Dyscalculia & the FAM - PowerPoint Presentation

1. Dyscalculia & the FAMLinda Taylor, PhDIdaho School Psychologist4-7 % of people have dyscalculiaISPA October 4, 2018

2. AgendaBrief neurology of mathematics Cognitive Processing & Math DeficitDyscalculiaFAMInterventions & Teaching StrategiesMath AnxietyMath Anxiety AssessmentsAssessment ofNumber senseCognitive deficits

3. Neuropsychology of Math (Feifer)Language Skills (Temporal Lobes)Early math skills tend to be verbally encoded. Most Asian language have linguistic counting systems past ten (ten-one, ten-two, etc) whereas English deviates from base-10 system (Campbell & Xue, 2001)Children with math disabilities frequently have delays in their language development. (Shalev et al, 2000)Word problems offer an intricate relationship between language and mathematics. Terms such as all, some, neither, sum, etc. may be confusing when embedded in the grammatical complexity of word problems (Levine & Reed, 1999).

4. 3 Basic Neural Codes to Format Numbers in the Brain(1) Verbal Code - numbers are encoded as sequences of words (twenty-four instead of 24). - Dehaene & Cohen, 1997Left perisylvan region of temporal lobes.No need to understand quantitative concept.Main strategy used by younger children learning basic math facts (two plus two equals four)Critical for memorization of over-learned facts, such as multiplication facts (nine times nine equals eighty-one).

5. 5Occipital LobePerisylvan RegionTemporal LobeFrontal LobeParietal Lobe

6. 3 Basic Neural Codes to Format Numbers in the Brain(2) Procedural Code - numbers are encoded as fixed symbols representing a quantity of some sort, and sequenced in a particular order. ( 24 instead of twenty-four). - Von Aster, 2000Bi-lateral occipital-temporal lobes.Critical for number identification skills.Circuitry involves the syntactical arrangement of numerals. Our internal number line.Critical in the execution of mathematical procedures for equations not committed to rote memory (e.g. subtraction with regrouping).

7. 7Occipital LobeOccipital-Temporal RegionTemporal LobeFrontal LobeParietal Lobe

8. 8(3) Magnitude Code - numbers are encoded as analog quantities. Allows for value judgements, such as “9” is bigger than “4”. (Chocon, et al, 1999) Bi-lateral inferior parietal lobes.Allows for semantic understanding of math concepts and procedures.Allows for the evaluation of the plausibility of a response. (9 X 4 = 94)Allows for the transcoding of more challenging tasks into palatable forms of operations.(15 percent of 80 becomes 10 percent of 80 plus half the value)3 Basic Neural Codes to Format Numbers in the Brain

9. 9Occipital LobeInferior Parietal LobeTemporal LobeFrontal LobeParietal Lobe

10. 3 Basic Neural Codes: formatting numbers in the brainTriple Code Model (processing networks):Verbal CodeAutomatic retrieval of over learned factsLeft hemisphereRegions surrounding basal gangliaDeep in primitive region of entorthinal temporal cortexInsular temporal cortex (automatic over learned rote verbalizations)Visual-Verbal CodeNumbers represent fixed symbols4 underlying concepts in order to learnClassificationOrdering1-1 correspondenceConservation (volume quantities constant despite spatial differences)Left & right occipital-temporal regionsPosterior tertiary zoneMagnitude CodeQuantitative number comparisonsRight hemisphereInferior parietal region in tertiary zones of both hemispheres

11. Summary of Triple Code Model11MATH SKILL BRAIN REGIONAddition Facts Perisylvan Region Left HemisphereMultiplication Facts Perisylvan Region Left HemisphereRegrouping Skills Bi-lateral Occipital-Temporal Long Division Bi-lateral Occipital-TemporalEstimation Skills Bi-lateral Inferior Parietal LobeGeometric Proofs Bi-lateral Inferior Parietal LobeFractions Bi-lateral Inferior Parietal Lobe

12. Math Fluency (Russell, 1999)

13. MATH FLUENCY (Russell, 1999)13Efficiency: Student does not getbogged down into too many stepsor lose track of logic or strategy.Flexibility: Knowledge of more thanone approach to problem solve. Allows student to choose appropriatestrategy and to double check work.Accuracy: A working knowledge of number facts, combinations,and other important numberrelationships.

14. Qualities NeededVisual-motor TasksCopying geometric shapes, numbers or lettersLine up numbersReading numbersMemoryEncoding basic facts into LTMRetrieving basic facts from LTMRemembering steps for problem solvingVisual-spatial ProcessingProblems learning: Up-down, Near-farPoor understanding of numbersDifficulties with pictorial representations

15. Qualities NeededAuditory ProcessingProblems following oral directionsProblems memorizing verbal information (x table, abbreviations)Language ProcessingMath symbols represent numerical conceptsNeeded for calculations, word problems, problem solving, computingReasoning

16. Qualities NeededAttentionNeed sustained attention to learnExecutive FunctioningIncludes attending, planning, self-monitoring, & decision makingAbility to regulate. Integrate, & coordinate several cognitive processes to work towards a goalPlanning Organize informationUnderstanding how to learn

17. Evaluation AreasGraphomotorNumbers poorly formed, inaccurateProblems copying geometric shapes & lettersMemoryRetention & retrieval of number facts & tablesForgets steps when doing a problemVisual-spatial ProcessingMisalignment of numbers in columnsConfusion with carrying & borrowingMisreading math signsProblems with directions up-down, left-right, near-far-across

18. Evaluation AreasAuditory Processing (Ga, AUD Gsm)Difficulty with oral drillsLinguistic-verbal processingProblems with:less thangreater thanmore thanReasoning Unreasonable solutions

19. Evaluation AreasAttentionDifficulty sustaining attention during instruction & directionsPlanning & OrganizingDifficulty problem solvingShift in Psychological SetApplying the practical procedure

20. Cognitive Processing & Math DeficitCrystalized Knowledge (Gc)Visual-Spatial Processing (Gv)Difficulty with word problemsPoor retrieval of over learned factsDifficulty with math terminologyDifficulty lining up equations/numbersPoor magnitude comparisonsGeometryMaps/Charts/GraphsCognitive AreaMath Implication

