Much of the thinking we do in Algebra class can be related to careers in quality control, error analysis, and design testing. One doesn’t have to earn an engineering degree to find a place in those environments. Indeed, there is much lower fruit for those who develop a basic comfort level with mathematical thinking. If our thinking is not interesting in math class, that is the fault of our curriculum and instruction. If our thinking is interesting, it makes perfect sense to point out its long-term usefulness whenever possible.
Asymptotes are no exception. Our current curriculum requires that students learn the three cases for horizontal asymptotes: Higher power in the numerator means no asymptote; for a higher power in the denominator the x-axis is the asymptote because…; if the powers are the same, draw an asymptote through the quotient of the leading coefficients because….
When do we ever draw asymptotes after high school if we don’t take calculus? We might use asymptotoes if we are describing a glass ceiling or a welfare safety net. Beyond that, I confess my ignorance and hope a reader will enlighten me. But the thought process described is very common in the workplace. With a little imagination, one can see an interesting generalization of the process as matching symbols with substance and response.
Beep-beep-beep, I check my dishwasher and am duly warned that the bottom drawer has flooded. I make sense out of the symbol and activate the appropriate response. Flash-flash-flash, the pressure is low in my right tire. Knowing how digital symbols relate to appropriate responses is how computer systems administrators earn their paychecks. The reports from department A do not look like reports from department B: Was there a change made in the computer code? Where?
Math teachers have options. We can require students factor fifth power rational functions through grueling repetition of the rational root theorem using long division. We could speed up the gruel by teaching synthetic division, confusing students’ understanding of long division. There is a reason why the Common Core writers left out synthetic division. Do I add or do I subtract? Do I bring that number down? Where do I put it? Surely connecting those processes with a career is likely kill most students’ interest in higher mathematics and related careers.
Another other option is to explore the math processes and then learn how technology becomes the priceless relief. It pays to understand connections and develop confidence in working with technology-generated symbols…literally pays! Students who can wrap their minds around that are likely be able to envision themselves there, set goals, and pursue the necessary learning. For these reasons, I have been learning everything I can about mathematical thinking in the workplace and finding new ways to “sell” those connections in an engaging classroom environment.