adapted from © Sharon deFur Summer 2004

Characteristics of Math DisabilitiesEric Shippee

K-8 Math SpecialistK-12 Special Education

AccommodationsAccommodations& Modifications& Modifications

areare purposeful changes educators make to the:purposeful changes educators make to the:• environment

• instruction

• assessment

• curriculum

• where, when, and with whom students learn

• how teachers teach so students learn

• how students demonstrate what they learn

• what the teacher teaches

AccommodationsAccommodations

• Expectations for the subject or test are not lowered or altered

• Students remain eligible for the same diplomas as their nondisabled peers

Purposes of AccommodationsPurposes of Accommodations

• Provide access to general education curriculum

• A “ramp” to the highway• Level the playing field• Minimize impact of the disability

Assessment AccommodationsAssessment Accommodations• Variety of

Assessment Tools– observations– probes– checklists– portfolios

• Test Administration– setting– timing/

scheduling– response – Presentation

Assessment Activities

• Objective assessment– Multiple choice, true-false, matching, short answer, fill

in the blank• Subjective assessment

– Requires evaluator judgment (Rubrics help!)• Explaining why a statement is or is not correct• Describing relationships• Drawing diagrams

• Performance tasks require integration of skills– Gathering and analyzing data– Posters– Projects

ModificationsModificationsSignificant purposeful changes

that teachers make to assessments or curriculum that result in moving students with

disabilities off the general curriculum.

Adaptations• Intentional lesson and unit design

changes intended to meet the needs of all students, but with particular consideration for those students who are experiencing challenges with the curriculum– E.g. instructional activities and routines that benefit

all students where the strategy is grounded in evidence-based research – Unit Organizer Routine represents an instructional adaptation that benefits those most challenged, but does not inhibit the learning of those who are at ease with the curriculum.

Accommodation, Modification, Adaptation?

Which one, when?Accommodati

onModification Adaptation

•Levels the playing field by alleviating or managing the “handicap”•Does not change the standard•Should be more difficult for the non-disabled person

•Enables access to the curriculum•Changes the standard•Allows full or partial participation

•Supports all learners, but specifically those who are challenged by the curriculum•Supports the standards•Benefits all students

Deal five cards (numbers up) in the center of the table. Then turn a sixth card up which will be the Objective Card. Each player will commence to use the numbers of each card so that the last solution equals the Objective Card number. Each of the five cards must be used. Each card may only be used once.

Krypto

Example:Cards: 1, 3, 7, 1, 8= 1 Objective Card 3 - 1 = 2 7 + 2 = 9 9 / 1 = 9 9 - 8 = 1

Crazy Krypto• You will have 5 minutes to solve the

Krypto problem on your card.• Each of the first 5 numbers must be used

once and only once • The sixth number is your solution number• When you have the answer turn your paper

over.

Types of math challenges…

• Perceptual– Figure – ground– Perceptual – closure– Discrimination– Reversals– Spatial-Temporal

challenges• Motor challenges

• Memory– Short term– Long term

• Executive Functioning

• Language– Expressive– Receptive

• Social–emotional concerns

• Academic

Figure Ground Perception• Definition: The ability to separate

objects from their backgrounds, for example, the ability to see the trees in the woods. In reading math problems, this skill is essential to enable the recognition of numerals and words from a body of text. Distractions can come from the page itself.

Did your student have figure-ground perceptual

challenges?• Visual

– May not finish all the items on the page

– Frequently loses place– Has difficulty

differentiating between operations

– Has difficulty visualizing groups

– Has difficulty reading multi-digit numbers

• Auditory– Has trouble

discerning a counting pattern

– Has difficulty attending in the classroom

Accommodations for Figure- Ground Perceptional

Challenges

• Larger Fonts• Index card

cutouts• Interactive

study guide• Fewer number

of problems

Perceptual Closure

•Definition: The tendency to perceive an incomplete pattern or object as complete or whole.

Did the student have difficulty with perceptual

closure?• Visual

– Has difficulty reading multi-digit numerals

– Has difficulty perceiving a group as a whole

– Has difficulty continuing visual patterns

– Has difficulty reading algebraic equations, decimal numbers

• Auditory– Has difficulty counting

on from a sequence

Accommodations for Perceptual Closure

• Visual– Use smaller

numbers in examples

– Change font– Use manipulatives– Smaller pattern

sequences– Chunk story events– Graphic organizers

• Auditory– Chunk directions – Keep directions

simple– Repeat directions– Provide a visual

Discrimination

•Definition: Seeing the difference between two similar objects, such as, the numerals ‘6’ and ‘9’ or symbols‘≤’ and ‘≥’. Persons with this problem see two similar objects as alike.

