Mathematics is a word that strikes fear in the hearts of many children and adults. Most students enter school eager to learn. Much of their play is mathematical in nature, and they intuitively use and learn new mathematical skills every day. As students get older, many start to shy away from mathematics, saying they are not good at it. Yet, in reality, research tells us that there is no such thing as a math gene.
We live in an age where students are being asked to learn mathematics at very high levels while becoming critical thinkers and problem-solvers. Given this state of reality, how do we cultivate a love of mathematics and help all students learn mathematics at a deep, conceptual level?
Think, Capture, Explain
As educators and parents encourage student ownership of their mathematical learning, three actions are at the heart of the learning process: think, capture, and explain (Figure 1).
Rather than learn procedures taught by others, students need to engage with rich mathematical tasks requiring them to think and reflect. These tasks must rely on the learning students have done while requiring them to use that knowledge in a novel way. They need to think about what they know, what they are being asked to do, what they already know, what they might try, what has worked and what has not worked. This is a messy, yet productive process.
Rather than learn procedures taught by others, students need to engage with rich mathematical tasks requiring them to think and reflect.
As they think, students must represent their thinking. This is where “capture” comes into play. Students may use words, pictures, symbols, and tables, alone or in conjunction with each other to represent their thinking. Capturing helps to make thinking visible to students and to those who work with them.
As students think and capture, they have mathematical conversations with their peers. Students explain their own thinking and give feedback to their peers. This process of mathematical discussion creates a cycle of thinking, capturing, and explaining that helps students find answers to problems presented to them.