When Will I Use This?
What I use the most from my undergraduate math education and optimism for the curriculum shift in British Columbia
A new semester is about to begin and I am not waiting for any student in my math classes to ask this question. We are going to discuss it on day one.
“When will I use this?”
Out of all school subjects it seems like this question is most often asked in math. There is a subtle flaw in this question — a misconception that needs to be exposed. When a student asks “when will I use this”, they are making an implication (perhaps subconsciously) that math should be learned for practical purposes. While math can be used in applications, it doesn’t need to be. It can be beautiful on its own — its own art.
Why Do Math?
Instead of asking when they will use math, I would love it if my students asked WHY they should do math. This latter question was eloquently addressed by Francis Su, president of the Mathematical Association Of America, in a 2017 address at the AMS-MAA Joint Winter Math Meeting. In his talk, Su explained how doing math within a mathematical community helps us flourish by satisfying five basic human desires: Play, Beauty, Truth, Justice, and Love.
Notice that solving practical problems did not make the list.
Of Su’s five reasons, the first three resonate strongly in me. I have fun playing with problems, I can see the beauty within the subject, and I think there’s nothing that contains more truth than a proven math theorem.
However, I feel that a limited percentage of high school students readily connect with Su’s reasons for doing math, no matter how zealously their teacher promotes it.
Another small cohort of students will diligently factor polynomials, solve trigonometric equations, etc. because they plan to go into engineering or another applied field where those skills may be required.
What about the rest of the students? Why should they do math? Or, when will they use it?
What I Use The Most From My Math Education
Near the end of winter break, this problem popped up on my Twitter feed:
Feeling nostalgic of my undergraduate days in math, I decided to give it a go. It took me three attempts using three different strategies before I got it — an hour and a half, in all.
Why did I do it? — Play, Beauty, Truth
When will I use it? — Never
Let me clarify. I will never use the result that I proved in “real life”. However, what I do use constantly in all aspects of my life are resilience, problem solving strategies, and logical reasoning. These were all required to complete the ‘problem of the week’. Doing math helped me grow in these areas, and doing math will help students grow in them as well.
One of the most important mindsets my math education helped me to develop is that of being resilient. It’s a mindset that serves one well any time they face a challenge. I often meet students who believe that if they can’t solve a math problem immediately or on their first try, then they won’t be able to solve it at all. It’s a handcuffing attitude that I strive to help change.
Problem Solving Strategies
Completing problem set after problem set in university really helped me to build up my repertoire of problem solving strategies. Many times I had to think outside-the-box and not be afraid to try unconventional methods. I find that many of these strategies and habits of mind can be applied to non-mathematical problems, too.
Mathematical proofs, with all the rigour they demand, are a great vehicle for improving one’s logical reasoning skills. Once developed, these reasoning skills are great assets any time one needs to make an important decision or provide a convincing argument.
Content Vs Competencies
British Columbia is in the middle of a major shift in its school curriculum. In the outgoing math curriculum, there were lots of “prescribed learning outcomes” (PLOs) and “achievement indicators” that listed the specific mathematical content students were supposed to know. It looked a lot like a list of topics and technical skills to be covered, and the types of problems students were expected to solve seemed very, well — prescriptive.
The province is shifting towards a more flexible curriculum that is focussed less on content and more on competencies. A few examples of their math competencies are:
- Use reasoning and logic to explore, analyze, and apply mathematical ideas
- Apply multiple strategies to solve problems in both abstract and contextualized situations
- Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
In the old PLO-based curriculum, things like resilience, problem solving strategies, logical reasoning, Play, Beauty, and Truth were somewhat implicit. It would take a well-trained math teacher to draw them out consistently throughout a year. In the new competency-based curriculum, these themes are now explicit. They are the curriculum.
While it will take time to adjust, I believe this will be a positive shift for mathematics education in British Columbia.