TExES EC-6 Mathematics Instruction & Problem Solving 3 — Questions and Answers
Question 1: A student solving 63 − 28 writes: 60 − 20 = 40, then 3 − 8, says 'I can't do that,' and stops. Which instructional strategy addresses this error most directly?
- Teach the student to always regroup before subtracting
- Use base-ten blocks to show trading a ten for ten ones so the ones place has enough to subtract (Correct answer)
- Tell the student to add the digits differently
- Switch to an easier subtraction problem first
Correct answer: Use base-ten blocks to show trading a ten for ten ones so the ones place has enough to subtract
Base-ten blocks make regrouping concrete by physically trading a ten rod for ten unit cubes, connecting the procedure to its meaning.
Question 2: Which representation best supports the transition from concrete to abstract understanding of multiplication for early elementary students?
- Memorizing the times table
- Drawing an array to represent 3 × 5 before writing the number sentence (Correct answer)
- Writing the algorithm vertically
- Solving word problems without diagrams
Correct answer: Drawing an array to represent 3 × 5 before writing the number sentence
Arrays provide a pictorial/representational bridge between physical objects and the abstract multiplication symbol.
Question 3: A teacher asks students to sort shapes into groups and explain their sorting rule. Which mathematical practice does this activity MOST directly promote?
- Computing fluently with multi-digit numbers
- Constructing viable arguments and critiquing the reasoning of others (Correct answer)
- Applying the standard algorithm for addition
- Memorizing geometric formulas
Correct answer: Constructing viable arguments and critiquing the reasoning of others
Sorting and explaining a rule requires students to construct and communicate mathematical arguments, a key mathematical practice.
Question 4: What does research identify as the MOST critical factor in helping young children develop number sense?
- Introducing formal algorithms early
- Providing rich experiences with counting, comparing, and composing/decomposing numbers (Correct answer)
- Emphasizing speed and accuracy on timed tests
- Focusing exclusively on written symbolic notation
Correct answer: Providing rich experiences with counting, comparing, and composing/decomposing numbers
Number sense develops through varied hands-on experiences that build flexible understanding of quantity and number relationships.
Question 5: A teacher uses a balance scale to introduce the concept of equality. A student adds 3 cubes to one side. What question BEST deepens algebraic thinking at this point?
- How many cubes are on the left side?
- What could you put on the right side to make the scale balance? (Correct answer)
- What color are the cubes?
- Can you stack the cubes in a tower?
Correct answer: What could you put on the right side to make the scale balance?
Asking what restores balance develops the concept that both sides of an equation must be equal, a foundation for algebraic reasoning.
Question 6: Which situation BEST illustrates the use of the 'think-aloud' strategy in mathematics instruction?
- Students solve problems silently at their desks
- The teacher verbalizes every step and decision while working through a problem (Correct answer)
- Students copy a model problem from the board
- The teacher assigns a problem and checks answers at the end
Correct answer: The teacher verbalizes every step and decision while working through a problem
Think-aloud makes the teacher's reasoning visible by narrating thought processes, which models metacognitive problem-solving strategies.
Question 7: A student can count to 20 but cannot tell that 15 is greater than 12 without recounting. Which concept is the student MOST likely lacking?
- Skip counting
- Cardinality
- Number magnitude and comparison (Correct answer)
- One-to-one correspondence
Correct answer: Number magnitude and comparison
The ability to compare numbers without recounting requires understanding number magnitude, which goes beyond rote counting.
TExES EC-6 Mathematics Instruction & Problem Solving 3
A student solving 63 − 28 writes: 60 − 20 = 40, then 3 − 8, says 'I can't do that,' and stops.
Which instructional strategy addresses this error most directly?