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TRANSCRIPT
Mathematics for Students
with Severe Disabilities
Dr. Brad Witzel
2011
Slide 1 Mathematics for Students with
Severe Disabilities
Brad Witzel, Ph.D.Associate Professor and
Special Education CoordinatorWinthrop University
Witzel, 2010 1
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Slide 2 Agenda
• Why is math a concern for students with severe disabilities?
– Transition
• Life skill
• Employment
• To help, should we focus on building their academic math skills or functional math skills?
Witzel, 2010 2
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Slide 3 Goals of changing math achievement
Academic
• With the higher math needs per career, we must increase our expectations and demand higher level mathematics.
• Those skills can be transitioned into functional and work-related settings.
Functional
• Since students with low-incidence disabilities struggle using math in real life settings, the focus should be application.
• Skills can still be taught and practiced within the functional curriculum.
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Slide 4 Content to be covered
• Number recognition
• Counting
• Quantification
• Basic Facts
• Vocabulary
• Instructional Delivery
• Bringing it all together
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Slide 5 Number Sense defined
The NMP defined number sense as “an ability to immediately identify the numerical value associated with small quantities, a facility with basic computing skills, and a proficiency in approximating the magnitudes of small numbers of objects and simple numerical operations” (2008, p. 27).
More advanced forms of number sense involve understanding of place value, composition and decomposition of number, and the concept of basic arithmetic operations (Chard, 2006; Gersten & Chard, 1999; NMP, 2008).
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Slide 6 Areas within Number Sense(Fuchs, Compton, Fuchs, Paulsen, Bryant, & Hamlett, 2005; Fuson, 1990, Gersten,
Jordan, & Flojo, 2005)
a) counting forward and backwards
b) fluent quantification and magnitude of number
c) number to numeral identification
d) base-10 and place recognition and recall
e) fluent use of arithmetic strategies
Focus on these in your assessment of early learners
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Slide 7 Make Numbers Relevant
• Cooking
• Hop scotch
• Calendar
• Sport scores
• Game boards
• Color by number
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Slide 8
Around the tree and around the tree,
that’s the way we make a three
Down and over and down some more, that the that’s the way we make a four
Dot notation (Simon & Hanrahan, 2004)
Wisniewski and Smith (2002) found that students with disabilities excelled in speed and accuracy when
taught using a dot notation format and transitioned to fluency.
Numeral and quantity
© Witzel, 2008 (updated 2011) 8
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Slide 9
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Slide 10 Some Basic Skills
a) Counting and counting on– Counting chart, unifix cubes, feed the monkey
a) Counting backwards (difficult until early elementary)– Counting chart, unifix cubes
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Slide 11 Number line (Gersten et al, p. 33)
© Witzel, 2010 11
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Slide 12 Ten Frames
Using patterns to earn numeracy skills and numbers (subitization)
• 3+4=7
• 5+2=7
12© Witzel, 2008 (updated 2011)
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13© Witzel, 2008 (updated 2011)
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Slide 14
14© Witzel, 2008 (updated 2011)
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Slide 15
15© Witzel, 2008 (updated 2011)
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Slide 16
16© Witzel, 2008 (updated 2011)
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Slide 17
17© Witzel, 2008 (updated 2011)
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Slide 18 The number code
Some people say that they like math because it logical….
Find the pattern in each of these groups of numbers.Is the pattern visual, auditory, both, or neither?
A. 1-9
B. 10-19
C. 20-29
D. 100-120
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Slide 19 Language Experiences
Teach base ten – Example- Understanding of 17
Try see-says and Race to 100
Tens Ones
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Tens Ones Tens Ones
1 1
1
1
1
1
1
1
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Slide 20 Building Fluency
• Students with developmental disabilities have made gains in oral and written fluency based on systematic and ongoing practice with addition and subtraction facts (Jolivette et al., 2006).
• Build practice and repetition within math class.
Witzel, 2010 20
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Slide 21 Extra Practice Options
(Chapman, 2010)
35
I have 35. Who has 6
groups of 8?
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Slide 22 Multiplication Assessment (Chapman, 2010)
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Slide 23 Instructional Delivery
• Daily routines (Browder & Cooper-Duffy, 2003) within explicit instruction
• Systematic instruction (Jackson et al., 2000)– Explicit think alouds and modeling
– Task analysis
– Practice practice practice
• Errorless response practice with delayed prompting (Ault et al,1989)
• Hands-on with relevance and stepwise procedures
Witzel, 2010 23
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Slide 24 Manipulative Objects: A Number Sense Teaching Tool
• Researched benefits span over:– Developing numeration -Basic facts -Fractions– negative #s -Area & perimeter -3D figures
• Manipulative objects do NOT teach children…. Teachers do!
