# data[].attributes.body
Use chunking technique

# data[].attributes.body
Organize content visually

# data[].attributes.body
Use the Concrete-Representational-Abstract (CRA) method. Start with concrete manipulatives, then to visual representations, and then to abstract symbols

# data[].attributes.attachment_link.title
| Training & Technical Assistance Center | School of Education | W&M School of Education

# data[].attributes.attachment_link.description
Emerging research suggests that students with moderate and severe disabilities can learn content aligned with grade-level standards while continuing to work on basic numeracy (Saunders, Bethune, Spooner, & Browder, 2013). Use of evidence-based instructional strategies and practices is critical to ensure students learn necessary content. Based on the findings from several studies, Saunders, Bethune, Spooner, and Browder (2013) developed a six-step approach to teaching mathematics that can be used in all math classrooms—both general and special education. The following example is from a seventh-grade class.

# data[].attributes.body
Incorporate key words/ vocab

# data[].attributes.body
Allow choices

# data[].attributes.body
For students with autism and sensory impairments: Modify available mathematics learning materials and provide explicit instruction

# data[].attributes.attachment_link.title
5 Strategies for Teaching Math to Special Education Students - Caffeine Queen Teacher

# data[].attributes.attachment_link.description
Teaching math the special education students can be tough. These 5 simple and effective strategies will make it easier and empower students.

# data[].attributes.body
Focus on core ideas

# data[].attributes.body
Incorporate culturally relevant examples to help students connect math to their real life and experiences

# data[].attributes.body
break up learning into small steps

# data[].attributes.body
Having regular conferences where you provide support and guidance to help students become more self motivated.

# data[].attributes.attachment_link.readable_text
In a nurturing learning environment, students and teachers build a place of mutual respect and appreciation. When everything is working, all students feel valued, and teachers are aware of how developmental needs affect learning. However, some students may develop their gifts or talents ahead of their age or experience. It is our responsibility as educators to engage and build up these gifts and talents.

Sometimes, categorizing and labeling students can make you shrink a little. After all, you know that all of your students are special in their own way. Giftedness is not fixed-all students have the ability and the potential to excel, and all students have special talents and strengths. The important thing is finding a way to nurture those talents and strengths in such a way that students can develop their potential to the fullest.

All students have the right to learn new things every day, but managing the range of academic levels within a classroom is a formidable task. Often, gifted or advanced learners may be underchallenged or understimulated. There can be a mismatch between how they preferer to learn and how they are taught. This can potentially lead to a host of behavior, confidence, and peer relationship struggles.

So, how can you support these learners as an educator? Let's take a look at a few teaching strategies and best practices!

Treat students as individuals

As you are building your approach and learner profile, keep in mind that exceptional students are unique. They may be twice-exceptional, intellectually gifted children who also have learning disabilities. They may be gifted in one area and not in another. Extraordinary talent in math does not always transfer to an equal talent in writing, art, or science. This can be frustrating for the student. Supporting gifted students usually involves a mixture of acceleration and enrichment of the usual curriculum. A first step is creating an interest survey for the whole class. By reviewing the results, a classroom teacher can personalize lessons and target topics of interest.

Let students explore their passions

Help students immerse themselves in a subject that sparks their passion by providing a topic library or by checking books and magazines out of the library and creating a resource of appropriate videos. Classroom teachers can structure art projects and writing activities about the topic of interest. There is no reason not to teach reading through the focus of trains or to teach math with counting marine animals with students. If they are older, why not explore impact of the topic on history? There are always opportunities to connect.

Infuse enrichment into activities

Students may speed through material as they master it. If the suggested pace is two chapters a week but your students can complete two chapters a day because the topic engages them, let them get ahead. Add to the instruction by allowing them to create a presentation, a project, or even a script for a podcast. Provide the space for deeper exploration and understanding. Arrange enrichment activities that gifted students can carry out by themselves at their desks. Allow students to do special projects. However, avoid finding busywork, as students will recognize it for what it is.

Build in time for flexible learning groups

You can intentionally create small groups for flexible learning with consideration of students' readiness levels, strengths, and/or interests. This thoughtful planning tool can be used to create a more dynamic learning environment. Keep in mind that the groups continually change based on assessment data related to students' needs. When the data are studied, students may bubble up and display previously hidden talents. Include identified gifted students in group work. Although gifted learners are capable of working independently, these students need opportunities to work with and socialize with their peers.

Embrace creative questioning

Gifted learners are often curious about the world around them, and they may ask detailed questions to satisfy their thirst for knowledge. This curiosity goes beyond simple interest in a topic and can extend to aspects that are seemingly outside of the scope of a lesson. Be respectful of your students' curiosity, and encourage the search for answers to impossible questions. Students may ask unexpected questions, so try to leave room for exploration when a quirky question comes your way by asking where this question came from and what it is connected to.

Look for evidence of learning by encouraging students to share their intuitive theories about a topic and by completing open-ended tasks in which they extend or apply what they have learned. Gifted children need less drill to master them on fundamental processes; be comfortable in leaving some gaps for students to bridge themselves.

Encourage self-directed learning with your students

Self-directed learning is a skill that can be developed with all students. While some children are more self-motivated than others, self-directed learning is crucial to becoming a lifelong learner. Have regular conferences to help students plan their work, and provide support for difficulties and evaluation. Focus on meaningful and relevant content that enriches the topic at hand.

Interested in learning more about how you can support students with gifted abilities in your classroom? Check out our blog post, Classroom Strategies to Support Advanced Learners at All Grade Levels.

# data[].attributes.attachment_link.title
Classroom Strategies: Teaching Gifted Students

# data[].attributes.attachment_link.description
Gifted or advanced learners may be under-challenged or under-stimulated. Here's how to support these learners as an educator.

# data[].attributes.body
Teach students to recognize that their math experience from the past are still relevant and important in the present tasks

# data[].attributes.body
Explicit instruction

Avoid memory overload

Visual and auditory examples

Make real-life connections

Utilize manipulative and technology

Provide reviews within a day or two of official learning

Utilize drawing

Use graph paper to keep organized

# data[].attributes.attachment_link.readable_text
Dyscalculia is a mathematics-related disability resulting from neurological dysfunction. Students who are diagnosed with Dyscalculia have average to above-average intellectual functioning and a significant discrepancy between their math skills and their chronological-age-peer norms. For a diagnosis of Dyscalculia, it must be determined that the math deficit is not simply related to issues such as poor instruction, vision, hearing or other physical problems, cultural or language differences, or developmental delays.

In Accommodating Math Students with Learning Disabilities, author Rochelle Kenyon lists the following strategies for teaching a student with math-related learning disabilities.

Avoid memory overload. Assign manageable amounts of work as skills are learned.

Build retention by providing review within a day or two of the initial learning of difficult skills.

Provide supervised practice to prevent students from practicing misconceptions and "misrules."

Make new learning meaningful by relating practice of subskills to the performance of the whole task.

Reduce processing demands by preteaching component skills of algorithms and strategies.

Help students to visualize math problems by drawing.

Use visual and auditory examples.

Use real-life situations that make problems functional and applicable to everyday life.

Do math problems on graph paper to keep the numbers in line.

Use uncluttered worksheets to avoid too much visual information.

Practice with age-appropriate games as motivational materials.

Have students track their progress.

Challenge critical thinking about real problems with problem solving.

Use manipulatives and technology such as tape recorders or calculators.

This list was adapted from the following source: Garnett, K., Frank, B., & Fleischner, J. X. (1983). A strategies generalization approach to basic fact learning (addition and subtraction lessons, manual #3; multiplication lessons, manual #5). Research Institute for the Study of Learning Disabilities. New York, NY: Teacher's College, Columbia University.

For additional resources on how to make mathematics accessible to students with disabilities, consult the DO-IT Knowledge Base article Where can I find tips on making math accessible to students with disabilities?

For more information regarding challenges faced by students with math-related learning disabilities, consult the DO-IT Knowledge Base article What are typical challenges students with math-related learning disabilities face?

# data[].attributes.attachment_link.title
What are strategies for teaching a student with a math-related learning disability?

# data[].attributes.attachment_link.description
Dyscalculia is a mathematics-related disability resulting from neurological dysfunction. Students who are diagnosed with Dyscalculia have average to above-average intellectual functioning and a significant discrepancy between their math skills and their chronological-age-peer norms. For a diagnosis of Dyscalculia, it must be determined that the math deficit is not simply

# data[].attributes.attachment_link.readable_text
Author: Rotigel, J. & Fello
Publications: Gifted Child Today
Publisher: Prufrock Press
Volume: Vol. 27, Issue 4, pp. 46-51
Year: Fall 2004
Today, as usual, Mrs. Johnson began her 3rd-grade math class by reading aloud a thinking puzzle: Charlie, the dog, was tied to a 2-meter rope. His favorite ball was lying in the grass at least 10 yards away from him. He managed to grasp the ball easily. How did he manage to do this? Nathan's hand flew into the air just microseconds after his teacher finished posing the question. While his classmates were pondering the problem, Nathan had already formulated the answer. Surprising even Mrs. Johnson, Nathan immediately found the lateral thinking puzzle required little effort and absolutely no math. While other students were converting meters to yards, moving decimal points, and drawing pictures, Nathan realized that the other end of the rope was not attached to anything; the dog merely had a 2-meter rope tied to his collar, but was not tethered at all.
Whether Nathan had heard the "riddle" before or whether he surmised that mathematics couldn't solve the scenario remains a mystery. Nevertheless, most teachers have had similar experiences with children who are talented in mathematics and strong in logical reasoning. Unfortunately, many programs for gifted children are inadequate and poorly designed (Heid, 1983), leaving classroom teachers to struggle to meet the needs of gifted children effectively. What resources are available for these students? What assessment tools are appropriate? Do these children need acceleration or enrichment? How can we meet their needs when there are so many other demands on teachers' time? This article will address these and other questions in an attempt to shed some light on the difficult issues of challenging and nurturing children who demonstrate talent in the field of mathematics.
Characteristics of the Gifted Math Student
Whether math problems require computation skills, problem-solving strategies, inferential thinking skills, or deductive reasoning, mathematically talented students are often able to discern answers with unusual speed and accuracy. Mathematically gifted students are able to see relationships among topics, concepts, and ideas without the intervention of formal instruction specifically geared to that particular content (Heid, 1983). Due to their intuitive understanding of mathematical function and processes, they may skip over steps and be unable to explain how they arrived at the correct answer to a problem (Greenes, 1981).

