For my Math 25 class I am trying to put together just what is in my metaphorical "toolbox" of math skills I use when thinking about how to approach real-life math problems.
I'm keeping track of this here.
I need to develop some lessons about this concept for the first week or two of Math 25 in future terms. One issue I have not fully processed is whose toolbox to teach about. I'm sure that my toolbox would look different than an A-level Math 25 student, and both would look different from a C-level Math 25 student. Do I try to teach "tools" at the most useful and advanced development of each concept, or the "tools" as they less useful but make more immediate sense to more students?
(For example, in my mind finding the percent of a whole number and the percent of another percent is one concept. But to most C-level Math 25 students these are two very distinct algorithms, since one involves changing every percent to decimal format and the other does not. As another example, when finding the percent change between two numbers is the final step "multiply by 100" or is that not a distinct step and merely part of how to see the decimal result of the earlier division?)