21. Cognitive Processing & Math DeficitNonverbal Fluid Reasoning(Gf-nonverbal)Verbal Fluid Reasoning(Gf-verbal)WISC-V: Similarities & ComprehensionPoor mental math skillsDifficulty with estimation skillsPoor pattern recognition skillsPoor strategy formation skillsDifficulty w/ word problemsLimited inferential learning skillsPoor understanding of Math terminologyCognitive AreaMath Implication

22. Cognitive Processing & Math DeficitMemory(Gsm)Processing Speed(Gs)Tendency to forget steps of an algorithm in multiple step math problemsPoor regrouping skillsDifficulty with mental rotation tasksPoor mental math skillsDifficulty with speeded skill drillsSlower visual pattern recognitionCognitive AreaMath Implication

23. Working Memory & Math SkillPhonological LoopStorage of auditory & verbal informationLeft temporal lobeWrite numbers from dictationTake lecture notes in math classRapidly retrieve math facts stored in language dependent codeHelp understand word problemsWorking MemoryMathematical Skill

24. Working Memory & Math SkillVisual-Spatial SketchpadHolds visual, spatial & kinesthetic information in temporary storage using mental imageryHoused along interior portion of right parietal lobeMental Math Problem SolvingHelps line up place value when problem solvingMagnitude representationRemembers sequence of steps or algorithm when problem solvingAids in geometryFacilitates solving proofsWorking MemoryMathematical Skill

25. Working Memory & Math SkillCentral Executive SystemCentral command post for modulating phonological loop & visual-spatial sketchpad systemsAllocates attention resources so multiple cognitive tasks can be executedPrimarily house in frontal lobesInhibits distractionsModulates anxietyRegulates emotional distressFacilitates selective attention to math operational signs & key words in math word problemsWorking MemoryMathematical Skill

26. Working Memory & MathematicsSymbolic Working MemoryRelated to executive capacity of working memoryEach symbol (regardless of presentation format (auditory or visual) allows for verbal rehearsal strategies to keep information active through an inner articulatory loop while simultaneously resisting distractionsMental math calculationNumber line facilitySequence of math steps (algorithm)Facilitate math facts retrievalNumeric pattern recognition skillCognitive representation of numbersFacilitates algebraic problem solvingWorking Memory SystemMath Skill

27. Working Memory & MathematicsSpatial Working MemoryReferred to as visual-spatial sketchpad of working memoryModulated by frontal & parietal lobe reionsA variable in the development of spatial & magnitude representation skillsAlignment of numbers in columnsMagnitude comparisonsEstimation skillsElaspsed timeVerbal spatial problem solvingFacilitates geometric problem solvingWorking Memory SystemMath Skill

28. Language/Math Delay CorrelationsOverall Language DevelopmentPervasive problems in expressive and receptive languageExpressive language only deficitsMath disabilitiesDeficits in number reasoning & arithmetic problemsDelays with overall counting skills (over 4)Language DifficultiesMath Difficulties

29. Neuropsychology of MathExecutive Functioning Skills: (frontal lobes)Executive control mechanisms such as planning, self-monitoring, organizing, and allocating attention resources to effectively execute a goal directed task.Executive functioning dictates “what to do when”, a critical process in solving word problems.Executive functioning allows students to follow an algorithm when problem solving.

30. Neuropsychology of Math: EFDorsal-lateral cortex - helps to organize a behavioral response to solve complex problem solving tasks. Orbitofrontal cortex - rich interconnections with limbic regions and helps modulate affective problem solving, judgement.Anterior cingulate cortex - allocates attention resources and modulates motivation.

31. Neuropsychology of Math: EF

32. Neuropsychology of Math: EF

33. Neuropsychology of Math: EF

34. Dyscalculia: DSM-5Specific Learning DisorderA neurodevelopmental disorder of biological origin manifested in learning difficulty and problems in acquiring academic skills markedly below age level and manifested in the early school years, lasting for at least 6 months; not attributed to intellectual disabilities, developmental disorders, or neurological or motor disordersSpecify if:315.00 With impairment in reading.315.2 With impairment in written expression315.1 With impairment in mathematicsSpecify current severity:MildModerateSevere

35. DefinitionFailure to achieve in mathematics commensurate with chronological age, normal intelligence, and adequate instruction. It is marked by difficulties with visualization;  visual-spatial perception, processing and discrimination; counting;  pattern recognition;  sequential memory;  working-memory for numbers;  retrieval of learned facts and procedures; directional confusion; quantitative processing speed;  kinesthetic sequences;  perception of time.

36. Neuropsychology of Math (Feifer)Math Disability (Dyscalculia)- refers to children with markedly poor skills at deploying basic computational processes used to solve equations (Haskell, 2000). These may include deficits with: (1) Poor language and verbal retrieval skills (2) Working memory skills (3) Executive functioning skills (4) Faulty visual-spatial skills

37. Terms for DyscalculiaSpecific Learning Disability / Disorder in Mathematics (SLD-Math) Math Learning Disability (MLD)Developmental Dyscalculia (DD)AcalculiaGerstmann’s Syndrome (severe type of dyscalculia)Math DyslexiaMath AnxietyNumerical ImpairmentNumber AgnosiaNonverbal Learning Disorder / Disability (NLD)

38. Geary & Hoard, 2005 Model Procedural Math DeficitsDifficulty following arithmetic procedures due to deficits in working memory and a poor conceptual understanding of numbersOne or more deficits in the ability to count, order, or sequence numbers and/or sequence mathematical procedures when problem solving. Deficits in left prefrontal cortexVisual-Spatial DeficitsDifficulties with spatial representation of numbers and limited magnitude representation skillsA disorder of the verbal representations of numbers and the inability to use language-based procedures to assist in arithmetic fact retrieval skills. Deficit in the posterior portion of the right parietal lobe

39. Geary & Hoard, 2005 Model Semantic DeficitsPoor ability to retrieve stored facts, usually due to long term memory and retrieval issuesCore deficit in both visual–spatial and conceptual components and an inability to decipher magnitude representations among numbers. Deficit in posterior region of the left hemisphere responsible for retrieving linguistic information

40. Types of Mathematical DisabilitiesDevelopmental DyscalculiaDifficulty acquiring simple math operations despite adequate cognitive skills and exposure to educationAcquired DyscalculiaDifficulty retrieving stored mathematical facts from memory due to a cerebral insult

41.

