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
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
Likely solutions strategies:
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
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?