For example, Mariah, an energetic, 6th-grade prealgebra student, often seems disinterested during her hourlong math class, as she doodles and appears to be preoccupied. While the teacher demonstrates the steps required for calculating the correct answer to 4b + 11= 2b + 23, Mariah leafs through her history folder. After all, she can solve these linear algebraic equations in just one step. Like many gifted students, she barely listens to the teacher's directions, does not write page numbers in her assignment book, and does not make eye contact with the teacher. Mariah views practicing step-by-step processes as a waste of time when solutions can be found by just looking at the problem.

Students who are talented in mathematics often demonstrate an uneven pattern of mathematical understanding and development, since some are much stronger in concept development than they are in computation (Rotigel, 2000; Sheffield, 1994). Gifted math students often want to know more about the "hows" and "whys" of mathematical ideas than the computational "how-to" processes (Sheffield). Since these children often prefer to learn all they can about a particular mathematical idea before leaving it for new concepts, a more expansive approach to mathematics based upon student interest may avoid the frustration that occurs when the regular classroom schedule demands that it is time to move on to another topic. A more linear approach to mathematics is often a better match for gifted children instead of the spiral curricula often found in textbook series and followed by classroom teachers. For example, when the topic of decimals is introduced, children with mathematical talent can be allowed to delve much further into the topic, learning practical applications for decimals and the connections between decimals and other mathematical topics.

Many of these students' gifted characteristics emerge during the preschool years. Bailey, a mathematically precocious 5-year-old, understands that numbers have patterns and relationships to real life. While watching a series of movie previews at the local theater, she can skillfully decide which new releases will occur before or after she turns 6 simply by noting their release dates in the upcoming year. Parents of preschoolers may report that their child demonstrates an unusual interest in mathematical concepts and particularly enjoys games involving numbers. At an early age, some gifted students note relationships between products and prices in the grocery store, the passage of time, changes in weather temperatures, and measurements of distances. Parents of these "number sense gurus" are fascinated by their children's precociousness, but are often unaware of the significance or relevance of these early mathematical discoveries.

By the time these emergent mathematical geniuses arrive for their first formal math lessons in kindergarten, they may have already established their own unique theories of number sense, sequences and patterns, problem solving, and computational strategies. Too frequently, the teachers following the curriculum merely touch on many math concepts, failing to recognize and nurture young mathematicians (Pletan, Robinson, Berninger, & Abbott, 1995). Formal instruction in elementary school classrooms often lacks challenge for the gifted learner since courses in regular classrooms sometimes have a relatively narrow range of topics, minimal investigation of concepts, repeated drill and practice, and yearly repetition. The basic mathematical concepts that are presented in kindergarten and 1st grade can be a particular problem for children who have already mastered number recognition, one-to-one correspondence, and counting. Recent studies indicate that few instructional adaptations are made to accommodate these young learners' needs (Archambault, Westberg, Brown, Hallmark, Emmons, & Zhang, 1993). Students gifted in mathematical thinking and problem solving need greater depth and breadth of topics and openended opportunities for solving more complex problems (Sheffield, 1994).
Challenges for School Districts
Misunderstandings regarding the nature of giftedness and talent abound, and busy teachers and administrators are sometimes at a loss to know how to nurture and challenge children whose abilities belie their age-based grade-level placement. However, according to the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000, p. 13), these students must be supported so that they too have an opportunity to reach their mathematical potential. All too often, the regular curriculum is insufficient in depth, breadth, and pace to meet the needs of the gifted child (Wolfle, 1986). In addition, the recent emphasis on state standardized testing programs has increased the use of basic skills instruction and drill in an attempt to assure that all students will be successful on these tests (Moon, Brighton, & Callahan, 2002). A great deal of research supports the conclusion that gifted students need to use advanced materials and curricula if they are to reach their potential (Reis, Westberg, Kulikowich, & Purcell, 1998; VanTassel-Baska, 1995, 1998a).

Most educational settings do not adequately address and meet the needs of gifted students, and most teachers make only a few minor modifications to the curriculum when attempting to teach them (Archambault et al., 1993). Planning for 12 years of mathematics instruction for all students has sent many administrators and district curriculum specialists scrambling for the latest research on best practices, and the notion of meeting the needs of mathematically advanced students adds complexity to the task. The dilemma of choosing between acceleration to an advanced math class placement and providing planned enrichment activities within the regular classroom setting plagues math coordinators, curriculum specialists, superintendents, and parents.
The Critical Role of Assessment
According to the Principles and Standards for School Mathematics (NCTM, 2000, p. 23), assessment and instruction should be integrated so that assessment provides information for the teacher to use to make instructional decisions. Children who demonstrate high achievement in mathematics should be carefully evaluated to determine the extent of their talent and provide a profile of their strengths and weaknesses (Lupkowski-Shoplik, Sayler, & Assouline, 1994). Grade-level achievement test results can be somewhat helpful, for if a student scores extremely well, it may indicate that mathematics is an area of strength for him or her.

If a child scores at or above the 95th percentile on a grade-level achievement test, it is possible that the test did not have enough items of appropriate difficulty for the child, thus the score may not indicate his or her true level of understanding. In this case, it may be necessary to administer an above-level test that will contain more items of higher difficulty. Julian Stanley pioneered this concept in 1971 when he began the talent searches (Stanley & Benbow, 1986), and 30 years worth of research have shown that out-of-level testing is a valuable tool for determining the level of programmatic modification that is needed for a gifted student.

Although a variety of standardized tests may be used for out-of-level testing, research has demonstrated the effectiveness of the EXPLORE test to identify talented elementary school students (Colangelo, Assouline, & Lu, 1994; Rotigel, 2000; Rotigel & Lupkowski- Shoplik, 1999). The EXPLORE (American College Testing Program, 1997) was developed for 8th-grade students and therefore contains a sufficient number of higher level items to allow students to demonstrate their proficiency more fully. According to ACT, the EXPLORE is directly related to student educational progress and includes a large number of complex problem-solving items and fewer measures of narrow skills. Many of the regional talent searches around the country offer EXPLORE testing in mathematics, as well as other subject areas.

No evaluation should be based simply on standardized testing, however. Teacher observations, classroom-based assessment, daily performance, and social and emotional needs must be included in the evaluation. It is important that data be gathered and analyzed by a multidisciplinary team of educators who are able to make and carry out educational recommendations for the student.
Program Evaluation and Curricular Collaboration
From the administrative perspective, a needs assessment could be conducted with all math teachers to determine each teacher's individual perceptions, teaching methods, and curricular successes or problems. An investigation of repeated topics, overlapping concepts, and ineffective activities could identify weaknesses in the math program. In order to meet students' needs, many concepts and topics in the curriculum could be compacted (Reis et al., 1998). For example, ratios and proportions could be coupled with simple fractional portions of sets. Some measurement or temperature concepts could be integrated into other curricular areas like science, thus allowing for more enrichment lessons in visual logic, inferential thinking, and deductive reasoning. According to VanTassel-Baska (1998b), efficient use of time is an important consideration in the development of talent.
Challenges for Teachers Differentiation of Instruction
Once a sufficient foundation of information is gathered, an individualized plan can be established for each mathematically gifted student. It then becomes the responsibility of classroom teachers to implement the program. The plan may include enrichment experiences; differentiation of instruction, including pretesting and compacting the curriculum; flexible cluster grouping by topic or mathematics achievement; grade skipping in math; mentoring; and increased use of technology. The decision regarding which level of intervention is necessary should be based upon the evaluation. Highly gifted students may require more intense modification such as grade skipping in mathematics. Rather than choosing one method over the other, research indicates that a combination of these approaches makes for a stronger program for divergent math thinkers (Stanley & Benbow, 1986). Daily ongoing assessment, teacher observations, achievement tests, and above-level testing can all be helpful in determining the type of program that will best meet the needs of each gifted child.

Defined by Tomlinson (1995), differentiated instruction is "the consistent use of a variety of instructional approaches to modify content, process, and/or products in response to the learning readiness and interest of academically diverse students." Teachers must add components to each lesson and modify the content for the high-ability students, as well as for those who need remediation. For example, a lesson on calculating the area of polygons might include just the basic formula for most students, but should provide various real-world applications of calculating area for gifted learners. The increased complexity of the problems should require higher order thinking skills and provide opportunities for open-ended responses. Effective differentiation of instruction is very different from the unfortunate practice of simply assigning 20 problems to the gifted child while the remainder of the class is given only 10. "More of the same piled higher" is inappropriate and may lead children to conceal their abilities in order to avoid the extra, unnecessary work.

The task of differentiating each lesson requires accessing additional resources, planning for small-group interaction, and perhaps even modifying lessons during delivery (Tomlinson, 1995). In most instructional settings, the mathematical understanding and performance of the students is diverse, so classroom teachers plan their instruction with a myriad of learners and learning styles as the focus. Using a pretesting component in the math program allows for the identification of attained skills, strategies, and achieved concepts prior to the beginning of a new unit. For the gifted population, this helps eliminate the repetition from year to year in the mathematics curriculum. Pretesting and compacting the curriculum allows for a diagnostic approach for planning the teacher's instruction and allows educators to have a more accurate account of the skills and concepts students have mastered and those they have yet to be introduced to or need to strengthen. This process provides the foundation for effective differentiation of instruction, as each student should receive instruction based upon his or her identified instructional level (Howley, 2002). As noted by Winebrenner (2003), gifted students whose programs have been compacted can spend time working on their differentiated activities while their classmates are preparing for state assessments.
Enrichment and Grouping
It is certainly possible to meet the needs of some gifted students simply by enriching and modifying the existing mathematics curriculum. Enrichment is designed to expose students to a variety of topics related to those of the regular education program and to allow for further investigation of them.

