Teaching Math among Adults with Learning Disabilities
Training Materials for Facilitators and Participants
CAEPA Conference Fall 1999Prepared by:
Leecy Wise, Coordinator
4 Corners Resource Center
502 S Madison, Cortez, CO 81321
Note: This segment is designed to follow an introductory presentation which has discussed the definition of the term "learning disability," the legal implications of serving learning disabled (ld) adults, and general screening and assessment strategies recommended for developing effective approaches for teaching ld adults.
Session Objectives - Participants will
- apply teaching strategies that encourage learning disabled adults to become independent, confident learners
- address math-related skill requirements with LD appropriate instruction
- practice math exercises and activities that reinforce the learning disabled student's strengths and make-up for specific learning deficiencies
- create math exercises that apply the principles of good teaching with learning disabled adults
- be happy
Materials: The materials used for this workshop are taken from "Bridges to Practice: A Reserach-based Guide for Literacy Practitioners Serving Adults with Learning Disabilities - A project of the National Institute for Literacy http://slincs.coe.utk.edu/special_collections/learning_disabilities/bridges-to-practice.html
Learning Disabilities Association of Canada 's Bringing Literacy within Reach: Identifying and Teaching Adults with Learning Disabilities -1991 (BLR)
Facilitaror's Notes and Agenda
A. Review and Practice (30 minutes)
I. Definition of Learning Disabilities (BP 1, pp 13-14)
- Learning disabilities is a general term that refers to a heterogeneous group of disorders...
- manifested by significant difficulties...
- in the acquisition and use of listening, speaking, reading, writing, reasoning, and mathematical abilities.
- These disorders are intrinsic to the individual...
- presumed to be due to central nervous system dysfunctions...
- and may occur across a lifespan.
- Problems in self-regulatory behaviors, social perception, and social interaction may exist with learning disabilities but do not by themselves constitute a learning disability. Although learning disabilities may occur econcomitantly with other handicapping conditions (for example, sensory impairment, mental retardation, serious emotional disturbance) or with extrinsic influences (such as cultural differences, insufficient or inappropriate instruction), they are not the result of those conditions or influences.
Discuss each aspect of the definition and have participants provide examples where appropriate.
II. Behavioral Characteristics of LD students http://edu-ss10.educ.queensu.ca/~lda/ldachar.htm
III. Indicators of LD
Review and discuss the information presented at these two sites and ask for confirmation or argument from participants. How would these items be recognized when teaching math?
IV. Elements of Good Instruction for LD students
A. The SMARTER Method (BP 4 - Section 3, p -11-18)
- Shape critical Questions
- Map critical content
- Analyze for Learning Difficulty
- Reach Instructional Decisions
- Teach Effectively
- Evaluate Mastery
- Revisit Outcomes and Plans
Go over the visual presented in BP4, just so participants can see how the map is developed.
B. Direct Instruction (Bridges to Practice [BP], Guide Book 4 - Section 4, p -21-23)
Phase 1 - Provide Objective
Phase 2 - Introduce and Model the Skill
Phase 3 - Provide Guided Practice with Feedback
Phase 4 - Encourage Independent Practice and Generalization
Discuss each phase in this approach. Bring out that this is a modification of the simplified steps, "I do it. I do it with your help. You do it with my help. You do it."
Teach the steps to soving the problem below (or any other of your choice) following the Direct Method).[DEMONSTRATION]
Example: Julia makes $15,000.00 a year. How much does she make each month if she works all year?
Introduce a similar problem and ask someone to review the steps in solving the problem applying the Direct Method. [PARTICIPATION)
C. Characteristics of LD- Appropriate Instruction (BP 4 - Section 6, p -41-46)
Provide information on each of the characteristics and have participants job down notes on what you say in the spaces around each item.
Remind participants to keep a check list of good practices and apply it after each session with the learner to remind themselves to include more and more characteristics as they go along.
Another good method for self-assessment is to give another person a checklist and have them check off characteristics that you have used in teaching an activitiy.
