Key Ideas from Effective Pedagogy in Mathematics

Strong Mathematical Focus

Realistic Expectations

Classroom Routines

Real World Context

Errors = Deeper Understandings

Modified Tasks and Alternative Pathways

Multiple Connections Within and Across Topics

Sharing Solution Strategies = Powerful / Fluent / Accurate Mathematical Thinking

Multiple Representations and Relationships

Less Focus on Right Answers, More Focus on Thinking That Leads to the Answers (Explain, Defend, Justify)

Revoicing = Repeating, Rephrasing, Expanding on Student Talk

Listen to Others, Debate, Resolve Conflict, Arrive at Common Understandings. Teacher Withholds Own Explanations Until Needed

Students Can Use and Generate Own Representations - It Provides Insight Into Student Thinking

With Guidance, Technological Tools Can Link to the Real World

Move Away From Tools as External Aids Toward a Part of Mathematical Reasoning

Independent Thinking Time

Whole-Class Discussion

Partners and Small Groups

Mathematical Struggle

Open-Ended Tasks Beyond "Right Answers"

Practice Activities (Big Idea Connections / Strategical Games

Observe Students / Conversations to Further Class Discussion

1-on-1 Interviews Highlight Diverse Learning Needs

Open-Ended Questions Provide Insight Into Student Thinking / Reasoning

Mathematical Language Versus Home Language

Code Switching Can Help Students Grasp Underlying Meanings (e.g., Moving From Similar Toward Ratio/Scale)

Model Appropriate Terms and Communicate in Ways Students Understand

Teachers See Potential in Tasks They Set, Leading to Sound Instructional Decision Making

Teachers Need a Grounded Understanding of Students as Learners (e.g., Conceptions and Misconceptions)

Teachers With Sound Knowledge More Apt to Notice Critical Moments and Modify Their Routines to Fit the Need