Math Problem-Solving
Why emphasize problem-solving in mathematics? We have so much to teach.
Problem-solving strategies from mathematics can be applied to other areas, such as writing.
C. Patrick Collier, Professor of Mathematics at the University of Wisconsin at Oshkosh remarked in a May 98 graduation speech at University of Wisconsin, Oshkosh,
"Being stuck is a natural consequence of accepting a problem. Expert problem solvers are stuck far more often than not. I came to realize that being stuck is not a sign of stupidity, but staying stuck while not trying to do anything about becoming unstuck is a sign of weakness. I learned that problem solving is the art of knowing what to do when you do not know what to do, and that doing something to get unstuck is far better than complaining about being stuck...I really learned to see the honor in being stuck by teaching mathematics."
Whether reading, writing, or solving math problems, being able to have strategies available to use is key to successful solutions. And the strategies we need to teach and practice in math can be applied to other disciplines to get "unstuck." Take writing as an example:
Look at the process of writing a poem, as in the example at: Writing Process Example
Math Strategy
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Writing Strategy
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Guess and check or
Guess and Improve
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Use a checklist and randomly list topics/ideas (web/cluster)
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Create an organized list or table
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List ideas and elaborate on each; create a table of categories and list related details under each category (key words, meetings, etc.)
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Make a model or drawing
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Visual people use art and sketches and color to illuminate ideas; webs/clusters; Venn Diagrams
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Find a pattern
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Poem, essay, story (graphic organizers for each)
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Act it out
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Movement, skits, replay events as mind movies
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Work backwards
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Refresh memory by working backwards through the topic; what caused what (cause/effect)
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Break it down into parts
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What part is most vivid? What does it relate to? Look at assignment; break into parts and begin with one part; checklists
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Make a simpler case
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Start with key ideas before elaborating
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Eliminate possibilities
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What doesn't work? What ideas are not relevant or connected to you or the topic?
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Write an equation
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For me to solve our poetry creation, my equations were:
a feeling is congruent to an object = metaphor
metaphor = (me as part of the synergy (no ONE is in charge) of collaboration) + (the results of collaboration, the details of the year)
Therefore: the leaves of the apple tree synergistically collaborates, shares, shines, learns from all the other leaves of expertise.
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Make a graph
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Graph our summaries: assessment, targets, instruction and the number of sharing/queries for each
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Use logical reasoning
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Analyze the most important sharing
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So, what I have learned through mathematics applies to reading and, in this case, writing. All areas are important; targets, assessment, and instruction are interconnected among the disciplines.
Heuristics is the process of solving problems: "I learned that problem solving is the art of knowing what to do when you do not know what do do" --and that the strategy used may not always result in success. We do learn and improve our successes from these processes.
We must offer our students access to the thought processes that generate options to solving problems in any area; mathematics has offered us a common language for solving problems. Let's use it.
Thoughts by Sheri Edwards
1C. Patrick Collier (1999). "Much of What I Needed to Know I Learned by Teaching Mathematics." Mathematics Teaching in the Middle School, Volume 4, Number 8, May 1999.
See: Hitchhikers Guide to The Galaxy by Douglas Adams
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