Discrimination?• Visual

– Has difficulty differentiating between or writing numerals

– Has difficulty discriminating between operation signs

• Auditory– Has trouble

distinguishing between endings of numbers (e.g. 13 and 30

– Has difficulty with decimal numbers

– Has difficulty discriminating between word parts (e.g. addition and edition)

PEMDAS-2(-3+5)-(4-8) +6/2=?

-2(2)-(-4)+6/2=?-2(2)-16+6/2=?

-4-16+3=?-17

-2(-3+5)-(4-8) +6/2=-17

Accommodations for Discrimination

• Peer checking• Teacher checks

periodically• Write, review, and

check• Teach procedure to

check with calculator• Highlighters• Group verbalization

to review problems

Spatial-Perceptual Challenges

•Definition: Knowing where objects are located in space. Processing whole-part relationships.

Spatial/Temporal Challenges?• Visual

– Has trouble writing on lined paper– Has difficulty with concepts such as

before-after; next to-above– Has trouble noticing size differences– Has trouble aligning numbers or

following computations up-down, across (directional challenges)

– Has difficulty writing fractions– Has difficulty copying problems,

setting up a page of work– Has difficulty grouping manipulatives– Has difficulty with a number line;

positive & negative number confusion

• Auditory– Has difficulty following

directions using ordinal numbers

– Has difficulty with spatial adverbs (first, next, last)

Accommodations for Spatial-Perceptual

Challenges• Paper variations• No lines• Graph paper• Model use of spatial

adverbs

Fine Motor Skills

•Definition: Eye-hand coordination that involves purposeful movement of the small muscles of the hands and fingers.

Motor Challenges?• Writes numerals from dictation

slowly, illegibly, and inaccurately• Has difficulty writing numerals in

small spaces (may write too large or too small)

So what might you do?• Use visual cueing

– Boxes, circles, lines• Color code• Reduce the number of items

on a page• Use centimeter square graph

paper or use unlined paper• Use templates and skill

guides• Reduce writing demands

when appropriate• Use verbal cues to scaffold

Short Term Memory

•Definition: Remembering information which has been heard recently. Relays information to active working memory and to long term memory.

Short term memory?• Visual

– Has trouble retaining newly presented material

– Has difficulty copying numerals from the board

• Auditory– Has difficulty with

oral drills– Has difficulty with

dictated assignments

Accommodations for Short-Term Memory Challenges

• Drill and practice• Study guides Never• Mnemonics Write• Unit packet for SOL In

being taught Red• Teacher modeling Ink

Working Memory• Definition: Linking of information

you already know with new information. Linking “knowns” with “unknowns”. You develop ideas in your working memory. It is a mechanism for holding together parts of a task while you are engaged in that task.

Working Memory?• Visual

– Difficulty solving word problems

– Difficulty continuing a pattern from midpoint

– Difficulty with multi-order computations

• Auditory– Difficulty

completing complex processes

– May have difficulty quickly or efficiently using “inner language”

Accommodations for Working Memory Challenges• Display key vocabulary• Problem solve daily• Games• Calculator use OK• Firm understanding of

concepts

Long Term Memory

•Definition: Seemingly limitless storage vaults for preserving knowledge, skills, and life experiences.

Long-term Memory?• Visual

– Cannot retain basic facts or processes over time

– Has trouble retrieving information at the needed time

• Auditory– Has trouble

retaining orally presented information for extended periods of time

Accommodations for Long-Term Memory Challenges

• Hold weekly review sessions• Teach material in different

ways• Provide hands-on experiences• Frequent use of graphic

organizers

Sequential Memory

•Definition: The ability to be able to put information in the correct order and to remember that information.

Sequential Memory?• Visual

– Trouble with complex operations

– Trouble accurately reading numerals

– Difficulty solving longer number sentences and equations

– Difficulty telling time– Difficulty with multi-

step word problems

• Auditory– Misperceives

numbers that are said (e.g. 32 becomes 23)

– Does not retain story problems that are dictated

© Sharon deFur Summer 2004

Memory Strategies?

