Wednesday, April 24, 2013

2013 NCTM Conference: "Using Problem-Based Learning Tasks to Foster Reasoning and Proof"

2013 NCTM Conference (4/18/13 - 11:00 am - Enrique Galindo, Julie Evans, and Jason Walton):
In this session several teachers from Indiana shared their journey of using problem-based learning in their classroom. These teachers worked together to create units based on problems that prompted students to respond to a question in such a way that they are actively engaged in the learning process and driven to learn appropriate skills and concepts.

The first example that one of the teachers gave was a PrBL which challenged students to consider how long they would have to grow their hair in order to donate it to Locks of Love. The students were required to research the necessary data, plot a graph of hair growth, and answer the question using mathematics to defend their opinions.
The students had to research the following questions:
What is the "starting point" of their hair now? Where would this point be on a graph?
What is the rate of growth for their hair? How does this affect the graph plotting hair growth?
The students made predictions of the rate of hair growth based on a video depicting the hair growth of a young man who grew out his hair for "Locks of Love". Students measured their own hair and researched how long hair must be in order to donate it.
Students then used the data to create a graph and to model it using an algebraic equation. They then gave a presentation on their findings and defend their predictions and mathematical calculations.

Another teacher provided an example PrBL which challenged students to create a new snack using chocolate and peanuts which could not exceed specified conditions regarding weight and fat content. This project required students to apply systems of inequalities to a real life scenario.

A third teacher provided an example PrBL which asked students to use trigonometry to analyze the "biorhythms" of the two quarterbacks in the superbowl to predict which quarterback would win the superbowl.

The teachers provided the following suggestions about implementing PrBLs:
First, student grouping and collaboration is important for driving discussion and investigation. They suggested allowing students some amount of choice in who they work with, so they are enthusiastic about working together. Students must be willing to discuss ideas in order to work together to achieve the expected results.
Second, the teacher should provide students with a rubric so that they have a goal to aim for. Students find it frustrating to work on a project if they are confused about what the teacher desires.
Third, the teacher should ask many questions to guide students' thinking. Instead of telling students "that's wrong", they should challenge the students to defend their ideas and use mistakes as a base for learning.
Finally, authenticity is extremely important. Students have to be "hooked" to get passionate about what they are doing.

PrBLs are excellent for developing 21st century skills, helping students understand how to really use math in their lives. Memorizing mathematical facts and formulas is not enough.

They provided the following site for people interested in PrBLs:

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