In cases where math students are grouped according to their understanding of mathematical concepts and ideas, teachers can cover concepts at an appropriate pace for the group. Pretesting and compacting of the curriculum are helpful here, as they allow the group of mathematically talented students to be appropriately challenged. In addition, a classroom of homogeneously grouped gifted students would enable a teacher to apply the Enrichment Triad Model (Renzulli, 1977). For example, once students have mastered basic algebraic concepts, additional learning opportunities would be provided in the area of divergent thinking, individual projects, and group activities that would connect those algebraic concepts with real-world events and scenarios.
Acceleration and Technology
Since many mathematically talented students have already mastered the basic skills, the enrichment activities and advanced projects their teachers have planned may not provide sufficient challenge. Indeed, for many talented youngsters, some degree of acceleration is needed based on their demonstrated achievement and ability. Simply working in the highest math class at their grade level may not meet gifted learners' needs, regardless of how well the teacher has differentiated the lessons. Gifted students may have already acquired the content and concepts presented in these classes, so acceleration to a math class at a higher grade level may be the most viable option. However, Lewis (2002) cautioned that acceleration should not be done unless it also meets the student's affective needs, which is sometimes difficult to determine.

Although accelerating a student to a higher grade-level class can present logistical problems for teachers and administrators, it is important to match not only the mathematical content with the learner's needs, but also to provide an appropriate pace of instruction for his or her rate of acquisition. Acceleration may be the only way to accomplish this. Classroom experience and research demonstrate that, even though they may be younger, children who are exceptionally talented in mathematics will learn material much more quickly and with fewer repetitions than the regular curriculum allows (Sowell, 1993). Thus, the repetitions of a spiral curriculum become redundant and mundane to a gifted math student. On the other hand, gifted students in accelerated classes have opportunities to work with advanced concepts, in-depth topic investigations, and problems with real-world applicability.

Many advances in technology can assist the classroom teacher in meeting the learning needs of gifted math students by providing opportunities to explore complex problems and mathematical ideas (NCTM, 2000, p. 14). Readily accessible classroom computers, supervised access to the Internet, and appropriate software programs offer opportunities for gifted students to advance at their own rate.
A Conclusion That's Outside the Box
Teachers sometimes experience frustration when gifted children can arrive at correct answers through nontraditional methodologies or when some of their questions are far beyond the scope of the lesson at hand. Since gifted students can often interpret, predict, and analyze mathematical situations and problems better and faster than their teachers, a significantly different instructional approach may be necessary. Successful teachers of gifted learners adapt their teaching strategies to accommodate the students' unusual thinking strategies and methodologies. Unfortunately, inexperienced or untrained teachers sometimes make provisions for the gifted by assigning them enrichment worksheets, independent projects, or reports on famous mathematicians. Quantity, in this case, does not always equal quality (Greenes & Mode, 1999; Wolfle, 1986).

Being sensitive and aware of the unique characteristics of gifted students enables teachers to set more realistic expectations in the classroom. Teachers need to be confident in their own mathematical knowledge and teaching abilities in order to accept the divergent thinking abilities of their gifted students. In Mariah's case, traditional expectations of step-by-step problem solving with paperand- pencil assignments may not be appropriate. When gifted students are able to arrive at the correct answer by following an unmarked thinking path, teachers should acknowledge this creative, divergent problem-solving strategy and not reprimand the student through missed points or a lowered grade because of not following more traditional techniques. Teachers should adapt the content where appropriate, condense the concepts where applicable, alter the pace of content acquisition, and allow for open-ended, multiple solutions to problems.

Meeting the needs of each learner is the goal of every teacher, and each grade level has its own unique challenges. Whether it is the preschooler, Bailey, who can often make math connections without formal instruction; Nathan, the 3rd grader with the quirky thinking style; or Mariah, the prealgebra student who "sees" the answer without doing the work, each student thinks "outside the box." Accessing all available resources, using a variety of assessment tools, and choosing appropriate placements for each student are all aspects of meeting the individual needs of each learner. Being aware and sensitive to the unique characteristics of gifted learners will assist teachers in providing a myriad of opportunities for growth in mathematical reasoning and problem solving.
Author Note
The authors would like to thank Michael Bosse and Jacquie Gentile for their helpful comments on an earlier version of this paper.

References
American College Testing Program (ACT). (1997). EXPLORE technical manual. Iowa City, IA: Author.

Archambault, F. X., Westberg, K. L., Brown, S. W., Hallmark, B. W., Emmons, C. L., & Zhang, W. (1993). Regular classroom practices with gifted students: Results of a national survey of classroom teachers.

Storrs: The National Research Center on the Gifted and Talented, University of Connecticut.

Colangelo, N., Assouline, S. G., & Lu, W. (1994). Using EXPLORE as an above-level instrument in the search for elementary student talent. In N.

Colangelo, S. G. Assouline, & D. Ambroson (Eds.), Talent development II: Proceedings from the 1993 H. B. and Jocelyn Wallace National Research Symposium on Talent Development (pp. 281-297). Dayton: Ohio Psychology Press.

Greenes, C. (1981, February). Identifying the gifted student in mathematics. Arithmetic Teacher, 14-17.

Greenes, C., & Mode, M. (1999). Empowering teachers to discover, challenge, and support students with mathematical promise. In L. J.

Sheffield (Ed.), Developing mathematically promising students (pp. 121-132). Reston, VA: National Council of Teachers of Mathematics.

Heid, M. K. (1983). Characteristics and special needs of the gifted student in mathematics. Mathematics Teacher, 76, 221-226.

Howley, A. (2002). The progress of gifted students in a rural district that emphasized acceleration strategies. Roeper Review, 24, 158-160.

Lewis, G. (2002). Alternatives to acceleration for the highly gifted child. Roeper Review, 24, 130-134.

Lupkowski-Shoplik, A. E., Sayler, M. F., & Assouline, S. G. (1994). Mathematics achievement of talented elementary students: Basic concepts vs. computation.

In N. Colangelo, S. G. Assouline, & D. Ambroson (Eds.), Talent development II: Proceedings from the 1993 Henry B. and Jocelyn Wallace National Research Symposium on Talent Development (pp. 409-414). Dayton: Ohio Psychology Press.

Moon, T., Brighton, C., & Callahan, C. M. (2002). State standardized testing programs: Friend or foe of gifted education? Roeper Review, 25, 49-61.

National Council for Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA.: Author.

Pletan, M. D., Robinson, N. M., Berninger, V. W., & Abbott, R.D. (1995). Parents' observations of kindergarteners who are advanced in mathematical reasoning. Journal for the Education of the Gifted, 19, 30-44.

Reis, S. M., Westberg, K. L., Kulikowich, J. M., & Purcell, J. H. (1998). Curriculum compacting and achievement test scores: What does the research say? Gifted Child Quarterly, 42, 123-129.

Renzulli, J. (1977). The enrichment triad model: A guide for developing defensible programs for the gifted and talented. Mansfield Center, CT: Creative Learning Press.

Rotigel, J. V. (2000) Exceptional mathematical talent: Comparing achievement in concepts and computation. Unpublished doctoral dissertation, Indiana University of Pennsylvania.

Rotigel, J. V., & Lupkowski-Shoplik, A. (1999). Using talent searches to identify and meet the educational needs of mathematically talented youngsters. School Science and Mathematics, 99, 330-337.

Sheffield, L. J. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics Standards (Report No. RBDM 9404). Storrs: National Research Center on the Gifted and Talented, University of Connecticut. (ERIC Document Reproduction Service No. ED388011).

Sowell, E. J. (1993). Programs for mathematically gifted students: A review of empirical research. Gifted Child Quarterly, 37, 124-129.

Stanley, J. C., & Benbow, C. P. (1986). Youths who reason exceptionally well mathematically. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 362-387). New York: Cambridge University Press.

Tomlinson, C. A. (1995). Deciding to differentiate instruction in middle school: One school's journey. Gifted Child Quarterly, 39, 77-87.

VanTassel-Baska, J. (1995). The development of talent through curriculum. Roeper Review, 18, 98-102.

VanTassel-Baska, J. (1998a). Excellence in educating gifted and talented learners (3rd ed.). Denver: Love.

VanTassel-Baska, J. (1998b). The development of academic talent. Phi Delta Kappan, 79, 760-764.

Winebrenner, S. (2003). Teaching strategies for twice-exceptional students. Intervention in School and Clinic, 38, 131-137.

Wolfle, J. A. (1986). Enriching the mathematics program for middle school gifted students. Roeper Review, 9, 81-85.

Disclaimer: The appearance of any information in the Davidson Institute's Resource Library does not imply an endorsement by, or any affiliation with, the Davidson Institute. All information presented is for informational and archival purposes only. The Davidson Institute bears no responsibility for the content of republished material. Please note the date, author, and publisher information available if you wish to make further inquiries about any republished materials in our Resource Library.

# data[].attributes.attachment_link.title
Mathematically Gifted Students: How Can We Meet Their Needs? - Davidson Institute

# data[].attributes.attachment_link.description
This article discusses the identification of the characteristics of the gifted math student, how school districts comply with the child's needs, and how

# data[].attributes.body
Use multimodes of representation

# data[].attributes.body
supply positive reinforcement and quality feedback

# data[].attributes.attachment_link.title
5 Tips for Culturally Responsive Teaching in the Math Classroom

# data[].attributes.attachment_link.description
Teachers can help all students feel like they belong in math classes by creating connections between course material and students’ lives.

