Dawn P. Flanagan, Ph.D. St. John’s University Yale Child Study Center, School of Medicine

1. Math Learning Disability within the Context of Current Research and Practice in SLD Identification and Treatment Dawn P. Flanagan, Ph.D. St. John’s University Yale Child Study Center, School of Medicine

2. Presentation Outline • Math Learning Disability (MLD) – Etiology and Incidence • Comparison of Typical achieving students with MLD and Low Math Achievers • Cognitive Correlates and Diagnostic Markers of MLD • Assessment – Overview of Progress in Theories and Measures of Intelligence • Relations between CHC cognitive abilities and processes and math achievement • Operational Definition of SLD (use of SLD Assistant) • Culture-Language Interpretive Matrix (C-LIM) • Overview of Cross-Battery Assessment – Identification of a “pattern of strengths and weaknesses” • Linking Cognitive Ability Profiles for Children with MLD and LA to Educational Strategies and Intervention

3. Math Achievement • Many children find mathematics difficult • “Mathematics is a complex and nuanced field that requires effort and focus for most people to learn” • About 7% of school aged children have a specific learning disability in math (MLD) due to underlying deficits or developmental delays in the cognitive systems that support mathematics learning (Barbaresi et al., 2005) • An additional 5% to 10% of children and adolescents will be LA Geary, Hoard, and Bailey (2009)

4. MLD Definition • There is no currently agreed upon cut-off score that is used to identify either MLD or LA (Geary et al., 2009) • It is important to distinguish between MLD and LA Geary, Hoard, and Bailey (2009)

5. General Cut-Offs • MLD • Children who score below the 10th percentile on standardized mathematics achievement tests for at least two consecutive years. • LA • Children who score below the 25th or 30th percentile across two (or more) consecutive years • Groups Differ • Severity and breadth of mathematics difficulties • Underlying sources of mathematics difficulties Geary, Hoard, and Bailey (2009)

6. MLD, LA, and IQ • In general, LA children have average IQs • In general, MLD have low average IQs, most likely related to underlying cognitive correlates Geary, Hoard, and Bailey (2009)

7. Etiology Twin and family studies suggest both genetic and environmental contributions to MLD Shalev and her colleagues found that family members (e.g., parents and siblings) of children with MLD are 10 times more likely to be diagnosed with MLD than are members of the general population. Geary, Hoard, and Bailey (2009)

8. Twin Study (Kovas et al., 2007) • A large twin study of academic learning in elementary school found that genetic as well as shared (between the pair of twins) and unique environmental factors contributed to individual differences in mathematics achievement and MLD. Geary, Hoard, and Bailey (2009)

9. Genetic Influences • There are no MLD genes, but there are genetic influences on MLD • Of the genetic effects: • 1/3 were shared with general cognitive ability • 1/3 with reading achievement independent of cognitive ability • 1/3 were unique to mathematics • about 2/3 of the genetic influences on mathematics achievement and MLD are the same as those that influence learning in other academic areas • 1/3 only effect mathematics learning. Geary, Hoard, and Bailey (2009)

10. Genetic Influences • The shared genetic influences may explain why many children with MLD also have reading disability (RD) or other difficulties that interfere with learning in school, such as attention deficit hyperactivity disorder. • Barbaresi et al. found that between 57% and 64% of individuals with MLD also had RD, depending on the diagnostic criteria used for MLD. Geary, Hoard, and Bailey (2009)

11. Deficits in Children with MLD • Three most consistently found deficits: number sense, semantic memory, procedural competence • Children may have deficits in one or more of these areas • The severity and the developmental course of the deficit may differ as well Geary, Hoard, and Bailey (2009)

12. Cognitive Correlates and Diagnostic Markers • Most commonly studied cognitive correlates • Working memory • Speed of processing • intelligence • Do deficits in basic cognitive areas cause or modify the expression of MLD and LA? Geary, Hoard, and Bailey (2009)

13. Working Memory • Holding mental representations of information in mind while simultaneously engaging in other mental processes • Not fully understood which component or components of working memory contribute to the math cognition deficits of children with MLD Geary, Hoard, and Bailey (2009)

14. Diagnostic Approach to MLD Identification • Children with MLD typically score below the 10th percentile on standardized math achievement tests for more than one grade (Geary et al., 2007; Murphy et al., 2007) (LA score between the 10th and 25th percentile for more than one grade) • Many children who score poorly in one grade may score average in the next grade (not associated with MLD or LA) • Children who score below 85 (or below the 16th percentile) on IQ are often excluded from the MLD category Geary, Hoard, and Bailey (2009)

