# Tag Archives: kindergarten

## Happy kindergarten surprises

I was at a table full of kindergartners playing with triangles, trapezoids, and concave hexagons. We were building and chatting. They wanted to know if I wanted to hear them sing in French. I said yes. The sweetest two minutes ensued as this table’s Frere Jacques spread to the next and then the next, and soon the whole classroom was singing and doing math.

A few minutes later I made this.

And then I went scrambling for my notebook.

Yup. Sure enough. $(a-b)^2+4(ab)=4(\frac{1}{2}ab)+c^2$ is equivalent to the Pythagorean Theorem.

## Kindergarten questions

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.

Girl: Yes.

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.

She pauses.

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.

1. What would these children have done if asked—prior to instruction—to make a pattern with their tiles?
2. 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.