Research can help us to discover powerful ideas, if we can just learn to unpack the ideas from the context of the researcher’s world and place it in the context of teaching children. Here is one idea I have found in the research that we have been unpacking.
There are many times in math when we have to think of more than one thing at a time. For example, when we think of multiplication, we think of groups and the number in each group. But, I remember being told you could not think of more than one thing at once. So… how do we help our students do this?
The metaphor I was given was that our mind is like a glass of water that can hold one thing at a time. Yet, I was constantly encountering people who claim to multi-task and there is the mathematical thinking that suggests the need to be able to do this. In the book The Shallows, Nicholas Carr refutes the idea of multi-tasking. He suggests that people move their attention from one thought to another. They are not thinking of two things at once, but they are moving back and forth, or bouncing around.
So how does a person then drink coffee and drive, or for that matter think about groups and the number in each group? The answer might be in what we define as “thinking” about something. They might be able to do one of those activities because they have done it so many times it has become part of a place in the brain where we no longer have to consciously think about doing something, like tying your shoes.
One way this applies to math is that our students learn math through many experiences until they no longer have to create the math concept with conscious thoughts in order to use the ideas. For example, students use counters to establish a number until they can use a pattern they have associated with that number, like a finger pattern for “5”. You will see them pop up the pattern from a place in their brain in which they don’t need to consciously think about it. This allows them to do mathematical tasks that are increasingly complex. Over time, they don’t need the pattern anymore and they can use the pointing acts alone or just the words they were saying when counting the objects in the pattern. Eventually, this accumulation of experiences becomes part of the brain where tying your shoes resides (if you can tie them without putting forth mental effort).
It takes time and it takes progressing from concrete experiences to less and less concrete ones, to develop this ability in mathematics. How much time and what is the progression of these experiences? Powerful ideas for another time…