42. 3 Subtypes of Developmental DyscalculiaVerbal Dyscalculia SubtypeDisorder of verbal representation of numbersInability to use language based procedures to assist in arithmetic fact retrievalDifficulties counting and rapid number identificationDeficit retrieving or storing over learned math factsDifficulties in reading and spellingSemantic Dyscalculia SubtypeBilateral inferior parietal areas (hold semantic knowledge about numeric qualities allow for estimation skills)Left perisylvan region (storage of rote verbal sequences corresponding with math facts)Inability to understand magnitude representation among numbers(von Aster, 2000)

43. 3 Subtypes of Developmental DyscalculiaProcedural Dyscalculia SubtypeDeficit processing and encoding numeric informationLeft & right inferior occipital-temporal regionFrontal & subcortical loops interface with posterior mechanism for arithmetic proceduresDifficulty recalling sequence of steps needed to perform multi-digit tasksBreakdown in Procedural Operations sequencingDifficulty transcoding numeric systems into meaningful language systemDifficulty reading number aloudDifficulty writing numbers from dictationDifficulty starting in right hand column when doing subtractionComorbid with ADHD(von Aster, 2000)

44. 3 Subtypes of Math Disabilities44(1) Verbal Dyscalculia Subtype: Main deficit is the automatic retrieval of number facts which have been stored in a linguistic code. Multiplication and addition often impaired Poor at math fluency tests.  Math algorithms often preserved.  Often have learning disabilities in language arts as well.KEY CONSTRUCT: Verbal Retrieval Skills (RAN)

45. Verbal DyscalculiaDifficulty accurately retrieving overlearned math factsSlower retrieving overlearned math factsSlower when rapidly naming & identifying numbersConfusion with math vocabulary termsDifficulty solving math word problems

46. Verbal Dyscalculia: Left PerisylvianCountingRapid number identificationRetrieval of stored factsAddition & multiplication factsMay have coexisting reading & writing difficultiesNumeric qualitiesComparisons between numbersUnderstanding basic conceptsVisual spatial skillsDeficitPreserved

47. Procedural DyscalculiaDifficulty remembering the algorithm of sequenced set of procedures when problem solvingFrequent errors in the execution of proceduresDifficulty skip counting forwards & backwardsPoor number line fluencyOver reliance on immature counting proceduresPoor ability to recognize math sequencesLimited symbolic working memory

48. 3 Subtypes of Math Disabilities48(2) Procedural Dyscalculia Subtype: A breakdown in comprehending the syntax rules in processing and encoding numeric information. Often associated with deficits in working memory.Difficulty writing numbers from dictation.Subtraction and division often impaired.Retrieval of math facts and magnitude comparisons often preserved. Key Constructs: Working Memory and Anxiety

49. Procedural Dyscalculia(Bilateral occipital temporal lobes)Writing numbers from dictationReading number aloudMath computational proceduresSyntactical rules of problem solvingDeficits with division and regrouping procedures in subtractionRetrieval of over learned factsComparisons between numbersMagnitude comparisonsDeficitPreserved

50. Semantic Dyscalculia Subtype:50A breakdown in comprehending magnitude representations between numbers and understanding the spatial properties of numeric relations. Can be associated with lower IQ and faulty executive functioning skills.Difficulty evaluating the plausibility of a response (e.g. 2 X 4 = 24)Inability to transcode math operations into a more palatable form ( e.g. 9 X 4 is same as (4 X 10) - 4).Poor magnitude comparisons.Key Constructs: IQ, Executive Functioning, Visual-Spatial

51. Semantic Dyscalculia(bilateral inferior parietal lobes)Magnitude representationsTranscoding math operationsHigher level math proofsConceptual understanding of mathEstimation skillsReading & writing numbersComputational proceduresRetrieval of over learned factsDeficitPreserved

52. Visual-Spatial DyscalculiaRight hemisphere white matter disorderGender biases (more females have it)Non verbal learning syndrome2 subtypesRight frontal dysexecutive syndrome impacts strategic development of novel concept formationRight posterior visual-spatial-holistic problem solving capabilitiesCombination of bothVisual-spatial aspects of attention and memory processing disrupts the orthographic code which results in sloppy, misaligned, two dimensional paper-pencil math problem solvingComorbid with surface dyslexia due to breakdown in orthographic code

53. Visual-Spatial Dyscalculia(bilateral occipital parietal lobes)Aligning a column of numbersVisual perceptions of numbersSpatial attributes s (i.e. size, location, orientation, mental rotation)Magnitude comparisonsRetrieval of stored factsReading numbersMath algorithmsVerbal strategiesDeficitPreserved

54. Math Facts Error Analysis(Feifer, S. & DeFina, P., 2005, p. 65)Math Fact 6 + 6 = 10Operand 6 - 5 = 11Algorithm 123 -87 44Place Value .70 +.75 . 145Word Problem DifficultiesVerbal retrieval errorProcedural error due primarily to poor attention & executive functionProcedural error due to poor working memoryProcedural error due to poor working memoryVerbal dysfunction & poor saliency determination

55. (FAM)Feifer Assessment of Mathematics

56. FAM (https://www.parinc.com/Products/Pkey/109)Age range: 5 - 21 yearsTime:PK: 35 minutes K-Grade 2: 50 minutes Grade 3+: 60 minutesScreening Form: 15 minutes Qualification level: SPrice: Comprehensive Kit: $502FAR & FAM: $891

57. FAM IndicesProcedural Index (PI)Verbal Index (VI)Semantic Index (SI)FAM Total Index (TI)FAM Screening Index

58. Procedural Index (PI)Number Forward CountBackward Forward CountNumeric CapacitySequences (deductive reasoning)The Procedural Index represents deficits in the ability to count, order and sequence numbers or mathematical procedures. It measures auditory memory for numbers, sequencing and deductive reasoning. Weaknesses in symbolic working memory (Numeric Capacity, AUD Gsm) can result in a variety of math difficulties such as losing one’s place when problem solving, poor mental math skills, and forgetting the series of steps (or algorithm) needed to solve more complex equations. This could be exacerbated by math anxiety. In addition, the Sequences subtest requires executive functioning skills and deductive reasoning (top down approach) to identify the underlying rule that holds the information together.