• Mnemonics• Visuals where A "picture is worth 1000 words.“• Tactile Memory• Kinesthetic Memory• Visual Memory• Rhyming or Rhythm• Remember … "Repetition is the mother of

retention.“• Making an association

Receptive Language?• Visual

– Has difficulty associating words with symbols

– Has difficulty with signs that have different meanings (e.g. fraction bar)

• Aural– Has difficulty

relating words to meanings

– Has difficulty with words that have multiple meanings

– Has difficulty writing numerals from dictation

– May have difficulty using inner language

Math is its own Language

• Therefore:– Language

(vocabulary concepts) instruction & supports are essential

46

What is the definition of this word ?

Mean

47

A Hostage Situation…Mean

What does it mean in everyday language?

What does it mean in mathematical language?

MEAN

48

How Could These Words Hold You Hostage?

• Odd• Difference• Similar• Product• Base• Fact• Power

• Mean• Range• Plane• Regular• Variable• Pi• Radical

Reading & Writing?• Word

recognition• Fluency• Comprehension

Executive Functioning Metacognitive skills?

• Cannot draw conclusions; therefore, has trouble noticing and continuing patterns

• Cannot use prior knowledge effectively to draw conclusions

• Has difficulty solving multi-step word problems• Has difficulty continuing a counting pattern

from within a sequence• Has difficulty applying learned operations

within a complex computation• Has trouble generalizing information without a

structured approach• Lacks strategies for problem solving

Social and Emotional Factors

• Impulsivity/ Organization– Careless mistakes– Inattentive to details– Frequently loses

homework• Distractibility

– Difficulty with multi-step computation

– Off-task– Does not complete work– Starts work, but does

not finish

• Passivity/Learned helplessness– Omits problems– Appears disinterested– Lacks strategies– Gives up easily

• Anxiety– Tension interferes with

math testing– Avoids math

Concrete, Representational, Abstract

Concrete– Students need to build, act out, or interact

with physical models.

By observing and participating in such activities you;

– engage the kinesthetic learner – create student ownership of content– Provide a strong memory to tie with the

content

Concrete, Representational, Abstract

Representational– Students need draw out or recreate their

experiences. By drawing out their prior experiences the

students;– improve their memory recall– are able to use past experiences to solve new

unfamiliar problems– Continue to have ownership of math concepts

Concrete, Representational, Abstract

Abstract– This is when student only use the symbols of math

to solve problems. (formulas, equations, expressions…)

– Students naturally progress from the representational to the abstract.

– Students who have worked on Concrete models and Representational models have less trouble dealing with and understanding an Abstract representation.

Effective Lessons that Meet Diverse Learning Needs

1. Expand the developmental part of the lesson – Multiple Means of Representation –

For example, – Provide personal experiences with real things – concrete

manipulatives to semi-concrete to abstract– Use mental imagery– Offer more visuals to support– Relate to prior knowledge– Use a wide variety of examples & non-examples with

discussion as to why and why not these are examples– Use inductive exploration with multiple examples

SEEK HIGH LEVELS OF ENGAGEMENT!

• Teachers can improve the level of involvement by– Being aware of the importance of

student involvement to effective instruction

– Seeking ways to increase student involvement, including student to student communication

– Monitoring “dead” time and change procedures to increase engaged time

Practice and ApplicationMultiple Means of Engagement

• Practice activities– Think time practice activities emphasize accuracy.– Speed-drill practice activities emphasize quick

answers (limited use)• Application activities

– Classroom applications include textbook examples and contrived examples to apply skills

– Real-world problems uses examples from the student’s world in which to apply skills.

References• http://www.net-optics.co.uk/glossary-of-terms.htm#f

• http://stfx.ca/campus/stu-sev/disabled-students/ld/types.htm/

• Levine, M. (2002). A mind at a time. New York: Simon & Schuster.

• Thomlinson, C.A. (2001). How to differentiate instruction in mixed-ability classrooms. Alexandria, VA: ASCD

• Marzano, R.J., Pickering, D.J., & Pollock, J.E. (2001). Classroom instruction that works: Researched-based strategies for increasing student achievement. Alexandria, VA: ASCD

• www.wm.edu/ttac

Contact Information

This power point will be available on our website http://tidewaterteam.wm.edu.

Eric Shippee: ewship@wm.edu

Thank you and have a great day!