# data[].attributes.body
model instruction

# data[].attributes.body
Give equitable feedback

# data[].attributes.attachment_link.readable_text
How Gifted Learners Differ from Classmates

Relationship to Mathematics Learning

1. Pace at which they learn

1. The sequential nature of math content makes pacing an issue.

2. Depth of their understanding

2. Deeper levels of understanding and abstraction are possible for most mathematical topics, so differentiation becomes important.

3. Interests that they hold (Maker, 1982)

3. If the interest is snuffed out early, the talent may not be developed.

Mathematically gifted students differ from the general group of students studying math in the following abilities: spontaneous formation of problems, flexibility in handling data, mental agility of fluency of ideas, data organization ability, originality of interpretation, ability to transfer ideas, and ability to generalize (Greenes, 1981). No list of characteristics of the mathematically gifted includes "computational proficiency," and yet at levels prior to Algebra I, this is commonly used as the criterion that determines who gets to move on to more interesting material. Furthermore, there is a myth that gifted students don't need special attention since it is easy for them to learn what they need to know. On the contrary, their needs dictate curriculum that is deeper, broader, and faster than what is delivered to other students.

Mathematics can be the gatekeeper for many areas of advanced study. In particular, few gifted girls recognize that most college majors leading to high level careers and professions require four years of high school math and science (Kerr, 1997). Students may drop out of math courses or turn toward other fields of interest if they experience too much repetition, not enough depth, or boredom due to slow pacing.

An Agenda for Action: Recommendations for School Mathematics of the 1980s (NCTM, 1989, p. 18) says, "the student most neglected, in terms of realizing full potential, is the gifted student of mathematics. Outstanding mathematical ability is a precious societal resource, sorely needed to maintain leadership in a technological world." By 1995, when the NCTM created a Task Force on the Mathematically Promising, not much had changed (Sheffield et al., 1995).
What do the Curriculum Standards of the National Council of Teachers of Mathematics (NCTM) say we should do about mathematically gifted students?
The NCTM Standards do not mention gifted students explicitly but recognize that students are not all the same. For all students, the Standards place a greater emphasis on areas that traditionally have been emphasized for the gifted. All students are now expected to complete a core curriculum that has shifted its emphasis away from computation and routine problem practice toward reasoning, real-world problem solving, communication, and connections. "The Standards propose that all students be guaranteed equal access to the same curricular topics; it does not suggest that all students should explore the content to the same depth or at the same level of formalism" (NCTM, 1989, p. 131). At the high school level, additional topics are suggested for "college-intending" students. The Report of the Task Force on the Mathematically Promising recognizes that there are special issues relating to the education of the mathematically promising student (Sheffield et al., 1995) and has made recommendations that include the development of new curricular standards, programs, and materials that encourage and challenge the mathematically promising.
What should be done to differentiate curriculum, instruction and assessment for the mathematically gifted in the regular classroom?
Historically there has been debate about the role of acceleration versus enrichment as the differentiation mode for mathematics. Most experts recommend a combination. The following are suggestions for differentiating for the mathematically gifted by using (1) assessment, (2) curriculum materials, (2) instructional techniques, and (4) grouping models. These opportunities should be made broadly available to any student with interest in taking advantage of them.

Give pre-assessments so that students who already know the material do not have to repeat it but may be provided with instruction and activities that are meaningful. In the elementary grades, gifted learners still need to know their basic facts. If they do not, don't hold them back from other more complex tasks, but continue to work concurrently on the basics.

Create assessments that allow for differences in understanding, creativity, and accomplishment; give students a chance to show what they have learned. Ask students to explain their reasoning both orally and in writing.

Choose textbooks that provide more enriched opportunities. Unfortunately, curriculum in this country is mainly driven by textbooks, which are used about 80% of the time (Lockwood, 1992). Math textbooks often repeat topics from year to year in the grades prior to algebra. Since most textbooks are written for the general population, they are not always appropriate for the gifted. Several series that hold promise for gifted learners have been developed recently under grants from the National Science Foundation; they emphasize constructivist learning and include concepts beyond the basics.

Use multiple resources. No single text will adequately meet the needs of these learners.

Be flexible in your expectations about pacing for different students. While some may be mastering basic skills, others may work on more advanced problems.

Use inquiry-based, discovery learning approaches that emphasize open-ended problems with multiple solutions or multiple paths to solutions. Allow students to design their own ways to find the answers to complex questions. Gifted students may discover more than you thought was possible.

Use lots of higher-level questions in justification and discussion of problems. Ask "why" and "what if" questions.

Provide units, activities, or problems that extend beyond the normal curriculum. Offer challenging mathematical recreations such as puzzles and games.

Provide AP level courses in calculus, statistics, and computer science or encourage prepared students to take classes at local colleges if the supply of courses at the high school has been exhausted.

Differentiate assignments. It is not appropriate to give more problems of the same type to gifted students. You might give students a choice of a regular assignment; a different, more challenging one; or a task that is tailored to interests.

Expect high level products (e.g., writing, proofs, projects, solutions to challenging problems).

Provide opportunities to participate in contests such as Mathematical Olympiads for the Elementary School (grades 4-6), Math Counts (grades 7-8), and the American Junior High School Mathematics Exam (grades 7-8) or the American High School Mathematics Exam (grades 9-12). Give feedback to students on their solutions. After the contests, use some of the problems as the basis for classroom discussions.

Provide access to male and female mentors who represent diverse linguistic and cultural groups. They may be within the school system, volunteers from the community, or experts who agree to respond to questions by e-mail. Bring speakers into the classroom to explain how math has opened doors in their professions and careers.

Provide some activities that can be done independently or in groups based on student choice. Be aware that if gifted students always work independently, they are gaining no more than they could do at home. They also need appropriate instruction, interaction with other gifted students, and regular feedback from the teacher.

Provide useful concrete experiences. Even though gifted learners may be capable of abstraction and may move from concrete to abstract more rapidly, they still benefit from the use of manipulatives and "hands-on" activities.

How can technology support the needs of the gifted?
Technology can provide a tool, an inspiration, or an independent learning environment for any student, but for the gifted it is often a means to reach the appropriate depth and breadth of curriculum and advanced product opportunities. Calculators can be used as an exploration tool to solve complex and interesting problems.

Computer programming is a higher level skill that enhances problem solving abilities and promotes careful reasoning and creativity. The use of a database, spreadsheet, graphic calculator, or scientific calculator can facilitate powerful data analysis. The World Wide Web is a vast and exciting source of problems, contests, enrichment, teacher resources, and information about mathematical ideas that are not addressed in textbooks. Technology is an area in which disadvantaged gifted students may be left out because of lack of access or confidence. It is essential that students who do not have access at home get the exposure at school so that they will not fall behind the experiences of other students.
What is the responsibility of schools and teachers in developing giftedness in mathematics?
Classroom teachers and school districts share the responsibility of addressing the needs of gifted students.

Teachers need training and support in recognizing and addressing the needs of the mathematically gifted.

Teachers who teach mathematics to gifted learners need a strong background in mathematics content. If the school has only a few students with special needs and does not have such a teacher, a mentor from outside the school should be located to work with individuals.

A coordinated curriculum plan needs to be in place so that the mathematical experiences for students are not duplicated or interrupted from one year to the next.

The school should have an organized support system that includes resource books, technology, and human resources.

Regular mathematics classrooms that offer sufficiently challenging and broad experiences for gifted students have the potential to enrich the learning community as a whole since other students will be interested in attempting, perhaps with help, some of the more challenging tasks. If math classes offer diversity in assignments, products, and pacing and monitor student needs, all students will be able to work at their own challenge level.
Return to Top References
Archambault, F. X., Westberg, K. L., Brown, S. W., Hallmark, B. W., Zhang, W., & Emmons, C. L. (1993). Classroom practices used with gifted third and fourth grade students. Journal for the Education of the Gifted, 16, 103-119.

Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28, 14-18.

Lockwood, A. T. (1992). The de facto curriculum. Focus in Change, 6.Maker, J. (1982). Curriculum development for the gifted. Rockville, MD: Aspen Systems Corporation.

Kerr, B. A. (1997). Developing talents in girls and young women. In N. Colangelo & G. A. Davis (Eds.), Handbook of gifted education (2nd ed., pp. 483-497). Boston: Allyn & Bacon.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.Sheffield, L. J., Bennett, J., Berriozabal, M, DeArmond, M., Wertheimer, R. (1995) Report of the task force on the mathematically promising. Reston, VA: National Council of Teachers of Mathematics.

Tomlinson, C. A. (1995). Deciding to Differentiate Instruction in Middle School: One school's journey. Gifted Child Quarterly, 39, 77-87.

Westberg, K. L., Archambault, F. X., Dobyns, S. M. & Salvin, T. J. (1993) The classroom practices observation study. Journal for the Education of the Gifted, 16, 120-146.

Dana Johnson is a mathematics instructor at the College of William and Mary
and also teaches enrichment classes through the Center for Gifted Education at the College.
Return to Top copyright ©2000 ERIC Clearinghouse on Disabilities and Gifted Education
URL: http://www.eric.ed.gov/

# data[].attributes.attachment_link.title
Teaching Mathematics to Gifted Students in a Mixed-Ability Classroom

# data[].attributes.attachment_link.description
Tips on how to teach math to gifted students in your regular classrooms.

# data[].attributes.body
Provide gifted students with activities that allow them to advance in math rather than enrichment sheets.

