NBPTS AYA Math study guide
NBPTS AYA Math · Work through your exam, one topic at a time.
National Board Certification in Adolescence and Young Adulthood (AYA) Mathematics is a voluntary, advanced professional credential for teachers of mathematics to students roughly ages 11–18. It is designed for experienced educators who want to demonstrate accomplished practice against the National Board’s standards, not for initial licensure. The NBPTS AYA Math study guide has 8 sections and about 2,241 words.
01Knowledge of Students and Mathematics Content
This section tests whether you understand mathematics deeply and understand the learners in front of you. Content expectations span number and operations, algebraic reasoning, functions, geometry, trigonometry, statistics, and probability at the adolescent level, plus the developmental realities of how adolescents build abstraction, tolerate ambiguity, and reason proportionally.
305 words, about 2 min02Instructional Design and Planning in Mathematics
Planning questions probe whether you can build coherent units backward from enduring understandings and standards, sequence tasks so that concepts emerge before procedures are formalized, and anticipate student thinking before the lesson begins. Backward design: enduring understandings → essential questions → evidence of learning → learning activities.
296 words, about 1 min03Instructional Delivery and Classroom Discourse
Delivery questions focus on how you orchestrate mathematical talk, press students to justify reasoning, and use questioning to move thinking forward without taking over. Talk moves: revoicing, restating, reasoning, adding on, wait time, and turn-and-talk.
284 words, about 1 min04Assessment and Use of Evidence of Student Learning
Assessment questions test your ability to gather valid evidence of understanding, interpret it accurately, and act on it instructionally. summative purposes: assessment for learning versus of learning.
277 words, about 1 min05Learning Environment and Equitable Access
This domain examines whether you build a classroom where all students can do mathematics-where mistakes are treated as information, participation is broad, and barriers are removed rather than lowered. Safe mathematical community: norms that value reasoning, revision, and respectful critique.
262 words, about 1 min06Reflective Practice and Professional Growth
Reflection questions ask you to examine your own practice with evidence, identify a specific problem, and choose a professional learning move that targets it. Reflective cycle: describe → analyze → interpret → plan next steps.
272 words, about 1 min07Collaboration with Families and Colleagues
This domain tests whether you can build productive partnerships with families and colleagues to support student learning, communicate clearly, and navigate disagreement professionally. Family communication: proactive, two-way, jargon-free contact focused on student learning and specific next steps.
261 words, about 1 min08Mathematical Modeling and Problem Solving
This domain asks whether you can engage students in genuine modeling: formulating a problem from a real context, building and revising a model, and interpreting results critically. Modeling cycle: identify a problem → make assumptions → build a model → analyze → interpret and validate → revise or report.
284 words, about 1 min