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 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. 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 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

Questions 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?

Method 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 Survey

Survey Answers Range 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 Strategies

Knowing if you are right

What Helps?

Needed Skills

Further 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 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 Test

Interpretation 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 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.

Portfolio 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