OGET OGET Mathematics Foundations & Pedagogy 1 — Questions and Answers
Question 1: Which instructional model moves students from physical objects, to pictures, to abstract symbols in mathematics learning?
- I Do, We Do, You Do
- Concrete-Representational-Abstract (CRA) (Correct answer)
- Direct instruction model
- Socratic method
Correct 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.
Question 2: A student solves 8 × 7 by thinking '8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56.' This demonstrates use of the:
- Commutative property
- Associative property
- Distributive property (Correct answer)
- Identity property
Correct 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.
Question 3: Which type of mathematical reasoning involves drawing a general conclusion from a set of specific examples?
- Deductive reasoning
- Inductive reasoning (Correct answer)
- Proportional reasoning
- Spatial reasoning
Correct 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.
Question 4: A teacher wants students to understand place value conceptually. Which manipulative is MOST appropriate?
- Algebra tiles
- Base-ten blocks (Correct answer)
- Fraction circles
- Geoboards
Correct 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.
Question 5: Which approach to problem-solving in mathematics encourages students to try multiple strategies and discuss their reasoning with peers?
- Rote memorization
- Standard algorithm drill
- Problem-based learning (Correct answer)
- Direct recall practice
Correct 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.
Question 6: When a student consistently makes errors computing with fractions because they add both numerators and denominators, the teacher should first address:
- Memorization of fraction rules
- Conceptual understanding of what fractions represent (Correct answer)
- Timed practice drills
- Calculator use
Correct 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.
OGET OGET Mathematics Foundations & Pedagogy 1
Which instructional model moves students from physical objects, to pictures, to abstract symbols in mathematics learning?