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Provide structures and scaffolds to facilitate organized note-taking and solution planning.
Provide structures and scaffolds to facilitate organized note-taking and solution planning.
Guided notes
Effectiveness in math education: (Cardetti et al., 2010)*
Integrating UDL in "guiding notes:" (Bertrand et al., 2025)*
"Scaffolding and fading:" gradually increasing the frequency and size of blank spaces as a term progresses (Krapf & Pfefferkorn, 2022; Reed et al., 2016)*
Use checklists and templates to support solution planning
Integrate activities and/or structures that help students monitor their progress.
Integrate activities and/or structures that help students monitor their progress.
Incorporate formative assessments (see resources for Expression and Communication)
Utilize questions/prompts that encourage metacognition and reinforce learning
Questions to encourage students to use intuition throughout problem solving
Examples modeling "pause and ponder" (The paradox of the derivative, Linear transformations and matrices)
Embed opportunities for self-reflection (see resources for Emotional Capacity)
Support the development of students’ metacognition to aid in problem solving.
Support the development of students’ metacognition to aid in problem solving.
Improve problem solving with regular use of metacognitive prompts such as "What are you doing? How are you doing it? (and) How does it help you?" (Schoenfeld, 1985; Star & Verschaffel, 2017)*
Polya's general problem solving approach (understand the problem, devise a plan, carry out a plan, look back and reflect)
*Bertrand, E., Keazer, L., & Phaiah, J. (2025). From guided to guiding: Optimizing note-taking scaffolds with universal design for learning. [Manuscript submitted for publication.]
*Cardetti, F., Khamsemanan, N., & Orgnero, M.C. (2010). Insights regarding the usefulness of partial notes in mathematics courses. Journal of the Scholarship of Teaching and Learning, 10: 80–92. https://files.eric.ed.gov/fulltext/EJ882128.pdf
*Krapf, R. & Pfefferkorn, L. (2022). How does the provision of guided notes affect student learning in mathematics? International Journal of Research in Undergraduate Mathematics Education, 8: 642-670. https://doi.org/10.1007/s40753-021-00160-x
*Reed, K. D., Rimel, H., & Hallett, A. (2016). Note-taking interventions for college students: A synthesis and meta-analysis of the literature. Journal of Research on Educational Effectiveness, 9(3): 307–333. https://doi.org/10.1080/19345747.2015.1105894
*Schoenfeld, A. H. (1985). Mathematical Problem Solving. Academic Press.
*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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