Thinking Like A Mathematician

Finally, our first post of 2017!

As always, it’s incredibly busy coming up to speed each year, introducing new students to our learning community, and getting back into routines. But now we have a moment to reflect, celebrate, and share progress so far.

Inquiring into new maths concepts, and continuing to develop maths skills, has gotten off to a solid start, so let us share with you some of what we’ve been up to.

One of the important concepts in mathematics that we belive in, is the ability to apply different strategies to solve problems. One great strategy, and one that underpins so much of our mathematical understandings, is “looking for a pattern”. You see patterns (a repeated design or repeated sequence), everywhere you look! And so we want students to be seeing patterns when they are inquiring into maths.

This is one of the things Mathematicians do, and we can certainly  all “think like a mathematician”.

Another thing that mathematicians do is ask “What if…?” questions. For instance, “What if I changed a rule in this pattern, what difference would that make?”. This is where deep thinking and deep investigation and deep inquiry takes off!

Today, one group of students modeled a problem, collected data, and began organsing the data to find a pattern. The problem was in a story format:

I was camping by a lake at the weekend and there were some lucky people who came to camp on the island in the middle of the lake. It must have been a couple of families because there were 8 adults and 2 children. Trouble was that their boat was missing. I helped them hunt around for it, but all we could find was an old canoe. We tested it and found that it could take the weight of one adult, or one child, or two children. At first it didn’t look like the canoe would do the job, but they figured out how to use it to cross the lake. Could you figure it out?

Students solved this by modelling it with concrete materials, by drawing a diagram, and by acting it out. All great strategies! It turned out that 33 trips across the water were required in order to get everyone across. Can you work out how?

However, we recalled that thinking like a mathematicians means that we could then ask: “What if we change one aspect of the problem? What would we find out”. We decided to change the number of adults involved in the problem. In groups, students replayed the problem with a different number of adults each time. For the chosen number of adults in the problems, students found out how many crossings it took.

So now we had some raw data that we could organise in a meaningful way to see what we could learn, and especially what patterns we could find. If we’re really clever, perhaps we can soon find a generalisation that can be turned into an algebraic equitation! (But maybe we’re getting a bit ahead of ourselves… )

At the same time, another group of students has started looking at the patterns of animals as they roam around Earth. Some websites are available that allow you to see the GPS tracking of various animals that has taken place. It’s surprising how far they have wondered.

So what sort of maths can we draw out of information such as this? Are there any patterns? Can we think like a mathematician and ask “What if…” questions?

We shall see… Stay tuned…

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