15. Diagnostic Approach to MLD Identification • Typical IQ score for MLD is around 90 (85-95) (sometimes lower based on the intelligence test used and underlying cognitive correlates) • LA children have average IQs (and often above 90-95) • Low achievement scores must be observed across several grades before the child should be considered LA (Geary et al., 2009) Geary, Hoard, and Bailey (2009)

16. Diagnostic Approach to MLD Identification • Children with MLD (and to a lesser extent LA) show a deficit or marked delay in their number sense, learning of arithmetic procedures, and in memorizing basic math facts • These difficulties are likely do to low average IQ and poor working memory for MLD, but not LA Geary, Hoard, and Bailey (2009)

17. Diagnostic Approach to MLD Identification • Whatever the underlying causes, the number sense and procedural difficulties appear to be more of a developmental delay than a deficit • LA about one year behind TA • MLD about three years behind TA Geary et al., 2004, 2009

18. Contemporary Cattell-Horn-Carroll (CHC) Theory Cross-Battery Assessment (XBA) School Neuropsychology Alternative research-based methods for identifying patterns of cognitive strengths and weaknesses Traditional Atheoretical assessment and interpretive approaches Subtest Analysis Limited to no attention paid to neuropsychology literature Ability-Achievement Discrepancy Cognitive Assessment

19. Overview of the Field of Cognitive Assessment

20. Continuum of Progress: Intelligence Theories and Test Batteries General Ability (g) Dichotomous Abilities Multiple Cognitive Abilities (Incomplete; not implicitly or explicitly CHC-organized Multiple Cognitive Abilities (Incomplete; implicitly or explicitly CHC-organized Multiple Cognitive Abilities (“Complete”; implicitly or explicitly CHC-organized g Broad Abilities Theory-Practice Consistency Spearman Original Gf-Gc Simultaneous- Successive Thurstone PMAs PASS (Planning, Attention, Simultaneous, Successive) Cattell-Horn Carroll (CHC) Theory of Cognitive Abilities Carroll Three-Stratum Theory Cattell-Horn Gf-Gc Theory Theory-Practice Gap Primary Theories (Neuropsych. Psychometric) WJ WJ III WJ-R Cross-Battery Assessment (XBA) applied to “incomplete” batteries Stanford-Binet LM SB-IV SB-V W-B WISC WAIS WPPSI WISC-R WAIS-R WPPSI-R WISC-III/WISC-IV WAIS-III/WAIS-IV WPPSI-III Applied IQ Batteries K-ABC KAIT KABC-II 1970s to Late 1990s 2000 to Present CAS DAS DAS-II

21. Cattell-Horn Gf-Gc Theory Cattell-Horn Gf-Gc Theory Gf Gq Gc Gsm Gv Ga Glr Gs CDS Grw Broad (Stratum II) Fluid Intelligence Quantitative Knowledge Crystallized Intelligence Short-Term Memory Long-Term Retrieval Visual Processing Auditory Processing Processing Speed Reading/ Writing Correct Decision Speed Narrow (Stratum I) 69 narrow abilities found in data sets analyzed by Carroll (1993)

22. A Landmark Event in Understanding the Structure of Intelligence Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. New York: Cambridge University Press

23. Reviews of Carroll’s Book “He has reviewed and reanalyzed the world’s literature on individual differences in cognitive abilities, collected over most of a century....No one else could have done it. No one else would have applied so consistent and impartial a system on the literature, and reached so balanced, complete, and useful a conclusion...It is a monumental contribution...it defines the taxonomy of cognitive differential psychology for many years to come.” Snow (1993)

24. Reviews of Carroll’s Book “This is truly a remarkable book. It is simply the finest work of research and scholarship I have read and is destined to be the classic study and reference work on human abilities for decades to come. Each of these chapters alone is a major literature review of research in a particular cognitive domain.” Burns (1994)

25. G General Intelligence General (Stratum III) Gf Gc Gy Gv Gu Gr Gs Gt Processing Speed (RT Decision Speed) General Memory & Learning Broad Visual Perception Broad Auditory Perception Broad Cognitive Speediness Broad Retrieval Ability Broad (Stratum II) Fluid Intelligence Crystallized Intelligence Narrow (Stratum I) 69 narrow abilities found in data sets analyzed by Carroll Carroll’s (1993) Three-Stratum Theory of Cognitive Abilities

