# "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:

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

She models several example rows from the table.

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.)

She summarizes the learning of the day.

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*.

In my view, the most effective teaching practice is one that strikes a balance between teacher control and student thinking, and adapts to the needs and strengths of individual students. This requires teachers to be responsive to student thinking, anticipate misconceptions, and provide targeted support and feedback. Ultimately, effective teaching is not just about imparting knowledge, but about facilitating learning and helping students develop the skills and confidence they need to succeed.

In Heibert, et al.'s book, "Making Sense: Teaching & Learning Mathematics with Understanding" (1997, Heinemann) there is a wonderful quote that has guided me about this tension in instruction. It's called 'The Dilemma.' "How to assist students in experiencing and acquiring mathematically powerful ideas but refrain from assisting so much that students abandon their own sense-making skills in favor of following the teacher's directions." (p 29) The authors then go on to say, "rather than resolving the dilemma by choosing one of the options, and rather than resisting or ignoring the dilemma, teachers should embrace it. By remaining open to the tension, teachers can remain sensitive to both the subject and the students... we believe it is possible for teachers to intervene in ways that stimulate and push students' thinking forward and, at the same time, promote students' autonomy... [by creating] an environment in which students reflect on and communicate about mathematics" (p.30)