I am spending a bit of time a couple days a week in kindergarten this year. It was part of the now-changed sabbatical plan, but important to me to follow through on.
Today was my first day. It was awesome.
The young ones are working on patterning. AB patterns, AAB patterns, ABB patterns and ABC patterns. I’ll leave the curricular questions for when I know more. Today I’ll take these activities at face value, which is to say: this is the mathematics these children were working on today.
The children were instructed to use square tiles to make an ABC pattern. If you haven’t spent time studying curricular approaches to patterning in early elementary, this means that they were to use the tiles to make something such as this:
Color is the only variable attribute of the tiles the children were using.
I had several interesting conversations about this task with children today. The one I want to report is the following.
I made this pattern:
I asked the girl sitting next to me whether I had made an ABC pattern.
Me: How do you know?
Girl: [blank look; long pause]
Me: Show me how you know it’s an ABC pattern.
She carefully points to each tile, saying one letter per tile in the following way.
Girl: And you need another C.
Learning is messy—beautifully messy.
I left today with two big questions on my mind; each relating to this exchange, and to others not documented here.
- What would these children have done if asked—prior to instruction—to make a pattern with their tiles?
- How does this kind of patterning work interact with learning to count?
I hope my readers will see that these are not questions I expect to be answered in the comments. I hope you will see that these are big and important questions worthy of wondering about for days, weeks, and beyond. I hope you’ll join me in wondering about these questions, and the consequences of potential answers to them.
I argued a while back that learning is having new questions to ask. I hope you’ll join me on my learning journey.
You didn’t ask, “If the pattern continues in this way, what color will the 379th tile be?” I’m shocked – SHOCKED!
Also, I’m not 100% convinced that you’re doing everything possible to help these children assail Mt. Calculus as soon as humanly possible. Disappointing. ;^)
Clearly the tiles didn’t understand the purpose of the investigation.
The 2nd of your two questions above has been on my mind this week. Here’s an example of a counting / pattern problem that gave my younger son ( 4th grade) a little trouble earlier this week:
The first time through was difficult for him – when he was working alone – and the second time through he was able to walk through the problem. That tells me he’s very close to understand some relationship between patterns and counting, but exactly what gaps need to be filled in are a complete mystery to me in all honesty.
This child seems to have a sense of structure/pattern and it looks like she was making a pattern that that suited her in terms of the relevant attributes (color & number). My wonder at this juncture is: what’s the differnce between the patterning activity itself and a child’s ability to abstract her pattern to symbolic form (A, B, C, etc)? I mean, how are colors and “ABC” related? That’s quite a leap between the reality and the “name” of the pattern.
Interesting. Perhaps an ABC pattern is a row of colors that contains a multiple of three tiles? Or perhaps it’s that you were an adult, so your pattern must be right?
When I tried patterning like this with my preschool-2nd grade kids awhile back, they all agreed that patterns had to repeat exactly. ABABAB, or ABCABC, but not ABCBA or ABABBABBB. I would lay out a row of tiles, asking if I had a pattern. “No … no …” They seemed concerned or almost sorry for me when my patterns didn’t repeat — pitying my inability to make it work. And then they cheered when I got one “right.” 🙂
I am so excited that you will be in a Kindergarten classroom and sharing what you see. I teach grades 5-7 so I see lots of that content. And, a lot (most?) of the #MTBoS content is for algebra and higher, so I am excited to see / hear / think about the youngest kids.
Trying to figure out what kids are thinking (like in this post) is the most intriguing part of this job. I am excited to read about what you observe in the kindergarten classroom!
P.S. Congrats on getting to work with the Desmos crew. I think they just hired a college friend of mine: Zan Armstrong. She is great!
Thanks, Tyler! I hope to do you all proud.
Yes, we are all big fans of Zan at Desmos. She’s a great mind and a great spirit!
I so enjoyed your talk at TMC15 this summer. I agree with Tyler that there are so many parallels between what we do in middle grades and the thinking that is built in kinder. Looking forward to following your work with these young mathematicians through the year.