26. Carroll’s Research-based Conclusions About the Cattell-Horn Model “The Cattell-Horn model...is a true hierarchical model covering all major domains of intellectual functioning...among available models it appears to offer the most well-founded and reasonable approach to an acceptable theory of the structure of cognitive abilities” Carroll (1993)

27. Which Model Should Be Used? Contemporary Psychometric Theory Applied to the Wechsler Intelligence Scales

28. An Integration of the Gf-Gc and Three-Stratum Theories of Cognitive Abilities Based largely on McGrew’s analyses in 1997-1999

29. Catell-Horn-Carroll (CHC) Theory of Cognitive Abilities/Processes

30. Verbal Ability FSIQ Nonverbal Ability

31. Summary of Relations between CHC Abilities and Specific Areas of Academic Achievement (Flanagan, Ortiz, Alfonso, & Mascolo, 2006) Refined and Updated Recently by McGrew & Wendling (in press)

34. CHC Domain-Specific Summaries: • Key to slides/figures • Bold font = WJ III cognitive test was a significantly related to designated WJ III achievement cluster (or test within the cluster; e.g., Letter-Word ID in Basic Reading Skills cluster) • Red font = significant cognitive clusters/tests based on McGrew @ Wendling (2009) CHC empirical research literature integration • Black font = significant clusters/tests based on review of non-CHC extant literature • Dashed broad CHC domain rectangle = broad CHC domain variable was not significantly related to achievement but at 1 (or more) narrow abilities within the broad CHC domain was. • DS = WJ III Diagnostic Supplement test or cluster requiring 1 or more DS tests

35. Processing Speed Gs (NA) Auditory Processing Ga Broad Domain Markers Narrow Domain Markers Most Relevant WJ III Clusters Most Relevant WJ III Tests Work Mem (MW) Working Memory Numbers Rev. (MW) Aud. Wrk. Mem. (MW) Under. Dir (MW/LS) Short-Term Memory Gsm • Perc. Speed (P) • (Number Facility-N) • AtnCon/ExFun (AC/EF) Processing Speed Perceptual Speed-DS Visual Matching (P/N?) Cross Out (P) Pair Cancellation (AC/EF?) Associative Mem. (MA) Naming Fac. (NA) Cognitive Fluency Associative Memory-DS Retrieval Fluency (FI) Rapid. Pic. Nam. (NA) Vis.-Aud.-Lrng (MA) Long-Term Retrieval Gen. Seq. Reas. (RG) Quant. Reas. (RQ) Fluid Reasoning Numerical Reas.-DS Number Series (RQ)-DS Number Matrices (RQ)-DS Analysis-Synthesis (RG) Glr Fluid Intelligence Gf Phonetic Coding (PC) Phonemic Aware. 3 Sound Aware. (PC/MW) Bridge research – real world practice WJ III clusters/test selected based on McGrew & Wendling (2009) plus expert-knowledge and clinical experience with WJ III battery Research foundation: From McGrew @ Wendling (2009) CHC COG-ACH relations research synthesis (prior slides) Basic Math Skills ages 6 to 8

36. Processing Speed Gs Crystallized Intelligence Gs Broad Domain Markers Narrow Domain Markers Most Relevant WISC-IV Clusters Most Relevant WISC-IV Tests or Supplemental Work Mem (MW) Working Memory Index Digit Span Letter-Number Sequence Short-Term Memory Gsm Perc. Speed (P) Number Facility (N) AtnCon/ExFun (AC/EF) Processing Speed Index Coding Symbol Search Semantic Memory and Retrieval Fluency Associative Mem. (MA) Naming Fac. (NA) Long-Term Retrieval Gen. Seq. Reas. (RG) Quant. Reas. (RQ) Perceptual Reasoning Index Matrix Reasoning Picture Concepts Glr Fluid Intelligence Vocabulary Knowledge (VL) Gf Verbal Comprehension Index Vocabulary Word Reasoning Bridge research – real world practice Research foundation: From McGrew @ Wendling (2009) CHC COG-ACH relations research synthesis (prior slides) Tests recommended by Flanagan and colleagues (2009) Basic Math Skills ages 6 to 8

