Delaware State University
SMILE Project and the Math Forum

August 31, 2011

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1: Worked in small groups to solve the College Algebra PoW A Pound of Valentine's Chocolate. The challenge: come up with as many ways to solve the problem as possible.

2: Discussed the group's problem-solving process. Here are the steps we took (and which should set the flow for the workshop sections):

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3: We also discussed what made the group process effective and worthwhile. Here's what we came up with... Check out the "What Worked" column below:

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In summary, it seemed like the group work helped us understand the problem more deeply. It was fun and exciting to hear other ways of solving the problem. But to be effective, everyone had to work independently to be able to contribute different ideas (whether they were complete or correct or not, they were still important contributions!). And everyone had to participate equally. And finally, everyone had to work actively to understand the other methods.

4: How does this compare to what students are used to in math class?

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5: How can we bridge the gap between what works in math class and what will make the workshops effective?

Here are our ideas (my apologies if I missed any!):

  • Reshuffle the groups. Group students who are "talkers" together in one group. Help the talkers experience the value of listening and learning from others strategies. Maybe some of the talkers who also value listening can help inspire and share with other groups.
  • Look out for good listeners (who ask things like, "so what you're saying is," or "that's similar to this because,") and have them assist you in facilitating the groups.
  • Value and praise good listening questions (like the ones above); maybe write them on the board as you notice them? Or reflect on the group process at the end of a session?
  • Have students present their ideas and findings to one another; by the end of the term, any student in the group should be able to present that group's work.
  • Don't write or tell the students what to do.
  • Don't check work for the students.
  • Enforce individual work time (5 - 10 minutes) before group sharing time.
  • Have the students each share something they understand about the problem at the beginning. Go around. Everyone can contribute at this stage.
  • Encourage the "talkers" to step back.

6: Those who were able to stay then discussed some of the hardest parts of the problem-solving process. We focused on writing the problem mathematically so it can be solved by calculation, solving for a variable, etc. If students get stuck at this stage:

  • Have them tell you in their own words what they know from the problem
  • Have them tell you in their own words what they are trying to find
  • Help them organize the known information like this:
    • Quantities in the problem [Name the quantities, then put the value in parentheses, like this: Time it takes Tristan and Isolde to eat a box of chocolate (2 weeks)].
    • Relationships in the problem [In words: Amount of chocolate in a box (1 lb) / Time it takes Tristan and Isolde to eat a box of chocolate (2 weeks) = Amount of chocolate they eat in 1 week (1/2 lb per week)].
  • If they can do that, you can help them shorten the writing into more mathematical sentences, or they might have an idea of how to solve the problem based on the relationships.

7: We also talked about what if students get bogged down in calculations or come across one they can't do. We decided that setting up the problems was the main focus of Math Workshop and that it was ok to have students use graphing calculators (which Dr. Shahin can provide if needed) to do the nitty-gritty work.

Please email us with any questions.
Max Ray and Suzanne Alejandre


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