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Ellerton, and Jinfa Cai, published by Springer This edited book of 26 chapters is divided into four parts: defining the field; mathematical problem posing in the school curriculum, mathematical problem posing in teacher education, and concluding remarks. It is not a slim book—there are pages contributed by 52 authors from 16 countries, such as the U. Despite these many and varied contributions, one gets the distinct impression that problem-posing research is still in its infancy. Why have students pose problems, in addition to solving them?
However, while problem solving has long been a fundamental activity in mathematics classrooms, problem posing has been neglected.
Mathematical Problem Posing: From Research to Effective Practice
Yet, in real life, problems must often be created or discovered by the solver. Thus, to prepare students for the future, problem posing needs to become a regular part of the mathematics curriculum. Indeed, it contains a great many problem-posing tasks, and ideas for implementing them, at a variety of levels, including 3rd, 5th, and 7th grades, high school, and college.
But there are other examples. An example of a free problem-posing situation is the following: There are ten girls and ten boys standing in a line. Make up as many problems as you can that use the information in some way. An example of a semi-structured problem-solving situation is the following: In the following picture, there is a triangle with an inscribed circle.
Make up as many problems as you can that are in some way related to the picture. The first time the doorbell rang only one guest arrived. Each time the doorbell rang, three more guests arrived than had arrived on the previous ring.go site
Table of Contents: Mathematical Problem Posing :
Explain how you found your answer. In contrast, many Chinese students posed problems similar to those they usually did in class. However, when asked, both US and Chinese students reported that they had had little or no experience in posing mathematical problems, but thought doing so might help them learn mathematics.
Low complexity problem-posing tasks call heavily on recall and recognition of previously-learned concepts and typically specify what the solver is to do, such as make a calculation or solve a one-step word problem. Moderate complexity tasks involve more flexibility of thinking and choice among alternatives—the solver is expected to decide what to do, such as solve a multiple-step problem, extend a pattern, or interpret a simple argument.
High complexity tasks make heavy demands on the solver, who must engage in more abstract reasoning, planning, analysis, judgment, and creative thought.
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Such tasks may ask a solver to use different representations to solve a problem; to describe, compare, and contrast solution methods; or to provide a mathematical justification. Results revealed that the preservice teachers were profi cient in solving simpler arithmetic tasks but had diffi culty generalizing and interpreting numerals in an algebraic form.
They were able to pose some basic and reasonable problems and to consider important aspects of mathematical problem solving when generating new tasks.
Thus, teacher educators should provide substantial educational experiences by incorporating both problem-solving and problem-posing activities into engaging instruction for preservice teachers. N2 - Empirical data were gathered from 51 middle-grade preservice teachers who were randomly assigned into one of two groups. AB - Empirical data were gathered from 51 middle-grade preservice teachers who were randomly assigned into one of two groups.
Abstract Empirical data were gathered from 51 middle-grade preservice teachers who were randomly assigned into one of two groups. Fingerprint teacher. Springer New York.
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