HOW NON-MATHEMATICIANS CAN HELP STUDENTS WITH … Webinar Handout - 2017.pdfa dislike of using computers. I have “a nearly non-existent visual memory”. I find it easier to work

UNDERSTANDING AND REMOVING MATH BARRIERSHOW NON-MATHEMATICIANS CAN HELP STUDENTS WITH LD, ADHD, AND ASD

Ibrahim Dahlstrom-Hakki, Ph.D.

© LCIRT 2016Do Not Copy Without Permission

Why Students Struggle with

Math2


Mathematics & Cognitive Load

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A Math Support Framework

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Effective Math Supports

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WHYSTUDENTSSTRUGGLEWITH MATH

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Struggling with Math• Sources of struggle

– Language processing

– Abstract thinking

– Visual-spatial skills

– Attention for extended periods of time

– Executive function coordination

– High working memory demand

7© LCIRT 2016Do Not Copy Without Permission

I have slight dyslexia, with very poor arithmetic skills, anda dislike of using computers. I have “a nearly non-existentvisual memory”. I find it easier to work algebraically withsymbols rather than with actual numbers. Numbers just don’tMake any sense. Mathematics and arithmetic are two verydifferent things.

Weaknesses:Reading difficulties, poor arithmetic skills, weakvisual memory, poor computer skills.

Strengths: Very high intelligence, creative, strong analyticalskills, strong algebraic thinking, strong oralcommunication skills.

Learner Profile: Emma

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Dr. Emma KingPhD in Cosmology and

Award Winning Mathematician


Dyscalculia• Developmental Dyscalculia manifests as

one or both of the following:– An impaired number sense

• An inability to estimate or compare quantities• Thought to be present at birth

– Difficulty in retrieving numerical facts• An inability to retrieve mathematical facts and

operations• Memory difficulty is usually math specific


Mathematics Processing in the Brain


Ansari (2008)


MATHEMATICS& COGNITIVELOAD

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Working Memory

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• Processing capacity is limited– Limited number of items can be held in

working memory at any one point– Gateway to information processing and

knowledge acquisition– Bottleneck in acquiring and expressing

knowledge– Needs to address intrinsic and extraneous

processing loads


Cognitive Load

Working MemoryExtraneousLoad

• Extraneous Loads– These loads are parts of a learning task that

are not integral to the learning goal• e.g. Spelling in a critical thinking essay• e.g. Reading in an algebra word problem

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Cognitive Load

Working MemoryIntrinsicLoad

• Intrinsic Loads– These loads are the core elements of a learning

task• e.g. Analysis in a critical thinking essay• e.g. Algebraic reasoning in an algebra word problem

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Cognitive Load

Working Memory

• Learning is efficient when cognitive load doesn’t exceed working memory capacity– When extraneous loads are low– When intrinsic loads are appropriate to the

learner’s ability level

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ExtraneousLoad

IntrinsicLoad


Cognitive Load

Working Memory

• Learning is slowed or stops when cognitive load exceed working memory capacity– When intrinsic loads are beyond a learner’s

ability level– When extraneous loads are high

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ExtraneousLoad

IntrinsicLoad


Cognitive Load

Working Memory

• Factors limiting available working memory– Weakness in memory, attention, or executive

functions– Language deficits– Poorly automatized skills– Anxiety or other affective issues

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• Skills and strategies can reduce extraneous cognitive load and free up working memory– Automatization of skills– Addressing confidence and other affective issues– Effective strategy use

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Working Memory

Cognitive Load


A MATHSUPPORTFRAMEWORK

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Mathematical Cognitive Load

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Symbolic Decoding

Computational Fluency

Ibrahim Dahlstrom-Hakki (2014)

Conceptual Understanding


Symbolic Decoding• Numbers

• Immediate intuitive sense of quantity represented

• Symbols• Immediate and accurate understanding of

the operation represented• Other decoding

• Language processing• Graph interpretation


Computational Fluency• Procedural knowledge

• How to perform a computational procedure or operation

• Problem solving approach• Knowledge of how to approach and tackle a

problem• Error checking

• Intuitive sense of expected answer• Efficient error checking procedure


Conceptual Understanding• Underlying concepts

• Understanding of the underlying mathematical and scientific concepts

• Translation across formats• Symbolic Notation• Language• Concepts

• Translation across contexts• Abstraction


Traditional Remediation

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Decoding Focused Practice


Procedural Drilling

© Dahlstrom-Hakki 2016Do Not Copy Without Permission

Concept First Approach


Representational Fluency


Procedural Efficiency


EFFECTIVEMATHSUPPORTS

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Reduce Math Loads• Help students separate decoding, conceptual,

and computational loads– Help students understand context based problems

without specialized language and symbols• Act out the scenario• Represent the problem using images or manipulatives

– Practice the computation process independently• Use manipulatives, e.g. Algebra tiles• Technology, e.g. DragonBox

– Develop fluency with relevant terms/symbols• Small set of most relevant terms/symbols• Explicit practice 20+ times

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Manipulatives


• Representational

• Abstract/Symbolic

1 + x = 3

?

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Manipulatives



Reducing Attention Loads• Reduce distracters

• Sensory distracters• Clutter and unnecessary complexity

• Enhance perceived importance of content

• Apply interest context to problem• Act out scenarios

• Avoid Split-attention effect• Integrate necessary information

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Information Integration

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Reducing Language Loads• Simplify Text

• Clear language• Formatting and spacing

• Provide visual/auditory supports• Mind-mapping• Text-to-speech/Speech-to-text• Graphical representations• Roleplay contexts

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Alternate Means of Conveying Concepts

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Roleplay Contexts

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© LCIRT 2016Do Not Copy Without Permission 35

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HOW NON-MATHEMATICIANS CAN HELP STUDENTS WITH … Webinar Handout - 2017.pdfa dislike of using computers. I have “a nearly non-existent visual memory”. I find it easier to work