Transcript Document

Characteristics of Math
Disabilities
Eric Shippee
K-8 Math Specialist
K-12 Special Education
adapted from © Sharon deFur
Summer 2004
Accommodations
& Modifications
are purposeful changes educators make to the:
• environment • where, when, and with whom
students learn
• instruction
• how teachers teach so
students learn
• assessment
• how students demonstrate
what they learn
• curriculum
• what the teacher teaches
Accommodations
• Expectations for the subject or
test are not lowered or altered
• Students remain eligible for the
same diplomas as their
nondisabled peers
Purposes of Accommodations
• Provide access to general
education curriculum
• A “ramp” to the highway
• Level the playing field
• Minimize impact of the disability
Assessment 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
Modifications
Significant 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?
Accommodation Modification
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
•Supports all
learners, but
specifically those
who are challenged
by the curriculum
•Supports the
standards
•Benefits all students
•Enables access to
the curriculum
•Changes the
standard
•Allows full or
partial
participation
Krypto
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.
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 figureground perceptual challenges?
• Visual
• Auditory
– 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
– Has trouble
discerning a
counting pattern
– Has difficulty
attending in the
classroom
Accommodations for FigureGround 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)
6
-2(-3 + 5) - (4 - 8) + = ?
2
2
PEMDAS
2
-2(-3+5)-(4-8) +6/2=?
2
-2(2)-(-4)+6/2=?
-2(2)-16+6/2=?
-4-16+3=?
-17
2
-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 • Auditory
– Has difficulty with concepts such as – Has difficulty following
directions using
before-after; next to-above
ordinal numbers
– Has trouble noticing size differences
– Has difficulty with
– Has trouble aligning numbers or
following computations up-down,
spatial adverbs (first,
across (directional challenges)
next, last)
– 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
Accommodations for SpatialPerceptual 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
Mnemonics
Unit packet for SOL
being taught
• Teacher modeling
Never
Write
In
Red
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 multistep word problems
• Auditory
– Misperceives
numbers that are
said (e.g. 32
becomes 23)
– Does not retain
story problems
that are dictated
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
© Sharon deFur
Summer 2004
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
What is the definition of this word ?
Mean
46
A Hostage Situation…Mean
What does it mean in
everyday language?
What does it mean in
mathematical
language?
MEAN
47
How Could These Words Hold
You Hostage?
•
•
•
•
•
•
•
Odd
Difference
Similar
Product
Base
Fact
Power
•
•
•
•
•
•
•
Mean
Range
Plane
Regular
Variable
Pi
Radical
48
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 multistep 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 Application
Multiple 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/disabledstudents/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: [email protected]
Thank you and have a great day!