• Some helpful hints– Practice using manipulatives before you teach– Provide language experiences while using
manipulatives– Develop a pictorial representation for transition to
abstract understanding… the ultimate purposeWitzel, 2010 24
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Slide 25 Concrete to Representational to Abstract
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Slide 26 Next Steps
• Consider
– General Education Access
– Planned modifications and accommodations
• What is the difference between accommodations and modifications?
Witzel, 2010 26
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Slide 27 Potential accommodations
• Extra wait time• Procedures clarification• Minimize classroom
distractions• Homework reminders and
planners• Weekly progress report and
home checks• Increased 1:1 assistance• Peer tutoring or reciprocal
teaching• Homework from previous
week
• Classroom signals for attention
• Visual organizer• Scribe or notetaker• Guided notes• Shortened assignments• “Chunked” lesson of brief
assessed activities throughout a lesson
• Frequent praise to teach proper academic and social behaviors
Any more????
© Witzel, 2008 (updated 2011) 27
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Slide 28 Potential modifications
• Altered grading procedures
• Alternate but related standard during lesson
• Different reading assignments
• Different questions
• Alternate assessment content and / or expectations
• Elimination of parts of assignments if they remove a standard
• Calculator during math fluency assignment
© Witzel, 2008 (updated 2011) 28
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Slide 29 Modifications and Accommodations
• What are modifications to a teacher’s instruction?– An algebra teacher is a teaching trigonometric ratios (sine,
cosine, tangent). You expect students to memorize the formulas to solve for angles and lengths of sides. How might you modify the assignment for a student with memory problems and calculation at the 2nd grade level?
• What are accommodations?– The same teacher decides not to modify the assignment
but instead provides accommodations. What accommodations could be applied and how?
© Witzel, 2008 (updated 2011) 29
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Slide 30 Warning for Accommodations and Modifications
• Before using accommodations, and even more so with modifications, one must make detailed preparations with the long term goal of their planned and successful omission.
• Unless the outcome allows an inclusion of their use (e.g., glasses), accommodations and modifications must be faded from instruction.
© Witzel, 2008 (updated 2011) 30
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Slide 31 Final Thoughts:Choose a pathway to helping students
with severe disabilities in math
1. Set Content - Choose an outcome
2. Organize Content - Set short-term goals and mathed assessments
3. Set Instructional Delivery - Choose a technique
4. Engage and Reassess the decisions and process
Witzel, 2010 31
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Slide 32
Witzel, 2010 32
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Slide 33 References
Ault, M. J., Wolery, M., Doyle, P. M., & Gast, D. L. (1989). Review of comparative studies in the instruction of students with moderate and severe handicaps. Exceptional Children, 55, 346-356.
Ball, C. (2003). Every stage counts in the journey to numeracy. Times Education Supplement (Oct. 10, 2003), 24.
Browder, D. M., & Cooper-Duffy, K. (2003). Evidence-based practice for students with severe disabilities and the requirement for accountability in “No Child Left Behind.” The Journal of Special Education, 37 (3), 157-163.
Gersten, R., & Chard, D. (1999). Number sense: rethinking arithmetic instruction for students with mathematical disabilities. Journal of Special Education, 33 (1), 18-28.
Geary, D. C., Hoard, M. K., & Hamson, C. O. (1999). Numerical and arithmetical cognition: patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74 (3), 213-239.
Jackson, L., Ryndak, D. L., & Billingsley, F. (2000). Useful practices in inclusive education: A preliminary view of what experts in moderate to severe disabilities are saying. Journal of the Association for Persons with Severe Handicaps, 25, 129-141.
Jolivette, K., Lingo, A. S., Houchins, D. E., Barton-Arwood, S. M., Shippen, M. E. (2006). Building math fluency for students with developmental disabilities and attentional difficulties using great leaps math. Education and Training in Mental Retardation, 41(4), 392-2000.
National Council of Teachers of Mathematics [NCTM], (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
Wisniewski, Z. G., & Smith, D. (2002). Hw effective is touch math for improving students with special needs academic achievement on math addition mad minute timed tests? ERIC (ED469445).
Witzel, B. S., & Ferguson, C. J. & Mink, D. (in-press). Developing early number sense for students with disabilities. Young Children.
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