Key Ideas from Effective Pedagogy in Mathematics

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Philosophical Foundations of Education and Curriculum Planning

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The Enlightenment

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Key Ideas from Effective Pedagogy in Mathematics

Teacher Knowledge

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

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

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

Mathematical Language

Model Appropriate Terms and Communicate in Ways Students Understand

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

Mathematical Language Versus Home Language

Assessment For Learning

Open-Ended Questions Provide Insight Into Student Thinking / Reasoning

1-on-1 Interviews Highlight Diverse Learning Needs

Observe Students / Conversations to Further Class Discussion

Worthwhile Tasks

Practice Activities (Big Idea Connections / Strategical Games

Open-Ended Tasks Beyond "Right Answers"

Mathematical Struggle

Arranging for Learning

Partners and Small Groups

Whole-Class Discussion

Independent Thinking Time

Tools and Representations

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

With Guidance, Technological Tools Can Link to the Real World

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

Mathematical Communication

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

Revoicing = Repeating, Rephrasing, Expanding on Student Talk

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

Making Connections

Multiple Representations and Relationships

Sharing Solution Strategies = Powerful / Fluent / Accurate Mathematical Thinking

Multiple Connections Within and Across Topics

Building on Student Thinking

Modified Tasks and Alternative Pathways

Errors = Deeper Understandings

Real World Context

An Ethic of Care

Classroom Routines

Realistic Expectations

Strong Mathematical Focus