Vicki Jacobs, CGI Conference 

October 2000 

 

Creating Classroom Communities that Talk Mathematics 

 

1. What types of questions can we ask to help children explain their 
strategies? 

• How did you solve this problem? How did you think about this problem? 
• What did you do (think about) first? 
• How could you prove that (convince us)? 
• How would you explain what you did to a younger child? 


 

2. What types of questions can we ask to help children who are stuck during 
problem solving? 

• What is the problem asking? Tell me what happens in this story. 
• Tell me one thing you know about the problem. 
• What could you do first? 
• Is this problem hard? If so, why -- what makes this problem hard? 
• Would it help to make these numbers a little bit smaller? 
• Would it help to talk with (or listen to) [another child]? 
• Does what you did make sense with the story? 
• Is there a way we could organize these _______ (e.g., cubes, tallies, pictures, etc.) so that it 
would be easier to keep track? 


 

3. What types of questions can we ask to help children extend their thinking? 

To encourage articulation of and reflection on specific parts of a child’s strategy: 

• Why did you _______? (e.g., switch to counting by 10s here, put out 6 cubes, etc.) 
• How did _______ help you solve the problem? (e.g., linking the cubes together in a long 
train, drawing all the leaves on the tree, etc.) 
• What makes using _______ difficult? (e.g., lots of tally marks, cubes, pictures, etc.) 
• What does _______ represent in the story? (e.g., this color cube, these circles, etc.) 
• If you were to do this problem again, would you do anything differently? 


 

To encourage (or reinforce) more sophisticated counting or strategies: 

• Are there other ways that you could count these _______ to make it easier (or faster)? 
• (e.g., cubes, tally marks, cupcakes, etc.) 
• Could you try what you just did with the _____ in your head? (e.g., the cubes, a picture, etc.) 


 

To encourage flexible use of strategies: 

• How could you solve the problem a second way? 
• How could you solve the problem using _______? (e.g., cubes, a picture, etc.)? 
• Remember how the other day you solved the ____ problem using _____, could you use that 
strategy with this problem? (could be in reference to a previous strategy of that child or a 
strategy discussed in class) 
• How would it change your work if _______ (e.g., the baseball cards came in groups of 11 
instead of 10, another group was added or taken away, etc.) 
• How could you write down how you solved your problem? 



4. What can we do to help children listen to and learn from each other? 

 

Suggestions for initial sharing discussions: 

• Consider having children begin sharing with an easy problem. 
• Consider working in small groups initially so children learn to share and listen in a more 
manageable environment. 
• Consider writing problems about the children in your class so that the child who is in the 
problem is especially motivated to share. 


 

Questions to encourage active listening: 

• Could anyone else explain how [child] solved the problem? 
• Can anyone explain why [child] did _______? (e.g., put the cubes in groups of four, circled 
each group of 10 tally marks, etc.) 
• Does everyone understand what [child] is saying? Does anyone have a question or 
compliment for [child]? 
• Who would like to share that has a different strategy? 
• Is [child’s] strategy similar to anyone else’s strategy we heard? If so, how are they similar? 
How is [child A]’s strategy and [child B’s] strategy similar? (different?) 


 

Other techniques to encourage listening to other children’s strategies: 

• Ask a child to begin explaining his/her strategy and then ask if anyone else could finish the 
explanation. 
• Ask a child to write his/her work on the board but not explain it. Ask other children to 
explain the strategy from looking at the written work. 
• Have children write their strategies on the board or overhead before the sharing discussion 
begins so no one has to watch the often time-consuming process of re-writing a strategy. 
• After a child has shared a strategy, ask the rest of the children to solve the next problem 
using the strategy that was just shared. 


 

Things to consider when choosing which child shares: 

• Should everyone share? 
• Has anyone had a particular breakthrough today? 
• Should the easier strategies come earlier in the discussion? 
• Should a more sophisticated strategy be shared – will anyone understand? 
• Which (if any) wrong answers should be shared?