NCTM’s Principles to Actions describes effective teaching practices, conditions, and structures to ensure mathematics learning environments that benefit all learners. A simple assessment of whether or not a mathematics classroom is learner-centered is to ask the following questions: **Who is carrying the cognitive load in your classroom during mathematics lessons? Who is doing the mathematics? Who is doing the thinking and talking?**

These curated resources, produced by reputable experts in the field, may help you create a dynamic learning environment that promotes mathematical understanding, thinking, and student voice.

**I. Creating Cultures of Thinking: The 8 Forces We Must Master to Truly Transform Our Schools**** (Ron Ritchhart)**

**II. Mathematical Tasks**

- Mathematical Tasks as a Framework for Reflection: From Research to Practice (Smith & Stein)
- Selecting and Creating Mathematical Tasks: From Research to Practice (Smith & Stein)
- Thinking Through a Lesson: Successfully Implementing High-Level Tasks (NCTM paid article)
- The October 2016 issue of
*Educational Leadership*offers other ideas on general lesson planning with some direct applications to mathematics classrooms! (Some articles are paid access)

**III. Promoting Student Discourse**

- How to Get Students Talking! Generating Math Talk That Supports Learning
- 5 Practices for Orchestrating Productive Math Discussions (summary)
- Never Say Anything a Kid Can Say! (NCTM paid article)
- Connecting Mathematical Ideas (book with classroom videos)

**IV. Using Questioning to Elicit Student Thinking & Promote Discourse**

- PBS TeacherLine Tips for Developing Mathematical Thinking
- The Art of Questioning in Mathematics (Robert Kaplinsky)

Some thoughts on questioning in the classroom:

- If you want to know what a student is thinking,
. This avoids the “guess what’s in my head” type of questioning which can typically be lower-level recall.**ask a question you do not know the answer to** - Ask a questions that
. How many of your questions require students to answer with a second sentence (or even a single sentence)?**require students to respond with a second sentence (or more)** - What questioning sentence starters could you post in your classroom to encourage student-to-student questioning and explanation of thinking? How can these questioning sentence starters become a classroom norm among teacher-student, student-teacher, and (ultimately) student-student interactions?

**V. Classroom Norms**

So often, it is teachers that design the learning environment and set up the classroom rules and expectations. But do students have a say in designing ** their** learning environment that meets

**needs? Some questions to ponder:**

*their*- Do students have choice and voice in your classroom?
- What is “tight” and what is “loose” in the classroom? Who decides?
- How often do students have the opportunity to provide you with feedback on how the class is running and what should be improved?

The Science Behind Classroom Norming

Some teachers have even adapted the Seven Norms of Collaboration from Adaptive Schools (or had students adapt these norms with their language) to build common collaborative school norms for students and adults alike.