You know how it is- you are doing an amazing number talk with your students. They are sharing all sorts of interesting mental math ways to solve the problems and you think, "This is good!" Then you realize that you only have maybe half of your students (and somedays that is a high estimate) really engaged in the process. The rest, and in my case, it is usually my lower kiddos are really not engaged or paying attention to the strategies. Either they are lost because the strategies are beyond their realm of thinking at the time or they just are not engaged. What can you really do and still maintain the structure and purpose of the number talk?
One quick fix is to prepare a set of double sided cards. You choose the colors- mine are blue and green. I used leftover cardstock and I cut 3 x 5 inch cards out of the cardstock and glued them together so I have blue on one side and green on the other. Then, I laminated them. At the start of the number talk, I give the cards to the students. I explain that they start with the cards in their laps. When they know the answer, they place the card on their desk- they can choose which side is up. If it's blue, that means they have an answer, but they don't want to share. If the card is green, they have an answer and they are willing to share their strategy. This is a quick way to make students accountable, and it makes it easy for you to choose someone to share.
Another way to make students accountable is to ask them at the end of the number talk to use finger signals to indicate the most efficient strategy. After students have shared their strategies (and you've numbered them) ask students to choose which strategy they think is most efficient. By doing this you can informally see where the students are in their thinking and can plan accordingly with additional number talks.
A third way to provide some accountability is to hold small-group number talks throughout the week. You can easily add a quick number talk to your small group math instruction. And, holding the number talk in a small group allows you to really hone in on particular skills that certain students need.
Class anchor charts explaining different strategies is another great way to hold students accountable. When you make the strategies visible in the classroom, it provides a great reference for the students and holds them accountable because the information is right there on the wall!
Another way to hold students accountable for the strategies they are learning in number talks is by asking them to solve an exit ticket problem. Give students an index card or half-sheet of paper. Pose a problem that will require them to use the strategies you've been working on. Ask students to use one side of the paper to solve the computation using a strategy that was shared during number talks. On the other side of the paper, they can solve it with their choice of strategy. Doing this give you a quick look at individuals and their understandings and misconceptions. It also helps you choose the next direction you want to go with further number talks. But, don't use these as a grade- simply use the information gathered to guide your instruction.