STEM Mathematics Teaching Methods 2 — Questions and Answers
Question 1: A teacher uses algebra tiles to help students model polynomial factoring. This approach best exemplifies which instructional principle?
- Rote memorization of procedures
- Concrete-Representational-Abstract (CRA) progression (Correct answer)
- Direct instruction only
- Summative assessment design
Correct answer: Concrete-Representational-Abstract (CRA) progression
The CRA framework moves students from physical manipulatives (concrete) through diagrams (representational) to symbolic notation (abstract).
Question 2: Which formative assessment strategy gives real-time data about student understanding during a math lesson without interrupting flow?
- End-of-unit test
- Mini whiteboards for simultaneous response (Correct answer)
- Portfolio collection
- Standardized benchmark exam
Correct answer: Mini whiteboards for simultaneous response
Mini whiteboards allow all students to display answers at once, giving the teacher immediate whole-class data.
Question 3: When differentiating a geometry lesson, a teacher offers three versions of a task at varying complexity levels. This strategy is called:
- Scaffolding
- Tiered tasks (Correct answer)
- Cooperative learning
- Think-Pair-Share
Correct answer: Tiered tasks
Tiered tasks present the same core concept at different levels of complexity to meet diverse learners' needs.
Question 4: A student consistently reverses the inequality sign when multiplying both sides by a negative number. The teacher's most targeted intervention is to:
- Assign more inequality practice problems
- Use a number-line demonstration showing direction reversal with a specific counter-example (Correct answer)
- Move on and revisit in a future unit
- Remove negatives from future inequality tasks
Correct answer: Use a number-line demonstration showing direction reversal with a specific counter-example
A concrete number-line counter-example directly addresses the misconception by making the sign reversal visually meaningful.
Question 5: Which questioning technique encourages students to justify mathematical reasoning rather than just state answers?
- Closed recall questions
- Funneling questions toward a single answer
- Focusing questions that probe student thinking (Correct answer)
- True/False questions
Correct answer: Focusing questions that probe student thinking
Focusing questions redirect attention to student reasoning and require explanation, deepening conceptual understanding.
Question 6: To address math anxiety in a high school classroom, the MOST effective environmental approach is:
- Timed drills to build fluency under pressure
- Eliminating all assessments
- Normalizing mistakes as part of the learning process through a growth mindset culture (Correct answer)
- Only assigning easy problems
Correct answer: Normalizing mistakes as part of the learning process through a growth mindset culture
A growth mindset culture reduces fear of failure and has been shown to lower math anxiety and increase persistence.
Question 7: A teacher wants students to discover the Pythagorean theorem before formally stating it. Which activity best supports this inquiry approach?
- Reading the theorem from the textbook
- Memorizing a² + b² = c²
- Drawing squares on each side of right triangles and comparing areas (Correct answer)
- Watching a video proof
Correct answer: Drawing squares on each side of right triangles and comparing areas
Building and comparing squares on triangle sides lets students observe the area relationship empirically before the formula is formalized.
STEM Mathematics Teaching Methods 2
A teacher uses algebra tiles to help students model polynomial factoring.
This approach best exemplifies which instructional principle?