Putting an End to Math Confusion

Confusion leads to frustration which leads to despair and ultimately to the belief that failure is inevitable. Confusion is often the foundation upon which math anxiety grows.

A teacher came to me with a problem similar to this in the first grade textbook. She felt frustrated because it barely made sense to her, and she knew that she wasn't explaining it clearly to her students.

So what's going on here?

Students are solving a three number addition problem by decomposing a number to make an easier problem to solve. In this case, students are making a ten. This is something that people often do mentally because it is easier to add tens. But, as the strategy is presented for first graders, it is more than likely too difficult for them to understand. The textbook is forcing a strategy, and students are expected to use this strategy to solve the lesson's problems.

What's a better way to introduce this strategy to students?

Allow students to model the situation with different color counters and ten frames. Start with only two numbers, 7 and 5. Ask, "How might we solve this problem?" Students should be encouraged to explain different strategies that can be used to solve the problem. Highlight the make a ten strategy by moving three of the red counters onto the ten frame to make a ten, and have students explain that 7 + 5 = 10 + 2. Next show 7 + 5 + 6, as shown above. Repeat the same process to uncover the students' understanding of adding three numbers. The make a ten strategy can be encouraged and discussed. Don't be surprised if some students use 3 from the group of 5 to make 10, while other students use 3 from the group of 6 to make 10. Just be sure to ask them to explain their thinking!

Strategies should be introduced, discussed, revisited, and encouraged. They should not be forced upon students. Math is built upon a foundation of understanding. Teachers provide experiences for students to stretch their thinking and build new understandings. For many students, forced procedures and strategies interfere with meaning making and create confusion, frustration, and even math anxiety.