1. Mathematics Disabilities Prepared by: Cicilia Evi GradDiplSc., M. Psi

2. Development of Math Knowledge Informal knowledge  arithmetic operational and math concepts before school age – Some are innate, but also influenced by environments Number sense  fluidity and flexibility with numbers, understanding of what numbers mean, ability to perform mental math and make comparisons  before Kindergarten

3. Development … (2) Formal knowledge  during school years  due to aging and instructions  including system of symbols, concepts, procedures that form the content of math instruction Children progress from primitive strategies to using more sophisticated and efficient strategies to solve problems  Unfortunately … instructions in schools does not match this progress

4. Development … (3) Sophisticated strategies – Manipulatives  using objects to understand math concepts – Place value  where children can learn that numbers can be multiples of 10, decimals – Read p. 456

5. Problems … Dyscalculia  severe or complete inability to calculate 6-7% school-age children show persistent, grade-to-grade, difficulties in learning some aspects of arithmetic or related area (Geary, 1999) More than half to students with LD have individual program goals in math

6. Problems in Cog Dev To develop math literacy  students must have an understanding of math facts, rules and knowledge and relationship Typically approach word problems in a mechanical fashion  looking for key words and not understand the problem Students need a sufficient and efficient knowledge base to draw info  to solve problems

7. Problems in Arithmetic Typical problems: – Writing numerals and math symbols correctly – Recalling the meaning of symbols and answers to basic facts – Counting – Following steps in a strategy for solving multistep problems  story problems, proper and improper fractions STAR strategy  p. 460-461

8. Assessments Achievements Tests  to make comparisons Formal Diagnostic Testing  fine-grained assessments to determine in which areas of math a student is having difficulties (P. 463) Informal Inventories  teacher asks the students to complete representative examples of different kinds of problems  developed or created by teachers (p. 466-469)

9. Assessments (2) Error Analysis  informal method by analyzing mistaken answers or errors – Incorrect facts  6 x 5 = 40 – Incorrect operation  performs addition when it should be multiplication – Incorrect execution of procedures – No pattern errors  random incorrect response – Combination of incorrect facts and incorrectly employed operations and/or algorithms (Mastropieri & Scruggs, 2002)

10. Assessments (3) Monitoring Progress – Curriculum-based Assessments  combined with consultation  higher achievements Set of shorts tests – Administered quickly and repeatedly – Need changes  to avoid students learning the answers – P. 471

11. Interventions Effective instructions – Takes place in groups – Teacher directed – Academically focused – Individualized Provide daily review, demonstrate new skills and offers extended opportunities to practice new skills under individualized teacher supervision and correction  p. 472

12. Interventions (2) Developmental Interventions  include developmental programs, which designed to foster the growth and improvement of math skills – Skills include : addition, subtraction, multiplication, and division – Basal programs  programs used for teaching beginners fundamental math concepts

13. Interventions (3) Remedial Interventions  introducing new concepts systematically, providing adequate practice and review, teaching big ideas – Includes scripts for daily lessons, workbooks to provide extensive practice opportunities Technology – Calculators – Computer-Assisted Instruction (p. 476-477)

14. Interventions (4) Effective Teaching Procedures – Modeling  p. 478 – 480 (table 14.3) – Reinforcement  when prerequisite skills are set – Strategy Training  students are given cognitive strategy to attack problems in math (table 14.4) – Self-instruction Training  p. 482