"When do I get to tell students the stuff I know?"

Here is a short video of some great teacher explanation.

"When do I get to tell students the stuff I know?" is a core question for a lot of math educators. Teachers are right to notice they already know a bunch of stuff about the subject students are trying to learn, stuff which sure seems like it might be of use to students at some point.

One group of educators has a very clear answer here which is, roughly, “Just tell ‘em! How is this even a question?” Some will emphasize Barak Rosenshine’s Principles of Instruction, which recommends you a) break the stuff you know into small steps, b) model those steps, and then c) ask students to practice those steps.

What’s great about this answer is that it is quite clear and also quite accessible to all the teachers who are wondering what to do with the stuff they know.

Another group of educators got together, formed an organization called the National Council of Teachers of Mathematics and occasionally publishes documents that have a lot of influence on the field of math education in the United States. For example, NCTM published Principles to Actions in 2014, a document with eight recommendations for teaching, all of which have a lot of wisdom. However, not one of them offers a clear or accessible answer to the question, “When do I get to tell students the stuff I know?” Check them out.

Groups that speak clearly and accessibly about the value of student knowledge need a perspective that is similarly clear and accessible about the value of teacher knowledge.

Here’s Schwartz and Bransford writing about the limitations of the “just tell ‘em!” model and offering a perspective on how teachers can create “a time for telling” (1998, p. 511):

Distinctions can seem obvious to experts who, therefore, do not bother to illuminate them. Moreover, the expert's ability to discern is often tacit and, hence, goes unrecognized. As a result, neither instructor nor students may recognize that students have missed important distinctions. 

Even when there is an attempt to help students differentiate, the task can be difficult when novices are simply told about distinctions they should make. It is relatively easy to tell a distinction to someone, if that person shares the same set of experiences. However, with respect to the content of instruction, shared experiences are exactly what novices and experts are missing.

For explanations to be effective, teachers and students need a shared set of experiences to talk about. 

These conversations are often too abstract so I want to offer a short excerpt of classroom video, shared with permission.

In this video, Liz Clark-Garvey shares her own knowledge of unit rates but does so only after having used an interactive activity to create a shared set of experiences with her students.

Have a look:

It’s worth noting what the teacher does with her explanation:

1. She reminds students of previous learning. (A number talk.)

2. She models several example rows from the table.

3. She responds to a student’s hypothesis by interpreting it through ideas offered by two students, Gael & Zoli. (This is an absolutely breathtaking moment IMO.)

4. She summarizes the learning of the day.

5. She invites students to try another example on their own.

Schwartz and Bransford’s research suggests the teacher’s students have learned more because of their shared experiences than they would have if the teacher had shared her knowledge straight away.

Moreover, students are always learning more than math in math class. I invite you to wonder what the teacher’s students have learned about their capacity to think valuable mathematical thoughts, about their relationship to power, about their value in that class, to have heard their teacher speak about the experiences they share, rather than just about the stuff she herself knows.