59. Procedural Index (PI)Number Capacity (average) > Number Count suggests that struggles more with mental manipulation and sequencing aspects of number processing. Forward Number Count > Backward Number Count suggests limitations in working memory and over reliance on fingers when skip counting, over rely on the number line, or struggle with most types of mental math.Backward Number Count> Forward Number Count suggests poor automaticity with skip counting despite an adequate understanding of arithmetic concepts. Barbati may have careless errors when problem solving. Interventions should be geared towards teaching base 10 counting strategies and helping Barbati develop number line fluency, practice skip counting and use 100 charts to better comprehend patterns and relationships among numerals.

60. Procedural Index (PI)Number Count > Sequences suggests Barbati has good auditory working memory and knowledge of arithmetic procedures but struggles with the executive functioning component of math due to poor deductive reasoning skills.Sequences > Number Count suggests Barbati has good deductive reasoning and pattern recognition skills but struggles with auditory working memory of numbers needed to execute mathematical tasks without a visual prompt or cue.

61. Procedural Dyscalculia: Instructional StrategiesTens frame chart or Number line on deskPractice skip counting from various points on the number linePlay math games to develop number line fluency skill (e.g., Chip’s Game from the book “Playing with Math: The Name of the Game”)Teach to concept development and reduce the amount of ‘busy work’Teach multiple methods of problem solving so s/he can select the one that s/he understands best

62. Procedural Dyscalculia: Instructional StrategiesHelp with Math Equations with multiple stepsDevelop a mnemonic code to help remember order of stepsEg., to remember the steps for long division Divide, Multiply, Subtract, Bring down = Dead Monkeys Smell BadReduce Math AnxietyUntimed testsRedo incorrect problemsTake tests in different location  Poor AttentionColor code math operation signsUse graph paper to complete work

63. Procedural Dyscalculia: Interventions63Freedom from anxiety in class setting. Allow extra time for assignments and eliminate fluency drills.Color code math operational signs and pair each with pictorial cue.Talk aloud all regrouping strategies.Use graph paper to line up equations.“Touch math” to teach basic facts. Attach number-line to desk and provide as many manipulatives as possible when problem solving.Teach skip-counting to learn multiplication facts.

64. PI: Working Memory StrategiesRead math problems out loud (or under your breath)Create acronyms to learn sequence of stepsExample: to remember the order of operations use PEDMAS =Please Excuse My Dear Aunt Sally = Parentheses, Exponents, Multiplication, Division, Addition, SubtractionCreate a checklist with visual cuesUse scratch paper (avoid mental math)See all information while problem solving (have all information on one page or see both pages on computer screen)Avoid having to use multiple handouts, flip through multiple text book pages or switch computer screens when doing homeworkUse 100’s chart (not calculator) for assistance while learning math factsCreate visual cue card (put the word acute inside the acute angle)Acute _________

65. Procedural Dyscalculia ProgramsOn Cloud Nine (Lindamood Bell)Helps develop visual imagery when working with numbers and equationsDo the Math Helps develop number operations

66. Verbal Index (VI)Rapid Number Naming (automatic number ID skills)Addition Fluency (automatic recall of overlearned facts)Subtraction FluencyMultiplication FluencyDivision FluencyLinguistic Math Concepts (define & reason w/ math vocabulary)Measures one’s ability to quickly retrieve information from long-term memory (Rapid Number Naming). Lower scores on the Verbal Index suggests deficit is the automatic retrieval of symbolic information stored in a linguistic fashion. The verbal subtype of dyscalculia often hinders one’s ability to use language based procedures in arithmetic fact retrieval of over learned skills. However, it does NOT hinder one’s ability to appreciate numeric qualities and understand mathematical concepts.

67. Verbal Index (VI): Subtest AnalysisRapid Number Naming > Math Fluency represents a typical LD due to poor retrieval skills of math facts only (problems with angular gyrus). Names of numbers are retained (language) but the ability to memorize and retrieve longer chains of numeric information stored in a math sentence is problematic. Flash cards tend to reinforce rote memorization of facts in the linguistic code without having any quantitative value. This creates a surface learner who can regurgitate acts but does not have an understanding of the symbols to be able to recall them over time.Educators should focus on reinforcing the nonsymbolic elements of numbers in order force students to use more spatial brain regions instead of over relying on linguistic concepts to develop more consistent and enduring earning.

68. Verbal Index (VI): Subtest AnalysisAddition & Multiplication > Subtraction & DivisionNeurological profileAddition > Subtraction>Multiplication > DivisionDevelopmental profileUse strengths to help weak area

69. Verbal Index (VI): Subtest AnalysisMath Fluency > Linguistic Math ConceptsCan rapidly retrieve information from long term memory but has a deficit in understanding math vocabulary and terminology. This suggests that Barbati may have memorized math facts in an efficient manner but has difficulty generalizing and applying mathematical thinking to real world problems. Because s/he has a lack of conceptual understanding of mathematical principles.Interventions may include writing or stating a verbal story from a math sentence in order to develop a better contextual understanding of numbers.Linguistic Math Concepts > Math Fluency Understands math vocabulary and terminology but has a deficit in rapidly retrieving information from long term memory

70. Verbal Index (VI): Subtest AnalysisLinguistic Math Concepts > Math Fluency Understands math vocabulary and terminology but has a deficit in rapidly retrieving information from long term memoryHas a good theoretical and conceptual understanding of mathTypical of students with a mathematical learning disability

71. Verbal Dyscalculia: Testing ProfileRAN – lowMath Fluency - lowDifficulties with Word ProblemsMath Problem Solving - lowPoor ReadingPoor Spelling

72. Verbal Dyscalculia Instructional StrategiesAutomatic Math Fact Retrieval StrategiesMath Fact Family Chart (create & keep close by)Use Dot Array Cards for addition & multiplication factsFlash card ringsPractice writing & verbalizing math facts using large physical movementsPaper Plate GamesPractice difficult facts by rolling a pair of diceMath WarPlay Egg Carton Shake up (practice math facts)Family Math Facts practiceUse mnemonics for easy to learn rulesMultiplication Go-Fish Game

73. Verbal Dyscalculia: Instructional StrategiesMath Vocabulary StrategiesCreate a Concept Web to represent different math vocabulary termsHighlight or draw a box around key words & phrases in math assignmentsLabel the problemCreate a chart of common key words used in word problemsTell a verbal story from a math equationCreate a math dictionary notebook

74. Verbal Dyscalculia: Interventions(Wright, Martland, & Stafford, 2000)Distinguish between reciting number words, and counting(words correspond to number concept).Develop a forward number word sequence (FNWS) and backward number word sequence (BNWS) to ten, twenty, and thirty without counting back. Helps develop an automatic retrieval skills.Develop a base-ten counting strategy whereby the child can perform addition and subtraction tasks involving tens and ones.Reinforce the language of math by re-teaching quantitative words such as more, less, equal, sum, altogether, difference, etc...

