Rethinking Subtraction: The Importance of Relational Thinking: On the article: “Relational Thinking: What’s the Difference?“. Read the full article here.
Subtraction is a cornerstone of early mathematics, but how students approach it reveals much about their cognitive flexibility. In “Relational Thinking: What’s the Difference?” the authors highlight the challenges young learners face when solving problems like 41 – 39 versus 100 – 3. Surprisingly, many first graders find 100 – 3 easier because their default approach to subtraction is rooted in “take-away” thinking or standard algorithms, which can be cumbersome and error-prone for problems requiring nuanced reasoning.
The Case for Relational Thinking
Relational thinking encourages students to view subtraction beyond mere “taking away.” Instead, it emphasizes reasoning about the relationships between numbers. For instance, recognizing that 41 – 39 can be solved by observing the small distance between 41 and 39 avoids the tedious process of borrowing or incremental subtraction.
This approach requires a mindful application of place value and an understanding of the properties of numbers and operations. Students who pause to consider the nature of the numbers in a problem before acting are practicing relational thinking. For example, understanding that 201 – 199 is simply the distance between two numbers avoids the mental strain of subtracting 199 incrementally from 201.
Teaching Subtraction Flexibly
Promoting flexible reasoning in subtraction involves teaching students to adapt their strategies based on the problem at hand. While the “take-away” model is helpful for simpler problems, others lend themselves better to relational reasoning. For example:
- Problems like 41 – 39 can be solved efficiently by reasoning about distance.
- Problems involving large differences, like 100 – 3, are more suited to counting back.
By fostering a habit of strategic decision-making, educators can help students become more accurate and efficient in their computations.
Key Takeaways for Educators
- Introduce subtraction as more than just “taking away.” Encourage students to think about it in terms of relationships and distances.
- Use classroom moments to highlight flexible approaches. For example, show how breaking down a problem like 41 – 39 into smaller, intuitive parts makes it easier to solve.
- Model and teach relational thinking as a habit, helping students develop a disposition to pause and consider their strategies before acting.
Conclusion
Subtraction is often taught as a rigid process, but adopting relational thinking opens doors to more meaningful and flexible approaches. By teaching students to see subtraction as both “taking away” and “finding the distance,” educators can equip them with strategies that enhance both accuracy and confidence in problem-solving.
Citation: Relational Thinking: What’s the Difference? (Schoen et al., 2016). Read the full article here.
Relational thinking involves a mindful application of place value and the properties of number, operations, and equality in solving mathematics problems (Jacobs et al. 2007)https://t.co/1GfNoiItLN
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