Making our first math posters –
What is a math poster anyway?
In math this week the students that I work with ages 7 – 8 made their first math posters.
What does this mean exactly – to make a math poster?
It is a crucial part of the math work we do here at Opal where we ask students to reflect on their work and show what they did to solve a problem. This requires one of the ideas we use often in connection with reading – the idea of metacognition. Metacognition in its simplest form is thinking about your thinking. This seems so simple, yet it is so easy not to do this. We have to train ourselves to ‘hear’ what is happening in our brains.
For instance – early in the week the students were solving two digit addition problems in relation to a context around measuring papers for an art show. They were doubling the paper size and so had problems such as 14+14, 32+32, 46+46 etc. Many of the students said that the work felt easy. When I looked at their work with them though, most students found it very difficult to say how they had gotten their answer. It seemed like it was a mystery.
I brought two of these ‘mysteries’ to the class the next day to see if we could use our detective skills to figure them out.
In one story the student said they used the problem 22+22 = 44 to figure out the problem 32+32 = 64 by just adding 20. This is very efficient mathematical thinking but when I asked where the 20 came from, the answer was “I don’t know.”
In another instance a student was trying to explain to their partner an idea about the problem 60+60. He said, “I did 60 + 50 and then added 10. Ok, great I said, so can you explain where the 50 came from? Answer: “I don’t know.”
These students clearly have some great math strategies going on in their brains but they are not aware of what is happening, what they are doing and how they are getting their answers. “I just knew it.” Is what I hear a lot. So, why do we need these students to explain? Why isn’t it good enough for them just to know it without being able to explain how they know it?
Well, I think there are many, many reasons – but here are a few:
If they are able to explain and name their strategies then as the numbers get harder and the mental math more difficult – instead of relying on I just knew it, they can rely on splitting, finding a friendly number, using 10’s. The numbers as they get bigger won’t get in the way of the strategies because the strategies once understood will be automatic themselves.
Explaining something is a sure way to understand it more clearly yourself. A math professor from Lewis and Clark remarked recently that having students talk about their process in math is an important step in their true understanding of the concepts and therefore their growing math ability.
Talking about how one did a problem allows others to see and consider possibilities different from what they typically use. It is great community work to take the time to share one’s process. It allows students to scaffold each other to the next idea they might be ready for.
After figuring out the ‘mysteries’ above as a class, we were able to see more clearly how we were trying to understand what went on in someone else’s brain. Students were then asked to choose one problem on their sheet of doubled measurements to write on a poster and then, they needed to show the steps of how they figured out their answer.
These are some of the posters students completed.
The next day we put all the posters out on the table and students were asked to go around and look at them. We modeled how to really study a poster. What does it look like when you are trying to understand someone else’s work?
“It looked like he was really thinking.”
“He was so focused and didn’t move around a lot.”
“He looked hard at the paper the whole time.”
We all gave it a try:
Finally we ended with a congress where we looked at a few posters in depth. Students explained their work and we listened, asked questions where we didn’t understand and tried to put their thinking into our own words. Congress is where a lot of the scaffolding happens, where students are challenged to notice strategies they are possibly not yet using but might decide to try out in the future. They are exposed to new ideas other students have learned. Through talking about the strategies and constructing their own words of understanding we are able to create a common language we can use as we continue our work in the future.
“I just knew it,” seems like such a powerful place for students to be initially. Their seems to be satisfaction in this mysterious knowledge, as if some math ideas are so clever you can’t even explain them. Yet, the real power comes in the explaining because with it comes the understanding. You can see the difference in the children’s eyes. “I just knew it,” has a vacant stare. A non-active, why are you asking me this again, let’s get on with it voice and no connection with anyone aorund them. Explaining your process has the look of hard work, busy brain, eyes intense and alive. The voice may be uncertain, but it is making an attempt and often ends up with excitement and pride when a students realizes they truly know their own brain. Even beyond that, others around are listening, hanging on their words seeing if their brains can meld for that moment of common understanding. And when they do, the satisfaction is enormous, the energy electrifying. Creating the space and culture for these moments – this is our work.