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Improving Mathematics Problem Solving Through Written Explanations Report on action research project by Janet Schlattmann

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My Background o Alliance Middle School o 7 th grade math 8 th grade algebra 23 years teaching-17 in Alliance Grades 7-8 currently Grades 7-12 in the past 100 students in 7 th grade 12 students in SWS and 14 in regular 7 th grade class in my study

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Problem of Practice Low problem solving scores on Terra Nova No confidence in problem solving Difficulty explaining answers or thinking NCLB requirement District’s math goal NCTM process standards of communication, reasoning, and problem solving

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Literature Review Kjos and Long, 1994 Millard, Oaks and Sanders, 2002 Ishi, 2002 Jurdack,1998 Pugalee, 2001 Research not found

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Purpose The purpose of this study is to determine the effects on low achieving students as well as other students of using written explanations and /or representations of thinking and reasoning in mathematical problem solving.

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Question and Methods 1. What is the effect of students expressing their thinking and reasoning through writing/representation in math problem solving on their ability to solve problems? Pretest and Post test of problem solving scored with a rubric on concepts and computation. Schools scores from District problem solving assessments (previous year and this year). Scores on problem solving assignments given during research time frame

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Question and Methods 2. How will student attitudes about themselves as problem solvers change when written communication is used? Attitude survey at beginning and end Observations kept as a journal Interviews

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Question and Methods 3. What is the effect on students’ ability to communicate their thinking when written communication is used? Pretest and post test scored with rubric on explanation and representation. Teacher observation and journal Scores of problem solving assignments scored with explanation and representation.

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Question and Methods 4. How will low achieving students’ problem solving growth compare to the scores of students in a regular class? Compare pretest and post test scores Compare scores of problem solving assessments Compare scores of problem solving assignments

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Analysis Mathematical Concepts

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Attitude 1. I am pretty good at math problem solving. 2. Writing about my thinking or my reasoning helps me to better understand the problems I am solving. 3. Writing my ideas and reasoning is easy for me. 4. I am improving at problem solving. 5. I understand more about problem solving than I am able to put down in writing.

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Attitude 6. The activities we are doing in class are helping me be more confident in problem solving. 7. Others would clearly be able to understand how I solve problems by reading my explanations and looking at my charts or models. 8. I am good at writing. 9. I like mathematics.

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Attitude 1. I am pretty good at math problem solving. 2. Writing about my thinking or my reasoning helps me to better understand the problems I am solving. 3. Writing my ideas and reasoning is easy for me. 4. I am improving at problem solving. 5. I understand more about problem solving than I am able to put down in writing.

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Attitude 6. The activities we are doing in class are helping me be more confident in problem solving. 7. Others would clearly be able to understand how I solve problems by reading my explanations and looking at my charts or models. 8. I am good at writing. 9. I like mathematics.

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Attitudes Interviews Did writing in problem solving help them? Did they like it? What helped them to be better problem solvers? Have feelings about problem solving changed?

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Attitudes Observations Negative behaviors Attempting problems Confidence and reliance on self instead of the teacher

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Explanation/Representation

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Observations Difficulty in expressing thoughts in writing Writing as they solved Writing for others to understand Variety of solutions More detail and depth of thinking

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Comparison

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Comparisons

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Interpretation Written expression slight improvement SWS improvement in problem solving over time Improvement in willingness to try Student differences on what helped them improve Writing explanations helped students think through steps Writing and problem solving takes time Writing helped me see the misconceptions students had about their mathematics and perceptions about problems

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Connections to Previous Research Jurdak, 1998 –positive effects of expository writing Pugalee,2001-metacognitive development through explaining actions Low achievers and problem solving not addressed in any research I found

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Implications For me Have students continue writing explanations in problem solving Start at the beginning of the year Incorporate more strategies to know how to express thinking Have students share solutions and explanations Continue collection of data to study effects of written expression

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Implications For others NCTM-process standards of communication, reasoning, problem solving Struggling students can show growth Attitudes not always positive when work is more difficult Writing can improve student growth in expression, problem solving and willingness to try

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Implications Further research More research is needed as there is little research on this topic More students need to be studied Study needs to be over a longer period of time Research is needed to study low achievers to find improvement in problem solving and reasoning

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All math staff will experience a problem solving session that entails using “Habits of Mind” problem, solving the problem, presenting solutions to the group and brainstorming modifications and uses for particular grade levels and classrooms. We will meet a minimum of once a quarter. We will display our solutions in our rooms or hallways to see what the different grades have come up with for solutions. We may collect data to measure growth if we can decide what the group wants to collect and how to assess it. School Plan

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Problem solve with written explanations once a week if possible. Teach writing strategies to help students get thoughts on paper. Teach more reading of problems Use “Habits of Mind” problems with my students and have them display and discuss solutions and explanations. Individual Plan

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