Slope … Fast?

Well, I’ve been somewhat discouraged by the latest test in our ‘math – applications for living’ course.  This test is all about understanding linear (additive) and exponential (multiplicative) change.  In spite of approaching these models in different ways, followed up by repeated work, students had considerable difficulty translating verbal descriptions to anything quantitative or symbolic.

One basic problem seems to be that students did not start with much understanding of slope for linear functions.  Every student in the class had completed beginning algebra (usually recently), where we do the usual work with slope — calculating it, using slope to graph, and finding the equation of a line given information about slope.  When faced with non-standard problems with information on slope, the transition to quantitative or symbolic statements was not easy.

One part of this difficulty is the connection between input  & output units and units in slope.  Like most traditional algebra books, ours does not make an issue out of units for slope in ‘applications’; as you know, slope must involve two units.  Because of this difficulty, students would see a percent change as a linear change.

Mostly, this post is a “note to self”:  Learning slope is not really a fast thing.  Repeated use, alternate wordings, and non-standard problems need to be used to build a more complete understanding.  We too often spend a week or two on all linear function topics in a beginning algebra course; to get that ‘sufficiently good’ understanding, we need to allow more time so we can really dig in to what slope and the linear form are doing.

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