## Participation in math class

Nothing you can do can guarantee that every child actively participates in your math class but there are some things you can do to increase the odds.

Source: Wikipedia

In a typical classroom a teacher asks a question, a student responds, the teacher indicates whether the response is incorrect or correct, and this is repeated until the class discussion is over. If this is the only type of interaction a teacher has with their students, this can be problematic.

1. It’s very difficult to keep track of who has participated and who has not which often leads to skewed participation in the conversation.
2. It’s impossible to know how each child understands the mathematical ideas being discussed.Here’s an example Dylan Wiliam uses to illustrate this point: If a teacher asks four questions in a row of four different children and the responses to the first three questions from children are incorrect but the fourth is correct, the only thing that can be concluded is that the fourth child was able to answer that question but what is typically concluded is that the class understands and so the teacher moves on. Unfortunately I myself am guilty of this many, many times. All too often we stop questioning when we get a correct response.

Fisher and Frey (2007) say the following on this matter:

a few of you will answer
for the entire class,
and we’ll all pretend
this is the same thing as learning.”

But what can we do differently? How can we minimize this kind of interaction? Note that it is probably not possible to completely eliminate these types of interactions, nor would it necessarily be advisable to do so, but there are some ways to reduce their impact on a classroom.

Turn and talk:

Prompt students to talk to each other about a question while you circulate and listen for responses (and hold students accountable for talking about what you want them to talk about). Come back to the whole class and ask a few people to share responses. This has the benefit of increasing the chance every student shares an idea with at least one person and increases the amount of time students have to process and think about the question.

Wait time:

The average amount of time teachers wait for a response after asking a question is less than one second. Just delaying this to five seconds (or even more sometimes) increases the amount of students who have time to process the question, think about it, and then formulate a response.

Whiteboards:

Instead of posing a question and waiting for one response, pose a question and ask students to, either individually or with a small group, construct a response that they can share on their whiteboards. This way you can walk around and see what ideas students have and every student has an opportunity to take their time to think about the question.

Use student generated questions:

There is some evidence that students do better when they own their learning. Having students generate questions they have and allowing students to answer each other’s questions (perhaps initially mediated by you) or you to answer questions they have, gives students more control over their own learning. Of course, students are often not used to this kind of interaction and will likely need support of some kind in generating questions.

It is extremely common to start class with a somewhat interactive description of how to solve a problem, give students opportunity for guided practice with lots of feedback, followed by independent practice, followed by a summary by the teacher or a student of what was learned that day. In this case, any questions that are asked within the context of the entire class can only really happen either during the initial describing of how to solve the problem at the beginning of the class or during the summary at the end.

An alternative to this approach is to start with a problem where you can be reasonably sure all students understand what the problem is and what they are trying to find out. Now when you initiate any full group discussion, students are much more likely to have questions and the answers to these questions are much more likely to be understood by everyone.

Note that I’m not a fan of cold calling students. With some students, having a teacher who cold calls raises their anxiety, making it more difficult for them to think about the mathematics. It might be a useful technique once you know every student feels comfortable and has something to say.

What other strategies can you use to encourage participation (even non-verbal participation) in your classroom?

• Thanks for this helpful post! Even though you know better it is easy to fall into trap of asking class Qs and moving on.
I often tell students they have to make a commitment and write down their answer, even if it’s wrong. Then I circulate and see what they wrote.

• Peter Smyth wrote:

This is how we can and should teach.
What we can’t afford to do is shortchange what it takes for a teacher to get here – in terms of background knowledge, preparation, practice, and reflection.
It takes what Deb Ball calls MKT: Mathematical Knowledge for Teaching.
It takes making your teaching a craft, and it’s long term.

• It was with college engineering students, but it should work anywhere. I would ask the question and write all the answers on the board, and say “What now?” or something similar.The ones who “knew” they were right were the most disturbed by this! After a sometimes lengthy discussion a single answer was agreed on.

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• I like the quote. Whiteboards are definitely the best instantaneous formative assessment of a whole class’ understanding. We all need to increase that wait time. If it’s just a short recall answer, I put my hand to my ear so they can shout it out, because I don’t want to waste wait time on a low cognitive question.

• I am using this quote. It so clearly states what is so easy to do “in the interest of time.”

This is a great reflection with some very practical solutions for increasing participation.

• Thought-provoking post!
Turn &I talk is my go-to strategy when I ask a question and the silence is deafening.

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