# data[].attributes.attachment_link.title
Meeting the Needs of Talented Elementary Math Students | Renzulli Center for Creativity, Gifted Education, and Talent Development

# data[].attributes.attachment_link.description
M. Katherine Gavin, Ph.D. Neag Center for Gifted Education and Talent Development As a math specialist in gifted education for over 20 years, I work with te…

# data[].attributes.body
Use "untimed" math fluency assessments: Incorporate less anxiety-producing evaluations to reduce stress for students with math disabilities

# data[].attributes.body
Collaborative learning

# data[].attributes.body
Respect thinking time

# data[].attributes.body
Cultivate a growth mindset

# data[].attributes.body
Verbalize mathematical reasoning

Visuals

Lots of examples

Provide feedback

Peer assistance

# data[].attributes.body
allow gifted students to discuss math with their peers of similar abilities

# data[].attributes.body
Address the barriers that may prevent ELLs from being successful in the classroom

# data[].attributes.attachment_link.title
17 Essential Strategies for Teaching Diverse Learners Effectively | EssayGrader

# data[].attributes.attachment_link.description
Discover essential strategies for teaching diverse learners effectively. This guide will equip you with tips to create an inclusive classroom environment.

# data[].attributes.body
Be aware of bias and stereotypes

# data[].attributes.body
Utilize audiovisual materials

# data[].attributes.body
give equal access to math thinking and learning

# data[].attributes.body
Use multiple teaching strategies: hands on, visuals, technology, etc.

# data[].attributes.body
revoice hard terms by using students’ everyday words before introducing formal math terms.

# data[].attributes.body
Create an inclusive and supportive learning environment to ensure that students embrace their mistakes and take risks

# data[].attributes.attachment_link.readable_text
In a prekindergarten classroom in an impoverished section of the city, Ms. Shepherd announced to the children that they were all going for a walk in the neighborhood. Her theme for that month was buildings.

During the walk the class came upon a house under renovation where the construction workers and electricians were happy to take a break to talk to the children. The children paid rapt attention to measurement, construction plans, and plum lines and levels. Over the next few weeks, Ms. Shepherd and the children returned to the building site several times, observing from a safe vantage point as the house took shape, cheering on the carpenters.

Back in the classroom, the children engaged in a variety of hands-on activities centered on buildings. Children created buildings in the block area, taking tools and measuring devices from the math center to help with their construction. The teacher assistant outlined a skyline of the city for the dramatic play area and the children added the windows and finishing touches to the mural. The class also interviewed a father who worked for a construction company, and he spent one morning showing the children the basics of how to measure and assemble a house. Throughout Ms. Shepherd's building theme, mathematical content was integrated everywhere!

Fostering young children's interest in math centers can be difficult. Children often overpopulate the dramatic play, art, and block areas but may have little interest in exploring the math center without prompting. This past year, we (as university-based researchers and consultants) have been intensively observing the math centers in eight publicly funded prekindergarten classrooms in a southern city. We sought to understand children's natural interactions with math manipulatives and materials during center time. All of the classrooms were relatively well supplied with math-related materials, but in some cases the centers were not set up to foster children's sustained interest or develop their mathematics understanding. Materials were similar across classrooms, but they did not change over time and were not organized in ways that provoked students' curiosity or attention.

Two major research findings support the importance of mathematics learning in urban prekindergarten classrooms that primarily serve children of color. One is that early math knowledge is a strong predictor of later school success-in reading as well as math (Duncan et al. 2007). The other is that racial disparities in children's math achievement are present at kindergarten entry (Friedman-Krauss 2016)-and these gaps remain large throughout elementary, middle, and high school (National Assessment of Educational Progress 2015).

In this article, we argue that creating engaging early math-learning opportunities is critical, especially for African American boys, and we recommend choosing materials and designing environments to optimize early math learning.

Supporting African American boys

At an early age, African American boys become aware of racialized stereotypes regarding their own math abilities (Nasir & Shah 2011). On average, African American boys are overrepresented in negative educational outcomes and underrepresented in positive outcomes. Although it is well established that these disparities are due to a wide range of issues regarding opportunities to learn (see Bowman, Comer, and Johns in this issue), a misperception remains among some members of the public (including some educators) that these disparities are due to innate differences in abilities. As a result, many African American boys are often confronted with lowered expectations even when they are high achieving(Berry III 2008; Zilanawala et al. 2017). Lowered expectations can lead to these children being denied access to rigorous math curricula, feeling unsupported in their math trajectories, and developing a negative attitude toward or perception of their abilities to do math (i.e., their self-efficacy) (Berry III 2008; Nasir & Shah 2011). Making matters worse, new research finds that young children's attitudes toward math are a powerful predictor of their achievement, even after controlling for cognitive abilities (Chen et al. 2018; Digitale-Stanford 2018).

Setting expectations and attitudes aside, research also finds clear disparities in access to high-quality math learning across educational settings. Young children of color attending urban schools in low-income areas tend to have fewer opportunities to master math knowledge. A study of urban prekindergarten classes showed that math teaching and activities take place much less frequently than literacy teaching and activities (Farran et al. 2017). Studies have also found that in the elementary grades (and beyond) African Americans are underrepresented in gifted programs. For example, a careful examination of gifted referrals in kindergarten, first grade, and third grade found that when Black children had a Black teacher, they were far more likely to be referred and assigned to gifted programs than when they had a non-Black teacher (Grissom & Redding 2016). Given these disparities in opportunities to learn throughout early childhood and elementary school, perhaps it should come as no surprise that, according to the National Assessment of Educational Progress (2015), only 13 percent of African American eighth-grade boys were proficient in math, compared with 43 percent proficiency among White boys.

Generally, urban schools, elementary through high school, in low-income areas do not have the rigorous math curricula or high-quality math instruction necessary to engage children and youth in deep math learning or to prepare students for college-level math courses. As a consequence, in higher education institutions, African American students are being assigned to remedial math courses at a higher rate than their White peers (Chen 2016; Preston 2017).

Early exposure to high-quality math environments is increasingly important in determining students' career trajectories. In 2002, according to the National Science Foundation, African American college students received only seven percent of the science, technology, engineering, and mathematics (STEM) bachelor's degrees awarded. In 2014, this percentage remained roughly unchanged. While STEM careers have typically been male dominated, this is not the case among African Americans. Fewer than half of the STEM degrees awarded to African Americans in 2014 went to males (National Science Foundation 2017).

African American males' accomplishments in mathematics remain an under-researched topic, especially from an early childhood perspective. Many successful African American men who have STEM careers have attributed their achievement largely to positive early math experiences. This suggests that by offering more challenging and supportive math learning environments-especially when children are young-teachers can improve children's math proficiency and, over time, open doors to STEM careers (Berry III 2008; McGee & Pearman II 2014; Zilanawala et al. 2017).

Providing engaging early math experiences is not simple. Significant efforts-such as reducing teacher turnover, increasing spending, and hiring more qualified teachers-have had little impact on improving African American males' math trajectories (Zilanawala et al. 2017). Increasing math involvement in early childhood classrooms serving children of color from low-income families requires fundamentally rethinking math learning opportunities.

Why Is Math So Important?

Exposure to high-quality early math experiences and environments allows children to plan, focus, and build on past experiences-actions that develop executive function skills. These skills include the ability to suppress distracting information, shift attention between multiple components of a task, and retain and process information, all of which facilitate learning and performance in the classroom (Fitzpatrick et al. 2014; Clements, Sarama, & Germeroth 2016). Engaging in math activities-like playing board games and sorting toys into sets (by color, shape, etc.)-enriches these essential skills.

The connection between math and executive function is especially important for children growing up in low-income homes and under-resourced communities, which as of 2016, included 34 percent of Black children (Annie E. Casey Foundation 2018). Recent neurological evidence shows that the areas of the brain most affected by early exposure to poverty are the ones related to executive function skills and reasoning (Noble et al. 2015). Because children from low-income families and under-resourced communities tend to have less-predictable routines and be exposed frequently to high-stress environments, they are less likely than children from wealthier families to have well-developed executive function and math skills (Ursache & Noble 2016). Boys in particular have a hard time focusing and persisting without strong environmental support, and boys from low-income, high-stress households have the most difficulty. Younger children are more dependent on the organization of the environment than older children. It is important to note that environmental support does not mean more teacher direction and control. Often, it means creating a math learning center that has enticing math materials, minimal distractions, and accessible organization to direct children's attention. The choice of materials matters (as we outline in the article), with some offering more support for learning than others.

To learn more about the development of executive function skills and mathematical abilities, see "From Design Copying to Mathematics in the Early Childhood Classroom" in the March 2018 issue of Young Children.

Choosing appropriate math materials

Through our work with teachers, we've seen that the supply of products and programs on the market claiming to facilitate math learning can be overwhelming. Based on questions from teachers, and on the day-to-day challenges we observed in their classrooms, we developed the following guidelines and strategies for selecting appropriate math materials and using them in enriching ways.

Provide sequential activities

In early childhood, the most effective math materials involve sequential learning. Sequential materials give children a logical order or sequence of steps to follow and often involve children creating a working plan. Using these types of materials, children engage in higher-order thinking, planning, reflecting, and problem solving. More engagement in sequential activities is linked to higher gains during preschool in both math and self-regulation skills (Farran et al. 2017). Examples of sequential materials for 3- to 5-year olds could include tangrams (matching patterns of increasing complexity); peg-sorting boards; and learning cubes with design cards (3-D construction based on 2-D pictures).

Select materials that give children feedback

While teacher-directed math instruction is important, math centers should help children learn independently as well. Materials that automatically provide feedback (sometimes called autodidactic or self-correcting) allow children to independently see when they have made a mistake. A simple example is a jigsaw puzzle with pieces that only fit together one way. The self-correcting feature allows children to extend their initial ideas into sustained math learning while enhancing working memory (Kirschner, Sweller, & Clark 2006; Willingham 2017).

Many successful African American men in STEM careers have attributed their achievement largely to positive early math experiences.

When choosing math materials, teachers should consider how much support children are likely to need to understand and learn from the activity. An introduction and sporadic support may be reasonable, but if children are likely to need continuous support, the product may not be appropriate for the math center. Puzzles are often great examples of autodidactic materials. In one common puzzle that teaches shapes and one-to-one correspondence, each shape has a particular number of holes that correspond with pegs on the puzzle board.

