Dear Link Community,
What a semester it has been! The math classes this year that I’ve taught have been full of moments of student insight and growth.
In Algebra 2, I find that I am able to teach a lot of math applications. One topic that I look forward to teaching every year is exponential growth. I love teaching about exponential growth because the main applications of exponential growth that I teach are quite interesting to me: investments, debt, and population growth. Students were taught that exponential growth is a powerful thing that you want working for you, not against you. It works against you in the form of debt, but for you in the form of investments. For example, we looked at how much $1000 of credit card debt could cost you in the long run, versus investing $1000, and the result is staggering: $1000 invested today could be worth $4000 in 24 years, but $1000 of credit card debt could cost you hundreds of dollars in the time it takes to pay it off. It is also interesting to look at population growth. Though the equations of population growth can be somewhat simple at the Algebra 2 level, I always make a point to point out how there are different factors that can change the growth rate of population over time, so it isn’t as simple as using one exponential equation to determine what the world population will be many years from now. This analysis shows students how to use equations in a way that gives them a better understanding of the phenomena, while at the same time, understanding the limitations of such models.
This year, I have had the pleasure of teaching Calculus BC, an AP course. What I love about calculus is its relation to infinity. In calculus, we look at the infinitely large and infinitely small and see that lots of useful applications arise from looking at these things. In fact, there are many examples of calculus that we run in our everyday lives without realizing it. The speed of your car, as measured by the speedometer, is an example of a concept in calculus called the derivative. When you add up the parts of something to find the whole, you are, in a sense, doing calculus.
One of the best examples of applying calculus from this semester comes from the topic of optimization problems. Using calculus, one can find the way to construct something in a way that maximizes the quantity of interest. While there are many applications of optimization problems in engineering, optimization problems have applications in other disciplines such as economics and business.
In Geometry, we’ve spent more time on proofs than ever before in any of my previous three Geometry classes. I love teaching proofs because I see proofs as a fantastic way to build critical thinking skills. With proofs, you start with facts that are so obviously true that you don’t need to prove them, then use these ideas to prove new facts, and then you keep building on what you’ve already proven to prove more and more facts. By having students practice proofs, they are practicing distinguishing between what they believe is true and what they know to be true. They also learn how to convince someone else that what they know is true is actually true. Lastly, proofs are creative; it can take a little bit of insight to discover a proof, rather than just following a procedure like in algebra. It has been a joy to watch students continue to grow their abilities to find proofs and become more confident in their abilities to do so.
-Gage Edgar, Math Teacher