How classroom games can help build reasoning skills

Students can discuss different strategies and probabilities by playing simple games.

While most students enjoy games, even the simplest kind—such as tic tac toe—can help children develop important 21st-century skills such as critical thinking and mathematical reasoning, experts say.

During a webinar hosted by edWeb, Sarah DeLeeuw and Patrick Vennebush from the National Council of Teachers of Mathematics demonstrated how basic games can help students become more engaged in math lessons.

Many rudimentary games give students a chance to make their own decisions, reflect on those decisions, and talk about strategies with their peers, the panelists said. In addition to promoting communication skills, students can learn from one another and explore different ways to play games.

Tips for teaching with games include:

  • Do not show children how to play at a higher level—let them advance on their own.
  • Encourage them to explore and do their own thinking while playing games.
  • Do not reinforce correct behaviors or try to correct the wrong ones.
  • Play with individual children whenever possible, to help them reflect on their own choices during game play.

Games can help educators adhere to the Standards for Mathematical Practice found in the Common Core State Standards, the panelists said. Those standards are:

  1. Makes sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

Games offer an opportunity for teachers and students to develop strategies, and teachers can incorporate the standards of mathematical practice in the natural progress of a game’s strategy.
Tic tac toe can be used to help students develop strategy skills and mathematical reasoning, DeLeeuw said, because students learn to focus on and prioritize different goals—do they make a move in order to win, or do they decide on a move in order to block their opponent from winning or advancing? And what skills do students use to prioritize between those two goals?

For instance, when playing tic tac toe, students can examine the likelihood of winning based on their own moves and calculate probabilities. They also can focus on their opponent’s likelihood of winning. Explaining their decision to place an X or an O in one square instead of another helps students develop reasoning skills. When they communicate their strategies, they engage in a natural dialogue and progress toward higher-order thinking skills.

Playing a game called Game of Nine Cards, students use math and reasoning skills to be the first person to identify three cards in their hand that add up to 15. Exactly three cards must add up to 15, even though students may draw more than three cards.

Teachers can visit for an online version of the game. Follow-up questions might ask students to describe their strategy and why they chose one card versus another.

“Communicating a strategy is a very important part of this reasoning and sense-making,” DeLeeuw said.

Vennebush said the game offers a number of questions and scenarios that educators can use to teach students how to reason and strategize. For instance, students can explain which numbers they should pick to reach 15, which numbers they might pick to prevent their opponent from reaching 15 before them, and which numbers students should not pick.

The game can be modified to focus on letters and words, or teachers could increase the number of cards needed to reach a certain numerical value.

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Laura Ascione

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