1. Dr. Robinson, EEX 4251, Spring 2008 Enhancing Problem Solving Abilities

2. Definition Problem-solving is a process that involves applying previous knowledge, skills, and strategies to novel problems Problem-solving is a process that involves applying previous knowledge, skills, and strategies to novel problems

3. Characteristics of Problem-Solving Instruction Focuses on the application and/or generalization of math skills to real-world tasks. Focuses on the application and/or generalization of math skills to real-world tasks. Requires new ways of thinking and deep levels of understanding Requires new ways of thinking and deep levels of understanding Involves use of word problems, technological tools and functional applications to develop realistic contexts for using mathematics. Involves use of word problems, technological tools and functional applications to develop realistic contexts for using mathematics. More challenging than computational skills. More challenging than computational skills.

4. Rationale for Enhancing Problem-Solving Abilities Increased emphasis on problem-solving and reasoning per national NCTM standards Increased emphasis on problem-solving and reasoning per national NCTM standards Used extensively in Used extensively in –the workplace –daily living –leisure activities

5. Real-World Problem Solving Examples Work Place Work Place –Determining pay –Figuring out over-time –Handling money Daily Living Daily Living –Balancing checkbook –Measuring recipe quantities –Telling Time Leisure Activities Leisure Activities –Playing board games –Determining gas mileage –Keeping score in sports

6. Students with disabilities have more difficulty with problem-solving than their peers without disabilities. Students with disabilities have more difficulty with problem-solving than their peers without disabilities. Students with disabilities have particular word problem difficulties Students with disabilities have particular word problem difficulties –Identifying relevant information –Reading the problems –Identifying appropriate operations –Performing the computation –Translating words to equations –Performing high-level reasoning

7. Planning Guidelines Develop appropriate word problems Develop appropriate word problems -complex grammar  simple sentence structure initially  complex sentences as language skills advance  graduated word problem sequence - vocabulary and verbal cues (or, key words) -story problem structure  temporal sequence problems - start with quantity, and then action occurs that results with larger or smaller quantity  comparison problems - involve two quantities and the difference between them  classification problems - involve super ordinate (e.g., birds) and subordinate (e.g., canaries) classifications - multiple operations -extraneous information

8. Sentence Structures Simple Simple –Juan has 2 dogs. Barry has 3 dogs. How many dogs are there in all? Complex Complex –During the play, Joan ate 4 candy bars. During the same play, Billy ate 3 candy bars and Sue ate 5 candy bars. How many candy bars were eaten altogether?

9. Integrate Authentic Problem-Solving Experiences Integrate Authentic Problem-Solving Experiences –Anchored Instruction –Functional Application

10. Procedural Strategies Four to eight sequential steps that lead to problem solution. Four to eight sequential steps that lead to problem solution. Important components Important components –Reading the problem carefully –Thinking about the problem via self-questioning or drawing, visualizing, underlining, or circling –Determining the correct operation or solution strategy –Writing equations –Computing and checking the answer

11. Schema-Based Instruction Involves the use of schema diagrams to represent various types of word problems (Figures 6.1 and 6.2) Involves the use of schema diagrams to represent various types of word problems (Figures 6.1 and 6.2) Two primary components Two primary components –Identifying the problem schema & checking to be sure salient elements of selected schema are present –Writing critical information on the diagrams and solving the problem