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 http://www.illuminations.nctm.org/deepseaduel 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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