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
"Much of school mathematics can be seen as the codification of answers to sets of interesting problems. Accordingly, much of the mathematics that students encounter can be introduced by posing interesting problems on which students can make legitimate progress."

(NCTM, 2000, p. 334)


What role can classroom technology play in problem solving?

Technology offers great opportunities and some challenges in teaching problem solving. Tools like graphing calculators, computer-based labs, computers with software programs like Geometer's Sketchpad or spreadsheets can vastly increase the range of problems and concepts teacher and student can pose and explore. To give one example which is discussed more fully in Session 6 of this course, Connections, using a motion detector to capture the motion of a falling ball and plot a curve, students in a 10th-grade class were able to make tangible their understanding of quadratic functions, scientific notation, and accuracy and precision in mathematical communication.

Used well, these tools can broaden the landscape of the high school classroom. For example, graphing calculators can allow students to graph and explore many classes of functions that would be tedious and potentially unhelpful to graph by hand. Large datasets of actual population data could be used as the basis for a data analysis and probability lesson about variation about the mean. Computer simulations can be used to check conjectures, reason about mathematical ideas, and refine thinking. Many of these tools put a much broader range of representations in the hands of students working on problem solving.

Technology tools are also good enforcers of mathematical rules. They can help students learn the facts of mathematics and put this knowledge to use in problem solving. They can help build ability to have to "explain" to a computer how to solve a problem step by step in developing a computer program. Computers are unforgiving as well, and embody mathematical rules and principles in ways that students can absorb. As Jeannie Shimizu-Yost, a teacher participant in the Teaching Math videos notes, teenagers are sometimes more willing to accept a rule from a calculator than from an adult! Although a teacher may explain to a beginning trigonometry student in the midst of developing a problem-solving strategy that the tangent of 90 degrees does not exist because division by 0 is impossible, when a student uses a calculator to find tan90° and sees that the result is "error," this is a chance for reinforcement of an idea.

Technology also provides an opportunity to find connections among problems. Graphing software makes it easy to compare and save graphs, which can build a progressive understanding of functions and their characteristics. Since these tools do not belong exclusively to any one mathematical subject area, they also build bridges across these areas, showing students in successive years how topics in geometry, for instance, can be connected to algebra.

Next  The role of the teacher in problem solving

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