As long as students understand the content, technology supports such as books in electronic format and text-to-speech can accommodate for reading difficulties and word prediction or speech-to-text programs can accommodate for writing difficulties.

In most cases, students with LDs at secondary school who are working at their appropriate level (i.e. Academic or Applied) would be working toward credit in all their courses, with accommodations.

For students with learning disabilities, social skills, anger management or organizational skills could come under Alternative Skill Areas if someone is specifically teaching them to the student, and assessing the student's progress based on the expectations, and they are not just being encouraged in the classroom.

Alternative Skill Areas can also be used when basic academic skill areas continue to be taught in higher grades. The 2004 IEP Resource Guide gives an example of an older elementary school student working on reading decoding and comprehension skills as an alternative skill area. This can be used as a way to continue to teach and assess basic academic skills while at the same time allowing the student to access the regular curriculum with accommodations.

Ministry References and Resources

The Individual Education Plan (IEP), A Resource Guide, 2004, is a guide intended to help educators working with students with special needs to develop, implement, and monitor high-quality IEPs. Click here to access the resource guide.

Samples of Individual Education Plans (IEPs) have been developed and posted on the EDUGains website to support the development and implementation of effective IEPs in Ontario. Click here to access the samples.

The document, Individual Education Plans: Standards for Development, Program Planning, and Implementation, 2000, describes province-wide standards that must be followed in the elaboration of student IEPs. Click here to access the standards.

The document, Special Education, A Guide for Educators, 2001, includes a section devoted to the creation and upkeep of a student's IEP. Click here to access Part E: The Individual Education Plan (IEP) of the document, including Individual Education Plans: Standards for Development, Program Planning, and Implementation, 2000.

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Accommodations, Modifications & Alternative Skill Areas

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The following article provides an overview of accommodations, modifications and alternative skill areas, and discusses where students with learning disabilities (LDs) fit in. Accommodations Accommodations are the special teaching and assessment strategies, supports and/or individualized equipment (including technology) that are required to enable a

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Open Ended, Open Middle, and Parallel Math Tasks

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Open Ended, Open Middle, and Parallel Math Tasks

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Consider how these type of problem solving questions can meet the diverse learning needs in a classroom.

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Instructional Decisions - Differentiating the Mathematical Problem.pdf

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Creating an Effective Learning Environment

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Creating an Effective Learning Environment

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Effective Lessons establish a clear purpose for both teachers and students

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Effective Lessons establish a clear purpose for both teachers and students

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5 Practices a new direction screen captures.docx

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Over 400 Gizmos aligned to the latest standards help educators bring powerful new learning experiences to the classroom.

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Hi there. We're ExploreLearning!

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Focuses on how students learn mathematics in the elementary grades.

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PRIME was developed as a research-based initiative, focused on understanding how students learn mathematics in the elementary grades. The research was designed to answer two key questions for each of the five mathematics strands: 1. What are the phases of development that students "travel" through while learning key mathematical skills and concepts?

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Diagnostic assessments and lessons to help close gaps in math knowledge.