NBPTS MC Math flashcards

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

Rational number definition

A number expressible as a fraction a/b where a and b are integers and b is not zero. This excludes division by zero and includes terminating and repeating decimals.

Proportional relationship test

Two quantities are proportional only if the ratio y/x is constant for all pairs and the graph passes through the origin. A linear graph with a nonzero intercept is not proportional.

Function vertical-line test

A relation is a function if and only if no vertical line intersects its graph more than once, meaning each input has exactly one output.

Interior angle sum formula

For a polygon with n sides, interior angles sum to (n minus 2) times 180 degrees. A quadrilateral therefore sums to 360 degrees.

Mean versus median choice

Use the mean with standard deviation for roughly symmetric data; use the median with interquartile range when data are skewed or contain outliers, because the median is resistant.

Independent events multiplication rule

For independent events, the probability of both occurring equals the product of their individual probabilities. Independence means one outcome gives no information about the other.

Decimal comparison misconception

Students who call 3.45 larger than 3.5 are comparing digit strings rather than magnitudes. Remediate with number-line placement and place-value decomposition.

Anticipating student strategies

Pedagogical content knowledge includes predicting methods students will use, such as counting on or making ten, and selecting tasks that reveal the underlying mathematical structure.

Independent entry scoring

Each ePortfolio entry is scored separately against its own rubric. Strength in one entry cannot compensate for a missing required artifact or unaddressed rubric element in another.

Evidence specificity requirement

Analysis must cite dated, specific evidence from submitted work, quoting student reasoning directly with identifiers substituted for names rather than making general claims about growth.

Before-and-after impact claim

A claim of impact needs baseline evidence, the instructional decision made, and post-instruction evidence tied to the same learning goal, so change can be attributed.

Reflection quality standard

Reflection explains why an instructional move suited those learners, including alternatives considered and rejected, rather than merely narrating the sequence of activities.

Video entry scoring focus

Video entries are judged on student mathematical discourse and the teacher's questioning moves. Editing that conceals the teacher's in-the-moment decisions weakens the evidence.

Differentiation evidence

Accomplished practice shows specific adaptations for named learner groups, such as English learners or students with disabilities, together with the reasoning behind each adaptation.

Word-limit compliance

Exceeding a stated maximum length can make a response unscorable. Plan the structure and argument before drafting so the required analysis fits within the limit.

Assessment center format

Assessment center exercises are timed, computer-delivered prompts specific to the certificate area, each scored holistically on a rubric scale such as 0 to 4.

Top rubric descriptor

The highest rubric level typically requires accurate mathematics, explicit and generalizable reasoning, and substantive attention to student thinking, not just a correct answer.

Zero-score conditions

A score of zero is reserved for responses that are off-topic, illegible, or fail to address the prompt. Mere inaccuracy usually lands at a low passing-range level instead.

Two-part prompt rule

Many prompts require solving a mathematics task and explaining the pedagogy. Omitting either half caps the score even when the other half is strong.

Reasoning over answer

A correct answer with no visible reasoning can score below a correct answer with clear justification, because the rubric rewards generalizable mathematical explanation.

Timed exercise budgeting

Skim all prompts first, allocate minutes per prompt in proportion to the number of required parts, and reserve time to verify arithmetic and units.

Misconception response structure

When asked for an instructional decision, name the misconception, cite the evidence revealing it, and specify the task or question that would address it.

Core Proposition One

Teachers are committed to students and their learning. Evidence includes high expectations for every learner and knowledge of how students develop mathematically.

Core Proposition Two

Teachers know their subjects and how to teach them. Evidence includes representing concepts in multiple ways and anticipating specific student misconceptions.

Core Proposition Three

Teachers manage and monitor student learning. Evidence includes varied assessment, clear learning goals, and adjusting instruction based on collected evidence.

Core Proposition Four

Teachers think systematically about practice and learn from experience. Evidence includes reflection, professional reading, and revising a lesson after examining student data.

Core Proposition Five

Teachers are members of learning communities. Evidence includes collaboration with colleagues and families and purposeful use of community resources.

Alignment traceability rule

Every portfolio claim should trace to a named Core Proposition or mathematics standard, with the artifact serving as proof rather than the assertion standing alone.

Process standards in evidence

Mathematics standards pair content with process goals: problem solving, reasoning and proof, communication, connections, and representation should all appear in submitted evidence.

Concrete-representational-abstract

Introduce concepts with manipulatives, move to drawings and number lines, then to symbols, checking that students can translate among all three representations.

Multiplicative versus additive

Adolescent learners must distinguish additive comparisons from multiplicative ones. Tasks should require explicit reasoning about ratio and rate rather than repeated addition.

Language supports in mathematics

English learners benefit from sentence frames for justification, visual glossaries, and paired discussion before written explanation, keeping mathematical demand intact.