I firmly believe that math can and should be learned through life and interest. I’ve written a few posts about that but today I want to discuss a step in the right direction between the way we teach math in schools now and my belief of a more natural way. It’s about the belief that there are three important parts of learning math, but that right now only one of those parts is being taught. I think this vision I have would help more people grow up loving math, because they would connect to it in different ways. Kids would also learn the material better because it would be more ingrained in the way they thought and did things. So let’s get into these categories:
Computation: I’m starting here because this is the part we’re most familiar with as a society. This is what is taught in most schools now. Formulas, graphs, solving problems posed by the textbook. It’s definitely helpful to be able to compute. Especially with higher math, one does need to be taught them (by which I mean they wouldn’t just pick it by chance, not that they couldn’t teach it to themselves) and one also needs to practice to reach proficiency. But computation is unhelpful without context. Particularly when you’re solving problems that the teacher or textbook already know the answer to, it often feels pointless, like you’re learning this thing that isn’t helpful in your life, is boring and already has been solved anyway. Which brings us to the next category.
Real life: Math really is everywhere all around you. I’ve written a post about this topic specifically, so here I’m going to talk about a few ways this idea could be integrated into a math curriculum. These ideas aren’t mutually exclusive, I think they would be best used all together, or at least using a few of them:
- On a most basic level, simply discussing ways the math being taught is useful. Particularly if those things aren’t just useful to some people, but actually useful to the people being taught.
- Engaging them in activities that utilizes the math they are learning to compute. Solving real problems (not problems that have already been solved), building things, etc.
- In an integrated curriculum learning about ways that math, especially more complex math like algebra and calculus, serve a purpose in understanding the world could be a project for the students to research themselves. They could read about the history of using and understanding the concepts and about how they are used today.
- Having guests come in to talk about how they use math in there jobs. They could be mathematicians and talk more about the problems they’re solving with math or someone like an architect.
Beauty, fascination and play: I think this may be the category most often neglected in a curriculum, which I think is terribly disappointing because it draws so many people in who might not find the others ways to look at math as interesting. Again, I’ve written a whole post about this way of looking at math, so here I want to talk about what it might look like in schools. Playing with numbers is so much fun. I think Vi Hart videos (more information about Vi Hart in this post) might be a good jumping off place. Hart has videos about all sorts of mathematical concepts and it’s quite likely that something being studied in school would have a Vi Hart video to go along with it. They are often focused around doodling as a way to explore the topics and I think inviting students to play with art would be a good next step. There are many books (some of which I’ve read and written about here and here) about how interesting math is. Reading and discussing those books would be another way for students to engage in this understanding of math. I particularly think the Measurement by Paul Lockhart (discussed here) would be a great one for small group discussions particularly because there is a lot in this book to try on your own. This is a big topic and I certainly can’t cover all the great resources available for diving in, but I will work to add more to my resource page so you could find at least a small subset of the many choices there.
There is a lot more to say about the subject of math in school and I hope to write more about the subject, but this post hopefully gives you a sense of one direction I would love to see math curriculums go.