NBPTS AYA Math flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Van Hiele levels

Five sequential levels of geometric thinking: visualization, analysis, informal deduction, formal deduction, and rigor. Instruction should match the student's current level.

Conceptual vs procedural knowledge

Conceptual knowledge is understanding relationships and principles; procedural knowledge is knowing how to execute steps. Both are needed for mathematical fluency.

Representational fluency

The ability to move flexibly among concrete, pictorial, symbolic, verbal, and contextual representations of the same mathematical idea.

Cognitive load theory

Learning is limited by working memory. Reduce extraneous load, chunk information, and use worked examples for novices to support schema construction.

Backward design

Planning process that starts with desired results (standards), then determines acceptable evidence (assessment), and finally designs learning experiences.

High-cognitive-demand tasks

Tasks that require reasoning, sense-making, and connections rather than memorization or routine procedures. They promote deeper learning.

Three-phase lesson structure

Launch (activate prior knowledge and set purpose), explore (students work on the task), and summarize (synthesize and formalize learning).

Universal Design for Learning

Framework providing multiple means of representation, action and expression, and engagement to support all learners.

Talk moves

Discourse strategies such as revoicing, restating, reasoning, adding on, wait time, and turn and talk that promote student-to-student mathematical discussion.

Five practices for discussion

Anticipating, monitoring, selecting, sequencing, and connecting student responses to orchestrate productive whole-class mathematics discussions.

Productive struggle

Allowing students to grapple with challenging mathematics within reach, building persistence and deeper understanding rather than rescuing too quickly.

Accountable talk

Classroom discourse in which students justify claims with evidence, respond to peers' reasoning, and hold each other accountable to the learning community.

Formative assessment cycle

Elicit evidence of learning, interpret it, act on it through feedback or instructional adjustment, and re-engage students in the learning target.

Hinge question

A single diagnostic question used mid-lesson to determine whether to move on or reteach based on student responses.

Validity and reliability

Validity means an assessment measures what it claims; reliability means results are consistent across occasions or raters.

Analytic rubric

Scoring tool that breaks performance into separate dimensions (e.g., conceptual understanding, procedural fluency, communication) with descriptors for each level.

Equity vs equality

Equality gives everyone the same support; equity provides differentiated support so all students can reach high expectations.

Culturally responsive teaching

Connecting mathematics to students' lived experiences and community contexts to make learning relevant and accessible.

Stereotype threat

Anxiety that one's performance may confirm a negative stereotype about one's group, which can impair performance; reduce by emphasizing belonging and growth.

Flexible grouping

Temporary, purposeful grouping of students based on learning needs or task, avoiding fixed ability groups.

Lesson study

Collaborative professional development in which teachers plan a research lesson, observe it, debrief, revise, and teach it again.

Reflection cycle

A structured process of describing an experience, analyzing it, interpreting meaning, and planning future action to improve practice.

Action research

Systematic inquiry by teachers: identify a problem, implement an intervention, collect and analyze data, and adjust practice.

Professional learning community

A collaborative team of educators focused on student data, shared goals, and collective inquiry to improve teaching and learning.

Family engagement

Building partnerships with families through regular communication, multiple modes, cultural humility, and invitations for input.

Cultural humility

An ongoing openness to learning about families' backgrounds and avoiding deficit assumptions about students and communities.

Co-teaching models

Collaborative arrangements such as one teach/one support, station teaching, parallel teaching, alternative teaching, and team teaching.

IEP/504 collaboration

Coordinating accommodations and modifications with special education staff and families to ensure equitable access to mathematics.

Modeling cycle

Identify a real-world problem, formulate a model, compute, interpret results, validate, and report; the model is an approximation of reality.

Pólya's problem-solving steps

Understand the problem, devise a plan, carry out the plan, and look back to check and reflect on the solution.

Assumptions in modeling

Simplifying conditions stated explicitly when building a model; they affect the model's predictions and limitations.

Model validation

Comparing model predictions with real data and assessing reasonableness, limitations, and potential sources of error.