Strategic Problem Solving for Increasing Student Performance in Mathematics

1. Strategic Problem Solving for Increasing Student Performance in Mathematics Rio Grande Valley Council of Teachers of Mathematics November 21, 2009 Sheila Hoza Cunningham, EdD drsgh@att.net www.sghedc.com

2. Strategic Understanding . . . quality student achievement includes and goes beyond achieving the highest rating awarded by state and national accountability standards.

3. Strategic Expectation We will raise the performance of all students and close the achievement gap.

4. Teaching Mathematics Through Problem Solving Instruction with a focus on problem solving… • focuses students’ attention on ideas and sense making • develops the belief in students that they are capable of doing mathematics and that mathematics makes sense • provides ongoing assessment data

5. Teaching Mathematics Through Problem Solving Instruction with a focus on problem solving… • is an excellent method for attending to a wide variety of student abilities • engages students …fewer discipline problems • develops “mathematical power” • is a lot of “fun”

6. Written Symbols Pictures Manipulative Models Oral Language Real World Situations Multiple Representations

7. Problem Solving Board

8. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable?

9. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable? What is the question asking me to do?

10. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable? What data do I have? (What data is not necessary and/or What data do I need?)

11. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable? • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards

12. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable? Plan/Work (use the back if more room is necessary)

13. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable? Picture/Diagram/Table/Rule/Graph/ Thinking Map

14. Problem Solving “the most helpful strategy that students can use to help them understand how to solve a problem is the use of drawing pictures to represent the quantities and their relationships” Dr. Randy Charles, 2007

15. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable? Final Answer (use a complete sentence)

16. 8.1B What is the question asking me to do? What data do I have? (What data is not necessary and/or What data do I need?) • Strategies • Draw a Picture or Diagram • Look for a Pattern • Guess and Check (Estimate) • Act it Out (Using Manipulatives) • Simplify the Problem • Eliminate Possibilities • Make a Table/List • Work Backwards Plan/Work (use the back if more room is necessary) Picture/Diagram/Table/Rule/Graph/ Thinking Map Final Answer (use a complete sentence) Check your answer. Is it reasonable? Check your answer. Is it reasonable?

17. What About English Language Learners?

19. Problem SolvingandTAKS

26. Grade 6 TAKS • Frank and Joe each bought a small pizza. The pictures below show how much of each pizza was left. What portion of the pizza did Frank and Joe eat together? Frank’s Pizza Joe’s Pizza

34. TEKS Connections

35. SE 3.3A The table at the right shows how far three students jumped. Write a number sentence that can be used to find how many inches farther Mai jumped than Peter jumped?

36. 3.7B Lars is doing his homework. He has finished 1 problem after 6 minutes, 2 problems after 12 minutes, and 3 problems after 18 minutes. If he keeps working at the same speed, how long will it take him to work 5 problems?

37. 4.3A There were 1,455,268 people living inWeston in 1990. In the year 2000 therewere 1,426,599 people. How manymore people were living in Weston in1990 than in 2000?

38. 4.6C Mr. and Mrs. Gómez ride bikes to exercise. The table shows The total number of miles they had ridden after different numbers of days. If the pattern continues, how many miles will Mr. and Mrs. Gómez have ridden after 28 days?

45. Classroom Considerations • Using this process allows for more depth and higher cognitive demand using a single problem. Students may complete fewer problems but will be working at a higher level of thinking.

46. It’s Your Turn! • Work one of the problems on the TAKS Quiz using the Problem Solving Board to answer each question.

48. Talk to Your NeighborHow can you use the PSB to improve student performance in mathematics?

49. Problem Solving “As teachers…we must teach skills and strategies together, instead of in isolation. The reality is that to solve a problem you need to use both a skill and a strategy, so keeping them separate has been more confusing than helpful to students’ success” Dr. Randy Charles, 2007

50. www.sghedc.com Where do I find handouts? • Scroll down to 2009 presentations • Download RGVCTM handout • Download Problem Solving handout