Offer problem-solving opportunities

Extending children's initial interest involves setting high expectations and inviting children to make sense of the world through problem solving. Positive early math experiences are a wonderful way to foster young children's natural curiosity. In our observations, we have found that boys are often attracted to open-ended building materials such as Legos, Bamboo Blocks, and Magna-Tiles because they allow for exploration and creativity. However, without some additional assistance, children may not use these materials in ways that provoke deeper thinking. Teachers should scaffold children's play, increasing challenges, and sparking new explorations over time.

Materials such as Legos and Magna-Tiles allow students to plan elaborate structures if teachers provide some assistance. Pictured below is a young boy independently engaged in building stairs for a structure. To determine the height of the stairs, he measured the stairs against the height of the Lego container. This required the boy to complete several phases of rebuilding and remeasuring to ensure that the stairs fit the structure properly. After several attempts, he was able to transfer the stairs to the structure, and the stairs fit. Play like this-involving complex problem solving-is essential to developing the executive function skills (e.g., shifting attention between multiple components of a task) discussed in " Why Is Math So Important? ". While solving this challenge, he remained deeply engaged in his project for the remainder of math center time (roughly half an hour). Providing models (like a laminated poster of stairs) with corresponding plans to follow and suggestions from the teacher can help children enjoy the cognitive benefits-and fun-of more sophisticated play.

Add a variety of explicit math content

In the prekindergarten classrooms we observed, many of the materials in math centers were variations of sorting and block building. But there is much more to math learning than these two activities. Moreover, sorting and building can happen without children actually learning much math. Boys may be attracted to these types of activities, but the math center should represent a wide range of math content, from patterns to counting and cardinality to spatial relations. Materials that do not at first seem math related can become so with the addition of supporting resources. For example, we have observed that children often used counting bears for dramatic play. If children do not know how to count, having counting bears will not, by itself, teach them. However, adding a lazy Susan with numerals or dots(or a combination of either with color coding) to the counting bears can provide children with actual math learning. The lazy Susan allows children to physically count the quantity of counting bears and match it to the quantity of dots displayed on the lazy Susan (i.e., one-to-one correspondence).

We often saw Bristle Blocks in math centers even though they teach little to no math. While some spatial learning may occur with materials like Bristle Blocks, too often children merely attach them without reference to constructing a shape. For Bristle Blocks to enhance math, teachers need to add some creative suggestions for how children can interact with the blocks. Teachers can take advantage of how attractive the blocks are to children by adding measuring tapes, rulers, and suggestions for their usage, giving children a means to use these materials mathematically.

Avoid materials that distract from math learning

Teachers need to be aware of the nonmathematical aspects of materials and activities that may compete for children's attention. For example, young children are often distracted by the features of a math manipulative, particularly color, and may have trouble recognizing the mathematical concept (Willingham 2017). Teachers need to consider if color is being used for mathematical purposes (such as comparing the quantities of red cars and blue cars) or if it is simply a distraction (such as a rainbow of hues in a game intended to focus on one-to-one correspondence or counting on).

It is important to note that materials in which a nonmathematical concept is redundant with the mathematical concept may impair children's math learning. For instance, many materials that aim to focus on sorting allow for both numerical and color sorting; examining these materials, it is clear that very often children could sort entirely by color and be correct without attending to the math features at all. In addition, recent research has shown that preschoolers can become overstimulated by materials with mulitple features and can have trouble distinguishing which one is most relevant (Willingham 2017). When materials have multiple features, children may need support to identify and attend to the mathematical aspects. For independent learning in math centers, materials with a minimal number of distracting features may be more effective.

Organize, label, and rotate materials

Young children are highly dependent on the organization of the environment to be able to engage with math materials in a meaningful way. Creating a space that is neatly organized, labeled, and engaging will garner far more attention than a poorly arranged center. When children can easily see all available materials, they can better plan their math-related play, be it building a pyramid or copying a design or sorting toy animals into different types of sets (perhaps by tail length). Maintaining their interest throughout the year requires adding new materials and/or enhancing old materials with new resources that allow children to do more with what is at hand. For example, teachers could provide children with sets of pattern blocks and simple designs to copy. As the children gain mastery, teachers can add more complex designs and invite children to create their own using the shapes. Teachers can also expand this design copying using other materials, such as beads or LEGOs.

Containers for materials are often labeled to make cleanup easier, but there is a more important benefit to labeling. Appropriately labeling materials with photos and/or text helps children access them easily. Labels can also be enhanced to remind children of more challenging ways to play with the materials. Children can then independently navigate centers, making informed decisions and plans about what supplies to work with. Many materials fit well into tubs that are easy to label. Oddly shaped and large materials can be placed on labeled shelves.

Refreshing materials after every unit of study by adding new items and changing the supporting materials helps re-engage children and maintain their attention. For example, if counters are currently present in the math center and are only used to practice one-to-one correspondence, the teacher can add pattern cards that prompt children to use the counters in new ways. There is not one prescribed timeframe in which teachers should rotate materials. Fewer children choosing the math center is a strong indication that the materials need updating.

Conclusion

Fostering high-quality early math experiences can have a tremendous effect on the long-term school success and career trajectories of African American males. While the guidelines we have outlined here are beneficial to all preschoolers, they are critically important to male children of color. Far too many schools are not providing the vigorous math activities, materials, and supports that children of color need, hampering their opportunities to later engage in advanced math courses or enter STEM-related fields.

Early childhood teachers can foster productive math experiences for African American boys by having positive individual interactions, providing opportunities for exploration, extending children's initial interests, and structuring the environment to continuously attract and engage children in math learning.

The way in which teachers and parents approach and communicate the importance of math learning has a direct link to a young boy's perception of his ability to enjoy and excel in math. It also impacts his self-regulation skills. Therefore, making math a meaningful and inviting experience is vital in all early childhood classrooms-especially those serving African American boys growing up in under-resourced communities.

# data[].attributes.attachment_link.title
Positive Early Math Experiences for African American Boys: Nurturing the Next Generation of STEM Majors

# data[].attributes.attachment_link.description
In this article, we argue that creating engaging early math-learning opportunities is critical, especially for African American boys, and we recommend choosing materials and designing environments to optimize early math learning.

# data[].attributes.body
Create an environment where students can explore

# data[].attributes.body
Scaffold instruction- provide visuals, work in pairs, model and think aloud, use manipulatives

Use a variety of learning modalities- auditory, visual, and kinesthetic

Promote language production- provide sentence frames, create low stakes discussions!

# data[].attributes.attachment_link.readable_text
Math has often been called "the universal language." While it's true that numbers work the same way regardless of the language you speak, teachers cannot assume that their English language learners (ELLs) will automatically excel in math for this reason alone.

Language proficiency is also closely related to the development of strong mathematical skills. Kristina Roberston writes, " Solving word problems, following instructions, understanding and using mathematical vocabulary correctly - all of these skills require a language proficiency...We tend to think of mathematics as a subject that does not require a strong command of language. In reality, however, mathematical reasoning and problem-solving are closely linked to language and rely upon a firm understanding of basic math vocabulary (Dale & Cuevas, 1992; Jarret, 1999)."

This blog will discuss specific ELL math best practices and math instructional strategies that you can use to boost student learning.

4 Best Practices for ELL Math Instruction

According to data from the US Department of Education's Academic Performance and Outcomes for English Learners, overall ELL performance in math has been significantly below the performance of native speakers.

For ELL students to fully participate in the math classroom, teachers must employ strategies to promote both their academic and linguistic development. The following best practices can help you support your ELLs' mastery of math skills.

1. Scaffold your instruction

As you consider how to engage students in math lessons, it's important to provide your ELLs with support in navigating the linguistic challenges of math. Jeanine Harvey, director of multilingual learner academics at The New Teacher Project says, " We know from our work that multilingual learners do not have the same access to grade-level assignments as their peers...All students could engage with grade-level assignments with the right supports. "

Scaffolding instructional strategies for math may involve the following:

Providing visuals.

Allowing students to work in pairs or small groups.

Modeling and thinking aloud during instruction.

Using manipulatives.

Giving students word banks.

By providing intentional and strategic instructional scaffolding, your ELL students will be more engaged and experience more growth.

All students benefit from instruction that incorporates a variety of learning modalities. Research has shown that when auditory, visual, and kinesthetic methods are combined, students retain information better.

Though all students benefit from hands-on learning activities, they are particularly important for ELLs. According to The National Math Foundation, " By 2009, Mulalic (et al.) discovered that the kinesthetic learning style was the most preferred learning style among ESL students. Studies in 1987, 1990, 1993, 1997, and 2001 reported that adult L2 immigrants and ESL students in the US favor kinesthetic styles over all others (Gilakjani, 2012)."

While there are many ways to incorporate kinesthetic activities in your ELL math instruction, manipulatives are one of the most powerful tools you can use to support your ELLs. Although they are often thought of as math tools for elementary students, they can be used with students at any level.

Manipulatives provide a common language for students to communicate their thought processes. This is especially important for newcomer ELLs, whose expressive English language skills are starting to develop.

When you're teaching math to ELLs, it's important to consider how you can deepen their understanding of math concepts as well as encourage their language skills.

However, your ELL students face a significant cognitive load during instruction in content areas- they're simultaneously learning a new language and new skills. It's important to minimize their cognitive load while maintaining academic rigor.

A student's proficiency in a language is dependent on both production and comprehension. ELL students' receptive language skills generally develop more quickly than their expressive language skills.

Teachers need to intentionally help them increase their language production. You can do this through scaffolding and supportive language practices, like those below.

Allow students to use their native language alongside English.
Doing so can help you gain an understanding of what students know in their native language and will help in making connections with prior knowledge.

Provide students with sentence frames for a math discussion.
For example, "I know that this is a ______ because it has ______ line segments and _____ vertices."

