Overview
This lecture, led by Dr. Stephen Pfeiffer, focuses on the neuropsychology of mathematics, addressing why students struggle with math, different subtypes of math learning disabilities, and introducing the FAM diagnostic math assessment. Emphasis is placed on understanding underlying cognitive processes, not just achievement.
National Math Performance & International Comparisons
- Only 40% of US fourth graders and 33% of eighth graders are proficient in math; trends have been flat or declined recently.
- US students rank below international averages in mathematical literacy; many Asian countries outperform the US.
- Factors affecting performance include language structure, calculator use, and time spent on math instruction.
Key Concepts in Math Learning
- Math learning disability (MLD) is an umbrella term for underachievement in math relative to age/grade expectations.
- Dyscalculia is a specific neuropsychological condition involving cognitive deficits such as language, executive function, or working memory.
- Working memory and anxiety are critical: anxiety can impair working memory, affecting math performance.
Building a 'Math Brain'
- Four pillars: Approximate Number System (innate sense of quantity), connectivity (linking non-symbolic and symbolic number knowledge), automaticity (rapid fact retrieval), and quantitative knowledge (conceptual understanding).
- Symbolic (number symbols) and non-symbolic (quantitative intuition) processing must be connected for math success.
- Automatic fact retrieval frees up cognitive resources for higher-order problem solving.
Math Learning Disability Subtypes
- Verbal Dyscalculia: Language-based deficits; trouble with math fact retrieval but can understand concepts.
- Procedural Dyscalculia: Working memory deficits; issues with multi-step problems, algorithms, or maintaining steps under stress/anxiety.
- Semantic Dyscalculia: Conceptual/visual-spatial deficits; struggle with visualizing problems, estimation, abstract concepts, and pattern recognition.
Intervention & Assessment Strategies
- Use games, visual aids (number lines, graph paper), and estimation activities to develop foundational skills and reduce anxiety.
- Math interventions should emphasize conceptual understanding, not just rote memorization or rapid answer-getting.
- Testing should identify why a student is struggling (diagnostic) to tailor interventions effectively.
Family of Assessment of Math (FAM) Test
- FAM is a neurodevelopmental math assessment for ages 4-21, designed to diagnose math learning subtypes (procedural, verbal, semantic).
- Includes subtests for fluency, working memory, conceptual knowledge, vocabulary, and visual-spatial skills.
- Offers both comprehensive and screener versions; not limited to psychologists—educators can administer it.
Q&A Highlights
- Slow processing speed affects timed fluency tests; consider situational specificity and anxiety effects.
- Developing automaticity should start with visual/spatial number sense, then advance to fact drills—use games, not just flashcards.
- Estimation tasks (like jars) help build non-symbolic skills and should be integrated into curricula.
- Intervention selection (e.g., Rx for Discovery Math) depends on the student’s specific needs and assessment findings.
Key Terms & Definitions
- Approximate Number System — innate ability to estimate and compare quantities without counting.
- Automaticity — quick, effortless recall of basic math facts.
- Dyscalculia — specific math learning disability tied to cognitive processing deficits.
- Executive Function — set of mental skills for planning, sequencing, and problem-solving.
- Working Memory — holding and manipulating information for short periods during tasks.
Action Items / Next Steps
- Review the FAM manual and consider which version (screener/full kit) fits your assessment role.
- Incorporate estimation and non-symbolic math activities into instruction.
- Use games and visual materials to build foundational number sense before focusing on rote memorization.
- For further details, explore resources on the Rx For Discovery Math program and neuropsychology of mathematics.