75. Semantic Index (SI)Spatial Memory (Gv + Gsm)Equation Building (Executive Functioning)Perceptual Estimation (Gv)Number Comparison (Gs)Knowledge: (semantic understanding of # relationships and # sense)Addition KnowledgeSubtraction KnowledgeMultiplication KnowledgeDivision Knowledge

76. Semantic Index (SI) includes deficits with non-symbolic representations of math such as difficulty with estimation skills, aligning numbers in columns, magnitude representation and visual pattern recognition skills and symbolic representations of numbers (poor number sense and poor conceptual understanding of basic mathematical principles). The visual-spatial component of the Semantic Index tends to affect non-symbolic representation of math including estimation, aligning numbers in columns, magnitude representation, and pattern recognition.The conceptual component (executive functioning skills) of the Semantic Index refers to an inability to develop number sense and tends to affect symbolic representation of numbers.The Equation Building subtest measures quantitative knowledge and executive functioning skills.

77. SI Subtest AnalysisPerceptual Estimation > Number ComparisonMore adept at using visually based strategies to determine math representation. Perceptual Estimation < Number ComparisonMore adept at using symbolic information to determine magnitude representation  Math Knowledge ComparisonsUse inverse operations to help understand the weaker area

78. SI Subtest AnalysisEquation Building > Math KnowledgeHave stronger quantitative reasoning and executive functioning skills for mathematics. Have a stronger conceptual understanding of mat due to a strong nonsymbolic understanding of space and time but lack core number sense to execute math calculation skills. Equation Building < Math KnowledgeHave good semantic understanding of numbers due to good symbolic reasoning skills but may have difficulty generalizing their number sense to apply to math problems in a real world context.

79. Semantic Dyscalculia: Interventions79Reinforce basic pattern recognition skills by sorting objects by size and shape.Have students explain their strategies when problem solving to expand problem solving options.Teach estimation skills to allow for effective previewing of response. Have students write a math sentence from a verbal sentence.Construct incorrect answers to equations and have students discriminate correct vs. incorrect responses.Incorporate money and measurement strategies to add relevance. Use “baseball” examples as well.

80. Semantic RecommendationsAvoid using flash cards & rote repetitive exercises to a new concept prior to task masteryPresent information in context, especially relating it to his/her background knowledge, experience and interestsPlay math games to increase general number sensePlaying with MathName of the Game

81. Semantic RecommendationsFacilitate Multiplication & Division (help develop number sense)Manipulatives/Hands on InstructionDice, dominoes, Unifix cubesNumber line on deskSkip countingTap with fingers when countingTeach math vocabularyUse music to overlearn factsPlay math games at homeEmphasize teaching estimation skills with magnitude representations to force student to think in picturesUse mnemonics to over learn math factsIncorporate an area of passion in all lessons(i.e., Minecraft, train on time fractions, etc.)

82. Semantic Dyscalculia StrategiesVisual Spatial StrategiesTurn notebook sidewaysUse graph paperAvoid crowdingEnlarge charts & graphsUse a ruler to draw shapes & diagramsConsider a vertical number lineUse manipulativesDraw a T when solving equationsCreate a pocket chart from a file folder to learn place valueColor code and number each step when problem solving with fractions and long division

83. Semantic RecommendationsTargeted Math Intervention ProgramsHot Math (helps 3rd graders transfer solutions strategies to word problems)Number Words (enhances core number sense)Dreambox Learning (develops deeper conceptual understanding of multiplication and division)

84. Semantic Index (sample write up)Lower scores in this index often suggest limitations with quantitative reasoning and number sense and also difficulty applying mathematical skills to solve reals world problems. A relative weakness was noted in with visual spatial memory. Specific weaknesses with visual-spatial memory can hinder estimation and magnitude representation skills and suggests s/he may be memorizing rote symbols (digits) void of magnitude representation.

85. Semantic Index (Sample write up)Student presented with a profile of a student with a math learning disability consistent with Semantic Dyscalculia. There were noted processing deficits with visual-spatial memory, perceptual estimation tasks, as well as with quantitative reasoning and numeric pattern recognition skills. S/he appears to memorizing math facts void of meaning due to a stronger symbolic working memory instead of developing a conceptual understanding of numerals.

86. Semantic Index (sample write up)Student’s limited visual-spatial memory also seemed to hinder his/her performance with perceptual estimation types of tasks. Furthermore, student also struggles with his/her conceptual understanding of basic addition, subtraction, multiplication and division (in Verbal Index). In fact, s/he performed much better on most fluency measures which suggest that s/he is most likely memorizing basic facts instead of conceptual knowledge of numerals build around core number sense.Lastly s/he had significant difficulty determining how to set up math equations when presented with a word problemLower scores in this area suggest difficulty comprehending higher level math concepts and applications

87. FAM Cross Index Comparisons:Rapid Number Naming (verbal) > Number Comparison (semantic)Have good number (symbolic) identification skills but lacks deeper understanding of the nonsymbolic value or magnitude that numbers represent. (too much rote (verbal) memorization of facts without understanding to quantity and magnitude of numbers). Rapid Number Naming (verbal) < Number Comparison (semantic)May be due to an underlying language based learning disability that is hindering rapid naming skills or non neuro-psychological factors such as anxiety, inconsistent task motivation, etc.

