- Math conferences between teachers and students can help broaden their understanding of a new concept as they work through problems.
- Allowing students time to ask questions or hear responses from their peers provides an active learning opportunity that can help strengthen their grasp of mathematics. These conversations can start as early as elementary school and continue through middle and high school.
- “When teachers are able to talk to students and have them make their thinking visible, they can then support that student to engage more deeply in mathematics, support their making connections, and help them build on their learning,” said Trena Wilkerson, president of the National Council of Teachers of Mathematics.
When applied to mathematics, active learning helps students develop into “thinkers and doers,” said Wilkerson. Student-teacher conferences, in which educators engage with young students as they work, can help parse how a student is thinking and provide scaffolding as needed. Additionally, this process gives students time to absorb new steps, which they can apply to other concepts down the road.
To Wilkerson, active learning is a far better technique than pure memorization. Students may be able to find an answer with that approach, but they won’t be able to apply those steps — or concepts — to the next level in math. As math tends to build on itself as students move from grade to grade, a conceptual understanding is preferable.
“When something is memorized without meaning and a person is interrupted in the middle of solving a problem, for example, they often have to start back at the beginning to continue the process. They must go back through the steps,” she said. “This approach to memorization of tricks without understanding invariably comes crashing down for the student. They are not able to make mathematical connections and utilize their learning in new situations.”
With elementary school students, educators can focus on a few ways to encourage their younger pupils to speak up and share, math curriculum writer Gina Picha writes for Edutopia. With frequent conversations, students begin to see how their peers appreciate their ideas, and it can also teach listening skills — a nice byproduct.
Conversations in themselves also change the focus for students. Instead of being driven to complete an assignment, pupils begin to put more thought into how problems are constructed and where they could be applied in other settings — and even consider other methods.
It's easier to show young students how to solve a problem, said Wilkerson. But if the expectation for learning is that students can apply what they’ve gleaned to subsequent lessons, they need to know how they came to a conclusion and why that makes sense to them.
“Young children can explore mathematics, pose questions, engage in problem-solving, and justify solutions,” she said. “In doing so they build a positive mathematics identity and have a strong sense of agency as a doer of mathematics This then can carry through in elementary on to middle and high school.”