Strategies to Build Mathematical Reasoning

Mathematical reasoning can be understood through three interconnected actions: analyzing, interpreting, and justifying. For example, when solving an equation, a student who reasons mathematically does not stop at finding the value of the variable. They verify their solution, explain each step and connect it back to the original problem.

• Analyzing: Breaking a problem into smaller, manageable parts.
• Interpreting: Making sense of numbers, patterns, or results in context.
• Justifying: Explaining why a solution is correct using logical arguments or evidence.

Mathematical reasoning is not limited to textbooks. It plays a vital role in everyday decision-making, like comparing discounts while shopping, interpreting data in news reports, managing personal figures, and evaluating risks and probabilities. Consider a simple scenario: a store offers a 20% discount followed by an additional 10% discount. A student with strong reasoning skills understands that this is not the same as a flat 30 % discount and can explain why. This ability to interpret and justify learning makes meaningful and practical.

Developing reasoning is an intentional process. The following strategies can make a significant difference with developing mathematical reasoning.

1. Encourage Inquiry: Create a culture where asking “Why “ and “How” is as important as finding the answer. Open-ended questioning promotes deeper thinking. See also inquiry-based learning strategies.

2. Use Real-Life Contexts: Connecting math to everyday experiences helps students see its relevance and apply their understanding meaningfully.

3. Promote Mathematical Discussions: When students explain their thinking to peers, they clarify their own understanding and learn to evaluate different approaches. Related: questioning in the classroom.

4. Incorporate Open-Ended Problems: Problems with multiple solutions or strategies encourage creativity and reasoning rather than rote application.

5. Use Visual Representations: Graphs, models, and diagrams helps students conceptualize abstract ideas and identity patterns.

6. Think-Pair-Share: In this strategy, students think about the given scenario, pair up with a peer and share their reasoning and strategies about the problem.

7. Error Analysis: Students are given a problem with solution that has some errors. Students analyze and identify the error.

8. Math Journals: Math journals are a great way to develop logical reasoning that helps develop mathematical reasoning.

9. Sentence starters: Providing students with sentence starters help students organize their thought process and develop their reasoning ability. I noticed that… This works because… Another way to think about it is… etc.

Allison Green
Boston Tutoring Services