Conversations- Getting students talking

Perhaps one of the most important parts of having students construct mathematical understanding and truly gain a deep conceptual knowledge of the mathematical content being taught, students must be given opportunities to talk about what it is they are learning. It is through this talk and discussions with peers and teachers, new ideas are constructed and connections are made. To reinforce the importance of talking Boaler (2008) talks about a young Irish woman, Sarah Flannery, who won the European Young Scientist of the Year award who developed a wondrous mathematical algorithm. In her autobiography, Flannery recalls the events that led to her success. Boaler (2008) states “Flannery writes: “The first thing I realized about learning mathematics was that there is a hell of a difference between, on one hand, listening to math being talked about by someone else and thinking that you are understanding, and, on the other, thinking about math and understanding it yourself and talking about it to someone else.” (p.47) The National Council of Teachers of Mathematics also agree. NCTM (2007) suggest that one goal of mathematics education is for students to develop and expand their reasoning abilities. It is the mathematics classroom that is the main and central environment where students speak and write mathematics. Therefore, NCTM (2007) continues “it is essential for teachers to offer students opportunities to communicate mathematically by having them make, test, discuss, and refine conjectures, ultimately accepting or rejecting them” (p.1).
Student understanding of mathematical concepts is what teachers strive for, or at least, what teachers should strive for. Classrooms that have students interacting, communicating and helping each other solve problems is a classroom where students actually understand the mathematical concepts being taught. Marian Small also agrees. Small (2008) notes that “it is through interactions with other students as well as with the teacher, and with the opportunity to articulate their own thoughts that students are able to construct new mathematical knowledge” (p.4). Small (2008) goes on to note that it is in these classrooms, one in which she calls constructivists classrooms, “students are given the opportunity to develop richer and deeper cognitive structures related to mathematical ideas and students’ development of a level of mathematical autonomy”(p.4).
When students have mathematical conversations, they begin to see math as more than a collection of rules and procedures. They begin to see that math as a subject where they can have their own ideas, methods and perspectives. They will eventually see math as a connected subject with organized concepts and themes. Silence in the math classroom, where students are not asked about their own ideas and perspectives may feel disempowered and ultimately choose to leave mathematics even though they were good at it. Students that see their thought and ideas are valued are more apt to feeling responsible for the direction of their work, as they are being asked to use their intellect.