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This point is an interesting crux of disagreement about methods, not just nitpicky. Technically, slope is the rate of change of the tangent to a function, and t

by gbhn 14y ago

This point is an interesting crux of disagreement about methods, not just nitpicky. Technically, slope is the rate of change of the tangent to a function, and the disagreement is about how to communicate that to students. Approach 1, Mathalicious: "Unless you give students the right information from the first, even if it is a bit more abstract, they won't be prepared later on." Approach 2, Kahn: "The best way to prepare students is to keep things simple. Later you can give them refinements about tangents and derivatives and such." This is an interesting point, and I'd be pretty surprised if there isn't already a wealth of knowledge surrounding it in educational research. (Neither Kahn nor Ani appeals to such research in the articles.)

rm999 14y ago
I think this debate does sadly just come down to semantics, and I tend to side with Kahn on that merit. Once I got past a certain point in my math education (first half of intro of calculus 1) "slope" wasn't used anymore. We moved to derivatives and gradients. In my education we've always used slope as a purposefully simple/geometric term for 1 dimensional lines plotted in two dimensional x-y planes.
- R_Edward 14y ago
  Agreed, "slope" is a rather useless concept beyond algebra. When you're plotting, say, a position function, the slope of the function at any given point is of limited meaningfulness--the velocity, on the other hand, much more so! Likewise, the slope of the velocity curve at any given point is of little import, but the acceleration is very meaningful. Of course, the slope of the position curve is the velocity; what I'm suggesting is that referring to it as slope detracts from understanding, while referring to it as velocity enhances understanding. Consequently, getting all wrapped around the axle over the canonical definition of slope is a shining example of majoring in the minors.

by gbhn 14y ago

rm999 14y ago

I think this debate does sadly just come down to semantics, and I tend to side with Kahn on that merit. Once I got past a certain point in my math education (first half of intro of calculus 1) "slope" wasn't used anymore. We moved to derivatives and gradients. In my education we've always used slope as a purposefully simple/geometric term for 1 dimensional lines plotted in two dimensional x-y planes.

R_Edward 14y ago
Agreed, "slope" is a rather useless concept beyond algebra. When you're plotting, say, a position function, the slope of the function at any given point is of limited meaningfulness--the velocity, on the other hand, much more so! Likewise, the slope of the velocity curve at any given point is of little import, but the acceleration is very meaningful. Of course, the slope of the position curve is the velocity; what I'm suggesting is that referring to it as slope detracts from understanding, while referring to it as velocity enhances understanding. Consequently, getting all wrapped around the axle over the canonical definition of slope is a shining example of majoring in the minors.