Forum Outposts

The Geometry Forum Newsletter

Spring 1995, page 3

Research in Math Education, Problem of the Week

• From grade school through college I badgered teachers with the question, "Why?" Why do we carry? Why do we use the quadratic formula to solve the quadratic equation? Where do our methods come from? Sadly, I never received an answer. My teachers sometimes implied, sometimes directly stated that they couldn't explain or did not know. I became convinced that math was a subject in which there was no reason why. -- Hannah Freedberg, Swarthmore College

• ... it may be that the not 'brighter' students (whatever that means) have grasped the principle but are unable to verbalize it using symbols. They may be blocked by the symbol-ridden language they are taught to use when speaking about math... It seems to me to make more sense to have students understand concepts in their own language and through the use of their real world knowledge before assigning numbers and symbols to their understanding. -- Emily Smith, Friends Select, Philadelphia

• The problem is with creating a symbol system which exceeds the needs of the students. Learning to use the symbol system can quickly overwhelm the making of mathematical meaning. Symbol systems should be an embodiment of the understanding that students have, at a time that it is useful to them as a 'short-cut' way of expressing something. To the degree to which the formalization outstrips the students' construction of mathematical meaning, the emphasis will shift to manipulating the symbols. -- W. Gary Martin, University of Hawaii

• One way to control the rush to symbols and shortcuts in math class is to let the students take the initiative, i.e., wait for them to ask "Is there an abbreviation for this?" or "Is there a faster way to do this?" If you are not lecturing, you can provide answers to the students seeking them and let the others catch up, or just do it the 'slow' way. -- Robert W. Hayden, Plymouth State College

• I also like to ask the students if they have any ideas about making it easier to say what they want in response to "Is there an abbreviation for this?" or "Is there a faster way to do this?" This is in the tradition of student-generated symbols and algorithms, but introduces new complications about whether this gets in the way of their learning the 'right' way, or if it will be confusing for them to make the transition to future classrooms and the rest of the world. -- Peter M. Appelbaum, William Paterson College

POW Feb. 27 - March 3:
How many ways can you construct an isosceles triangle?

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