Embedded Files
Embed review of prerequisite skills in course materials.
Embed review of prerequisite skills in course materials.
Highlight and support student exploration of patterns, critical features, big ideas, and relationships.
Highlight and support student exploration of patterns, critical features, big ideas, and relationships.
Support student exploration of patterns and relationships through questioning to guide information processing
Calculational and Conceptual Orientations in Teaching Mathematics (Thompson et al., 1994.)*
Questioning 5 Talk Moves
Use "Explanatory Questioning" (cognitive science practice) by asking "Why?" questions and encouraging students to engage in self-explanation think alouds or discussing with others (Star & Verschaffel, 2017)**
Model concepts using multiple examples and non-examples.
Model concepts using multiple examples and non-examples.
Worked Examples (cognitive science practice): Lighten cognitive load by asking students to examine multiple worked examples before moving into problem solving practice (Star & Verschaffel, 2017)*
Compare & Discuss / Contrasting Cases draw on cognitive science research to highlight big ideas:
Compare & Discuss Algebra Materials, Compare & Discuss routine, Research evidence, Algebra Worked Example Pairs, blank template
Design problem strings to progressively release problems with increasing complexity and scaffold thinking.
Design problem strings to progressively release problems with increasing complexity and scaffold thinking.
How to design problem strings; Problem string curricula examples: Algebra; Precalculus
Chapter 9 on thin slicing in (Liljedahl, 2020)*
Use discourse strategies to hold students accountable for collaborative information processing.
Use discourse strategies to hold students accountable for collaborative information processing.
Talk moves Discourse: Simple Moves that Work, "Math Talk"
Building community norms: Shifting mathematical authority, classroom norms, RUME classroom authority
Include strategies from cognitive science for facilitating practice (e.g., interleaved practice, spaced practice, retrieval practice).
Include strategies from cognitive science for facilitating practice (e.g., interleaved practice, spaced practice, retrieval practice).
Resources from cognitive science for facilitating practice (retrieval practice, spacing, interleaving): Research summary
Retrieval Practice: Spaced retrieval practice
Interleaving: Interleaving mathematics practice
*Liljedahl, P. (2020). Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning, Grades K-12. Corwin.
*Thompson, P. W., Philipp, R., & Boyd, B. (1994). Calculational and conceptual orientations in teaching mathematics. In 1994 Yearbook of the NCTM
*Star, J., Verschaffel, L. (2017). Providing Support for Student Learning: Recommendations from Cognitive Science for the Teaching of Mathematics. In J. Cai (Ed). Compendium for Research in Mathematics Education. NCTM.
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