The Big Ideas in Patterning
In Ontario, there are five math curriculum strands that must be covered each year in elementary school. Of the five, I always gave patterning short shrift. I never really understood why having the kids make strings of red, yellow, and blue beads was relevant, and it was usually something I left to the last minute, or something I had the kids do while I assessed students or worked with small groups on “important” math.
Then, last year, I decided to find out more about it, and this past May, I presented my research and exploration of patterning at the Ontario Association of Mathematics Educators conference in Toronto. Unfortunately, I only had about 70 minutes, which, judging by the saucer eyes I saw staring back at me, was only enough time to turn my workshop participants on their heads and send them out the door, walking on their hands.
Therefore, over the next few months, I’d like to use my blog to go into more depth and engage in some discussion about what I’ve learned and the activities I’m developing.
The first thing I want to share is my list of what I consider to be the big ideas that students should learn about patterning. These are compiled and cobbled together from the NCTM standards, readings from Van de Walle and Small, and research by Joanne Mulligan. I have no idea, anymore, which ideas are theirs or mine, so lets just assume it’s all part of a Jungian zeitgeist and carry on.
- patterns are models
- patterns model relationships and structures
- patterns simultaneously represent consistency and change in those relationships and structures
- understanding pattern means being able to recognize, extend, replicate, predict and exploit those relationships and structures
- understanding pattern means being able to identify, diagnose, and perhaps repair breakdowns in those relationships and structures
These are some pretty big ideas indeed, and they seem a bit too grand to be achieved by stringing beads together. They are very likely not something most primary teachers keep in mind when chanting “red, yellow, blue, red, yellow, blue” with their students, during calendar time.
But as I post, I will endeavour to always refer back to these ideas, and we’ll see what other, perhaps more effective ways there are to discover and explore them. More to come.
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So, how would this then be pushed at home?
At an early primary level, I connect patterns to their experiences. So, morning routines are the same each week. The relationship between each part of the pattern is order, and what makes sense to do first, second, etc. For example, we don’t put on our school clothes before we shower. We brush our teeth after eating, not before. You can discuss why you use that order, and what would happen when that order is changed. You can also talk about how these routines change on weekends, and why they change.
Cause and effect is another pattern (ababab). If you yell at me, you get a time out. If you yell at me, you get a time out. I’m not letting you stay up, because every time you do you are cranky in the morning and that wrecks our morning routine.
Later, we make the mathematical connections, that patterns can have the same relationships. You go up the slide, then down, you go up the toboggan hill, then go down, etc.
We continue to use the colours and shapes because they are symbols of the parts, and that becomes algebra in later years.
My mom taught reading under Title I to elementary students. Your points remind me of what she said about teaching children to read. Words are patterns of shapes strung together. Children who had difficulties learning to read often usually had problems with this, and could be re mediated through patterning with shapes and color pattern practice.
I believe this is true. My blogs about the flash cards discuss the patterning in language. Phonics is one pattern. Grammar is another. Once my students understand pattern, I use the application to teach other things, like the properties of geometric shapes, or the order of numbers, or how life cycles work and what might interrupt those cycles.
Useful Video to Learn Basics on – Patterns in Numbers and Shapes @ http://youtu.be/0HzXapUeL5Y