I've been doing number talks with my classes for the past year and a bit. I think they are the single most effective way we as teachers can help our classes develop number sense, fact fluency, and fluency with computation strategies. They really do make that much difference, in my experience.
Along with number talks, I'm also a fan of JUMP maths. The founder of JUMP maths, John Mighton, is convinced that we can narrow the achievement gap between our most and least able maths students by making sure that mathematical ideas are broken down into small, understandable steps.
For me, number talks is a huge part of 'breaking down concepts' for children, so that the concepts are accessible to everyone, and not just the children who 'get' maths intuitively. Except teachers aren't the ones breaking the concepts down - children are doing that for themselves, as they reason about numbers, share their reasoning with their classmates, or explain the computation strategies used by someone else. We know that children learn and retain the most when they are teaching others. Number talks expect them to do just that - in a very real sense, our students teach each other, as they explain the strategies they have used to solve the problems we pose.
We've all had children in our class who just seem to 'get' maths - everything about numbers comes intuitively to them. Conversely, we've all also had children who seem to struggle with even simple mathematical concepts. In my brief experience with number talks, I've found that they allow the children who struggle to access numbers in a powerful way. And when we expect ALL of our children (and not just the high fliers) to articulate their mathematical thinking, we send an equally powerful message about their capabilities and our faith in their capabilities.
Number talks empower our students in maths. They take a subject that children are often afraid of, and turn it into something they teach! I love the excitement of children desperate to share with the class 'how they got the answer'. These kids are desperate to teach their classmates, when we provide the structure and setting through number talks. No wonder this is such a powerful mathematical routine. I'm looking forward to digging a bit deeper over the next few weeks of the book study.