Strong instruction requires both deep content knowledge and the ability to interpret and respond to student thinking. Teachers must not only understand mathematical concepts but also anticipate how students engage with them, allowing for responsive, effective instruction.
​
-
Mathematical Knowledge for Teaching (MKT) (Ball, et al) highlights that effective instruction requires understanding how students reason mathematically, anticipating misconceptions, and guiding discussions that deepen understanding.​
​
-
Building Thinking Classrooms in Mathematics (Peter Liljedahl) shows that students learn best when they actively engage in problem-solving, collaborate with peers, and construct their own understanding through discussion and exploration.
Rather than focusing on getting the correct answer quickly, students need opportunities to grapple with mathematical ideas, communicate their reasoning, and make sense of problems in multiple ways. Rich discourse and productive struggle are essential to this process.
​
-
The 5 Practices for Orchestrating Productive Mathematics Discussions (Margaret S. Smith & Mary Kay Stein) provides a framework for facilitating meaningful mathematical conversations that encourage reasoning and sense-making.
​