88. FAM Cross Index Comparisons:Linguistic Math (verbal) > Equation Building (semantic)(check Verbal Index > Semantic Index)The student understands the language of mathematics (Linguistic Math Concepts) but has difficulty with the symbolic understanding of mathematics (Equation Building). This suggests one has the verbal ability to explain the problem but has difficulty formulating a mathematical sentence in symbolic form. This requires numeric coding of verbal information, quantitative reasoning and executive functioning skills to cue the math mathematical processing centers in the brain to identify the sequential order of calculations (a frontal-parietal network).

89. FAM Cross Index Comparisons (cont.)Linguistic Math (verbal) > Equation Building (semantic)(check Verbal Index > Semantic Index)This response pattern suggests a core deficits in executive functioning skills pertaining to math symbolic information. This response pattern suggests that the student understands math vocabulary terms but may struggle with the logical arrangements of symbolic codes when engaged in quantitative reasoning.Specific interventions should be geared towards encouraging students to learn math context more relevant to their background, knowledge and experiences to develop a greater understanding of a particular concepts. The use of manipulatives (e.g., dice, dominoes, Unifix cubes) can help to strengthen magnitude representations before learning mathematical shorthand or symbolic information. Using a Bar graph similar to the Singapore Math Approach (Hoven & Garelick, 2007) with word problems can be an intermediary step to expressing the problem is in symbolic form.

90. FAM Cross Index Comparisons:Linguistic Math (verbal) < Equation Building (semantic)Suggests poor expressive vocabulary or limited conceptual understanding of math concepts. Often color coding words in math sentences, teaching math vocabulary terminology separately or having the student write a verbal sentence for math equation are helpful.

91. FAM Cross Index Comparisons:Numeric Capacity (procedural) > Spatial Memory (semantic) Auditory memory for numbers is significantly better than visual-spatial memory. Weaknesses in spatial memory affect estimation skills, align problems into columns and disrupts overall magnitude representations.Specific interventions include using graph paper, providing visual cues and use paper/pencil problem solving to mediate visual-spatial working memory weaknesses.

92. FAM Cross Index Comparisons:Numeric Capacity (procedural) < Spatial Memory (semantic) Visual-spatial memory is significantly better than auditory memory for numbers. Therefore, barbate may struggle mental math skills, may forget algorithms on multistep equations and/or difficulty sequencing numeric informationAnxiety can be a mitigating factorInterventions include teaching efficient strategies for problem solving, use mnemonics, providing number lines or tens frame chart to assist with ordering and sequencing information.

93. FAM Cross Index Comparisons:Number Count (procedural > Math Fluency (verbal)Suggests Barbati has a good conceptual understanding of number relationships but lacks the ability to use memory strategies to automatically retrieve stored facts from LTM. This is a typical response pattern of students with language-based learning disability.Check to make sure math anxiety is not impeding the automaticity of math fact retrieval skillsNumber Count (procedural < Math Fluency (verbal)This response pattern is typical of students who have memorized math facts in a rote manner but has poor automaticity with skip counting and may over rely on visual cues when skip counting (i.e. counting on fingers).

94. FAM Cross Index Comparisons:Sequences (procedural) > Perceptual Estimation (semantic)May have better top-down executive functioning skills, including strong deductive reasoning skills. May do well with symbolic reasoning math course (i.e., algebra).Sequences (procedural) < Perceptual Estimation (semantic)May have better “bottom’s up” processing for magnitude representation

95. FAM Cross Index Comparisons:Math Fluency (verbal) > Math Knowledge (semantic)Typical response pattern of students who have who have memorized math facts in a rote manner and lack a deeper understanding of number sense. This could also be due to poor instruction. Math Fluency (verbal) < Math Knowledge (semantic)Have a good appreciation of number sense, but lack the ability to shift to memory based processing and the automatic retrieval of information stored in a language based code.Anxiety may also impede the automatic retrieval of math facts.

96. FAM ScreenerVerbal Index:Linguistic Math Concepts (LMC)Procedural IndexSequences (SEQ)Semantic IndexNumber Comparison (NCO)Best predictors of math skill in each type of dyscalculia

97. Math CalculationsWJ-IV Math Calculation Skills ClusterWIAT-III: Numeric OperationsKTEA-3: Math ComputationForward Number CountBackward Number CountAddition Knowledge (60 sec)Subtraction KnowledgeMultiplication KnowledgeDivision KnowledgeIdaho SLDFAM

98. Math FluencyWJ-IV Math facts FluencyWIAT-III Math FluencyAdditionSubtractionMultiplication Addition FluencySubtraction FluencyMultiplication FluencyDivision FluencyIdaho SLDFAM

99. Math Problem SolvingWJ-IV problem Solving ClusterWIAT-III Math Problem SolvingEquation BuildingLinguistic Math ConceptsIdaho SLDFAM

100. Memory (Gsm)WISC-V WMIAWMIVWMIWJ-IV COGWorking MemoryNumeric CapacitySpatial MemoryFAM

101. FAM CritiqueNeurologically basedGood interventions/strategiesIn depth information on student’s deficitAdministration goes quickly and less stressful for student as many math subtests are only 30 secondsNo statistical cluster score for SLD areaAdvanced interpretationsOK for teachers to interpret?No index scores for Idaho SLD areasExpensiveHand ScoredProsCons

102. Math Apps & Instructional WebsitesMath is FunResources, targeted worksheets, games, exercises, lesson ideasIlluminationsQuality standards based resourceInteractive tools for students & instructional supports for teachersMath CrunchFast way to get math help on your phoneCool MathExplanations for higher level math (algebra & calculus)Coolmath4kidsFor children under 12Games and activities

103. Delivering Math Instruction(2008 Meta analysis)Small group instructionAddress skills necessary for the UnitBe explicit & systematicUse graphic representationsBalanced Curriculum

104. Pedagogy SuggestionsMetacognitive trainingTeach proper decision making skillsAlgorithmic proceduresProfoundly influences math achievement (p. 66)

105. Pedagogy SuggestionsUse graph paper for students who have difficulty organizing ideas on paper.Work on finding different ways to approach math facts; i.e., instead of just memorizing the multiplication tables, explain that 8 x 2 = 16, so if 16 is doubled, 8 x 4 must = 32.Practice estimating as a way to begin solving math problems.Introduce new skills beginning with concrete examples and later moving to more abstract applications.For language difficulties, explain ideas and problems clearly and encourage students to ask questions as they work.Provide a place to work with few distractions and have pencils, erasers and other tools on hand as needed.

