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Teaching Mathematics

Fraction misconceptions, algebraic thinking, word problems.

Ready-made classroom8 turns
Mathematics room
fraction addition
T
Student says: “I added the tops and the bottoms. 1 plus 1 is 2, and 4 plus 4 is 8. So 1/...”
1 · Mathematics

Student Adds Fractions Wrong: 1/4 + 1/4 = 2/8

Rehearse this
Diagnose procedural vs. conceptual understanding and use concrete representations to build meaning
Signal
misconception
Move
diagnose
Output
feedback
Ready-made classroom8 turns
Mathematics room
algebraic equality
T
Student says: “3 + 4 = ___. That's easy, it's 7! But ___ = 3 + 4? That doesn't make sens...”
2 · Mathematics

Equals Sign Means 'The Answer Is'

Rehearse this
Transform a relational misunderstanding using balanced representations (balance scale, true/false equations)
Signal
misconception
Move
diagnose
Output
feedback
Ready-made classroom8 turns
Mathematics room
multiplication with decimals and fractions
T
Student says: “0.5 times 6... that can't be 3. Multiplying makes things bigger. It has t...”
3 · Mathematics

Multiplying Always Makes Numbers Bigger

Rehearse this
Replace a limited mental model with a more general one while maintaining student confidence
Signal
misconception
Move
diagnose
Output
feedback
Ready-made classroom8 turns
Mathematics room
integer multiplication rules
T
Student says: “I know negative times negative is positive because you told me. But WHY?...”
4 · Mathematics

Why Is Negative × Negative = Positive?

Rehearse this
Explain a mathematical truth conceptually when the standard procedural explanation is insufficient
Signal
misconception
Move
diagnose
Output
feedback
Ready-made classroom8 turns
Mathematics room
mathematical modeling and word problems
T
Student says: “I can do 3 times 4.50. That's 13.50. But when you say 'Maria bought 3 not...”
5 · Mathematics

Student Can Compute But Can't Do Word Problems

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Distinguish content knowledge gaps from language/reading barriers and teach mathematical text comprehension str...
Signal
misconception
Move
diagnose
Output
feedback
Ready-made classroom8 turns
Mathematics room
metacognition and process visibility
T
Student says: “I got 42. It's right. Why do I need to write all those steps? I can do it...”
6 · Mathematics

Why Do I Need to Show Work If I Get the Right Answer?

Rehearse this
Motivate process documentation without diminishing the student's legitimate computational strength
Signal
misconception
Move
diagnose
Output
feedback