Books

This series of books provides formative assessment probes, along with descriptions of types of errors and possible interventions for each misconception, based on student responses:

Uncovering Student Thinking About Mathematics in the Common Core, Grades K-2
Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5
Uncovering Student Thinking About Mathematics in the Common Core, Grades 6-8

This series of books delves deeper into developmentally appropriate instructional strategies and learning progressions for different grade level spans:

Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2
Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5
Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8

The following book outlines the 5 practices for teachers to facilitate successful math discussions. This is similar to the process used by Brian Tash in his trainings, with more detail about the planning and steps:

5 Practices for Orchestrating Productive Mathematics Discussions

These books discuss mindsets and misconceptions about math, helping teachers, students, and parents to think differently about the subject:

Faster Isn't Smarter
Smarter Than We Think