The Neuropsychology of Math NASP 2012 conference Attended by our School Psychologist Jane Mendoza, M.A. Ed.S. School Psychologist

Constructs Working Memory Visual Spatial Functioning Ability to hold representational knowledge in mind, coupled with mental flexibility to manipulate this knowledge in whatever manner we choose Visual Spatial Functioning Ability to think in pictures Executive Function What to do: Developing a plan/strategy

Disorders in Math Verbal Procedural Semantic Visual-Spatial

Disorders in Math: Verbal Students who have difficulties with counting and rapid number identification skills, deficits in retrieving or recalling stored math facts Represents a disorder in the verbal representations of numbers, and the ability to use language-based procedures to assist in arithmetic fact retrieval skills – These students may also have difficulties in reading and spelling DEFICITS: counting, rapid number identification, retrieval of stored facts, addition and multiplication facts, may have coexisting reading and writing difficulties

Disorders in Math: Procedural Represents a disorder in the ability to transcode numeric systems into meaningful language systems Just as children must ultimately link phonemes with graphemes in order to learn the phonological code to reading, children must also learn the language of math by linking the verbal name of a numeral with its numeric representation Children with this subtype often have difficulty reading numbers aloud, and may struggle to write numbers from dictation Children with a procedural error subtype tend to have learning difficulties solely related to math. DEFICITS: writing numbers from dictation, reading numbers aloud, math computational procedures, syntactical rules of problem solving, deficits with division and regrouping procedures in subtraction

Disorders in Math: Semantic An ability to decipher magnitude representations among numbers Knowledge of the operations Allow for value judgment and evaluation of plausible response DEFICITS: Magnitude of representations, transcoding math operations, conceptual understanding of math, estimation skills

Disorders in Math: Visual-Spatial Difficulties with aligning a column of numbers; visual perception of numbers Spatial attributes such as size, location, or orientation and mental rotation, magnitude comparison

USA Decline in Math According to the trend in International Mathematics and Science Study 2004 (TIMSS, 2004), over the past 30 years math and science scores of American students have remained stagnant, while scores from industrialized nations have soared. Upon closer inspection – much information for educators to glean from data:

Four Reasons for Decline: Time Too much focus on the answers Dry and boring material Language of math matters

Time Science and math not a priority, math is taught late afternoon and for only short periods of time.

Focus on answers Too much focus on the answers There’s a difference between getting answers and learning procedures rather than learning to think quantitatively about numbers

Dry and Boring Material Dry and boring material! Math needs to be fun and be presented in games and activities to eliminate the anxiety factor. Cushion Syndrome – born with too much cortisol in the brain Anxiety creation of cortisol in the brain may mimic Cushing Syndrome which can result in a working memory deficit.

Language of math matters Building numbers around base 10 matters Most European-derived languages such as English or French do not correspond to simple base-ten ordinal structure of the Arabic number system On the other hand, most Asian languages possess linguistic structures much more consistent with a numeric counting system: i.e., Asian languages count past ten by going ‘ten-one’, ten-two’, ‘ten-three’, etc., whereas English deviates from the base-ten counting structure and counts past ten as ‘eleven, twelve, thirteen,’ etc. Consequently, most American children conceive of ‘twelve’ as a collection of 12 disparate objects Asian children have built into their linguistic counting structure a more lucid representation of ‘twelve’, as being the collection of one set of ‘ten’ objects and one set of ‘two’ objects.

Days of School Work ethic deficit relative to Asian countries United States 180 days of school 6 hours per day South Korea 220 days of school 10 hours per day Japan 240 days of school Work ethic deficit relative to Asian countries

The vast majority of American children have lost interest in math and science: 84% of American students surveyed would rather do any one of the following than their math homework: a) clean their room, b) eat their vegetables, c) go the dentist, or d) take out the garbage. 1/3 of students surveyed reported they liked math (2/3s don’t like math) 43 % of students reported they had a difficult time understanding math and 45% indicated math was boring.

Difficulties - Calculator usage by students resulted in poor math performance Overseas, calculators are not used Calculators do not help to develop number sense Use double check work (self-monitoring), otherwise you’re robbing students of number sense Visual Spatial Sketch Pad – Working memory processing deficit = erased visual spatial sketch pad Students resort to use fingers to count – We need to help them with an externalized visual spatial sketch pad Set emotional climate/tone in class. Anxiety interferes with cognition

Interventions # line on desk Calculator (for checking work) Reduce anxiety in classroom Encourage use of visual cues (pencil/paper jot down equations) to help anchor work Use mnemonic techniques to help with recalling algorithmic steps/procedures Teach multiple ways to problem solving – No more than 3 otherwise too confusing – let student select easiest way for him/her. Avoid skill drills (creates anxiety) Color code math signs Use graph paper and label the columns Teach students within a context, not in isolation

Thank You Jane Mendoza, M.A.Ed. S. School Psychologist jamendoza@gesd32.org