1. Characteristics of Students with Learning Disabilities and the Impact on Learning Mathematics.

2. Information Processing How sensory input is: Perceived Transformed Reduced Elaborated Stored Retrieved Used (Swanson, 1987)

3. Information Processing Weaknesses That Affect Math Visual deficits Auditory-processing difficulties Motor disabilities Memory deficiencies Attention deficits Expressive language difficulties Receptive language difficulties

4. Visual deficits Spatial perception Reversals Figure ground Visual discrimination

5. Auditory-processing difficulties Ability to analyze, interpret and process information obtained though the ear. It does not apply to what is received by the ear drum, or to deafness.

6. Motor disabilities Includes limited mobility or movement In most cases can be accommodated through assistive technology.

7. Memory deficiencies If the information is to be learned, it will either be transferred to and stored in long-term memory, or a strategy will be utilized to keep the information in short- term memory.

8. Attention deficits Abilities to focus on the material for extended time

9. Expressive Language difficulties Taking processed information from the brain, and expressing it to others so that they can assess knowledge Underdeveloped vocabulary

10. Receptive Language difficulties Inability to convert language input to usable data within the brain. Underdeveloped vocabulary

11. Cognition Cognition – understanding, knowing Cognition in Math may include: –Reading (Comprehension) –Paraphrasing (Translation) –Visualizing (Transformation) –Hypothesizing (Planning) –Estimating (Prediction) –Computing (Calculation) –Checking (Evaluating) (from Montague’s cognitive & metacognitive model of mathematical problem solving)

12. Metacognition Thinking about Thinking Also called self-regulation or executive control “The active control over learning-related behaviors, self-regulation of motivation and affect, and control over various cognitive strategies for learning, such as rehearsal and memory strategies” (Pintrich, 1994). Metacognition in Math may include: –Self-instructing –Self-questioning –Self-monitoring (from Montague’s cognitive & metacognitive model of mathematical problem solving)

13. Cognitive & Metacognitive Issues Students with cognitive and/or metacognitive barriers may have issues with: –Assessing their abilities to solve problems –Identifying and selecting appropriate strategies –Organizing information –Monitoring problem-solving processes –Evaluating problems for accuracy –Generalizing strategies to new situations

14. Maintaining Positive Attitudes Toward Learning Mathematics Attitude affects achievement Attitudes can be influenced by: –Curriculum design –Teacher behavior –Past experiences

15. Any questions? ?

16. Connect to Think Aloud How does Think Aloud address any of the barriers encountered in the “Clinking Glasses” problem? How could the problem be differentiated to address the different barriers students may encounter?