On May 18, 2013, at 6:52 PM, Anna Roys <firstname.lastname@example.org> wrote:
> ANNA COMMENTS/QUESTION: Students use the table to answer the following question. (However, an alternate time and height data table could be built from experiential data where students were outdoors testing and collecting their own data for height and speed. How might this not be considered part of the math problem?)
There isn't much text supplied with the problem you quoted but the intent appears to be a lesson regarding the technical nuances/differences between "speed" and "velocity" as well as the meaning and application of "units". Speed is a magnitude (a number) while velocity involves both a magnitude and a direction (the sign in this case). The units in this example involve distance, time and a rate of change (distance versus time).
Speed, velocity, distance, time, sign, direction, magnitude, absolute value, rate of change and of course, number. All abstract (and generic) concepts that weave our mental senses and our reasoning together in 100's if not 1000's of use cases.
While doing the actual experiment (measuring parachute velocity) might have merit for other reasons, such as engagement for example, it does not address the "math problem". The "math problem" involves those abstract concepts listed above and their application to the context and data. Even if you did the actual experiment, you would still be at square one with the "math problem". A somewhat similar separation occurs in reading. In one section we focus on the abstract notions of linguistics like grammar, spelling, punctuation and morphology and at other times we focus less on the linguistics and more on the whole. When we are focused on the linguistics the examples are generic and uninteresting so as not to become distractions. We do not read books to study linguistics (other than maybe a book on linguistics). This where "whole language" fell short.
I realize that many students do not thrive in an environment like mathematics where the "stride" comes when one example of a mathematical situation after another is presented and the student is able to distill the "math" through exposure and discussion. But that is eventually both the essence of teaching mathematics and being successful at mathematics (or anything else for that matter). I think their problem is with thinking itself. Many unfortunately do not seem to understand the (mental) point. They don't recognize these insightful revelations for what they are, whether during traditional exposition or hands on activities. I would like to see more attention to that.