Organizational scaffolds promote clarity, reduce cognitive load, and support effective problem solving.
Guided notes support students to make connections and get deeper into the learning process.
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
Include reflection questions to encourage students processing in the guided notes and pause to reflect with students during the lesson. Sample questions:
What is the main idea or principle behind this problem/concept?
Which steps or strategies in my solution were most effective, and why?
Did I encounter any points of confusion? How did I address them, or what do I still need to clarify?
How does this concept connect to previous material or other areas of mathematics?
If I were to explain this solution or concept to a peer, what key points would I emphasize?
Progress-monitoring structures support self-regulation, identify growth areas, and guide strategy adjustment.
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)
Metacognitive supports help students plan, monitor, and evaluate their thinking for more effective reasoning.
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. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 35(8), 849-865. https://doi.org/10.1080/10511970.2025.2571608
*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.