Create opportunities for low-stakes discussion through activities like think-pair-share.
Jeff Zwiers, a senior researcher at the Stanford Graduate School of Education and the director of professional development for the Understanding Language initiative, stresses the importance of giving ELLs time to talk with each other and ask questions. Zwiers states, "Very few kids will raise their hand and say 'Can you explain that?' to the teacher, particularly multilingual learners, who need it the most, they won't do that. But with one other person, it's a safer setting."

4. Focus on word problems

As word problems become increasingly difficult over time, it's important to note that reading skills play a vital role in math.

Brenda Krick-Morales writes, " Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation - ELLs who have had formal education in their home countries generally do not have mathematical difficulties; hence, their struggles begin when they encounter word problems in a second language that they have not yet mastered (Bernardo, 2005)."

When using word problems with ELL students, it's important to consider the following questions:

What background knowledge do my students need to have to understand this problem?

Are there any multiple-meaning words or phrases that my ELL students may not be familiar with in this problem?

Will my students need to distinguish between necessary and unnecessary information in this problem?

High-Impact Strategies to Teach ELL Math Vocabulary

Vocabulary instruction plays a key role in ELL math achievement. ELLs need explicit, intentional vocabulary instruction to successfully gain math skills.

Focus on academic vocabulary

Math is full of challenging words like quadrilateral and vertices -and your ELL students may or may not have a prior understanding of these concepts in their native language.

ELL students benefit from pre-teaching academic vocabulary terms in a lesson, as it provides them with a foundation of understanding. It is also important to give them multiple exposures to math words-research on vocabulary development shows that students retain vocabulary better when they learn words in context rather than in isolation.

The following ideas can help you develop and reinforce academic math vocabulary:

Use a math word wall with visuals for ELLs.

Create personal "word walls" customized for math vocabulary.

Use precise vocabulary when discussing terms AND give a kid-friendly definition.

Incorporate graphic organizers to help students develop and expand their understanding of word meanings.

Get creative with teaching definitions-give students numbers and have them line up from least to greatest or give students string and call out different shapes for them to create. You can have a little fun while engaging your students in different learning styles.

Teach "tricky words"

Math vocabulary includes both specific terminology and everyday words that have different meanings in the context of math. Take a look at the example below:

Did the student "find x"? Technically, yes!

Words like "face," "table," and "carry" (and even the word "and!") have different meanings when they're used in math. Provide your ELL students with many opportunities to practice using these tricky words in the context of math.

Don't forget about homophones

Whether you're a native speaker or new to English, homophones can present a challenge. Many math vocabulary words are homophones: some and sum, raise and rays, won and one, wait and weight...the list goes on!

Consider creating a chart for your ELLs to reference to help them differentiate between common homophones.

Math and language skills are inextricably linked. By keeping language in mind when you plan your ELL math instruction, you can help your students develop important math skills.

Check out our Marvelous Math Pinterest board for engaging math ideas and support for students in all grades!

# data[].attributes.attachment_link.title
Elevate ELL Math Achievement With These Top Tips and Strategies | Continental Educational Publisher

# data[].attributes.attachment_link.description
This blog will discuss specific ELL math best practices and math instructional strategies that you can use to boost student learning.

# data[].attributes.body
Give pre-assessments: so students can be provided with instruction and activities that are meaningful

Create assessments: allow differences of understanding

Choose textbooks: provide more enriched opportunities

Use multiple resources

Use higher-level questions

Differentiate assignments

Provide useful concrete experiences

# data[].attributes.body
Including visual examples can help ELLs connect what they see to prior knowledge they may have.

# data[].attributes.attachment_link.readable_text
Listen to this post as a podcast:
A note on terminology: The acronym ESL is used less often now in schools than it used to be, because we recognize that many students who are learning English already speak several other languages, so English would not be a "second" language. I use it several times in the post because schools sometimes refer to the teachers as ESL teachers, and the term is still widely used as a search term for this topic. My intent in using the acronym is to make this post easier to find online.

You have a new student, and he speaks no English. His family has just moved to your town from Japan, and though he receives English as a Second Language (ESL) support, he will also be sitting in your room every day to give him more exposure to his new language. How can you be a good teacher to someone who barely understands you?

According to the National Center for Education Statistics, an average of 9 percent of students in U.S. public schools are English Language Learners (ELLs); that number is closer to 14 percent in cities. Although many of these students start off in high-intensity, whole-day English programs, most are integrated into mainstream classrooms within a year, well before their English language skills would be considered proficient.

How prepared are you to teach these students? If you're like most classroom teachers, you have little to no training in the most effective methods for working with English language learners (Walker, Shafer, & Iiams, 2004). So that means we have a problem here: Lots of ELL kids in regular classrooms, and no teacher training to ensure the success of that placement.

Below, three ESL teachers tell us what they know about the things regular classroom teachers can do to improve instruction for ELL students. These 12 strategies are simple, they are not very time consuming, and best of all, they will help everyone in your class learn better:

1. Make it Visual

"Avoid giving instructions in the air," says Melissa Eddington, an Ohio-based ESL teacher. "ELL kids have a harder time processing spoken language." So instructions - even basic directions for classroom procedures - should be written on the board whenever possible. Challenging concepts should be diagrammed or supported with pictures. And modeling the steps of a process or showing students what a finished product should look like can go a long way toward helping students understand. "Sometimes showing our students what to do is all they need in order to do it," Eddington says. Not only will this kind of nonlinguistic representation improve comprehension for ELL students, it will help all of your students grasp concepts better.

2. Build in more group work.

"Kids aren't just empty glasses that we pour stuff into and then at the end of the day they dump it back onto a test," says Kim, an ESL teacher who was the subject of my very first podcast interview. "If you really want the kids to learn, they've got to be engaged." That means less teacher-led, whole-class instruction, and more small groups, where students can practice language with their peers in a more personal, lower-risk setting. And if ELL students attend your class with a resource teacher, make use of that person: In most cases the resource teacher doesn't have to work exclusively with the ESL students; they can work with smaller groups that happen to contain these students, helping to improve the teacher-student ratio and give kids more time to practice.

3. Communicate with the ESL teacher.

Mary Yurkosky, a former ESL teacher in Massachusetts, credits much of her students' success to the strong relationship she had with the regular classroom teachers. "The classroom teachers were always talking to me about what they were doing in their classes," she says. "They made it so easy for me to support them: If a teacher was going to be doing a unit on plants, I could make sure we used some of that same vocabulary in the ESL class."

Ideally, this could be systematized, where ESL teachers could regularly get copies of lesson plans or collaborate with regular classroom teachers to build solid back-and-forth support, but "it doesn't have to be that much work," Yurkosky insists. "Just talk to each other. Talk about what's going on in your classrooms, invite each other to special presentations, share what your students are learning, and the words will naturally find their way into the ESL class."

4. Honor the "silent period."

Many new language learners go through a silent period, during which they will speak very little, if at all. "Don't force them to talk if they don't want to," says Eddington, "A lot of students who come from cultures outside of America want to be perfect when they speak, so they will not share until they feel they are at a point where they're perfect." Just knowing that this is a normal stage in second language acquisition should help relieve any pressure you feel to move them toward talking too quickly.

5. Allow some scaffolding with the native language.

Although it has been a hotly debated topic in the language-learning community, allowing students some use of their first language (L1) in second-language (L2) classrooms is gaining acceptance. When a student is still very new to a language, it's okay to pair him with other students who speak his native language. "Some students are afraid to open their mouths at all for fear of sounding stupid or just not knowing the words to use," Yurkosky says. "Letting them explain things or ask questions in their first language gets them to relax and feel like a part of the class."

And this doesn't only apply to spoken language. If you give students a written assignment, but the ELL student doesn't yet have the proficiency to handle writing his response in English, "Don't make them just sit there and do nothing," Eddington says. "Allow them to write in their first language if they're able. This allows them to still participate in journal writing or a math extended response, even if you can't read what they write." There has even been some evidence that allowing second-language learners to pre-write and brainstorm in L1 results in higher-quality writing in L2 in later stages of the writing process (Yigzaw, 2012).

6. Look out for culturally unique vocabulary.

"For most of these kids, their background knowledge is lacking, especially with things that are unique to American or westernized culture," says Eddington. It's important to directly teach certain vocabulary words: "Show them videos of what it looks like to toss pizza dough, show pictures of a juke box or a clothing rack - things that are not common in their own language."

One way to differentiate for ELL students is to consider the whole list of terms you're going to teach for a unit, and if you think an ELL student may be overwhelmed by such a long list, omit those that are not essential to understanding the larger topic at hand.

7. Use sentence frames to give students practice with academic language.

All students, not just English language learners, need practice with academic conversations. Sentence frames - partially completed sentences like "I disagree with what _________ said because..." - show students how to structure language in a formal way. Keep these posted in a highly visible spot in your classroom and require students to refer to them during discussions and while they write.

For this kind of language to really sink in, though, Kim says it has to become a regular part of class. "They won't do it if it's not the norm in the class, because they'll be embarrassed to use it among their peers," she says. "But if they can put it off on the teacher and say, Oh, well, you know, Miss Kim makes me talk like this, then they don't look as hoity-toity as they would otherwise."

8. Pre-teach whenever possible.

If you're going to be reading a certain article next week, give ESL students a copy of it now. If you plan to show a YouTube video tomorrow, send a link to your ESL students today. Any chance you can give these students to preview material will increase the odds that they'll understand it on the day you present it to everyone else. "That kind of thing is wonderful," Yurkosky says. "The kids feel so empowered if they've had a chance to look at the material ahead of time."

