Equal Sign Explorations

Last spring when I attended the NCTM conference in D.C. I went to a workshop on Number of the Day for Algebra. The leaders of the workshop shared some research done with elementary math students. Students were given the open number sentence 8 + 4 = ☐ + 5. They were asked what number should go in the box. Not only did a majority of younger elementary students provide a wrong answer (usually answering either 12 or 17), but a majority of students through sixth grade did. Fascinated by the workshop, I sought out the book they referred to in their presentation, Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.

So how can we help students develop a more accurate understanding of what the equal sign means? The book suggests in part a framework of using true and false number sentences and “open number sentences” (such as in the research above) to get children thinking and talking together about this topic. For children who “get” what the sign means and what that means in terms of the relationships between the numbers involved, it provides a chance to solidify their thinking as they work to explain it. For children who do not fully understand what the equal sign means, it provides a chance for them to hear their classmates explanations, which can help their developing understanding.

I have begun exploring true and false number sentences with my math group. Over time I will also introduce open number sentences in which they need to provide a missing number. It will be interesting to see how these activities and the math talk that they generate will affect the student’s thinking about numbers and equality.