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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. Strategic Understanding.

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strategic problem solving for increasing student performance in mathematics

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

strategic understanding
Strategic Understanding

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

strategic expectation
Strategic Expectation

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

teaching mathematics through problem solving
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
teaching mathematics through problem solving5
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”
slide6

Written Symbols

Pictures

Manipulative Models

Oral Language

Real World Situations

Multiple Representations

slide8

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?

slide9

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?

slide10

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?)

slide11

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
slide12

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)

slide13

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

problem solving
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

slide15

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)

slide16

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?

grade 6 taks
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

slide35

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?

slide36

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?

slide37

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?

slide38

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?

classroom considerations
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.
it s your turn
It’s Your Turn!
  • Work one of the problems on the TAKS Quiz using the Problem Solving Board to answer each question.
problem solving49
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

where do i find handouts

www.sghedc.com

Where do I find handouts?

  • Scroll down to 2009 presentations
  • Download RGVCTM handout
  • Download Problem Solving handout