1. copyright (c) 2003 Allyn & Bacon Chapter 14 Helping All Students Succeed in Mathematics This multimedia product and its contents are protected under copyright law. The following are prohibited by law: any public performance or display, including transmission of any image over a network; preparation of any derivative work, including the extraction, in whole or in part, of any images; any rental, lease, or lending of the program.

2. copyright (c) 2003 Allyn & Bacon Current Trends Mathematic literacy National Council of Teachers of Mathematics – Curriculum standards

3. copyright (c) 2003 Allyn & Bacon Difficulties in Learning Mathematics Cognitive Factors Educational Factors Personality Neuropsychological Patterns

4. copyright (c) 2003 Allyn & Bacon Nonverbal Math Difficulties (Johnson & Mykelebust, 1967) Social immaturity Disorientation Deficits in visual, motor, and self-help skills Problems estimating distance and time

5. copyright (c) 2003 Allyn & Bacon Effective Math Instruction for All Learners Inappropriate or inadequate instruction Evaluate the math criteria – Teach directly to the student – Teach concept until all students learn it – Provide practice with problem-solving and real- life application – Consider prerequisite skills – Walk students through text section by section

6. copyright (c) 2003 Allyn & Bacon Selecting Appropriate Math Content (Carnine, 1997) Avoid “spiral curriculum” Teach big ideas Make strategies conspicuous Use instructional time effectively Make instruction on strategies clear and explicit Provide appropriate practice and review

7. copyright (c) 2003 Allyn & Bacon Curricular Programs Project Math DISTAR Arithmetic Program Computational Arithmetic Program Key Math Teach and Practice Corrective Mathematics Program NCTM Navigation Series Real Math Program Touch Math ETA/Cuisenaire

8. copyright (c) 2003 Allyn & Bacon Goal Setting and Self-Monitoring Strategies (Leon & Pepe, 1983) – Teacher models and verbalizes the procedure – Teacher guides student through problem and solves it – Student verbalizes procedure while teacher monitors progress – Student whispers procedure to himself/herself

9. copyright (c) 2003 Allyn & Bacon Cooperative Learning Peer tutoring Small groups Team-Assisted Instruction

10. copyright (c) 2003 Allyn & Bacon Appropriate Instruction Demonstration- prompt-practice routine Explicit instruction – step-by-step instructions – Information about why learning this skills is important Assurance that students understand directions and task demands – Monitoring Maintaining positive reinforcement, varied practice, and ensuring motivation

11. copyright (c) 2003 Allyn & Bacon Comprehension “Talk aloud” Constant time delay Correction and immediate feedback Providing Practice

12. copyright (c) 2003 Allyn & Bacon Providing Practice for Mastery “Counting by Numbers” Guidelines for Games (Larson & Slaughter, 1984) – Choose games that reinforce present instruction – Consider complexity – Foresee potential problems – Provide answer key – Play at least one round of game with with students – Use aides or parents to assist in monitoring

13. copyright (c) 2003 Allyn & Bacon Strategies for Helping All Students Acquire Basic Math Skills Prenumber – Seriation – Classification Numeration – Estimating – Regrouping Place Value – Grouping – Naming Tens Fractions – Systematic practice – Separation of confusing terminology – Wide of elements to illustrate concepts

14. copyright (c) 2003 Allyn & Bacon Strategies for Computation Skills Patterns of Computation Errors – Spatial organization mistakes – Visual detail mistakes – Procedural error – Failure to Shift operation – Motoric problems mistakes – Memory problems – Difficulty with zero

15. copyright (c) 2003 Allyn & Bacon Strategies for Problem-Solving Skills FAST DRAW Word Problem Solving Algebra Problem Solving