This blog is a repost of a four-part series I wrote for NCTM’s Blogarithm in 2016. Read the original post here.
Walk down the halls of most schools, and you’ll no doubt hear students talking. In ELA classrooms, students may be heard discussing author’s intent or characterization. In social studies classrooms, there may be debate on events that lead to war, or the resulting fallout. Students collaborate in labs during science class, and compare their results. Knowledge is acquired through active participation in classroom discussions. Across the hall in the math classroom, an entirely different scene is playing out. Students recite answers and procedures. They are still talking, but very little discussion is taking place. At first glance, this seems like a trivial distinction.
There has been a lot of talk about re-imagining the modern mathematics classroom. Many blog posts and think pieces have been dedicated to answering the question familiar to all math teachers: “When am I going to use this?” Unlike ELA and other classes, the new focus of math education too often appears to be emphasizing real-world application above all else. This is important, but it also feels hollow, as though the sole measure of mathematics is its practical usefulness. There is a lot to be said for the beauty of pure mathematics. Logical reasoning, trial and error, cause and effect, viable proofs – these are all real world skills, even if the content used to teach these skills is not considered necessary.
There was public outcry when interpretations of the Common Core State Standards appeared to favor technical nonfiction over literature, and with good reason. While students won’t necessarily use their knowledge of Shakespeare when they enter the workforce, there is no question that it has a place in our schools. The study of literature contributes to learning compassion, empathy, and critical thinking. Students benefit from classroom discussions that challenge their preconceived notions, and compare different interpretations of the same text. At the same time, we know that it is not enough to simply read literature. The benefits of studying literature lie in the search for historical context, discussion of underlying themes, and critical analysis of the text. Much in the same way, mathematics cannot be boiled down to procedures and step-by-step directions, or comparing unit prices at competing supermarkets. Discussions in the math classroom allow students to formulate logical arguments, and strengthen their reasoning skills. Both subjects are enhanced by robust discussion amongst learners where ideas are spoken aloud and challenged.
If you need further convincing that discussion is a necessary component of a well-rounded math classroom, look no further than the Common Core Standards of Mathematical Practice. These standards, written to apply across the entire K-12 math curriculum, highlight important and necessary characteristics of a proficient mathematician. Several standards address the need for communication, but none so clearly as MP.3: Construct viable arguments and critique the reasoning of others. This cannot be done without giving students the opportunity to have conversations about what they are learning, and giving students space to be imperfect. The importance of communication between learners is also heavily emphasized in the NCTM publication, Principles and Standards.
Mathematical communication is a way of sharing ideas and clarifying understanding. Through communication, ideas become objects of reflection, refinement, discussion, and amendment. When students are challenged to communicate the results of their thinking to others orally or in writing, they learn to be clear, convincing, and precise in their use of mathematical language. Explanations should include mathematical arguments and rationales, not just procedural descriptions or summaries. Listening to others’ explanations gives students opportunities to develop their own understandings. Conversations in which mathematical ideas are explored from multiple perspectives help the participants sharpen their thinking and make connections.