Alignment With the Five Core Propositions and Mathematics Standards
The framework
The Five Core Propositions describe what accomplished teachers do: commit to students and their learning; know the subject and how to teach it; manage and monitor learning; think systematically and learn from experience; and participate in learning communities. The Mathematics Standards name the certificate's expectations, including Knowledge of Mathematics, Knowledge of Students, Equity, Diversity, and Fairness, Curriculum, Instruction, Assessment, Learning Environment, Technology, Collaboration, Reflection, and Professional Growth.
Core rules
- A citation is not evidence. Name the proposition or standard, then describe the behavior that shows it.
- Equity means access to challenging mathematics with the support each student needs, not identical tasks for all.
- Monitoring learning requires a source of evidence: exit tickets, interviews, error analyses, assessment data.
- Reflection means naming a specific decision and a specific revision, not praising the lesson.
- Collaboration includes work with families and colleagues, not only meetings attended.
Worked example
A teacher notices that multilingual students are silent during group work, though their written work is strong. She introduces structured talk moves, assigned roles, and a sentence frame ("I agree because..."). She monitors with a participation tally and a short exit prompt. This maps to Proposition 1 (commitment to students), Proposition 3 (monitoring learning), and the Equity standard, and the tally gives evidence rather than assertion. Sharing the results with the department maps to Proposition 5.
Traps that cost marks
Listing proposition numbers without describing behavior; treating equity as "same task for everyone"; using technology as a checkbox; describing reflection as retelling; and claiming collaboration without an artifact or outcome.