106. Strategies to Facilitate Working Memory in Classroom (p. 67)Teach multiple ways to problem solveAvoid speed competitions with studentsLink problem solving with passionSet algorithmic procedures to songEncourage visual cues

107. General Dyscalculia InterventionsFreedom from anxiety in class settingMnemonic strategiesTalk aloudUse graph paperStudent directive algorithmsTeach multiple methods & allow student decide which to useVertical number linesManipulatives

108. General Dyscalculia InterventionsManipulativesEstimation gamesTeach skip counting by drummingTeach base-10 counting strategiesTeach patterns and relationshipsProvide worksheets with answersConstruct an equation from verbal sentencesReinforce the language of mathematicsApply math to real life (batting averages, recipe, stocks, interest)

109. Common InterventionsGraphomotorTape record notesUse keyboard Oral-input software for composingMemoryUse multi-sensory strategies w/repetitionUse graphic organizersTape record lecturesVisual-spatial ProcessingPrecise & clear verbal instructionsVerbal repetitionUse highlighting for visual a focus (operating signs)

110. Common InterventionsAuditory ProcessingSlow down pace of instructionUse pictures & other visualsFocus on non-verbal cuesLinguistic-verbal ProcessingSlow down pace of instructionAsk student to verbalize what they are doingReasoningUse graphic organizers to show relationshipsTeach generalization & application across contextsCreate routines with frequent breaks

111. Common InterventionsAttentionDevelop routines with frequent breaksCreate cue sheets & mnemonicsPlanning & OrganizationCreate flow charts/graphs/cognitive websHighlight & color-code important information

112. Attention StrategiesCircle math operation signsWrite a small number above each step in the directionsWrite down all formulas before solving a problemHighlight, circle, or color code math operational signsTalk aloud when problem solvingDivide longer assignments into partsDouble check work by tapping the eraser on each number

113. Strategies for AdditionEstimation: is the answer reasonable?Use graph paper to set up problemsApply knowledge to place valueUse manipulatives (base 10 blocks) to represent place valueUse number lines & 100 charts for skip countingRecognize the patterns in numbersUse mental math strategies

114. Subtraction StrategiesUse base 10 blocks to represent valuesUse place value matsUse tens frameDraw pictorial representations

115. Multiplication StrategiesEstimation: Is the product reasonable?Use place value strategiesBreak the problem apart26 x 13 = (26 x 10) + (26 x 3)16 x 4 = (10 x 4) + (6 x 4)Know basic factsUse tally marks to group numbers

116. Strategies for DivisionSkip counting to help find equal groupsKnow fact familiesDrawing a pictorial representationExplore using manipulativesPlace value formatScaffolding (Feifer, p. 149)

117. Interventions for Lower Cognitive Skills117Manipulatives and hands-on type of instruction.Number-line situated on student’s desk.Drill and repetition.Focus on algorithm.Skip counting.Tap a drum beat when counting.Check for plausibility of response.Have student tell a number story to insure comprehension.Teach “math vocabulary”Utilize music, especially rap, to over-learn facts.Incorporate an area of passion in all lessons (e.g. baseball statistics, Yu-Gi-Oh life points, NASCAR standings, etc.)

118. Interventions for Poor Visual-Spatial Skills118Turn a visual problem into a verbal problem.Have students talk their way through a problem.Use graph paper to help line up equations.Make sure problems are written vertically as opposed to horizontally.Attach number-line to desk.Greater emphasis teaching estimation skills and magnitude representations.

119. Interventions for Lower Working Memory 119Number-line situated on student’s desk.Use a calculator.Reduce anxiety in the classroom.Increase number sense through games such as dice, domino’s, cards, etc..Encourage paper and pencil use while calculating equations.Use mnemonic techniques to teach math algorithm’s and sequential steps to problem solving.

120. Assessment: Number Sense ScreenerProven to be highly predictive of math disability in kindergarten and first gradeDeveloped by Nancy Jordan, EdD, University of Delaware, "Number Sense Screener," published by Brookes Publishing

121. Executive Functioning & Math Deficits: NEPSY/D-KEFSTowerAuditory Attention Response SetVisual AttentionDesign FluencyPlanning, inhibition, self-monitoringCognitive flexibility, sustained attentionVisual attention to math symbols, processing speedNonverbal strategy formation skills, planning, comparisonsExecutive Functioning AreaMath Implication

122. Executive Functioning & Math Deficits: NEPSY/D-KEFSPhonological ProcessingSpeeded NamingComprehension of InstructionsPhonological awareness, syllable segmentation contribute to accurate reading of word problemsVisual/verbal retrieval skills key for over learning math factsAuditory working memory, receptive language skillsExecutive Functioning AreaMath Implication

123. Sensori-Motor Functioning & Math Deficits: NEPSY/D-KEFSFingertip tappingImitating Hand PositionsVisuomotor PrecisionMotor speed and dexterityVisual perception, praxis, spatial awarenessVisual-motor integration, graphomotor coordination, manipulating a pencilSensori-Motor Functioning AreaMath Implication

124. Visual-Spatial Functioning & Math Deficits: NEPSYDesign CopyArrowsVisuomotor integrationvisual perception of abstract shapesSpatial orientation Lining up math equationsVisual-Spatial Functioning AreaMath Implication

125. Memory & Math Deficits: NEPSYMemory for FacesMemory for NamesNarrative MemoryVisual perception of details and memory for nonverbal informationVisual/Verbal retrieval skillsAuditory working memorySequencingVisual-Spatial Functioning AreaMath Implication

126. Anxiety & Math

127. The Anxious Brain and Mathematics127 Math Anxiety + Time Constraints = Poor PerformanceMales have stronger SAT math scores than females (SAT mean boys = 595 vs SAT mean girls = 554) Girls reported more anxiety and less self-confidence on visual spatial problem solving tasks (Casey, 1997)

128. The Anxious Brain and Mathematics128SUMMARY: MATH ANXIETY (Casey, 1997):Math anxiety alone not solely responsible for differences between boys and girls.Students with cognitive flexibility to use either a verbal or a visual-spatial strategy when solving a math problem are inherently less likely to become anxious than students with a singular methodology. Anxiety itself may serve as a double-edged sword in that the more anxious we become, the less cognitive flexibility we have to use alternative problem solving strategies.

