Everyone Knows Something About Everything
Most curriculum wastes that valuable resource.
This extraordinary bit of tweetcraft from Christopher Danielson reminded me this week of one of the most important principles in the whole of teaching:
Everyone knows something about everything.
All learning interacts with earlier knowledge. So whatever you’re trying to teach an old kid right now is interacting with knowledge they developed as a young kid which is interacting with knowledge they developed as a very, very young kid and so on.
We might wish learning worked a different way, a way where I say stuff the way I understand it and then you immediately understand that stuff the same way I do no matter what you knew before I started saying stuff. But we go to the classroom with the principles of cognition we have not the principles of cognition we might want.
That early knowledge is a responsibility for teachers. We need to let students know that their knowledge and experience are as essential to their learning as their teacher’s knowledge and experience.
But that early knowledge is a resource for teachers as well. It’s a gift. It makes teaching easier. When a student says, “it’s not only round, it has little bumps,” we have resources that can help us all move in the direction of new ideas.
Okay you’re saying this one is bumpy. How do you know this one isn’t bumpy? Which of these shapes is most bumpy and least bumpy? Can we come up with a rule to figure out if a shape is bumpy or not?
Jere Confrey said, “Students are our most underutilized resource in school” and I believe she was referring to resources like “bumpy.”
The failing of most math curricula is that they waste the gift of early student thinking.
For example, this is the first paragraph in a unit from a major math curriculum called “Circles in Math.”
In Maths or Geometry, a circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the centre. The distance from the centre of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The vast majority of math textbooks make no use of early student thinking. They make no room for it. Those textbooks share the formal, developed thinking of an adult and then ask students to develop their own ideas on those terms.
Those textbooks have no use for “bumps.”
This is why teachers modify their curricula, but they shouldn’t have to.
When teachers modify their curriculum, they’ll often describe their efforts to make it more “engaging.” But another name for what they’re doing is j”creating room,” creating room for early ideas from students and finding ways to treat those ideas like the resource, the gift, that they are. This makes teaching easier for the teacher. And, for the student, there are few experiences more engaging than experiencing some knowledgeable other person as deeply engaged in you.
A big change in my teaching came from asking myself "What can I ask them before I teach them anything?". It took me 10 years of teaching to get to that question, but it's made the following three years a lot more satisfying.
When I think about scaffolding or editing OUR or other materials for class, then number one thing I am thinking about is how to make "bumpy" part of the journey and how to utilize and celebrate the thought that went into "bumpy." Thank you for voicing this!