Key Ideas from Effective Pedagogy in Mathematics
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
