Today’s math classes aren’t what they used to be. Remember how students used to sit and listen to teachers explain the “hows” of mathematical computation, then work countless practice problems? Increasingly in math classes across the country, teachers are moving away from this traditional mode of instruction and are encouraging greater student engagement.

Raising the bar

A primary reason for this shift is the recent adoption of more rigorous mathematics standards by many states. Now students are required to learn more than computational skills. To be successful in meeting the new math standards, learners must also acquire a comprehensive understanding of both mathematical concepts and practices—the kind of knowledge that they can apply in real life situations.

Because of increased expectations in math classes, students are called upon regularly to communicate their mathematical thinking. They benefit from this change in four important ways. Imagine a student who is asked to consider whether a square is a rectangle and then share her thinking with other students in the class.

Four ways students benefit

First, her mathematical understanding is bolstered as she considers what she knows about both rectangles and squares. In explaining her thinking, she must understand and use mathematical vocabulary such as “right angle,” “parallel,” “sides” and “equal.” The thinking processes she uses in determining the relationship between the two shapes increase her understanding of geometry and makes it more likely that she will remember and be able to use what she has learned.

“[T]heir students gain not only a better understanding of math but also invaluable life skills.”

Secondly, communicating mathematically helps develop her thinking skills. She must be logical and creative in expressing herself so others clearly understand her ideas. The process of sharing her thinking encourages her to reflect more deeply and critically about mathematics (in this case about the attributes of the two shapes).

Thirdly, in addition to mathematical benefits, having to communicate in this way fosters her social skills. She learns to consider how her ideas are received by others. By clearly explaining her mathematical reasoning to others, her ability to communicate in all contexts is improved.

Finally, as she shares her ideas with others to gain a better understanding of the relationship between the two shapes, she is learning to work collaboratively. Her classmates may not agree with her thinking, but by talking about it together, she and her peers will better understand geometric relationships.

When students are expected to talk and write about mathematics in math class in additional to practicing computational skills, teachers find that their students gain not only a better understanding of math but also invaluable life skills.