Dear Link Community,
The end of the year was packed academically! Students took their finals, seniors did senior
projects, and everyone presented their POLS (presentations of learning). We will miss the
seniors next year, but we are confident that they will go on to do wonderful things in their lives.
In my Geometry class, a large portion of April was spent working on developing proof writing
skills. Proofs in Geometry are a step up in difficulty from anything that students have
encountered before. Before learning about proofs, the math concepts students encounter are
very formulaic. Students learn a procedure and apply that same procedure to similar problems.
They then build on previous knowledge to learn more complicated procedures; however, even
the most advanced concepts in algebra still follow this same structure. Proofs are a little
different. While there are general principles that apply to every proof, every proof is different in
the sequence of steps required to complete them. Also, solving the range of different proofs
encountered in this class requires students to recall a variety of different concepts from the
entire year.
The reason I emphasize proofs so much is because I find proofs to be an incredibly useful skill
to help critical reasoning skills. While students, after Geometry, are unlikely to need to create a
mathematical proof ever again, they will often encounter situations where they will need to
evaluate the validity of an argument or create their own logical argument. Though they get
practice writing arguments in English, it certainly doesn’t hurt to get more practice in Geometry.
In fact, Abraham Lincoln learned the reasoning skills necessary to become a lawyer by studying
Euclid’s Elements, the first known text on geometry. To study proofs, I had students practice
proofs in class for a couple of weeks. During this time, I helped them tweak their proofs and
gave them pointers on how to make them better. The formalism of proofs can be challenging for
students, but it is necessary, because being able to articulate your argument precisely is key to
making sure you are being completely logical. While proofs can be challenging, the students did
a great job with them.
Another concept that I see as being particularly useful for students to learn is financial math. At
the end of Algebra 2 this year, students learned how to calculate how big an investment will be
at some time in the future. In exploring these concepts, students learned that if one saves 25%
of their income each month every month until their initial investment quadruples, then they can
retire and live off of their investment indefinitely. Of course, saving 25% of one’s income is not
practical for everyone, so there are limitations to this idea. However, by introducing students to
these concepts, I hope that they were able to see the value of investing early, see how powerful
compound interest is, and internalize these concepts so that they make wise decisions with their
money in their futures.
-Gage Edgar, Math Teacher