A number talk is a 5 to 15 minute daily opportunity for students to use and describe mental math strategies. First several answers are accepted and recorded. Then students are asked to defend their work by describing how they computed the problem. The teacher records their thinking in a way that mirrors the child's process but most likely expands their understanding of how math can look. This process is repeated a number of times with other strategies, so all students get to hear and see several perspectives.
The goal is to increase the students' abilities to compute with accuracy, flexibility, and fluency. Number talks excite me, especially when I think of what would happen if every classroom in a school embraced this practice. These daily conversations across the grade levels would be priceless.
I would highly recommend this book for all classrooms K-5. An added bonus is that it comes with a DVD, which I found to be very helpful. It wasn't the cheapest book, but I saved some money by finding a used copy. It's money well spent though!