My first attempt at PBL

This week, a couple of things. First, I read my students' reflections on our Personal Finance lesson. Second, many of my students are diving headfirst into their projects - Yay!

The personal finance lesson discussed Credit Cards, High-Yield Savings Accounts, and IRAs. I gave the class different financial scenarios, and they worked in groups to recommend products for the hypothetical people using resources on NerdWallet. They got really into it - Imagine a room of 45 18–20-year-olds arguing about interest rates! What a sight!

The most important thing about that day was the casual mathematical discourse happening. Remember, a lot of these students don't like math. That's why they're not STEM majors. I think bringing up this topic made them realize that whether they like it or not, math can be really useful in our everyday lives - and most importantly, DON'T wait until you're 35 to start an IRA.

For homework, they had to reflect on the finance lesson - whether they felt comfortable talking about these topics with family and friends and if they planned to use what they had learned to inform their own finances. Many of them reported talking to their parents after class, some said they would like to do more research, and a couple talked about opening up HYS accounts and IRAs as soon as they got done calling their parents. 

This taught me that it is possible to get students who have a negative outlook on math to appreciate its value and instill some curiosity about how math can help improve their lives (financially at least). 

This week in class, we learned a bit about Graph Theory, paired with How to Read Mathematics. I started class on Tuesday by having the students explore in small groups a textbook from my personal collection. These ranged both in publication year (1950s-2000s) and subject (High School Algebra to Graduate-Level Mathematics). We discussed how the way mathematicians communicate through writing hasn't changed much in 70 years, but it is a little different depending on the mathematical maturity of the audience.

Then, as a class, we tackled the first couple of pages in Chartrand, Lesniak, and Zhang's Graphs and Digraphs, which was my master's Graph Theory textbook. The students volunteered some words they didn't understand, and as a group, I explained how we could use context clues to understand definitions, even if they contained many unfamiliar words. We also discussed the importance of mathematical definitions (and accompanying figures) as a way for mathematicians to verbalize abstract ideas.

Then, we talked about Theorems, and one student asked if Theorems are like mathematicians' thesis statements. That was one of the best moments in my six years of teaching!

Thursday, we continued the theme of graphs, but I taught them how to start drawing and analyzing graphs in yEd, because why not? We started with counting nodes and edges and progressed to running a basic centrality analysis. Then, they just played around with the software for the rest of the class. Once we were done with the main lesson, one student, who was planning to do her project on Puzzle Boxes, approached me with an idea for her project (Side note - I couldn't find anything that's been done connecting math to Puzzle Boxes, but they seem inherently mathematical). She asked if she could use graphs to model her Puzzles, and I replied "YES! PLEASE DO!" Let me tell you, it's a great moment as a teacher when a young math student comes up with an original idea.

Next week, I plan to teach about Data Visualization and the students will be finalizing their project topics.