D. Additional Remiders, Teaching Strategies, Techniques, and Approaches for Use With Adults Who Have Learning Disabilities (Thank you Ardith R. Loustalet Simons - ESL and Learning Disabilities)
- Use a student-centered approach
- Know your students learning strengths and weaknesses
- Set achievable goals
- Establish a comfortable learning environment
- Eliminate possibility of hearing problems
- Eliminate the possibility of vision problems
- Eliminate the possibility of hunger
- Make sure lighting is appropriate
- Eliminate distractions
- Schedule breaks that suit the students needs
- Permit movement as needed
- Avoid boring, repetitive drill
- Keep assignments short
- Give immediate feedback
- Promote enjoyment
- Allow for and build in ongoing success
- Select relevant and appropriate materials
- Provide highly-structured learning sessions
- Review regularly
- Use appropriate drills
- Use a multi-sensory approach
- Encourage/teach study skills
- Support and encourage
- Use compensatory techniques as indicated:
- Encourage learner to develop skill in another medium (e.g., photography, drawing)
- Use media other than paper print to expand horizons (videos, computer programs, etc.)
- Help develop protective vocabulary or information sheets (words to recognize in restaurants, street names, information asked for on applications, etc.)
- Encourage use of tape recorders
- Encourage use of books on tape
- Encourage use of mechanical spell-checkers
- Teach self-monitoring techniques for problem areas
- Model the skill
- Use graphic organizers
- Evaluate progress/mastery and redefine goals
- Provide opportunities for guided and independent practice
Distribute the list of additional strategies and review it briefly.
Suggest that participants develop a lesson-plan checklist.In creating lesson plans WITH the student, remember to compare expected outcomes to the items listed above. Also, make sure that you develop activities that meet the standards for quality instruction for LD students, previously discussed. Checklists are invaluable. You may not hit every item every week, just as you won't please all people all of the time; however, you can always apply strategies that reinforce the student's strengths while creating different avenues to build skills that had previously been impossible for him or her to acquire. And, that, folks, is the essence of good teaching, and the secret to building independent and confident learners.
Helping Students Overcome Difficulties and Disabilities while Learning Math
- Work in pairs or in groups.
- Identify the likely learning disability involved in each challenge a student faces in the list below.
- Develop one activity to help an ld student overcome two of the challenges below and correlate the activity to one or more of the characteristics and learning strategies discussed earlier.
- Present the item to the other participants.
Student can't translate simple fractions into percentage no matter how often this is taught.
Student is unable to interpret graphs.
Student cannot give the answer to a one-digit times one-digit multiplication question.
Student can't change the quatities given on a mixture container.
Student can't do work problems accurately
Student has difficulty with metric measurement
Student doesn't include all the important infromation required in factual writing.
Review of Session and Wrap-Up
The Math Student with a Learning Disability
The following material has been inspired or borrowed, with permission from Learning Disabilities Association of Canada - Bringing Literacy within Reach: Identifying and Teaching Adults with Learning Disabilities -1991 (BLR)
The student's perspective
The following questions might help you get an idea of how the student feels about math: (BLR p. 69)
1. Can you carry out the math needed in your daily life?
2. What kinds of math tasks are difficult for you?
3. What do you do when you have difficulty with math?
4. What kinds of things do you use to help you? (e.g., calculator, writing down, "in- head" strategies such as counting or finger counting)
5. Do you have difficulty remembering math facts (e.g., the multiplication or times tables)?
The Challenges Facing Students Learning Math
Math subskills which are likely to provide barriers to some learning disabled students are listed below. The sequence is presented roughly from "input" to "understanding/reasoning" to "output." (BLR p. 70)
Letter/word/sign recognition and identification
The student must be able to recognize and identify signs for mathematical procedures in both "sign" and written forms. This skill is somewhat dependent on adequate visual-spatial and language skills.
Activity: Participants provide a list of the most common signs.