129. The Anxious Brain and Mathematics129Working Memory and Anxiety:Students with elevated levels of math anxiety perform more poorly than students with lower math anxiety on all levels of mathematical problem solving (Kellogg et al, 1999).Central executive system (which functions to inhibit negative distracters), is often rendered useless when anxious (Anterior Cingulate). This paves the way for worrisome and negative thoughts which overburden the system (Hopko et al, 1998).

130. 5 Ways to Reduce Math Anxiety130Teach multiple ways to problem solving :Students who utilize both visual/spatial and verbal strategies outperform students who over-rely on just a singular methodologyAvoid skill drills:Speed and competition creates anxiety. Obtain fluency without classroom competitions.Link problem solving with passion:Attach personal meaning to the harshness of cold problem solving. Baseball batting averages or Yu-Gi-Oh life points are a fun way to learn math operations.

131. 5 Ways to Reduce Math Anxiety131Set algorithmic procedures to a song:Lower anxiety leads to better working memory and better working memory lowers anxiety. Set math operational steps to a song or rap, as verbal strategies often serve as a memory enhancer.Encourage visual cues:Students who take the time and effort to jot down equations on paper as opposed to working out equations in their head, put less stress on working memory systems.

132. Math Anxiety StrategiesWrite anxious thoughts on paper before beginning a testVisualized where you studied and completed practice problems for the testLearn mindfulness techniques when breathingSurvey the entire test prior to beginningPositive Self talkSmileHave a back up planMinimize unit test coverage

133. Math Anxiety InterventionsUse paper and pencilScratch paper with steps to solve problemEliminate timed testsUse mnemonic techniquesUse manipulativesUse a calculator judiciouslyUse to minimize rote calculations

134. Math Anxiety InterventionsReduce classroom anxietyPositive classroom environmentEncourage risk taking, asking questions, & personal growthLess emphasis on high stakes testsAllow a take-overContent & meaningStudent directed algorithms

135. Math Anxiety Assessments (Young)Mathematics Anxiety Scale for Young Children (12 questions)Children's Anxiety in Math ScaleChild Math Anxiety QuestionnaireCMAQ-RMath Anxiety Questionnaire – Scales C & D

136. Abbreviated Math Anxiety Rating Scale(5 point scale)Having to use the tables in the back of a math bookThinking about an upcoming math test the day beforeWatching a teacher work a difficulty equation on the board Taking an examination n mathBeing given a homework assignment in many difficult problems due the next dayListening to a lecture in math classListening to another student explain a math problem being given a “Pop” quiz in Math classStarting a new chapter in a math book

137. ReferencesD’Amato, Fletcher-Janzen, & Reynolds (2005). Handbook of School Neuropsychology. John Wiley & sons: Hoboken, NJ.Feifer, S. & DeFina, P. (2005). The Neuropsychology of Mathematics: Diagnosis and intervention. School Neuropsych Press, LLC: Middletown, MD

138. Resources Math Learning Disability Resource http://www.dyscalculia.org/Designing Mathematics Instruction: A Direct Instruction Approachexcellent book for assessing & teaching math

139. FARFeifer Assessment of Reading

140.

141. FARPhonological IndexFluency IndexMixed IndexComprehension IndexFAR Total Index

142. Phonological IndexPhonemic AwarenessNonsense Word DecodingIsolated Word ReadingOral Reading FluencyPositioning Sounds

143. Fluency IndexRANVerbal FluencyVisual PerceptionIrregular Word Reading FluencyOrthographic Processing

144. Phonological IndexFluency IndexMixed Index (Double Deficit)

145. Comprehension IndexSemantic ConceptsSynonyms & antonymsWord RecallMorphological ProcessingSilent Reading Fluency: ComprehensionSilent Reading Fluency: Rate

146. Rapid Automatic Naming (Glr-NA)WISC-V Rapid Naming IndexCTOPP-2 Rapid Symbolic Naming CompositeWJ-IV COG Retrieval Fluency subtestRapid Automatic Naming subtestIdaho SLDFAR

147. Phonological Awareness/Coding (Ga-PC)WJ-IV ACH Phoneme/Grapheme ClusterWord AttackSpelling of SoundsWIAT-III Basic Reading Skills subtestPhonemic AwarenessPositioning SoundsIdaho SLDFAR

148. Basic Reading SkillsWJ-IV ACH Basic Reading Skills ClusterLetter Word IDWord AttackWIAT-IIIWord ReadingPseudoword DecodingNonsense Word DecodingIsolated Word ReadingIdaho SLDFAR

149. Reading FluencyWJ-IV ACH Reading Fluency ClusterWIAT-III Reading Fluency Typical Reading Fluency FormatGORT-5 Reading FluencyTypical Reading Fluency FormatTypical Reading Fluency Format:Silent Reading Fluency: RateOral Reading Fluency Single Word ReadingVerbal FluencyIrregular Word Reading FluencyIdaho SLDFAR

150. Reading ComprehensionWJ-IV ACH Reading Comprehension ClusterWIAT-III Reading Comprehension Typical Reading Comprehension FormatText available for referenceGORT-5 Reading ComrehensionTypical Reading Comprehension FormatText not available for referenceSilent Reading Comprehension subtestText not available for referenceSemantic Concepts (synonyms & antonyms)Idaho SLDFAR

151. FAR CritiqueGood correlations to appropriate reading interventionNeurologically basedIn depth information on where deficits lieExpensiveAdvanced interpretationsOK for teachers to interpret?Often non-unitary Index ScoresNeed to use CHC model to get an SLD Index scoreOnly 1 true reading Comprehension subtestCan use a vocabulary subtest to make an index scoreProsCons

152. Linda Taylor, PhDlinda.taylor@vallivue.orgVallivue School DistrictCaldwell, IDComplete FAR presentation will be presented at the Boise Professional Development Class beginning January 2019Thank you!