Math Talk Learning

Math Talk is not just taking turns telling your method or meandering undirected talk. It is an instructional conversation directed by the teacher but with as much direct child-to-child talk as possible. Math Talk is focused on developing understanding for all children in the class.

The NCTM Standards emphasize the importance of developing mathematical language and communication in order to understand concepts rather than merely following a sequence of procedures. Math Expressions seeks to build a community of learners who have frequent opportunities to explain their mathematical thinking through Math Talk and thereby develop their understanding. children are asked to solve problems, explain their solutions, answer questions, and justify their answers. They use proof drawings as a reference for their

explanations. The dialogue that takes place helps everyone understand math concepts more deeply, and it helps children to increase their competence in using mathematical and everyday language. While children engage in dialogue, the teacher acts as a guide to maintain the focus of the discussion and to clarify when necessary.

Children gain greater understanding and ownership of mathematical concepts as they develop and express their own ideas. Describing one’s methods to others can clarify one’s own thinking. Similarly, hearing and analyzing others’ approaches can supply one with new perspectives; and frequent exposure to different approaches engenders flexible thinking. Math Talk provides opportunities for children to understand errors they have made and permits teachers to assess children’ understanding on an ongoing basis. By building understanding, Math Talk also prepares children for taking tests. When children encounter complex problems in testing, they can rely on their knowledge of the underlying mathematical concepts, developed through Math Talk activities, to successfully unravel and solve the problems. Math Talk also helps with test items that require explaining an answer.

Children use discussion to support the mathematical learning of everyone in the class. In a mature community of this type, children:

• develop and share their own mathematical thinking

• listen carefully to the mathematical ideas of others and restate them in their own words

• ask questions about and provide insights into the mathematical ideas of others

The development of such a way of learning is a gradual process that may take several months. The classroom is transformed as children and teacher take on new roles and responsibilities in a variety of areas. At the beginning of this process, teachers model Math Talk for children and elicit responses. Teachers wait patiently and refrain from intervening immediately to correct children’s errors in order to create space and support for children’s voices to emerge. Teachers eventually guide children from the side or the back of the classroom so that children can sense that their questions, ideas, and discoveries are the focal point of instruction.

Elements of the gradual transformation include:

• a shift from teacher as sole questioner to both children and teacher as questioners

• children increasingly explaining and articulating their math ideas

• a shift from teacher as the source of all math ideas to children’s ideas also influencing the direction of lessons

• children increasingly taking responsibility for learning and for the evaluation of themselves and others

• increasing amounts of child-to-child talk with teacher guidance as needed

Within such a community, being able to use appropriate math vocabulary, language, and proof drawings helps math become personally meaningful to children and provides a context through which children can share their ideas.

Structures for Developing Math Talk Skills. The key supports for Math Talk are the various “participant structures,” or ways of organizing class members as they interact. You can easily familiarize yourself with the most common Math Talk structures described in Math Expressions:

• Solve and Discuss (Solve, Explain, Question, Justify): Have four to five children go to the board, and each child solves the problem, using any method he or she chooses. Their classmates work on the same problem at their desks with paper or Math Boards. Then ask two or three children at the board to explain their methods. Children at their desks are encouraged to ask questions and to assist each other in understanding the problem and solution.

• Step-by-Step: In this variation of the “Solve and Discuss” method, several children go to the board. This time, however, different children perform each step of the solution, describing the step before everyone else does it. Children at the board and at their desks carry out that step.

• Student Pairs: Two children work together to solve a problem, explain a solution method to each other, role-play within a mathematical situation, play a math game, or help a partner having difficulties.

• Whole-Class Practice and Student Leaders: In Math Expressions children develop into leaders with Quick Practice activities. You can blend this strategy into your daily instruction. Initially children who understand a concept and are beginning to achieve speed and fluency lead the class; eventually everyone is a Student Leader.

• Scenarios: The main purpose of scenarios is to demonstrate a mathematical relationship in a visual and memorable way. In a scenario, a group of children is called to the front of the classroom to act out a particular situation.

• Small Groups: You can encourage unstructured groups to form spontaneously if there is room. For some activities, you may prefer to assign children to specific groups. When children finish, the groups present results, with each member explaining one part of the solution or project.

In this way, you will familiarize children with Math Talk and begin to develop a Math Talk learning community in your classroom.