How Games Strengthen Mathematical Thinking

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Many students are so inundated with homework assignments, practice problems, and workbooks that they lack time to play games. However, this gameplay is just as important to student progress as these assignments are. Yes, the academic content in these assignments is important, but games can be used to teach broader thinking skills such as the standards of mathematical practice. Playing certain games addresses these practices and can benefit students’ thinking skills long term.

The standards for mathematical practice (http://www.corestandards.org/Math/Practice/) focus not on content, but on how to help student develop the habits of mind that are essential to be successful in the discipline of mathematics. These standards steer students away from simply implementing procedures and focus on giving students the flexibility to problem solve and apply their knowledge to new situations and problems. The goal is for students to engage with mathematics on a deeper level. Games are an easy way to help students engage.

The first standard for mathematical practice is to “make sense of problems and persevere in solving them”. A game like Connect Four does just that. Players have a set task to achieve (get four of their color in a row), but are faced with the challenge of their opponent blocking them. This helps students get accustomed to developing a strategy, but then revising that strategy over and over again. Despite a failed first attempt, players continue to develop new plans and begin to anticipate the future moves of both players in the game.

The second mathematical practice is to “reason abstractly and quantitatively”. The focus here is for students to be able to both contextualize and decontextualize mathematics. For example, a game like Battleship requires students to recognize the board space as a grid as well as a map with ship locations. Students use their knowledge about the size and shapes of the ships to contextualize their strategy, while still representing their “hits” and “misses” abstractly.

The 7th and 8th mathematical practices (look for and make use of structure and look for an express regularity in repeated reasoning) both deal with finding and using patterns to make generalizations. Games like Sequence and Mastermind help students do just this. Sequence allows students to find patterns in the board game itself as well as patterns in their opponents’ moves. Mastermind relies heavily on structure, patterns, logic, and skills of deduction. Students guess a sequence of colored pegs and then must use the information they are given to reason through their next play. The goal is to successfully identify the pattern in the smallest number of moves.

Of course, there are many other games that can help students engage with these essential practices. A large number of games (including the ones mentioned above) help develop more than just one practice. Any game that requires players to strategize, think about their next move, alter their decisions based on an opponent’s turn, or look for patterns is worth playing. So, when the assigned homework is done, break out a board game for a low stakes and fun way to keep the learning going.

 

Elizabeth Masalsky is a 6th, 7th, and 8th grade mathematics teacher at Battery Park City School in Manhattan. She has a post-baccalaureate in mathematics from Brandeis University and her master’s in secondary math education from Bard College. Elizabeth is a Math for America Master Teacher and continues her professional development through workshops with Math for America, Metamorphosis and Math in the City.