The Case for Communication in Numeracy
Currently, one my school's goals is to improve our student's numeracy by having them develop their communication skills. I have been a big proponent of this drive for communication. My reasons are: my students are not very good at communicating their thought processes, their strategies, or even their attempts at thinking. Why do I think this kind of mathematical communication is important? My students are pretty good at calculation, they can solve problems, they are not bad conceptually, and they do have strategies for tackling mathematical thinking. They are NOT good though, at explaining their thinking. And I think this kind of articulation is important because I think it will help them to solve similar or different problems in the future.
The case against? Blink
During Spring Break, I get a chance to read for pleasure but I also listen to a lot of audio books. So while I am catching up on spring cleaning, I listen. Right now, I am re-reading (actually re-listening to) Malcolm Gladwell's Blink. It is about how people can make fairly accurate and discriminating decisions in the blink of an eye. Though Blink is not an education book per se, it is making me rethink my stance on having my students communicate their mathematical thinking.
Jam and Math
In one story, Gladwell describes how researchers gave a focus group a number of different jams and had them rank the jams in order of preference. When the group ranked the jams in these circumstances, they ranked them in almost the same order as a field of jam experts. But when a focus group was first asked to key on different qualities of each jam (such as colour, texture, taste, etc.), there was almost no correlation with the expert rankings. It is as if getting people to focus on these qualities inhibited them from being discerning jam tasters because they were distracted by a number of factors.
How does this relate to articulating mathematical thinking for elementary students? Sometimes we ask students to do things that work counter to the end goal, in this case for example, the ability to be numerate or to solve mathematical problems. Maybe getting students to overthink communication is getting in the way of being strategic in math the same way preloading the focus group with parameters distracted their jam judgement.
I just know.
Over the years when I ask some of my best math students to explain their thinking, they will say, "I just knew." I thought it was a cop out when they would say that, and when I would press them on it, they would get frustrated, not being able to articulate their thought processes. I took that as evidence for increased emphasis on communication because I thought such emphasis would increase their ability to explain their thinking.
Now, I am not so sure this is logical. I think back to my own youth. I used to love puzzles and logic problems. I'd like to think that my thinking was ordered and strategic, but even now as an adult, I can say my thinking is never linear or organized. Usually, when I am confronted with a problem or I am creating something, I think and I think and I think. Then I sleep. Then I think and I think and I think. Then I eat. I think and I think and I think. You get the idea. I load myself with a whole lot of thoughts, and then during a random moment of clarity (usually in the shower, when my brain unclenches), I reach through the maelstrom of thought and get an idea or a solution or a weird glimpse that will lead to a solution. (I am thinking of keeping a set of markers in the tub or at least some more absorbent towels handy). But like my poor math students, how are you supposed to articulate this thought process?
So what do I do about my students' ability to communicate numeracy? Abandon communication entirely? No, but then, what? I've never been a fan of word walls, especially because in my classroom design journey I've come to realise that they can become visual noise. No, I think the integration of math and communication has to be more organic than that: lots of reflection and discussion during the thinking process, and lots of sharing after the problem solving process. I still hope to expand my students' toolkits of strategies through sharing among each other, but also reinforce students internal metacognition strategies.