What makes a pattern?

Last year, a large fraction of the small amount of math that Katie did in Kindergarten consisted of basic patterns.  “Red, blue, red, blue, red” what comes next?  And the more advanced version of that with three repeating colors or objects.  Today, I happened to ask Katie what they had been learning about in math class recently.  Then we had the following conversation:

K: We’ve been doing patterns.
Me: Like the kind you did last year, “A, B, C, A, B, C…”
K: Well we sometimes do “A, A, B” or “A, B, B” – but anyway, they’re so easy.
Me: Are they always easy or do you sometimes get tricky ones?
K: There are no tricky patterns – they’re all easy!
Me: What about the pattern I gave you recently where you first had to add 1, then 2, then 3…, that was a bit tricky for you.
K: That’s not a pattern!
Me: No?
K: A pattern has to repeat.
Me: So 2, 4, 6, 8, … is not a pattern?
K: Well…(clearly thinking) I guess that’s a pattern because the 2 repeats – you add 2 each time.
Me: I see. But 1, 3, 6, 10, … is not a pattern?
K: (looking confused and frustrated) Oh, I don’t know. All I know is that my teacher said that a pattern has to repeat!

My main issue with the way Katie has been learning about patterns in school is not so much with this definition, but rather with the paucity of the examples.  If kids understand the pattern “A,B,C” then they also understand “dog, cat, mouse” and there’s no need to give them fifty variations of this but with different objects.  I do think that the way the word “pattern” can be used in math and similar disciplines can be hard to define, but we can definitely give kids the flavor of it and let them play around with the concept.

“Triangle, square, circle, triangle, square, circle,…” is not a geometric pattern, but a fractal is.  Arithmetic patterns do not have to be computationally complicated to be rich and interesting.  For example, I love the patterns discussed in this post, and they were presented to (and understood by!) kindergarteners.  Why do schools feel the need to turn everything about math class into a boring routine?


About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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4 Responses to What makes a pattern?

  1. It’s great reading how you are questioning the pattern/math activities that your daughter is doing. This connection between patterns and math is something I’ve thought about, mostly because this assumed connection between math and patterns never was clear to me. Now I’m acknowleging that patterns happen without the deliberate overlays of math. Math is introduced when we choose mathematical language and concepts describe, decipher an/or predict patterns. The question to ask is, If your daughter gets it in her head that patterns are something that is immediately recognized then what’s the point of connecting these patterns to math? In fact, the power of math is revealed when we can use it to find pattern than are not easy to see. Buffon’s Needle experiment is way out of the radar of a first grader, but what’s so compelling about it is that is a compelling example of how we can find patterns that are completely invisible until we think about a situation in a math-like way.

    Sure, learning A B A B is a place to start (and it’s a great way system to make jewelr) but hopefully your daughter’s teachers will teach her that this A B A B is the first graders introduction to investigating patterns that are much trickier to decipher.

    It’s such a pleasure to read your posts!


  2. Joshua says:

    Before I started teaching, I wrote down a bunch of pattern ideas. You might like it:Patterns, Estimation, Communication

    One that I’d particularly highlight is: play a simple piece (e.g., twinkle) and stop before the last note. Is there a pattern? How do they know that the song doesn’t feel finished? This is just for discussion, no real expectation to have deep answers.

    I have done most (all, not sure?) of these at home with my kids, usually at random times, relatively unscripted or structured. However, I only did a small number in the classroom (written up here.) For some reason I don’t quite understand, the other ideas require better classroom management and local language skills than I have.


  3. Sannichka says:

    i wonder if you could offer the teacher some of your math resources. It’s tricky to do it tactfully, in a helpful and unobtrusive manner. depending on the personality of the teacher…


  4. David says:

    To be cynical, it could be that this nice, clean definition of ‘pattern’ is suitable for elementary teachers, many of whom have very little mathematical training themselves and would feel less comfortable with more involved and disparate examples. To be slightly less cynical, doing it this way also reduces the workload for usually over-worked, under-paid, and under-appreciated teachers.


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