Chapter 7— Mathematical Disabilities Sousa How The Special Needs Brain Learns

Some Basic Facts (starts at p.141) Humans are born with a number sense (simple adding & subtracting before age 1; recognize greater than and less-than relationships with numbers as great as 5 by age 2) Parietal and frontal lobes are responsible for basic mental mathematics (counting forward & doing calculations) Mathematical ability is independent of language processing (each use different brain areas) A male’s brain is about 6% to 8% larger than a female’s brain; studies show that males may have a better visual-spatial ability while females have the advantage at processing language “About 6 to 8 percent of school-age children have serious difficulty processing mathematics.”

DYSCALCULIA (pp.143-144) Defined as “the condition that causes persistent problems with processing numerical calculations” People with Dyscalculia have difficulty doing the following: -mastering arithmetic facts -learning time, direction, and sequencing of events -acquiring spatial orientation, space organization, and mechanical processes, and reading maps -following directions and rules and keeping track of scores in sports/board games -following sequential directions, organizing detailed information, and remembering facts and formulas for calculations

TYPES OF MATHEMATICAL DISORDERS-(p.146-147) Number Concept Difficulties Counting Skill Deficits Difficulties with Arithmetic Skills Procedural Disorders Memory Disorders Visual-Spatial Deficits

POSSIBLE CAUSES OF MATHEMATICAL DISORDERS(p.144) Attitude--of some parents & students--mathematics failure as acceptable or normal; “students with positive attitudes about what they are learning achieve more than students with poor attitudes” (Singh, Granville, & Dika, 2002). Fear of Mathematics--negative experiences, anxiety, lack of success & confidence Quality of Teaching--“Studies show that student achievement is strongly linked to the teacher’s expertise in mathematics” (NSF, 2004). Neurological and genetic causes--Gerstmann syndrome, Turner syndrome

WHAT EDUCATORS NEED TO CONSIDER (pp.148-153) Source of the problem--use a standardized test, such as the Brigance Coomprehensive Inventory of Basic Skills (Revised), to determine prerequisite skills: 1. Follow sequential directions 2. Recognize patterns 3. Estimate by forming a reasonable guess about quantity, size, magnitude, and amount 4. Visualize pictures in one’s mind and manipulate them 5. Have a good sense of spatial orientation, space organization, and telling horizontal, vertical, and compass directions 6. Do deductive reasoning-general to specific 7. Do inductive reasoning-specific examples to generalization

WHAT EDUCATORS NEED TO CONSIDER (pp.148-153) Assessing Learning Difficulties--five critical factors that affect mathematics learning: 1. Level of Cognitive Awareness--similar to meta-cognition 2. Mathematics Learning Profile--Quantitative learners & Qualitative learners 3. Language of Mathematics--words/sentences translations to mathematical expressions/equations 4. Prerequisite Skills--“must be mastered before even the most basic understandings of number concepts and arithmetic operations can be learned.” 5. Levels of Learning Mastery—Level 1-connects new knowledge with existing knowledge/experiences; Level 2-searches for concrete material to model the concept; Level 3-illustrates the concept with a diagram; Level 4-translates the concept into mathematical symbols, expressions, and equations; Level 5-applies the concept correctly to real life; Level 6-teaches or communicates concept to others successfully

WHAT EDUCATORS NEED TO CONSIDER (pp.148-153) Less is more--studies show that “spending more time on fewer key concepts leads to greater student achievement in the long run” Use of manipulatives and computer software can help students learn abstract concepts and arithmetic relationships and help maintain focus The use of intensive drill and practice in searching for patterns can help many children with learning disabilities, including those with math disorders. Build on students’ strengths--on what they already know how to do to build up their weaknesses; make it practical, useful, and relevant as much as possible

STRATEGIES TO CONSIDER (p.154-5) General Guidelines for Teaching Mathematics Help students develop conceptual understanding and skills. Consider giving more oral and fewer written tests. Develop meaningful (relevant) practice exercises. Maintain reasonable expectations. Build on children’s strengths. Use manipulatives appropriately. Help students make connections. Determine and build on a student’s informal learning strategies. Accommodate individual learning styles as much as is practicable. Use technology appropriately.