Attitudes Toward the Practices

The Practices are possibly viewed as a short, surface-level list of suggestions teachers may consider before and during mathematics instruction.  But they also may be viewed as a multi-layered instructional guide for how teachers should teach and students should learn mathematics.

There is a vast difference between these two points of view. Adopting the first will have minimal or no impact on mathematics instruction and student learning, while the second, if enacted, will revolutionize school mathematics. With nothing to lose, and everything to gain, photowhy not go for the revolution?

Transformation through Games

In order to meaningfully implement the Standards for Mathematical Practice, teachers need a reasonable and manageable place to begin. We suggest you start with mathematics games. Games can drive the inclusion of research-based instructional strategies. Some of the strategies are . . .

  • Active student engagement
  • Instructional grouping and collaboration
  • Student discourse
  • Teacher questioning
  • Student thinking, reasoning, and metacognition
  • Student applications and knowledge transfer
  • Student time on task

While not a comprehensive list, the strategies identified deliver the point that successful concept-games implementation opens the door to successful strategy implementation.  Another point, however, is vital: implementation of the Standard for Mathematical Practice relies on effective use of these same strategies.

The Mathematical Practices

1.  Make sense of problems and persevere in solving them.

Students learn to struggle through the process of solving challenging problems by actually working on challenging problems. Concept games present students with various challenging problems in a venue students are motivated to complete successfully.

2. Reason abstractly and quantitatively.

Students must reason when engaged in the concept game and after play as teachers ask probing questions related to the game, such as:

  • What did you find easy about the game? Why?
  • What did you find difficult about the game? Why?
  • While playing, did you develop strategies to help you win? What strategies? Did they seem to work?
  • Did you raise any issues about any game rules? What issues and which rules?

3. Construct viable arguments and critique the reasoning of others.

Each time a game is played, students need to clarify their understanding of the mathematics involved. Students are involved in defending their thinking, as well as analyzing other ideas and understandings for reasonableness and accuracy.

4. Model with mathematics.

Students should compare and contrast various representations that are modeled in the game and in other instructional materials. Discourse during play provides opportunities for students to shift models or words into mathematical symbols, and mathematical symbols into words, pictures, or physical models.

5. Use appropriate tools strategically.

During concept games, tools such as manipulatives or calculators should be used as directed by the game. In other situations, the concepts developed during the game are reinforced and clarified by the students working with mathematical tools.

6. Attend to precision.

Clarity, accuracy, and logical reasoning are desired outcomes of concept games. As discourse increases, vocabulary also increases. When stating understanding, students should organize their thoughts and include correct mathematical terms.

7. Look for and make use of structure.  
When engaged in playing concept games, students are encouraged to look for patterns or structures that may emerge in various aspects of the mathematics.  Identified patterns are to be explored during classroom discourse about the games.

8. Look for an expressed regularity in repeated reasoning.

As students gain insight on concepts, they begin noticing that certain aspects of the mathematics involved continue to repeat for each turn or game.  This regularity provides students opportunities to adjust their thinking in general or specific ways.

Conclusion

There is a definite link between the Standards for Mathematical Practice, research-based instructional strategies, and conceptual understanding. Concept games provide teachers with an instructional tool that makes the link obvious, provide an excellent launching point for increasing instructional strategies, and assure student buy-in and engagement in learning mathematics.