PROBLEM-SOLVING

Review  What is the difference between a diagnosis and remediation and a correction?

Review  What are the general correction procedures?

Review  What are the steps in diagnosis and remediation?

Review  Example Selection—What are general principles?

Math Problem-Solving  Students with learning disabilities (LD), have difficulty solving math word problems  Most textbooks are not very helpful when it comes to teaching students how to solve math problems.  (a) read the problem, (b) decide what to do, (c) compute, and (d) check your answer.  Guess, check, & revise  Draw a picture  Act it out or use objects  Look for a pattern  Work backward

Math Problem Solving  Many students with LD do not easily acquire the skills and strategies needed to “read the problem” and “decide what to do” to solve it.  Need explicit instruction in mathematical problem solving skills and strategies to solve problems in their math textbooks and in their daily lives.

Math Problem-Solving  Mathematical problem solving is a complex cognitive activity involving a number of processes and strategies.  Problem solving has two stages:  problem representation and  problem execution.

Generic Problem Solving strategy  Read the problem for understanding.  Paraphrase the problem by putting it into their own words.  Visualizing or drawing a picture or diagram  Hypothesize  Estimate or predict the answer  Compute.  Check

Explicit Problem Solving strategies  Addition and Subtraction  Introducing the Concept  Number-Family Strategy  Temporal Sequence, Comparison, & Classification  Using Tables  Multiplication and Division  Multistep Word Problems

Addition and Subtraction Introducing the Concept  What are the preskills needed for problem solving?  What vocabulary should one teach in advance?

Addition and Subtraction Introducing the Concept  Format 11.1  Part A—demonstrating with semi-concrete objects  Part B—structured worksheet—students read, draw pictures, read again, and write the symbols.  What are the example selection guidelines?

a. Jim has six marbles. He finds two more marbles. He ends with how many marbles? b. Jim has six marbles. He gives away two marbles. He ends with how many marbles? marbles

Addition and Subtraction Number-Family Strategy  What is the number family?  How is it illustrated?  If only 2 numbers are given, how do students determine the missing number: 7  137 6

Addition and Subtraction Number-Family Strategy  Format 11.2  Part A—Introduces rule for subtraction, When the total number is given, we subtract.  Part B—Introduces the rule for addition, When the total number is not given, we add.  Part C—Structured worksheet—examples?  Part D—Less structured worksheet—what does the teacher ask?

Addition and Subtraction Problem Types  What are the three addition/subtraction problem types?

Addition and Subtraction Temporal Sequence Problems  What are these problems?  Strategy page 208: 1. Determine if the person starts or ends with more. 2. Label number-family line with starts or ends. 3. Fill in numbers. 4. Determine if add or subtract and find the unknown.  Format ll.3 Part C

Addition and Subtraction Temporal Sequence Problems What are the example selection guidelines?

Addition and Subtraction Comparison Problems  What are these problems? Note: the larger quantity compared is the total, the smaller quantity and the difference are parts of the total.

Addition and Subtraction Comparison Problems Strategy: 1. Read and determine the total number (larger quantity). 2. Fill in the diagram with the label for the total number 3. Fill in the known numbers 4. Determine whether to add or subtract

Addition and Subtraction Comparison Problems  Model Format 11.4, Structured Worksheet  What are the example selection guidelines?

Addition and Subtraction CLASSIFICATION Problems  What are these problems?  What preskills are necessary?

Addition and Subtraction CLASSIFICATION Problems  Strategy: 1. Read the problem and underline the classes. 2. Write the biggest class over the total number place. 3. Write the numbers for the smaller classes. 4. Determine whether to add or subtract and solve the problem.

Addition and Subtraction CLASSIFICATION Problems  Model Format 11.5, Structured Worksheet  What are the example selection guidelines?

Using Tables to Solve Classification Problems  Use tables for problems which present more data.  Uses fact family strategy  Requires teaching students how to use tables;  then integrating fact family knowledge with use of tables.

Integrated Review  What are the guidelines for integrated review for the Addition/Subtraction problems?

Multiplication and Division Problems  These problems address equal sized groups.  Words indicating equal sized groups: each, every, per, or in a box.  The word following each refers to a small number— for example: There were 5 retrievers in each pack. There were 3 packs. How many dogs in all?

Multiplication and Division Problems  If the problem gives the number of groups and the number in each group, multiply.  If the problem gives the total and asks either how many groups or how many in each group, divide.

Multiplication and Division Problems  Model Format 11.8, Structure Worksheet

Multi-step Problems  Made more difficult by  The number of quantities  The number of different operations  The order in which the information is given  Easiest type involves adding three numbers  First complex type involves two operations (addition/subtraction)  More complex are those that have students add or subtract and then multiply and divide.

Distractors  What are they?

Diagnosis and Remediation  Describe the 5 types of error patterns and general remediation for word problems. 1. Fact error 2. Computation error 3. Decoding error 4. Vocabulary error 5. Translation error

Other types of word problems  Ill-structured  Don’t fit a single strategy  Require Generic problem solving strategies Deep conceptual knowledge Fluent computational skills

Example  The Art Club is having a cookie sale. Each box of cookies costs $2.00. The first day Jennifer sold 6 boxes, Carlos sold 7, and Alex sold 3. How much did the Art Club make the first day of cookie sales?

Example  The 24 students in Mrs. Smith’s class formed a line. Every third student was wearing red. Every fifth student was wearing blue. What was the fifteenth student in line wearing?

Generic Problem Solving strategy  Read the problem for understanding.  Paraphrase the problem by putting it into their own words.  Visualizing or drawing a picture or diagram  Hypothesize  Estimate or predict the answer  Compute.  Check Montague, 2004

Think, Plan, Solve, Look Back

Read  Say: Read the problem. If I don’t understand, read it again.  Ask : Have I read and understood the problem?  CHECK : For understanding as I solve the problem.

Paraphrase  Say: Underline the important information. Put the problem in my own words.  Ask: Have I underlined the important information? What is the question?  What am I looking for?  CHECK: That the information goes with the question.

Visualize  Say: Make a drawing or a diagram. Use manipulatives to show the relationships among the problem parts.  Ask: Does the picture fit the problem? Did I show the relationships?  CHECK: The picture against the problem information.

Hypothesize  Say: Decide how many steps and operations are needed. Write the operation symbols (+, -, x, and /).  Ask: If I …, what will I get? If I …, then what do I need to do next? How many steps are needed?  CHECK: That the plan makes sense.

Estimate  Say: Round the numbers, do the problem in my head, and write the estimate.  Ask : Did I round up and down? Did I write the estimate?  CHECK : That I used the important information.

Compute  Say: Do the operations in the right order.  Ask : How does my answer compare with my estimate? Does my answer make sense? Are the decimals or money signs in the right places?  CHECK: That all the operations were done in the right order.

Check  Say: Check the plan to make sure it is right. Check the computation.  Ask: Have I checked every step? Have I checked the computation? Is my answer right?  CHECK: That everything is right. If not, go back. Ask for help if I need it.

Instructional Approaches  Sequence and segment  Repetition and practice  Directed questioning  Both process and content  Controlled difficulty  Strategy cues  Verbal Rehearsal  Process modeling/thinking aloud  Peer Coaching

Application Items for next week  Chapter 12, #11  Chapter 13, #1  Chapter 14, #4