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The Problem With Problem Solving

By Jessica Smith
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"How do mathematicians communicate their ideas to each other and to the public? If math is just numbers and symbols, how can we talk about math?"
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Grade Level: 5

Curriculum Areas:
Focus: Mathematics
Secondary: Writing, Speaking , Technology

Topic:
Math problem solving strategies

Themes:
Communication, Teamwork

Duration:
20 weeks
Summary
A class of 20 fifth graders will participate in two trimesters of problem solving lessons as part of the math curriculum. A demonstration problem and strategy is presented each Monday. Students are assigned a similar problem using the same strategy that is due on Friday. In the demonstration problem, the teacher models problem solving dispositions as well as math skills. For full credit students must explain their entire process in a written paragraph that a fifth grader with equal math abilities could follow. Students will work in groups throughout the week to solve the assigned problem and write the paragraph explaining the process. Students will evaluate their approach using checklists and rubrics. Students and groups may be required to submit multiple drafts and revise their work until a solid understanding is demonstrated. All student work will be kept in a portfolio for the second phase. During the second trimester students will reflect on the work in their portfolio and each group will choose one strategy to publish in an iMovie. The iMovie will feature students demonstrating problem solving strategies. Students must storyboard and script their movie prior to filming. Students must also learn how to use the iMovie software to effectively communicate their message in a concise and technologically appropriate way. The audience will be other fifth grade students in the school or the district. The movie component and real-world audience provides motivation and gives a deeper purpose to the writing piece of the problem solving assignment. Routine conversations with the teacher will ensure that students are on track during movie production. Students will also have the opportunity to evaluate themselves on a group work rating scale. The finished product will be a collection of movies created for students and by students that demonstrates how to solve complex word problems. The goal is to eliminate the problem with problem solving, that is that math is only numbers and the right answer is all that matters. Students will uncover a deeper understanding of what it means to communicate mathematical ideas, itís a process that requires logic, organization, and collaboration. Sometimes numbers and computation are only needed in the final step.

Rationale
Students often view math as a black and white subject area. For instance, if they have a number 7 written down for the answer to problem 20, and the answer happens to be 7, then they are right. If they donít have 7 written down, they are wrong. There is nothing in between. Thereís very little consideration for process. In computation itís manifested through showing work. Fifth grade math curriculum is particularly challenging in this area because there is significant time spent on computation with decimals, fractions, and constant review of math facts. Students always ask, ďdo we have to show our work?Ē Teachers and mathematicians view this question as almost ludicrous. The answer or solution to a math problem is typically just a number, and in isolation that number is meaningless. Students must realize that math is about communicating ideas. There is a process that involves words and symbols and sometimes the process ends up somewhere between right and wrong. A result in this gray area simply means there is more work to be done. If the work is thoroughly documented, then more people can participate in the discussion and understand the thinking that went into the process. Shifting the math focus from an outcome orientation to a process orientation can help students to uncover the true purpose of mathematical thinking.