Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Exploring Problem Solving
 Introduction | Cuisenaire Rod Patterns | Reflection Questions | Your Journal

Think about the Cuisenaire Rods Interactive Activity and reflect on the following questions. When you've formulated an answer to each question, select "Show Answer" to see a sample response.

 Question: In this activity, there were three tools -- manipulatives, a table, and a graph -- to work towards a solution. Did each aid in problem solving? What did you learn from each? Show Answer
 Sample Answer: Each representation prompted thinking about the pattern in a different way. The understanding of how to assemble and count the pattern that is provided by the rods can be captured in the table, and the values in the table, in turn, can be used to plot the points. Without the table, it would have been difficult to keep track of the values and see the general rule. The graph made it clear that this is a quadratic; the graph, however, is continuous and represents the related function, not the data in the table, which is discrete.
 Question: As a problem solver, were you aware of moving from one phase to another in your work? Could you have worked in a different order? Show Answer
 Sample Answer: In this problem, in which the tasks were structured in phases, it's reasonable to go forward in this way. But it's important to remember our own experience is often more like "messing around" with a problem, particularly when we are developing and applying a strategy. If we think of a problem as moving in only one direction, without some "sideways" connections or excursions to related topics and approaches, we may limit our own problem-solving effectiveness and our ability to assess and help students in developing theirs. When you are in the middle of a problem, you may not know which direction is "forward"; that is part of the task.
 Question: How did you keep track of what you had learned in the course of solving the problem? Did you make mistakes, and did you learn from them? Show Answer
 Sample Answer: Remembering, recording, and reviewing work as you solve a problem is a key task, and sometimes an overlooked one. Adult or student problem solvers are often in a hurry to "get it" –– that is, to find the answer. In this rush, people can forget to take time to record ideas and data, question results and conjectures, and backtrack effectively. Yet these are key aspects of problem solving, and as problems become more challenging, these steps become more essential. If we wish to help students in developing this habit, we must attend to it ourselves.

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