Abstract
The present study reports the design, implementation, and evaluation of a training program aimed at developing Chinese students’ problem-posing abilities, problem-solving abilities, and their beliefs about, and attitudes toward, mathematical problem posing and problem solving. In this study, a framework for teaching and assessing problem posing was developed. Results revealed that the training program had a significant positive effect on the originality of the problems posed by the students (but not on the appropriateness, complexity, and diversity of the problems posed), as well as on their problem-solving abilities and on their problem-posing and problem-solving beliefs and attitudes.
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Notes
- 1.
The term “instructor” refers to the researcher who was acting as the teacher in the first series of special problem posing training units and to the regular classroom teacher in the second series of lessons wherein problem-posing activities were integrated into the regular mathematics lessons.
- 2.
To be considered appropriate, a problem, first, should involve a quantity which is not given in the situation, but which can be computed by means of one or more mathematical operations with the given numbers. Second, the problem should satisfy the requirements of the problem situation (e.g., posing two different word problems was required for each item) or relate to the given problem situation (i.e., using at least one of the knowns, or the goal provided in the situation). Third, the problem should be solvable, i.e., the problem should provide sufficient information to obtain its answer or its goal should be compatible with the given information. Finally, the problem should accord with real-world constraints. (For more details, see Chen, Verschaffel, & Van Dooren, 2011.)
- 3.
Since its requirements state “Pose one mathematical problem whose solution would require only addition or subtraction, and one mathematical problem whose solution would require at least one multiplication or division,” it does not make sense to evaluate the diversity of the posed problems with these specific requirements.
- 4.
The PPQ and PSQ with different item order were used before and after the intervention.
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Chen, L., Van Dooren, W., Verschaffel, L. (2015). Enhancing the Development of Chinese Fifth-Graders’ Problem-Posing and Problem-Solving Abilities, Beliefs, and Attitudes: A Design Experiment. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_15
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