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## Teaching Math to Students with Disabilities

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**Teaching Math to Students with Disabilities**Present Perspectives**“Math is hard” (Barbie, 1994)**• US 15 year olds ranked 24th (among 29 developed nations) in the 2003 International Student Assessment in math literacy and problem solving • 7% of US students scored in the advanced level in the 2004 Trends in Math and Science Study • Almost half of America's 17 year olds did not pass The National Assessment of Educational Progress math test • 2006 Hart/Winston Poll found that 76% of Americans believe that if the next generation does not work to improve its skills it risks becoming the 1st generation who are worse off economically than their parents**How did we get here?**• Math skills have received less attention than reading skills because of the perception that they are not as important in “real life” • Ongoing debate over how explicitly children must be taught skills based on formulas or algorithms vs a more inquiry-based approach • Teacher preparation – general concern about elementary preservice training programs • Little reference to students with disabilities in NCTM’s standards • Debate over math difficulties vs math disabilities**Developmental dyscalculia**• developmental difficulties or disabilities involving quantitative concepts, information, or processes • Dyscalculia is where dyslexia was 20 years ago it needs to be brought into the public domain • Jess Blackburn, Dyscalculia & Dyslexia Interest Group**What defines mathematical learning disabilities?**• Genetic basis • Presently only determined by behavior (which behaviors: knowledge of facts? procedures? conceptual understanding? Speed and accuracy?) • Depending on the criteria incidence can include from 4 to 48% of students • Mathematical difficulties vs. mathematical disabilities: different degrees of the same problem or different problems?**National Mathematics Advisory Panel**• Established in 2006 • To examine: • Critical skills & skill progressions • Role & appropriate design of standards & assessment • Process by which students of various abilities and backgrounds learn mathematics • Effective instructional practices, programs & materials • Training (pre and post service) • Research in support of mathematics education**NCMT final Report (2008)**• Curricular content • Focused: must include the most important topics underlying success in school algebra (whole numbers, fractions, and particular aspects of geometry and measurement) • Coherent: effective, logical progressions • Proficiency: students should understand key concepts, achieve automaticity as appropriate; develop flexible, accurate, and automatic execution of the standard algorithms, and use these competencies to solve problems**What is the structure of mathematical learning disabilities?**• Issues with retrieval of arithmetic facts • Difficulties understanding mathematical concepts and executing relevant procedures • Difficulties choosing among alternate strategies • Trouble understanding the language of story problems, teacher instructions and textbooks**Math instruction issues that impact students who have math**learning problems • Spiraling curriculum • Teaching understanding/algorithm driven instruction • Teaching to mastery • Reforms that are cyclical in nature**Promising approaches to teaching mathematics to students**with disabilities • Math Expressions • Saxon • Strategic math Series • Touch Math Number Worlds Curriculum • Montessori methods and materials • What works clearing house**Resources for teaching math**• Illuminations • MathVids**Teaching Math to Students with Disabilities**Strategies**Application of effective teaching practices for students who**have learning problems • Concrete-to-representational-to-abstract instruction (C-R-A Instruction) • Explicitly model mathematics concepts/skills and problem solving strategies • Creating authentic mathematics learning contexts**Concrete-to-Representational-to-Abstract Instruction (C-R-A**Instruction) • Concrete: each math concept/skill is first modeled with concrete materials (e.g. chips, unifix cubes, base ten blocks, pattern blocks) • Representational: the math concept is next modeled at the representational (semi-concrete) level (e.g. tallies, dots, circles) • Abstract: The math concept is finally modeled at the abstract level (numbers & mathematical symbols) should be used in conjunction with the concrete materials and representational drawings.**Concrete-to-Representational-to-Abstract Instruction (C-R-A**Instruction) • Concrete: each math concept/skill is first modeled with concrete materials (e.g. chips, unifix cubes, base ten blocks, pattern blocks) • Representational: the math concept is next modeled at the representational (semi-concrete) level (e.g. tallies, dots, circles) • Abstract: The math concept is finally modeled at the abstract level (numbers & mathematical symbols) should be used in conjunction with the concrete materials and representational drawings.**Concrete-to-Representational-to-Abstract Instruction (C-R-A**Instruction) • Concrete: each math concept/skill is first modeled with concrete materials (e.g. chips, unifix cubes, base ten blocks, pattern blocks) • Representational: the math concept is next modeled at the representational (semi-concrete) level (e.g. tallies, dots, circles) • Abstract: The math concept is finally modeled at the abstract level (numbers & mathematical symbols) should be used in conjunction with the concrete materials and representational drawings.**Important Considerations**• Use appropriate concrete objects • After students demonstrate mastery at the concrete level, then teach appropriate drawing techniques when students problem solve by drawing simple representations • After students demonstrate mastery at the representational level use appropriate strategies for assisting students to move to the abstract level.**How to implement C-R-A instruction**• When initially teaching a math concept/skill, describe and model it using concrete objects • Provide students multiple opportunities using concrete objects • Provide multiple practice opportunities where students draw their solutions or use pictures to problem solve • When students demonstrate mastery by drawing solutions, describe and model how to perform the skills using only numbers and math symbols • Provide multiple opportunities for students to practice performing the skill using only numbers and symbols • After students master performing the skill at the abstract level, ensure students maintain their skill level by providing periodic practice • Example**Explicit Modeling**• Provides a clear and accessible format for initially acquiring an understanding of the mathematics concept/skill • Provides a process for becoming independent learners and problem solvers**What is explicit modeling?**Teacher Mathematical concept Student**Instructional techniques….**• Identify what students will learn (visually and auditorily) • Link what they already know (e.g. prerequisite concepts/skills, prior real life experiences, areas of interest) • Discuss the relevance/meaning of the skill/concept**Instructional techniques….(con’t)**• Break math concept/skill into 3 – 4 learnable features or parts • Describe each using visual examples • Provide both examples and non-examples of the mathematics concept/skill • Explicitly cue students to essential attributes of the mathematic concept/skill you model (e.g. color coding) • Example**Implementing Explicit Modeling**• Select appropriate level to model the concept or skill (concrete, representational, abstract) • Break concept/skills into logical/learnable parts • Provide a meaningful context for the concept/skill (e.g. word problem) • Provide visual, auditory, kinesthetic and tactile means for illustrating important aspects of the concept/skill • “Think aloud” as you illustrate each feature or step of the concept/skill • Link each step of the process (e.g. restate what you did in the previous step, what you are going to do in the next step) • Periodically check for understanding with questions • Maintain a lively pace while being conscious of student information processing difficulties • Model a concept/skill at least three times**Authentic Mathematics Learning Contexts**• Explicitly connects the target math concept/skill to a relevant and meaningful context, therefore promoting a deeper level of understanding for students • Requires teachers to think about ways the concept skill occurs in naturally occurring contexts • The authentic context must be explicitly connected to the targeted concept/skill • Example**Implementation**• Choose appropriate context • Activate students’ prior knowledge of authentic context, identify the math concept/skill students will learn and explicitly relate it to the context • Involve students by prompting thinking about how the math concept/skill is relevant • Check for understanding • Provide opportunities for students to apply math concept/skill within authentic context • Provide review and closure, continuing to explicitly link target concept/skill to authentic context • Provide multiple opportunities for student practice**Now it’s your turn…**• Using your case study information apply at least one of the three selected teaching strategy (C-R-A, Explicit Modeling or Authentic Concepts) to your group’s focus student • Think about the student’s strengths & needs • Review the student’s IEP and corresponding curricular framework • Be prepared to share your ideas with the class