This kind of summer programming up in the city finds me working with kids whose backgrounds I know nothing about. I don't know where they came from or where they're going, so I mostly just try and go with the flow, try to meet them every day where they're at instead of where I think we should be.

Although grant sources require some 'evidence' of learning or growth, my job is to do the best I can in four days. To the kids I describe our work as using and making and understanding patterns of all kinds, and we spend most of our time doing just that; instead of explicitly talking about patterns, we're just trying to make and use them. As a result, kids may or may not have absorbed new vocabulary to use when it's time to assess their learning on the final day. I think my goal is simply that they have a reserve of experience to call on when they're back in school learning math with their paper and pencils.

But, like I said, I still need to ask them questions at the beginning and at the end. Here are the questions I asked this week. I'm still not sure that the first question is a helpful one for assessing learning but, as you'll see, it did provide me with some very interesting information:

**Question One: "What is a pattern?"**

**First of four days, summer camp children ages five to twelve:**

Something that is ABB and it keeps going...

Two or more things on paper...putting it on paper over and over.

Square then rectangle, keep going.

Repeats.

Something that gets put together.

Different colors.

Numbers -- 1, 2, 1, 2...

**Last day:**

Numbers, shapes

Rhythm

Nature

Sequence, repeating.

Heel, heel, toe, toe... (a clogging step)

Circle, circle, square, hexagon (We studied a hexagon as one of our nature's patterns inquiries.)

Take things and put them in order.

You know it's a pattern when it's the same, something that repeats, like red, yellow, red, yellow...

**Question Two: How can you make patterns with your feet?**

First day:

First day:

Different kinds of shoes and socks.

Switch shoes.

1,2,3 on one foot, 1,2,3 on the other foot.

Bang them.

Mix with other people's feet.

Big foot, small foot...

(Alternate) movement.

Switch shoes.

Number of taps.

Last day:

Last day:

Steps, slides, jump, turn.

(Use directions) left right front back diagonal.

(Put your feet) together, split, crossed.

Big, small, big, small (movements)

Heel, heel, toe, toe (a clogging step)

Sounds

Use toes, heels, kicks.

It's heartening to see that the answers to the second question showed much more understanding after four days of dancing.

**As for the first question, it's clear to me that, even after four days of playing around with patterns, the**

*idea*of pattern these children (and pretty much every other child I've seen this summer) have internalized is a very narrow conceptualization limited to colors and shapes that repeat in a linear way one after another, almost always "on paper."Driving home today (it's over an hour each way) I had a lot of time to think. I was thinking of all the ways we can harness kids' love of doing and making in the elementary years to the goal of engaging in an deep and meaningful exploration of patterns of all kinds. And that, in the the process of this kind of exploration, kids would get a chance to represent and experiment with this oft perceived 'simple' concept in a multitude of ways: 2D on the page (so many ways to do this), 3D with their bodies as well as all the great math building materials out there, and even 4D using time and rhythm.

While I drove I also had a lot of questions in my head: How can kids learn to see patterns in numbers if all they know is 'red, blue, red, blue'? How can they understand what patterns are if they don't have personal experience with constructing them, taking them apart again to explore the pieces, and transforming them into something completely different?

I am certain it is possible to provide deep, meaningful, artistic, open ended explorations of patterns at the elementary level. We do it all the time in Math in Your Feet with percussive dance; I am starting to understand how I might move this approach toward other mediums. (To see a really nice curated collection of math art, go to the Math Munch blog.)

I have a lot more thinking and learning to do on this topic, but for now I'm clear on one thing:

Almost every one of the 180 kids I encountered this summer, no matter their age or their dancing ability, were unable to identify or describe patterns outside the standard textbook context. I think they can handle more. Not only that, I think they want more.

So interesting! Did the kiddos answer the questions verbally, or in written format? Do you think a different format would inspire different answers?

ReplyDeleteHey Julie -- It was a whole class, verbal reflection. I do think that a different format *might* inspire different answers (easier to draw than to say) but I'm not sure in this case the answers would be different -- I'm pretty confident I'd get a lot of linear "circle, square, circle, square" kinds of drawings. It's a great thought, though, and maybe next time I'll have some paper handy for this particular question. :)

ReplyDeleteMalke is there some way you could do a project kind of learning assessment - such as have them demonstrate a pattern they come up with????

ReplyDeleteLinda -- yes, absolutely. This kind of assessment is built into the school version of Math in Your Feet. We have a final presentation on the last day and, through the week, they learn how to analyze and talk about the patterns they and their friends are making. I'm still experimenting with the visual/nature patterns activities which are all new to my teaching repertoire. Actually, I sort of feel like I have a full year of curriculum in me on this topic, but I don't think I'll ever have that kind of opportunity. It would be a lot easier to assess understanding of this concept in a longer-term situation than in four random days where not every kid is there every day.

ReplyDeleteYou are absolutely right that these kids can understand more deeply than we give them credit. I just read "An Ethic of Excellence: Building a Culture of Craftsmanship with Students" by Ron Berger (2003), and it affirmed many of my ideas about teaching and learning. It's a must read as now I'm recommending it anyone who works with children.

ReplyDeleteThanks for the recommendation, Donna! I can't wait to read it.

ReplyDeleteMaria and I discussed patterns a few times in the course of writing the book. One of the things we talked about was how typical patterning problems (i.e. worksheets) do not allow young children to really explore patterns, but instead box them into a very narrow definition. Children do understand patterns more deeply than we give them room for. We once observed a young boy exploring a deck of cards. He laid them out like a road. At first he would put down whatever card was nearest to him. But after 3 or 4 cards a pattern started to emerge as he began to be more selective and purposeful. In the end, it was a very sophisticated structure that relied on at least 2 properties (horizontal v vertical placement of each card) and suit up/down.

ReplyDeleteI like the idea of offering children different formats in which to express their ideas. I had this experience with my son today. He was working with the Pattern and Sequence workbook today (something we hardly ever do). I came over to check on him and noticed that he did ALL but 1 of the "continue the pattern" exercises incorrectly. When I asked him why he thought the next element in the pattern had to be "X" and not "Y", he said this: "I know it should be the other one, Mom, but this one is much easier to draw".

Thanks for sharing your thinking process, it's really helpful. And, I think that the active exploration and identification of patterns in context are much more meaningful and impactful than being able to 'define' what a pattern is. Which is why I will change the question to something else next time. ;-)

ReplyDelete