MATH IN THE MIDDLEMICHAEL A. COBELENSMATH IN THE MIDDLEMICHAEL A. COBELENS

€

M2

2004

2006

∑

€

M2

2004

2006

∑

Problem SolvingProblem Solving

• Identify Learning Experiences

• Purpose: Methods of Teaching Problem Solving and Computational Skills

• Addition, Subtraction, Multiplication, Division

• Identify Learning Experiences

• Purpose: Methods of Teaching Problem Solving and Computational Skills

• Addition, Subtraction, Multiplication, Division

Problem of PracticeProblem of Practice

• Students do not use computational skills consistently.

• Students do not transfer skills to other situations.

• How can my teaching practices improve student performance?

• Students do not use computational skills consistently.

• Students do not transfer skills to other situations.

• How can my teaching practices improve student performance?

Literature ReviewLiterature Review

• Kendrick (2004): drill and practice very important in the retention of basic math skills

• Ashcroft (1981): multiple teaching methods reinforce learning, drill and skill enhance memory for retrieval

• Pajares and Graham (1999): self-efficacy• Ball (1999): Teacher Knowledge key to student

learning• Tims Tutor (2002): basic facts need to be

learned, important component in problem solving

• Kendrick (2004): drill and practice very important in the retention of basic math skills

• Ashcroft (1981): multiple teaching methods reinforce learning, drill and skill enhance memory for retrieval

• Pajares and Graham (1999): self-efficacy• Ball (1999): Teacher Knowledge key to student

learning• Tims Tutor (2002): basic facts need to be

learned, important component in problem solving

QuestionsQuestions

• What learning experiences help math processes become more concrete?

• What activities best help students learn math processes and where they apply?

• How do students determine which math process to use to solve a problem and whether they chose the correct method?

• What learning experiences help math processes become more concrete?

• What activities best help students learn math processes and where they apply?

• How do students determine which math process to use to solve a problem and whether they chose the correct method?

MethodMethod

• Student views on Problem Solving Survey• Student journals and reflections of

mathematics lessons• Daily personal journal of lessons and

observations• Student and Principal Interviews• Problem Solving Pre-test• Problem Solving Post-test

• Student views on Problem Solving Survey• Student journals and reflections of

mathematics lessons• Daily personal journal of lessons and

observations• Student and Principal Interviews• Problem Solving Pre-test• Problem Solving Post-test

Analysis of Student SurveyAnalysis of Student Survey

Feelings on Word Problems

30%

13%

9%

22%

26%

Don't Like This stinks I hate this Read to find info Neutral

Feelings on Word Problems

30%

13%

9%

22%

26%

Don't Like This stinks I hate this Read to find info Neutral

Survey AnswersRange from Strongly Agree to Strongly Disagree

Survey AnswersRange from Strongly Agree to Strongly Disagree

• I learn math concepts pretty easily 15/23 Agree

• There is only one way to get the right answer to a math problem 12/23 Strongly Disagree

• Knowing basic facts helps when solving problems 12/23 Strongly Agree

• I learn math concepts pretty easily 15/23 Agree

• There is only one way to get the right answer to a math problem 12/23 Strongly Disagree

• Knowing basic facts helps when solving problems 12/23 Strongly Agree

Student StrategiesStudent Strategies

Strategies for solving word problems

39%

26%

9%

22%

4%

Write down facts Identify key words Draw pictures Solve and check Rewrite

Strategies for solving word problems

39%

26%

9%

22%

4%

Write down facts Identify key words Draw pictures Solve and check Rewrite

Knowing if you are rightKnowing if you are right

How do you know you are right

70%

13%

17%

Check it Strong feeling I don't

How do you know you are right

70%

13%

17%

Check it Strong feeling I don't

What Helps?What Helps?

What helps you learn math

22%

39%

17%

22%

Practice

Listening andtalking Listening andpractice Visuals

What helps you learn math

22%

39%

17%

22%

Practice

Listening andtalking Listening andpractice Visuals

Needed SkillsNeeded Skills

Needed skills to solve word problems

66%

13%

17%

4%

Knowing basic facts

Ability to read

Logic

Patience

Needed skills to solve word problems

66%

13%

17%

4%

Knowing basic facts

Ability to read

Logic

Patience

Further AnalysisFurther Analysis

• Homework and in class activities promote learning

• 78% say, “Listening and talking along with practice.” “I see how to work problems out, step by step”“When we work together I get to see the answer, it’s easier than working alone.”“Learning is easier when I know how to add, subtract, divide, and multiply.”

• Homework and in class activities promote learning

• 78% say, “Listening and talking along with practice.” “I see how to work problems out, step by step”“When we work together I get to see the answer, it’s easier than working alone.”“Learning is easier when I know how to add, subtract, divide, and multiply.”

Personal Daily JournalPersonal Daily Journal

• Retention of mathematical processes and computation need continuous review.

• Multiple step problems are difficult with only 11% of students completing correctly on problem solving test.

• Most effective learning experiences include practice, application, and talking.

• Retention of mathematical processes and computation need continuous review.

• Multiple step problems are difficult with only 11% of students completing correctly on problem solving test.

• Most effective learning experiences include practice, application, and talking.

Pre and Post TestPre and Post Test

75

76

77

78

79

80

81

Percentages and variation

Mean Median

Pre-test and Post-test Results

Pre-test

Post-test

75

76

77

78

79

80

81

Percentages and variation

Mean Median

Pre-test and Post-test Results

Pre-test

Post-test

InterpretationInterpretation

• Problem solving is difficult

• Assessment at point of instruction does not promote retention

• Story problems are not always problem solving

• Students need challenge and opportunity to apply learned skills

• Problem solving is difficult

• Assessment at point of instruction does not promote retention

• Story problems are not always problem solving

• Students need challenge and opportunity to apply learned skills

Plan of ActionPlan of Action

• Mastery of basic facts while challenging students to problem solve.

• Students provide multiple solutions to problems and explain how they solved the problems.

• Habits of Mind type problems to promote deeper the thinking.

• Mastery of basic facts while challenging students to problem solve.

• Students provide multiple solutions to problems and explain how they solved the problems.

• Habits of Mind type problems to promote deeper the thinking.

PortfolioPortfolio

• Teacher knowledge of Mathematics impacts student learning

• Pedagogy empowers teacher as authority• Action Research suggests problem solving is a

process• Leadership implies intellectual leader within the

learning community• Finally I plan to implement MIM strategies and

Habits of Mind problems

• Teacher knowledge of Mathematics impacts student learning

• Pedagogy empowers teacher as authority• Action Research suggests problem solving is a

process• Leadership implies intellectual leader within the

learning community• Finally I plan to implement MIM strategies and

Habits of Mind problems