Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Problem SolvingSession 03 Overviewtab atab bTab ctab dtab eReference
Part C

Defining Problem Solving
  Introduction | Introducing New Content Via Problems | A Positive Problem-Solving Disposition | Problem-Solving Techniques and Examples | Working Backwards | Technology | The Teachers' Role | Your Journal

 
  Using problems to introduce new content is a key part of the Problem-Solving Standard. To explore it, let's take the example of the introduction of logarithms in an Algebra II class. One approach would be to provide a formal definition of a logarithm, present and solve practice exercises, and then assign similar problems for student experience. A richer approach is to introduce the concept with a problem that requires a solution. One way of doing this can be found in the "Alice to the Moon" video in the Teaching Math series.

The teacher, Ms. Lynch, has explained to her students that each time Alice eats an ounce of cake, her height increases by a power of 10. She then asks students how much of this "base-10 cake" Alice must eat in order to stretch to the Moon. When this is combined with other information asked for by the students, like "But how big is Alice?" and "How far is the Moon?" the class is able to arrive at a restatement of the problem "What power of 10 equals 239,000 miles?" This approach will help students understand the relationship between powers of 10 and logarithms in base-10, which will be presented in follow-up lessons. It provides a context and motivation for understanding a concept that may at first seem very forbidding.


Not all content in the high school curriculum gives itself to this approach equally well. But it is always worth considering how a problem relates to a new concept and how it might be used to introduce mathematics content. When professional mathematicians move to a new aspect of content, they often do so by confronting a new problem or by reviewing work done previously on a problem. Students should be given the opportunity to progress in their own work in this fashion whenever feasible.

Next  Fostering a positive problem-solving disposition

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