Do we make learning math harder than it needs to be?
One of the "feature" concepts in first year algebra is the "slope-intercept" form of a linear equation, y=mx+b, where m is the slope and b represents the y-intercept. It seems to me we traditionally present this in some of the most counter-intuitive ways imaginable.
First and most obviously, we represent two key values using letters that have no apparent association with those quantities. Jeff Miller has undertaken a detailed study of the origin of the symbol m to denote slope. The consensus seems to be that it is not known why the letter m was chosen.*
Neither, so far as I can tell, is there any sort of agreement as to why the y-intercept is identified using the letter b. These seemingly arbitrary choices can be confusing to students looking for connections.
Further, if you consider that in a "real world" context slope defines the rate at which a quantity changes over time and that the y-intercept is an initial baseline value for that quantity, why don’t we teach the "intercept-slope" form of linear equations as y=b+mx (conceding the m and b), where we start with the initial value b which then changes according to the values of x and m. Would students not find this to be more intuitive than the traditionally taught form where change is being applied to a yet to be established quantity?
Sometimes I think we're like medieval monks, reluctant to allow just anybody to share the "secret knowledge" we possess.
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*Weisstein, Eric W. "Slope." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Slope.html