Wednesday, October 21, 2009

Math Intuition

In the classroom where I am placed at Chief Sealth, I am noticing that many students do not have good mathematical intuition or do not tap into it to help them solve problems. Frequently I find students stuck on problems that are conceptually quite simple because they “don’t remember how to do this [type of problem].” Today, students were having trouble converting from inches to centimeters. Some were stuck because they didn’t know how to set up the proportion (which is just one way of solving this problem) or how to solve for the unknown variable once the proportion was set up (many don't seem to understand what cross-multiplying is or why it works) or if they should multiply or divide by 2.54 (the conversion factor). Students did not seem to exhibit an awareness that there were multiple ways to solve this problem and that they can use a different approach if one doesn’t work for them, or that they could use reasoning to help answer their own questions. (For example, a student could reason: A centimeter is smaller than an inch, so a measurement in inches is going to be a smaller number than the measurement in centimeters. So to convert 20 centimeters to inches I would have to divide by 2.54 instead of multiply.) When I approach a situation like the ones I'm describing above at SGS, I'm used to either 1) asking other students in the group to explain how they did it and why, 2) asking students to explain their reasoning and poking at the parts that don't make sense until a student understands the problem for themselves, or 3) trying a simpler problem with a student to unveil the concept that is at work so that the student can arrive at a solution themselves. At Chief Sealth, I feel like these same techniques are not as useful. Students seem frustrated that I don't go right to "Here's how you do it..." or confused when I begin to throw different problems and solutions at them. So right now I'm wondering about the best ways to help students at Chief Sealth tap into their own intuition so that they can become more flexible problem solvers...

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