I am a believer in the many benefits of using math games in the classroom. Besides the fact that games can motivate and engage students in thinking about and applying concepts and skills, math games can foster mathematical communication as students explain and justify their moves to one another.
Games afford students an opportunity to communicate their ideas and justify their thinking. In using games, the teacher plays an important role in encouraging students to explain their thinking and in keeping students focused on mathematical ideas. Requiring students to explain and justify their moves during a sample round of the game played as a whole class models the type of thinking and communicating that is important for students to use later when they play the game in pairs.
The ability to pose questions that elicit, extend, and challenge students’ thinking is essential to creating a classroom environment in which intellectual risks, sense making, and deep understanding are expected. In daily lessons, teachers must make on-the-spot decisions about which points of the mathematical conversation to pick up on and which to let go, and when to let students struggle with an issue and when to give direction.
While the students are playing a game, it is the teacher’s responsibility to ask probing questions, such as:
• What card do you need?
• Which cards would not be helpful?
• Prove to me that a ____ is what you need.
• Why do you think that?
• How did you know to try that strategy?
• How do you know you have an answer?
• Will this work with every number? Every similar situation?
• When will this strategy not work? Can you give a counterexample?
• Who has a different strategy?
• How is your answer like or different from another student’s?
• Can you repeat your classmate’s ideas in your own words?
• Do you agree or disagree with your classmate’s idea? Why?
• What can you do to help yourself? Use your fingers to count? Count the dots on the dice or cards? Use manipulatives to figure it out? Draw a picture? Start with something you already know?
The power of questioning is in the answering. As teachers, we not only need to ask good questions to get good answers but need to ask good questions to promote the thinking required to give good answers.
While playing a math game, students’ abilities to learn from, and work with, others should expand. They should become more skilled in speaking to one another and in convincing or questioning their peers. The discourse should focus on making sense of mathematical ideas and on using mathematical ideas effectively in modeling and solving problems. When thinking is discussed regularly in the classroom, students feel comfortable describing their thinking, even if their ideas are different from the ideas of their peers. Discourse is not a goal in itself; rather, the value of mathematical discussions should be judged by whether students are learning important mathematics as they participate in them.
Effective teaching involves observing students, listening carefully to their ideas and explanations, and using the information to make instructional decisions. Through their teaching, teachers can also continue to deepen their understanding of the mathematics they teach, by learning with and from their students and then reflecting on that learning. The ability to reflect on and refine mathematical understanding as well as instructional practice is essential to achieving the vision of an effective mathematics classroom, whatever the grade.
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