Ben asks,
Why did I spend four years in high school, and then several more in college learning math that I’ve long since forgotten?
Think back on your high school and college courses. If you were to take the final exam today, how would you do? What does that tell us?
What should it tell us?
I
responded:
Great questions, Ben. As a former high school math teacher, I’ve thought along the same lines for hours on end. It seems that folks in math education circles can’t all agree on the purpose of K-12 math. Perhaps this is the same in other content areas as well?
Some math folks assume K-12 should prepare students for what I’ll call the “math careers” that require a working knowledge of advanced math in which symbolic manipulation (a la “Algebra”) is important. Engineers, physicists, mathematicians, and…well, the list is fairly short. We’ll call this the “math careers” rationale.
Then there are those that trump the “higher education" card. These are the folks that acknowledge slope-intercept form and polynomial division aren’t really valuable tasks, but they’re needed to pass the typical credit bearing college algebra course. That credit bearing course is important for anyone who is pursuing a bachelors’ degree. Ask your local community college instructor and he/she can likely tell you about the remedial math course market. I often told my unmotivated students it was in their best interest to learn math in high school on the public’s dime than it would be to pay for the exact same classes for no credit at college, just so they could eventually take a credit-bearing math course that met graduation requirements. We’ll call this rationale ”delayed meaning.”
The third camp of folks I encountered were those who thought symbolic manipulation was not needed at all for the masses. “If they want to become a mathematician, they can learn that stuff after high school.” Instead, the purpose of K-12 math should be overly practical. Financial literacy, career and technical measurements and math formulas form the foundation of this mindset. These people think every student should learn about loans, mortgages, how to balance a check book, converting various measurements needed in technical jobs, etc. We’ll call this the “application rationale.”
A few other folks I knew claimed that math taught students how to think. Completing the square or using Pythagorean’s Theorem to “solve for x” were two ways students could stretch their brains. If a student can stretch his/her brain in math class, it could surely be used in other contexts, too. I call this the “math as a way of thinking” rationale.
I do not have any solid sources to back up the categories I just described, but instead they come from my own experiences and discourse with other secondary math educators. From my perspective, the current educational system attempts to balance (perhaps not equally) all of these rationales. The state I live in requires financial literacy in its content standards as well as a fairly deep coverage of symbolic manipulation. The result appears to be your question/experience: “Why did I spend four years in high school, and then several more in college learning math that I’ve long since forgotten?”
What should this tell us? I think it tells us that we are currently unable to agree on the purpose of math education. Any of this make sense?
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