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MATH IN THE MIDDLE MICHAEL A. COBELENS. Problem Solving. Identify Learning Experiences Purpose: Methods of Teaching Problem Solving and Computational Skills Addition, Subtraction, Multiplication, Division. Problem of Practice. Students do not use computational skills consistently. - PowerPoint PPT Presentation
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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
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