How do you teach problem solving strategies?

How do you solve problems? What strategies do you use?

After doing a search in Thinkfinity, I found some interesting online games in CalculationNation  created by the National Council of Teachers of Mathematics for developing and practicing problem solving strategies: SlamBall and Fraction Fued. So here are a few of my ideas about how these could be used with students:

In Fraction Feud, students rely on number sense to create fractions greater (or less) than their opponent’s fraction). At first, the teacher can play against the computer to demonstrate the game while talking out loud about her decisions (providing a model by using think aloud process):

• ex. From the numbers given, I am going to choose this number for the denominator because that will leave me with this number for the numerator. Since my opponent used these numbers to create their fraction, I think I will use these numbers. Since I have to go first and make the smallest fraction, I think I will use these numbers because …

Students can work with partners to play Fraction Fued game. Students will be encouraged to first play together against the computer and share their thoughts/strategies with each other. If students would like, they may play against each other toward the end of the designated time. Following the playing of Fraction Fued game, students can write in their math journals about what strategies they used that did and did not work for them and their partners as they played the game.

For the other online game, the teacher can provide students with the link to the SlamBall game with the only instruction being that this will be another chance to practice problem solving strategies. 

Students may continue to work with a partner or may choose to play this game alone. Students will again be encouraged to start off playing against the computer but then may choose to play against each other. The object of the game is to slam the ball off the sides of the game board to send it on a path that collects the most tokens. One side of the game board may be moved around and you can choose to start the ball in an upward or downward motion. 

The strategies needed to success in the game are different from the strategies needed to succeed in the fraction game. At the end of the designated time, students will write in math journals about what strategies they used that did and did not work playing this game.

After students play both games and write about strategies, the class can have a discussion about what worked and what did not in each game. The teacher can have some guiding questions to get students thinking about their thinking and to keep the discussion going:

• What strategies did you use that worked well?
• What strategies did you use that did not work well?
• How did you decide what to try? If that did not work, how did you decide what to try next?
• Did you find the same strategies worked all the time? Why?
• Did the same strategies work in both games?
• What strategies will you try when you play either of these games again? Why?
• What do you mean by …. ? (asking clarifying questions)

These two games provide students with the ability to engage in a fun computer activity, while practicing two math skills. One being fraction size and the other spatial geometry. The goal is to develop flexibility. Flexibility is the ability to choose different approaches in response to the situation or problem. That skill is best developed by trying a variety of options and sharing with others about what did and did now work.  This lesson/activity is designed with pieces that encourage the development of that skill.
  

I don't think these activities would be as successful without the reflection piece. The reflection activity gives students a chance to solidify what they have learned a strategy to be. The reflections and discussions occurring throughout the lesson encourage students to think about their thinking (metacognition). Students may have some difficulty with this at first, but hopefully with continued practice they will begin to realize some of the reasons that they make the choices to use certain strategies at certain times. Sharing with a partner and participating in full class discussions will allow students to hear about strategies they may not have thought about before. 

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