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Tool: Teaching for mathematical content

More and more teachers are involving their students in problem-solving discussions. Having children present solutions to the class offers them the opportunity to explain their thinking. Also, presenting multiple solutions for any problem helps children to see mathematics as flexible and creative. It also allows them to make connections between various mathematical ideas.

However, if the discussion goes no further than the presentation of several solutions, then valuable opportunities for learning are lost. It is the role of the teacher to make connections between children's solutions, to highlight the mathematical values of efficiency and accuracy and to pull big mathematical ideas out of children's work. Although much of this teaching happens in-the-moment, planning ahead can help you recognize and act upon opportunities for learning when they occur.

Teaching for mathematical content during problem solving

The Problem:




Likely solutions strategies:

1. 2. 3. 4.


Remember, variety is not a goal in and of itself. Sometimes students will continue to use manipulatives long after they need them simply to have a “different” solution. We want children to be able to use algorithms and abstract thinking. Which of these strategies is most efficient? How might you move more children in the class toward abstract solutions?

Which solution strategies will you want presented to the class? What Big Idea will you want students to take away from each of the solutions presented? How can you facilitate the conversation so this happens?



How will you wrap up the lesson? Can you make connections across solution strategies? Should you work toward encouraging other children to try a certain strategy tomorrow? Can you use the problem to transition into an exploration of a new mathematical topic?