9. Learn about the cultural background of your students...

Our second-language populations grow more diverse every year. Taking the time to learn the basics of where a child comes from - exactly, not 'somewhere in the Middle East/South America/Asia/Africa' - tells the student that you respect her enough to bother. Kim remembers one time when she had to set the record straight about the diverse South American population at her school: "I was listening to the teachers talking about the 'Mexican' kids in our building," she says, "and I was like, 'We don't have any Mexicans.'" Not taking the time to at least correctly identify a child's country of origin, much like not bothering to pronounce their name correctly, is a kind of microaggression, a small, subtle insult that communicates hostility toward people of color. Make a commitment to be someone who bothers to get it right.

Once you have the country straight, take things up a notch by learning about students' religious and cultural practices. If he is a practicing Muslim, he should be told if one of the pizzas you ordered for the class party has sausage on it. If she comes from a culture where eye contact with adults is viewed as disrespectful, you'll know not to force her to look you in the eye when she's talking.

10. ...but don't make a child speak for his entire culture.

In her podcast interview, Kim shared a story about watching a teacher ask a new Iraqi student how he felt about the war in his country, right in the middle of class. "That's not cultural inclusiveness," she explains. "I've seen teachers do this and then pat themselves on the back. The students' English is limited so they can't express themselves very well, and they don't want to 'represent'; they just want to be there." If you anticipate a theme coming up in your class that's going to be relevant to one of your students, have a conversation with them in advance, or check with your ESL teacher to see if they think it's appropriate for in-class discussion.

11. Show them how to take themselves less seriously...

By modeling the risk-taking that's required to learn a new language, you help students develop the courage to take their own risks, and to have a sense of humor about it. "I tried to say the word 'paint' ( pinta) in Portuguese and instead I said the word for 'penis' ( pinto). They all roared with laughter while I stood there with a What?? look on my face," Yurkosky says. "When they explained what I'd said, I laughed so hard! I told them that laughing was fine because sometimes mistakes are really funny, but ridicule is never okay."

12. ...but always take them seriously.

One of Kim's pet peeves about how teachers interact with English language learners is the way they often see students' efforts as 'cute,' missing the whole point of what the student is trying to say. "A student will be desperate to communicate, and the teacher will get distracted by the delivery and miss the message," she says. "That's painful for me to watch." It bothers her when teachers mistake a lack of language for a lack of intelligence or maturity. When a child can't express themselves as well as they would in their native language, it's far too easy to assume the concepts just aren't in their heads.

"It breaks my heart when I hear teachers say (ELL kids) don't know anything," says Eddington. "These are brilliant kids and they know a lot. They just can't tell us in English yet." Make a conscious effort to see past the accent and the mispronunciations and treat every interaction - every student - with the respect they deserve.

"They're doing twice the job of everybody else in the class," Kim adds, "even though the result looks like half as much." ♦

Further Reading

The ESL/ELL Teacher's Survival Guide is one of the highest-rated books on teaching English-language learners available. In addition to offering an overview of the research on second-language learners and best practices in teaching ESL, it also includes a whole section on teaching ESL in the content areas and another specifically geared toward teaching ELL students in mainstream classrooms.
References:
Walker, A., Shafer, J., & Iiams, M. (2004). "Not in my classroom": Teacher attitudes towards English language learners in the mainstream classroom. NABE Journal of Research and Practice, 2(1), 130-160.

Yigzaw, A. (2012). Impact of L1 use in L2 English writing classes. Ethiopian Journal of Education and Sciences, 8(1), 11-27.

If you thought this was helpful, stick around.
Join my mailing list and never miss another post. You'll get weekly tips, tools, and inspiration - in quick, bite-sized packages - all geared toward making your teaching more effective and joyful. To thank you, I'll send you a free copy of my new e-booklet, 20 Ways to Cut Your Grading Time in Half. I look forward to getting to know you better!

Click here to get a PDF of this article.

# data[].attributes.attachment_link.title
12 Ways to Support English Learners in the Mainstream Classroom

# data[].attributes.attachment_link.description
Advice from three ESL teachers on the things regular classroom teachers can do to help English language learners thrive in mainstream classrooms.

# data[].attributes.body
By giving students physical instructions, they can make a connection between body movement and language comprehension, enhancing their language acquisition through kinesthetic learning.

# data[].attributes.headline
Strategies for recognizing a gifted student can include:

# data[].attributes.subject
Strategies for recognizing a gifted student can include:

# data[].attributes.body
Thinks quickly

Recalls facts easily

Impulsive and acts before they think

Long attention span

great deal of curiosity

Wants to understand the way things work

Independent characteristics

# data[].attributes.attachment_link.readable_text
Differentiated Instruction

Early childhood educators can use differentiation to help young students who may be gifted to thrive academically.

Educators have long been working on how to develop a more equitable curriculum that caters to all learners. Many times, however, teachers don't consider gifted students when they plan and implement differentiated learning strategies.

The late Barbara Clark-former professor emerita of California State University, Los Angeles, past president of the World Council for Gifted and Talented Children, and author of Growing Up Gifted: Developing the Potential of Children at School and at Home-defined gifted as the inborn biological superior development of various brain functions in the areas of cognition, creativity, academics, leadership, or the arts. But Clark also made clear that the "growth of intelligence depends on the interaction between biological inheritance and environmental opportunities."

In this claim, Clark urged us to consider the strong, rich, and timely connection between nature and nurture. Gifted children need to have the chance and the means to develop inherited traits of information processing with rich and inspiring schooling and environmental experiences.

Has advanced vocabulary and expresses themselves well

Thinks quickly

Recalls facts easily

Wants to know how things work

Began reading before starting school

Puts unrelated ideas together in new ways

Gets bored easily

Likes grown-up things and being with older people

Has a great deal of curiosity

Is adventurous

Has a good sense of humor

Is impulsive and acts before they think

Tends to dominate others if given a chance

Is persistent and sticks to a task

Has good coordination and body control

Is independent and self-sufficient in looking after themselves

Is aware of their surroundings and what is going on around them

Has a long attention span

Wanted to do things for themselves early

How to Recognize a Possible Gifted Child

They have unfinished work, which may be the result of varied interests and the inability to narrow down a topic.

Poor class work by gifted students is often a sign of disinterest in the subject matter. Gifted children may question the appropriateness of classroom activities for their needs but will work diligently on topics of high interest.

Sensitivity to the attitudes and perceptions of others may cause gifted students to fall into the perfectionism trap or to fear failure. These feelings can lead to unfinished work, procrastination, or underachievement.

Poor group work; gifted students may prefer to work alone because of feelings that their ideas will be misunderstood or unappreciated by the group.

Bossiness in group work could be an indicator of younger students practicing their leadership abilities to find the most effective leadership style.

Overbearing behavior also may stem from gifted students' desire for control in their lives, as well as their traits of independence and nonconformity.

Emotional outbursts or periods of withdrawal in gifted students may be due to their highly sensitive nature.

According to experts in gifted child development, from an early age gifted children show certain characteristics that might indicate to teachers and parents that these children have special needs. A young child who has many, but not necessarily all, of the following characteristics is likely to be gifted:

Together with the above characteristics and in accordance with what experts in the field say, from my experience as a teacher there are also certain classroom indications that a child might be gifted:

Should teachers and/or parents recognize these features in a child, they may want to ask a specialist for a formal assessment.

Approaches, Strategies, and Tips

Active pedagogies such as Montessori and Reggio Emilia share the common ground of allowing learners to construct their learning from their interests. These pedagogies base their approach on generating open topics to enable research and discovery through differentiated strategies and techniques.

For example, one recurring topic in all syllabi from K-2 and even higher is the weather. How can we guide the development of gifted children's interest in this topic? One way is to invite the class to go outside and ask the whole group to notice any special fact about the weather, using their senses to collect information about a weather condition the teacher may have decided to use as a starting point.

From here the teacher asks what the children may want to know about the weather. At this moment, gifted children may come up with questions that lead to deeper research because they will need accurate answers. They may ask, for example: Why does the weather change? Why are there different weather conditions at the same time in different areas of the country? Why is it that the weather varies in the different seasons? Why do seasons occur? When these questions arise, it's important for teachers to work with the learners to find the answers.

Skills Development

All young children develop skills in the area of STEAM through sorting, grouping, and adding and subtracting, using technology as an aid in finding images and videos, and typing labels they may need. With the weather, learners can observe the sky with the different kinds of clouds and make models and sculptures using a variety of materials such as clay, mud, wire, pipes, stones, flashlights or lamps, and pieces of cloth of different sizes.

In the case of gifted learners, the development of STEAM skills will require that the teacher be open to offering different contexts and resources that involve all of the above but may also demand more challenging and meaningful actions, where the learners have voice and choice so they have the chance to bloom and exceed expectations.

Language development: For reading and writing, invite gifted learners to read and label drawings, diagrams, flashcards, and signs, and to read, copy, and create short sentences. They can also learn poems and songs related to the weather and listen to or even read fiction stories and nonfiction books. While gifted learners will again show that they develop fast and steady, they might need some help with tracing letters and writing due to the development of their fine motor skills, which will probably be at their age level.

Motor skills: Young gifted children will frequently excel in their development of gross motor skills, but they'll need to control their anxiety and develop resilience in the field of fine motor skills. Offer them enough time to explore, and dramatize, for example, the movements of the tides, wind, currents, and the earth-drawing, writing, modeling.

Gifted learners, like all the children in the group, have the right to have an appealing and challenging learning context in order to thrive. It's important to bear in mind that giftedness is not a synonym for academic excellence, and most of the time, gifted children don't succeed in formal education, mainly because the topics that the curriculum offers, and almost certainly the approach, are not interesting to these children.

# data[].attributes.attachment_link.title
Connecting With the Very Young Gifted Child

# data[].attributes.attachment_link.description
Early childhood educators can use differentiation to help young students who may be gifted to thrive academically.

# data[].attributes.body
Incorporate more group work so students can use each other to bounce ideas off of one another rather than struggle alone.

# data[].attributes.body
By connecting math to real-life situations students can connect to math more personally.

# data[].attributes.body
Set high but achievable expectations with structured support