There is a special vocabulary in mathematics. The student must appreciate the meaning of signs, such as "+" and "-." He must know, for example, that "plus" is the opposite of "minus." This ability is part linguistic and part concept-formation.
Activity: Participants list other relationships among signs (i.e. multiplication and division)
Comprehension of correct rules and procedures
The student must be able to identify the rules and procedures that are necessary for the solving of particular problems. For example, "+" calls for plus rules and procedures to be used, while "X" calls for multiplication rules and procedures to be used. This comprehension involves concept-formation and problem-solving skills, as well as memory.
Memory for rules and procedures
The student must be able to remember the rules and procedures for addition, subtraction, multiplication and division. He must also have memory for content, such as for the multiplication tables.
Application of the procedures Some procedures need to be done in a particular order. e.g.,
2 (8+1) - 3: 8 + I = 9, then 2 x 9 = 18, then 18 -3 = 15
The application of procedures is largely a question of understanding, problem-solving and the capacity to benefit from feedback.
Activity: Participants give an example of other order-driven procedures.
Graphic and oral representation of answers
Handwriting, word-processing, or some other form of graphic output is usually needed in order to express an answer. This ability relies on visual-spatial organizational skills.
The way in which a student organizes written calculations is an important consideration, affecting both the communication of answers and the actual computations themselves.
Sometimes, the output requirement is to express an answer orally. This ability is dependent upon adequate linguistic skills.
Example: Jan left home at 7 AM. She drove by McBoo's to grab a cup of coffee on her way to work. That took 10 minutes. She then stopped by the Post Office to drop an important letter in mailbox, which took another 7 minutes. She then drove to work, arriving there 8 minutes after she left the Post Office. What time did she get to work? Explain your reasoning for solving the problem orally and express the answer in a complete written sentence.
Most everyday requirements for mathematical literacy require that output be fairly rapid (e.g., when making change). Calculation speed is largely a function of ease of problem-solving and, under some circumstances, level of development of visual-spatial organizational skills.
Everyday Numeracy and Calculation Activities
The following are some examples of everyday activities that require people to work with numbers and carry out calculations. An instructor may wish to draw on this list when developing testing and teaching activities in numeracy and calculation.
- calculations relating to business transactions
- calculations necessary for reading a bus or train schedule
- procedures for computing sales tax and dealing with other percentages, such as those involved in income tax
- reading simple graphs, such as those describing interest rates
- map reading and the calculation of distances on maps
Activity (10 minutes): Five groups- each group develops an example of each ( Examples will be used later to teach using LD-appropriate instruction)
To assess the student's ability to perform in the above areas, BLR (p.p.72-76) includes assessment questions and observation checklists to help the instructor develop a curriculum to address the gaps observed in the student's academic development.
Math and Learning Skills ( Refer to list and details skills in BLR (p.p.147 - 162)
Math-related skills required for the adult learner to function independently in most environments are grouped around predictable topics:
- Use of Calculators
- Time Calculations
- Graphs and pictorial Representations
- Spatial Concepts
- Ratios and Proportions
The learning disabilities related to acquitting the math skills listed are grouped around topics that can represent difficulties for most students in one form or another:
- Visual and Auditory Memory
- Visual-Spatial Skills
- Auditory Processing
Optional Practice Session with Math Items (40 - 45 minutes)
- Participants clarify any items among the definitions, instructional planning, and characteristics of good teaching that is not clear.
- Participants get into sub-groups. Each group will have ten minutes to develop simple teaching plan for a math item and ten minutes to teach it to the rest of the group.
- Group 1 - Develop and teach a simple math skill demonstrating the Direct Instruction (B- above)
- Group 2 - Develop and teach a simple math skill demonstrating the SMARTER (C - above)
- Group 3 - Teach a simple math skill demonstrating the first four characteristics of LD-Appropriate Instruction (D - above)
- Group 4- Teach a simple math skill demonstrating the last four characteristics of LD-Appropriate Instruction (D - Above)
http://www.std.com/anpn/index.html - ANN Numeracy Standards for Adults