TExES EC-6 Mathematics Instruction & Problem Solving 5 — Questions and Answers
Question 1: A teacher wants to assess whether students understand division conceptually, not just procedurally. Which task BEST reveals conceptual understanding?
- Solve 36 ÷ 4 using the standard algorithm
- Explain what 36 ÷ 4 means using a real-world sharing or grouping situation (Correct answer)
- Complete a division drill with 20 problems in 3 minutes
- Recite division facts in order
Correct answer: Explain what 36 ÷ 4 means using a real-world sharing or grouping situation
Connecting division to real-world contexts demonstrates whether students understand the meaning of the operation, not just the procedure.
Question 2: Which of the following BEST describes the purpose of using open-ended problems (with multiple solution paths) in mathematics instruction?
- To make grading easier for the teacher
- To promote flexible thinking and allow students to demonstrate different levels of understanding (Correct answer)
- To ensure all students get the same answer
- To eliminate the need for procedural practice
Correct answer: To promote flexible thinking and allow students to demonstrate different levels of understanding
Open-ended problems support differentiation and develop mathematical flexibility by valuing diverse valid approaches.
Question 3: A student solves 5 × 0 = 5, reasoning that 'multiplying makes things bigger.' Which instructional approach BEST corrects this overgeneralization?
- Mark the answer wrong and ask the student to redo it
- Show that 5 groups of 0 objects total 0 objects using a concrete model (Correct answer)
- Tell the student the zero property rule and have them memorize it
- Provide extra drill problems involving zero
Correct answer: Show that 5 groups of 0 objects total 0 objects using a concrete model
Modeling 5 groups of 0 with physical objects directly refutes the misconception by showing that the product must be zero.
Question 4: Which approach BEST helps students understand that the equal sign means 'the same as' rather than 'the answer comes next'?
- Always write equations with the answer on the right (e.g., 3 + 4 = 7)
- Present equations in varied formats such as 7 = 3 + 4 and 3 + __ = 7 (Correct answer)
- Avoid using the equal sign until third grade
- Teach students to write the answer immediately after the sign
Correct answer: Present equations in varied formats such as 7 = 3 + 4 and 3 + __ = 7
Presenting equations in non-standard formats builds understanding of equality as a relationship between two equivalent expressions.
Question 5: A teacher integrates a real-world project where students calculate the cost of supplies for a class party. Which best describes the primary mathematical benefit of this task?
- Students practice writing numbers neatly
- Students apply mathematical skills in context, developing problem-solving and reasoning (Correct answer)
- Students learn to use a calculator correctly
- Students are motivated by the party rather than the math
Correct answer: Students apply mathematical skills in context, developing problem-solving and reasoning
Real-world contexts develop the ability to apply mathematical reasoning to authentic situations, which deepens understanding and engagement.
Question 6: Which intervention strategy is MOST appropriate for a student who understands single-digit addition but struggles to transfer the skill to two-digit addition?
- Reassign single-digit addition worksheets as remediation
- Use place-value charts and base-ten blocks to make the structure of two-digit numbers explicit (Correct answer)
- Move the student to a lower math group permanently
- Focus solely on memorization of two-digit addition facts
Correct answer: Use place-value charts and base-ten blocks to make the structure of two-digit numbers explicit
Making place-value structure explicit with visual tools helps students see how single-digit strategies extend to larger numbers.
Question 7: A teacher presents this data to students: the class collected 12 cans Monday, 9 Tuesday, 15 Wednesday. She asks students to find the total and decide whether they met a 40-can goal. Which skill does this task PRIMARILY develop?
- Geometric reasoning
- Multi-step problem solving with data interpretation (Correct answer)
- Measurement conversion
- Identifying geometric patterns
Correct answer: Multi-step problem solving with data interpretation
Students must add multiple quantities and then compare the sum to a target, integrating computation with data-based reasoning across multiple steps.
TExES EC-6 Mathematics Instruction & Problem Solving 5
A teacher wants to assess whether students understand division conceptually, not just procedurally.
Which task BEST reveals conceptual understanding?