I had an idea for a proposal which I put in the TED-ED forums for a TED talk on Math in the Real World. Here’s my presentation, notes are below the presentation.
Hi all. My name is David Wees, and I’m a learning specialist for technology and mathematics teacher for Stratford Hall, in Vancouver, BC.
I want to first state that I don’t believe that doing mathematics is the same as doing computations or following algorithms.
Many math teachers seem to be stuck on the notion that teaching kids how to do computations out of context is the same as learning how to do mathematics.
So what exactly is a mathematician, and what is mathematical thinking?
Mathematicians think. A lot. They spend much more time thinking about problems than doing computations to solve those problems.
A mathematician is someone who problem solves using mathematics as their tool.
As proof that change in how we teach mathematics is necessary, we can look at the overall numeracy of our society. Numeracy levels in Canada are pretty abysmal, despite years and years of formal mathematics instruction occurring in schools.
It is a badge of honor in our society to admit that you are bad at mathematics. Almost no one would admit that they are illiterate, why do so many people celebrate their lack of numeracy?
Perhaps it’s time to try something new?
The problem, I see, with most mathematics instruction, is that we start by choosing the mathematics curriculum we want covered, and then find problems to suit this curriculum.
The flaw with this plan is that choosing a compelling problem to fit a particular area of mathematics is really difficult, and many math teachers don’t even try.
As a result, much of mathematics instruction lacks motivation in the eyes of the learner.
Here’s the crux of my argument. We’ve had curriculum which is mostly unrelated to experiences in kid’s lives for multiple generations which has only compounded the problem.
What I suggest instead is that we look at the world, and we find problems kids find compelling, and then we tease out the mathematics which is relevant to those problems. This is more difficult for math teachers to do, but will result in kids never asking the question, "Why do we need to know this."
Note that we can teach most of what we teach now to a motivated kid in a few years, rather than spreading it over all 12 years, so this way of exploring mathematics shouldn’t stop kids who are really interested in mathematics from exploring it further.
It is clear that our world has some deep mathematical structures. Which of those structures do we share with our students? Why isn’t more of the world we live in shared throught the lens of mathematics? If mathematics truly is the language of the universe, our current approach has kids learn some of the vocabulary, but never construct any sentences.
Trees for example have a fractal structure which is worth investigating. It is not hard to see that there is a mathematical formula of some kind which helps determine tree growth, but we can also see the idea of replication errors, and environmental factors that play a role as well. It also means that kids get a better connection between nature and the mathematics they learn.
Dan Meyer suggests finding "real" examples, rather than pseudo-context is key to developing student understanding of the world. The questions about the world have to be real, and from the students. The textbooks we use today include lots of "word" problems but for what purpose? Most of the textbook word problems are too poorly constructed to be obvious representations of the world, so why bother? What purpose does exposing kids to a bunch of pretend problems serve?
Outside of our own world, the whole universe has a strong mathematical structure on a large scale.
How often is this mathematical structure shared with students?
Or the relationship between this fractal and the previous picture of the galaxy?
Fractals and chaos theory are an important part of our world, mathematically speaking, yet neither one sees much "playing time" in our curriculum.
This is a complex project I’m working on where I am attempting to model mathematically the transfer of information in a classroom, and hence compare a didactic classroom to a cooperative learning classroom.
It’s not near done yet, so I can’t share any results, but if I do manage to complete it, the project will involve percentages, probability, graph theory, statistical distributions, geometry, Cartesian coordinates, and algorithms.
Flash card apps and other ways to memorize computations and algorithms aren’t going to improve our problems with numeracy. In fact, I don’t think these are really examples of technology at all, since they do nothing new. If you are going to use technology in your teaching, you should at least be using it effectively. Graphing programs, computer assisted algebra and calculus, multimedia to emphasize patterns, all of these are much more effective uses of technology than the current generation of apps for education.
To summarize my argument so far. Most people lack sufficient numeracy skills for our complex world. Our mathematics instruction really hasn’t changed in most schools for decades. Perhaps it’s time for a change? I’d recommend a focus on relevance to the real world, rather than a hierarchy of algorithms.
First, put aside that useless textbook with all of the prepackaged problems.
Start by finding an interesting problem that your students find compelling and look at the mathematics involved in that problem.
Better yet, turn your kids into investigators and have them find the problems and bring them to class. Finding interesting mathematics problems isn’t hard.
Don’t worry about that test so much. If your kids can solve real problems, and those problems are in some way related to your curriculum, they will do fine on the tests.
It would be nice if we could dump our current curriculum and replace it with something more aligned to the world views of our students, but that’s not really possible, so in the transistionary stage, we should find ways to include more of what kids experience in your teaching. Don’t be so afraid to experiment, if even a few of your kids recognize math outside of your classroom, you’ve done the world a huge service.
Slides 18 through 21:
So what does this look like? I did a project with my students last year where we explored the cost of owning a cell phone, based on the number of minutes used.
First we graphed the initial cost to join a cell phone plan, and then we graphed the cost of the cell phone plan. This got us talking about graphs, equations of lines, horizontal lines, and slope. As we went through the unit, I introduced the mathematics in pieces as the students needed more to explain the problem. For example, when students asked how we could find out exactly where the two lines met, we did a couple of lessons on algebra.
Then we recognized the optimal solution was actually the green line. We ignored the negative numbers, since they didn’t represent real values, and we focused on the part of the graph which was actually our solution to the problem. We discussed domain and range, within the context of a problem the kids understand. Notice also that our solution wasn’t a single number.
Finally, we needed to tidy up our solution so that we only represented what was actually the solution the problem. Clearly, without labels on the axis, the graph of our solution to the "what is the cheapest cell phone plan" didn’t make a lot of sense. I had the kids keep the first steps, so they can talk about their solution and communicate the reasoning they went to solve the problem.
There are lots of other examples like this one of real things kids want to know that involve challenging mathematics. We don’t need to dumb down the curriculum for students, we need to reenvision it. If we had a curriculum which emphasized the purpose of mathematics much more, I think we’d see a change in a single generation of students.
Here’s my contact information and the license for this presentation.