OGET Mathematics Foundations & Pedagogy Flashcards

Which instructional model moves students from physical objects, to pictures, to abstract symbols in mathematics learning?

Answer: Concrete-Representational-Abstract (CRA)

The CRA (Concrete-Representational-Abstract) progression, supported by research, builds conceptual understanding by first using manipulatives, then drawings, then symbols.

A student solves 8 × 7 by thinking '8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56.' This demonstrates use of the:

Answer: Distributive property

The distributive property states that a(b + c) = ab + ac; here the student distributes 8 across (5 + 2) to decompose a harder fact into easier ones.

Which type of mathematical reasoning involves drawing a general conclusion from a set of specific examples?

Answer: Inductive reasoning

Inductive reasoning moves from specific observations or examples to a general rule or pattern, commonly used when students discover mathematical relationships through exploration.

A teacher wants students to understand place value conceptually. Which manipulative is MOST appropriate?

Answer: Base-ten blocks

Base-ten blocks represent ones, tens, hundreds, and thousands as physical units, helping students build a concrete understanding of place value and regrouping.

Which approach to problem-solving in mathematics encourages students to try multiple strategies and discuss their reasoning with peers?

Answer: Problem-based learning

Problem-based learning presents open-ended, real-world problems that require students to apply mathematical thinking, collaborate, and justify their reasoning.

When a student consistently makes errors computing with fractions because they add both numerators and denominators, the teacher should first address:

Answer: Conceptual understanding of what fractions represent

Adding denominators shows the student lacks conceptual understanding of fractions as equal parts of a whole; instruction should rebuild this foundational concept before procedures.