37. Broad Domain Markers Narrow Domain Markers Most Relevant WJ III Clusters Most Relevant WJ III Tests Processing Speed Gs (NA) Auditory Processing Ga Work Mem (MW) Working Memory Numbers Rev. (MW) Aud. Wrk. Mem. (MW) Under. Dir. (MW/LS) Short-Term Memory Gsm • Perc. Speed (P) • (Number Facility-N) • AtnCon/ExFun (AC/EF) Processing Speed Perceptual Speed-DS Visual Matching (P/N?) Cross Out (P) Pair Cancel. (AC/EF?) Naming Fac. (NA) Long-Term Retrieval Retrieval Fluency (FI) Rapid. Pic. Nam. (NA) Glr Number Series (RQ)-DS Number Matrices (RQ)-DS Analysis-Synthesis (RG) Gen. Seq. Reas. (RG) Quant. Reas. (RQ) Fluid Reasoning Numerical Reas.-DS Fluid Intelligence Gf Phonetic Coding (PC) Phonemic Aware. 3 Sound Aware. (PC/MW) Lang. Dev. (LD) Listening Ability (LS) Comp-Knowledge Verbal Comp. (LD/VL) Bridge research – real world practice Crystallized Intelligence WJ III clusters/test selected based on McGrew & Wendling (2009) plus expert-knowledge and clinical experience with WJ III battery Research foundation: From McGrew @ Wendling (2009) CHC COG-ACH relations research synthesis (prior slides) Gc Basic Math Skills ages 9 to 13

38. Broad Domain Markers Narrow Domain Markers Most Relevant WJ III Clusters Most Relevant WJ III Tests Numbers Rev. (MW) Aud. Wrk. Mem. (MW) Sound Aware. (MW/PC) Under. Dir. (MW/LS) Work Mem (MW) Working Memory Short-Term Memory Gsm • Perc. Speed (P) • (Number Facility-N) • AtnCon/ExFun (AC/EF) Processing Speed Perceptual Speed-DS Visual Matching (P/N?) Pair Cancellation (AC/EF?) Processing Speed Gs Naming Fac. (NA) Rapid. Pic. Nam. (NA) Retrieval Fluency (NA) Crystallized Intelligence Gc Long-Term Retrieval Number Series (RQ)-DS Number Matrices (RQ)-DS Analysis-Synthesis (RG) Gen. Seq. Reas. (RG) Quant. Reas. (RQ) Fluid Reasoning Numerical Reas.-DS Glr Lang. Dev. (LD) Listen. Ability (LS) Comp-Knowledge Verbal Comp (LD/VL) Fluid Intelligence Gf Bridge research – real world practice WJ III clusters/test selected based on McGrew & Wendling (2009) plus expert-knowledge and clinical experience with WJ III battery Research foundation: From McGrew @ Wendling (2009) CHC COG-ACH relations research synthesis (prior slides) Basic Math Skills ages 14 to 19

39. Auditory Processing Ga Broad Domain Markers Narrow Domain Markers Most Relevant WJ III Clusters Most Relevant WJ III Tests Numbers Rev. (MW) Aud. Wrk. Mem. (MW) Under. Dir (MW/LS) Work Mem (MW) Working Memory Short-Term Memory Gsm Visual Matching (P/N?) Cross Out (P) Pair Cancellation (AC/EF?) • Perc. Speed (P) • (Number Facility-N) Processing Speed Perceptual Speed-DS Processing Speed Gs Number Matrices (RQ)-DS Number Series (RQ)-DS Analysis-Synthesis (RG) Quant. Reas. (RQ) Gen. Seq. Reas. (RG) Fluid Reasoning Numerical Reas.-DS Crystallized Intelligence Gc Phonetic Coding (PC) Phonemic Aware. 3 Sound Aware. (PC/MW) Fluid Intelligence Gf Lang. Dev. (LD) General Info (K0) Listen. Ability (LS) Verbal Comp. (LD/VL) General Info (K0) Comp-Knowledge Bridge research – real world practice WJ III clusters/test selected based on McGrew & Wendling (2009) plus expert-knowledge and clinical experience with WJ III battery Research foundation: From McGrew @ Wendling (2009) CHC COG-ACH relations research synthesis (prior slides) Math Reasoning ages 6 to 8

