Thursday, 7 March 2013

The Password of Mathematics is "Pattern"

We've done a lot of inquiry-based activities in maths over the last year. It has been fascinating to watch the kids (and their teacher) develop their understanding of mathematical thinking.

But as I reflected back on what we have been doing, I started to wonder if my inquiry maths journey was more than just a series of fun activities. Shouldn't inquiry go a bit deeper?

Well, I had made an effort to link our maths to what our unit of inquiry was that we were investigating. We are a PYP school (International Baccalaureate Primary Years Programme) and we have 6 units of inquiry each year. Making authentic links is central to true transdisciplinary learning. 

But is this enough?

And what about those left-over bits of content that don't fit authentically into any of the 6 units of inquiry? You still have to teach them. We often refer to them as the "stand alone" bits of the curriculum.

Or for those who don't teach PYP, how would you approach teaching maths as an inquiry? Where would you start? Where would you go?

Numbers Patterns - A Reflection

Last week, we launched into an inquiry into number patterns. It was something we had to "cover" (don't you hate that expression - sounds like you're making a bed or tiling a bathroom floor rather than inspiring children to learn...).

Here's where we went on our journey.

Tuning In

We started with the provocation - "The Password of Mathematics is Pattern" - taken from one of my favourite books: "The I Hate Mathematics Book" by Marilyn Burns.

What did this statement mean? Does it apply for ALL mathematics? And what type of patterns are we talking about? And what is a pattern?

This was a very interesting discussion.

We followed up with the kids creating 10 of their own patterns. They shared their patterns with a partner. The partner was asked to add the next number to the pattern and explain what was happening.

Here's a few patterns they came up with. See if you can find the next number:

1, 2, 4, 8, 16, .....

8, 20, 32, 44, .....

2, 6, 7, 21, 22, 66, 67, ......

100, 50, 25, 12.5, 6.25, ......

50 000, 5 000, 500, 50, 5, .....

The debrief was interesting. Here's a few of the comments:

"Can this have 2 answers?"

"I know these two are the same but I don't know what they're called."

"Is it a pattern if you add and multiply?"

"It's a pattern if the change is regular."

"What does it look like?"

We also found one of my all-time favourite movies on Youtube:

Donald in Mathmagic Land - a 1959 Donald Duck classic. I remember watching this (several times) when I was in high school on a 16mm movie projector. 

Finding Out

Next step was to find out a bit more about patterns. Some independent research uncovered several different types of patterns. We found out about:

  • arithmetic sequences
  • geometric sequences
  • triangular numbers
  • square numbers
  • cubed numbers
  • Fibonacci sequence

Students were able to share what they found out about each type of number pattern and discussed how the patterns looked. came in handy here.

Sorting Out

Now we knew a bit about different sorts of patterns, the next step was to see if we could sort out a few examples. I provided about 20 examples of different patterns, some written numerically, some as pictures or diagrams. 

Using our 6 groups of patterns that we had identified, we proceeded to spend the next hour arguing about what went where and why. Some were easy - others less so.

Here is how it looked:

It's a bit hard to see properly but there were 22 patterns that the kids had to place in one of 6 groups.
There's a diamond-shaped pattern that is in the "Geometric Sequence" group that proved difficult.

Going Further

There are some great clips on Youtube that we had a look at, to see what other people had learnt about patterns.

Two favourites were:

Amazing Number Patterns - this we great - we watched it a few times and paused the video frequently to discuss the patterns that were presented

Nature by Numbers - an awesome visual exploration of patterns by Etereae Studios 

Then we grabbed the i-pads and headed outside to photograph any patterns that we found. Finally, we imported the photos into the Comicbook app and annotated our comic strip. This provided an opportunity for the kids to demonstrate their understanding of patterns.

Here's some examples of these:


This inquiry cycle was conducted over 7 days. After it was concluded, I had a few questions for myself:

  • Did we actually go any further than just doing a series of fun activities?
  • Did the final activity actually provide the opportunity to show an understanding of a diversity of number patterns?
  • If "patterns" are the "password of mathematics" then shouldn't this inquiry run for a bit longer than 7 days? In fact, shouldn't it underline everything we do throughout the year?
  • And why is it being taught outside the rest of the inquiries that we are pursuing in the classroom? 
  • And where were the kids in the process? Had I pushed them in directions that I chose for them rather than letting them have a voice in the process?

Ahhh....teaching is learning!

1 comment:

  1. Hi Bruce,

    I'd love to see some of the example comics you discuss near the end of this post, but the comics don't seem to be visible.

    Thanks for sharing your process here, and this idea. I'm going to share this with my colleagues.



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