TEACHING STRATEGIES

To assess a student’s understanding of math concepts rather than just his ability to apply methods and procedures mechanically, a tutor should use strategies that emphasize conceptual reasoning, critical thinking, and connections between topics. Here are some effective ways to do this:

1. Ask Open-Ended Questions

• Instead of asking, “What is the answer?”, ask, “Why do you think that works?” or “Can you explain this in your own words?”

• Example: If solving an equation, ask, “Why do we move terms to one side?” instead of just instructing Alberto to do it.

2. Encourage Multiple Solution Methods

• Challenge Alberto to solve problems in different ways.

• Example: For solving 12 \times 25, ask, “Can you break it down differently?” (e.g., using distributive property: 12 \times (20 + 5)).

3. Use Real-World Applications

• Connect math concepts to real-life scenarios.

• Example: When teaching probability, discuss real-life situations like predicting the chances of rain or winning a game.

4. Have Him Teach Back the Concept

• Ask Alberto to explain a concept as if he were teaching another student.

• If he struggles, it indicates gaps in understanding.

5. Give Non-Routine Problems

• Use unfamiliar problems that require reasoning, not just rote application of formulas.

• Example: Instead of “Solve for x in 2x + 5 = 11”, ask “Create a real-world situation where you would use this equation.”

6. Use Conceptual Comparison Questions

• Ask “What is the difference between an equation and an expression?” or “How are fractions and decimals related?”

• These questions push Alberto to think beyond procedures.

7. Ask for Justifications and Counterexamples

• Have him prove why a rule works or find a counterexample to a false statement.

• Example: “Is it always true that multiplying makes numbers bigger?” (Introduce fractions to challenge this idea.)

8. Encourage Visual Representations

• Use diagrams, graphs, and number lines to reinforce understanding.

• Example: If teaching algebraic expressions, use a balance scale to visually demonstrate equality.

9. Introduce “What If?” Scenarios

• Change one part of a problem and ask, “How would this affect the solution?”

• Example: “What if the denominator of this fraction were zero?”

10. Use Concept-Based Assessments

• Instead of just giving computation exercises, include conceptual tasks like:

• Explain why a certain step is valid.

• Compare and contrast two methods of solving a problem.

• Describe a situation where a concept applies.