40. Auditory Processing Ga Broad Domain Markers Narrow Domain Markers Most Relevant WJ III Clusters Most Relevant WJ III Tests Work Mem (MW) Working Memory Numbers Rev. (MW) Under. Dir. (MW/LS) Aud. Wrk. Mem. (MW) Short-Term Memory Gsm • Perc. Speed (P) • (Number Facility-N) Perceptual Speed-DS Visual Matching (P/N?) Cross Out (P) Pair Cancellation (AC/EF?) Processing Speed Gs Lang. Dev. (LD) General Info (K0) Listen. Ability (LS) Comp-Knowledge Verbal Comp. (LD/VL) General Info (K0) Oral Comp. (LS) Crystallized Intelligence Gc Phonetic Coding (PC) Phonemic Aware. 3 Sound Aware. (PC/MW) Gen. Seq. Reas. (RG) Quant. Reas. (RQ) Fluid Reasoning Numerical Reas.-DS Number Matrices (RQ)-DS Number Series (RQ)-DS Analysis-Synthesis (RG) Fluid Intelligence Gf Bridge research – real world practice WJ III clusters/test selected based on McGrew & Wendling (2009) plus expert-knowledge and clinical experience with WJ III battery Research foundation: From McGrew @ Wendling (2009) CHC COG-ACH relations research synthesis (prior slides) Math Reasoning ages 9 to 13

41. Auditory Processing Ga Broad Domain Markers Narrow Domain Markers Most Relevant WJ III Clusters Most Relevant WJ III Tests Work Mem (MW) Working Memory Numbers Rev. (MW) Under. Dir (MW/LS) Short-Term Memory Gsm • Perc. Speed (P) • (Number Facility-N) Perceptual Speed-DS Visual Matching (P/N?) Processing Speed Gs Lang. Dev. (LD) General Info (K0) Listen. Ability (LS) Comp-Knowledge Verbal Comp. (LD/VL) General Info (K0) Oral Comprehension (LS) Story Recall (LS/MM) Crystallized Intelligence Gc Phonetic Coding (PC) Phonemic Aware. 3 Sound Aware. (PC/MW) Gen. Seq. Reas. (RG) Quant. Reas. (RQ) Fluid Reasoning Numerical Reas.-DS Number Matrices (RQ)-DS Number Series (RQ)-DS Analysis-Synthesis (RG) Fluid Intelligence Gf Bridge research – real world practice WJ III clusters/test selected based on McGrew & Wendling (2009) plus expert-knowledge and clinical experience with WJ III battery Research foundation: From McGrew @ Wendling (2009) CHC COG-ACH relations research synthesis (prior slides) Math Reasoning ages 14 to 19

42. Cross-Battery Assessment: The Key to Pinpointing Processing Deficits for SLD and Informing Interventions

43. Cognitive Assessment Differential Diagnosis Specific Learning Disability v. General Learning Disability (Slow Learner) Categorical NO Cognitive Assessment Achievement Testing only Non-categorical Current Debate in the U.S. versus

44. Why is Classification Important? When things are sorted into groups it makes them easier to understand and it makes it easier to see the relationships between them and to study them.

45. Correspondence Between Diagnosis and Treatment as syndromes/disorders become more discretely defined, there may be a greater correspondence between diagnoses and treatment Kratochwill and McGivern's (1996; p. 351)

46. No Cognitive Assessment = No Differentiation Between Children Who Have Markedly Different Learning Needs and Abilities Cognitive Assessment = IQ-Achievement Discrepancy Analysis

47. Defining Processes in a Cognitive Context (McCloskey, 2007) • Processes and Abilities both refer to mental capacities that enable learning and production • Processes are narrower, more specific mental capacities; Abilities are broader, more overarching mental capacities

48. Defining Processes in a Cognitive Context (McCloskey, 2007) • Ability deficits constrain learning and production; the degree of deficit places an upper limit on learning and production; compensatory or by-pass strategies typically are not very effective in countering ability deficits • Severe ability deficits result in cognitive impairments, that greatly constrain learning and production, such as mental retardation/intellectual disability

49. Defining Processes in a Cognitive Context (McCloskey, 2007) • Process deficits obstruct learning and production, but often can be by-passed or compensated for at least to some degree; in some instances their effects can be significantly reduced if addressed during early developmental stages with a good intervention program • Severe process deficits result in learning disabilities and/or producing disabilities involving slowed and/or inconsistent learning and production

50. Identification of Learning Disability in Mathematics • Consideration of the ability to reason with numeric information along with working memory capacities, basic processing related to mathematics skill development (e.g., processing speed), and executive function processing capacities assist in clarifying the differences between TA, MLD, and LA students