
06271459
j
2014c.00464
Flores, Alfinio
Braker, Jaclyn
Developing the art of seeing the easy when solving problems.
Math. Enthus. 10, No. 12, 365378 (2013).
2013
Information Age Publishing (IAP), Charlotte, NC; University of Montana, Department of Mathematical Sciences, Missoula, MT
EN
D59
G30
G40
I30
problem solving strategies
preservice teacher education
teaching
learning to see the easy
alternative approaches
alternative solutions
mathematical model building
geometry
arithmetic series
proportion
area
circles
trapezoids
thinking back about problem solving experiences
http://www.math.umt.edu/tmme/vol10no1and2/14FloresBraker_pp365_378.pdf
From the introduction: In this article we will focus on learning the art of seeing the easy, by using an example of a problem posed to future secondary mathematics teachers. De Finetti indicates that it is often difficult to see the easy things, that is, to be able to distinguish, in the complexity of circumstances present in a problem, those that are enough to formulate the problem or that allow one to do the formulation as several successive steps that can be carried out easily. The problem presented below was posed as part of a modeling course. According to Lesh and Doerr, we need to put ``students in situations where they are able to reveal, test, and revise/refine/reject alternative ways of thinking.'' We will first present the strategy used by a group of future teachers, and then an approach gained by looking back at the problem and trying to see it at a glance. We finish with a brief discussion of why it would be worthwhile for prospective teachers to look back at this and other problems.