Teaching math requires actually understanding math, and people who understand math have always been in short supply, in and outside of the teaching profession. So a different, simpler explanation for the failure of students to learn math is that there aren’t a lot of excellent teachers out there teaching math. Technology doesn’t enter into the picture.
Where it does enter the pictures is in a new and completely unexpected change in mathematics education. Excellent teachers who use technology can increase access to higher mathematics for students with poor computational skills, by allowing these students to reason about concepts without getting bogged down in computation. This year, my AB Calculus class included some students who couldn’t reliably add fractions. By the end of the course, almost all of them could explain what the derivative of a function means (in abstract and contextual terms), how it is calculated, and what it could be used for. They could do all this because they used calculators with computer algebra systems—calculators that give algebraic answers, not just numbers—to do the heavy lifting.
Finally, Kakaes never engages what is, to me, the central question that technology poses to the mathematics teacher, namely, what of the traditional pencil-and-paper mathematics is worth teaching?
“The argument should be about when and how often students should be taught to use their calculators,” Karafiol writes.
Kakaes responds here.