Key Ideas from Effective Pedagogy in Mathematics
Effective teaching in mathematics requires a deep understanding of both the subject and students' learning processes. Teachers with robust knowledge are better equipped to identify critical moments in the classroom and adapt their teaching strategies accordingly.
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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
