For my masters I need to do a capstone project this term. I pick a subject and then develop a series of lectures that are intended to be an ‘enrichment topic’, and likely targetted at upper year HS students.
Here’s the outline:
Students create a mini-course on a single mathematical enrichment topic. The course created
will be roughly three one-hour lessons that include both teaching and mathematical problem
• An “enrichment topic” means a topic that is outside of the union of the curriculum documents
(including courses that are not mathematics) for a generic jurisdiction. For example, teaching
calculus to Grade 10 students would not count as an enrichment topic.
• The mini-course can be aimed at any level from Grade 9 to Grade 12 (or college for college
• The mini-course can be approached from a number of different angles, including an historical
angle, a contest preparation angle, etc.
And here’s some possible ideas:
Applications of … (eg. Logarithmic Functions,
Complex Numbers, etc.)
Arithmetic, Geometric and Harmonic Means
Chinese Remainder Theorem
Compass and Straightedge Constructions
Cubic Equations and Polynomials of Higher
Euler Phi Function
Fermat’s Last Theorem
Fermat’s Little Theorem
Graphing Polar Curves
History of … (eg. Trigonometry,
Indian Mathematics, Fibonacci)
Limits of Sequences
Mathematics of Gambling
Mersenne and Fermat Numbers
Nine Point Circle
Open Problems (eg. Goldbach’s Conjecture,
Do any odd perfect numbers exist?)
Pencils of Planes
Platonic Solids and Polyhedra
Properties of the Pedal Triangle
So I have it narrowed down to two ideas.
Pros: I think it’s a cool enrichment topic and I’m personally interested in it.
Cons: I don’t know squat about the golden ratio. So in addition to developing the course, I have to learn and understand something about it. Like right now I couldn’t even do an outline of what I’d be teaching. And I’m concerned that the math behind it may be too much for a HS enrichment course. So basically, unsure if this is too much for me to handle over the summer.
Mathematics of loans
Pros: Easy for me to do, zero learning, The opposite of 1), I’d likely be done this early since I’d be just drafting an outline, screwing around in latex and spending some time building out some interesting exercises like ‘calculate PV/FV’ and ‘build an amortization schedule’.
Cons: Less certain this is a viable ‘enrichment’ topic.
Looking for your opinion on which way I should go. And if you choose 1) would welcome guidance on what area of the golden triangle I should focus on (I did some reading on this over the weekend, and holy crap that ratio is everywhere).
I suppose I could do #28 on the list, graphing polar curves. I plan on getting a tattoo once I’m done the degree and was thinking of getting a unit circle, which would tie in nicely. But, a golden ratio tattoo opens up some interesting possibilities as well.
Even before I had finished reading, Interest Theory had come to mind.
It’s math. It’s algebraic. It’s interesting (I think) It is outside the scope of anything in a HS curriculum. And since virtually every student borrows money from a bank at some point, it is a GD useful tool that could actually be life altering for some students.
I’ll just throw out there that I had a lot of fun introducing a class of high school students to the basics of actuarial math by having them calculate auto insurance rates given some very simple data, etc.
Auto insurance costs are something high school juniors and seniors are interested in for some reason…
Miss me with that P&C stuff because I know less about auto insurance actuarial-donking than I do about the golden ration :). It’s actually an interesting idea, but once I’m done mocking the whole P&C industry I have no idea where I’d even start.
Auto insurance pricing, how do you even.
Also, I would include a very brief overview of utility theory—WhoTH cares if you’re a millionaire when you retire if your roof is leaking now and the furnace doesn’t heat the house and you’ve had ramen noodles for your last twelve meals.
Fair enough. But I’m not going to start teaching HS kids about the benefits of leveraging lol.
Maybe I could do some work around increasing caution on variable rate mortgages. People are taking an absolute kicking on this right now. Rates jump up, people are starting to have to sell their houses because they can’t afford the payments and IIRC, in Canada they push out the amortization period to a max of 40 yaers and then start increasing payments. And when that becomes unaffordable, time to sell the house.
It takes the idea of approaching your whole financial life as the present value of future expenses and revenue.
I can’t find my copy, so I probably lent it out.
Highly valuable (IMO) to upper level high school students.
Could easily turn into a discussion on Utility Theory, as some students will choose to purchase (or buy on loan) something while others don’t.
Geez, I’m looking at taht book on amazon. On ‘.com’, it’s like 10 bucks, with a bunch available used for like $3. But, shipping from the US. Head over to amazon.ca, and it’s fREAKIN $40 and shipped from australia. What the heck.
I find the “wow, that’s a lot of interest” discussion innumerate. You pay a mortgage on a house because you cannot afford it all at once. One should consider interest as the “rent of money” and the payment of principal as an investment in a house (with an unknown rate of return). then discuss financial leverage.
Same goes for a car, so, “lease or own” decision exercise. It always makes me laugh a bit when someone says “never lease a car” without all of the inputs required to make such a decision. I mean, if someone offered to lease you a $40,000 car for $10/month, why wouldn’t you (after checking all of the conditions, of course)?
Can also see what the Present Value is when someone chooses to save by going farther to the cheap gas station every time for a lifetime. (Spoiler: I don’t think it’s a lot, relative to other items.)
Or, the current (heh-heh) discussion of EV versus ICE, or whether to buy Solar Panels or continue to pay for electricity (what inputs are required? is the big thing here so practical application of math).