Date of Award

July 2016

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Teaching and Leadership

Advisor(s)

Joanna O. Masingila

Keywords

Mathematical problem posing, Mathematical problem solving, Prospective elementary teachers

Subject Categories

Education

Abstract

This study examined the patterns of problem posing shown by United States (US) and Chinese prospective elementary teachers during problem-posing processes when problem-solving activities were involved in an alternating manner. It further explored the features of the relationship between problem posing and problem solving. Data were collected by asking 32 US and 55 Chinese prospective elementary teachers to pose problems for Translating, Comprehending, Editing, and Selecting processes (Christou, Mousoulides, Pittalis, Pitta-Pantazi, & Sriraman, 2005) before a problem-solving task, and then to pose two more problems after that problem-solving task, namely, problem posing after the problem solving process. All participants completed the first set of tasks, and 43 of them completed the similarly structured second set of tasks.

Participants’ posed and solved problems were quantitatively analyzed. For problem solving, the results showed that (1) 25% of the 32 US participants and 98% of the 55 Chinese participants completely solved the given problem during the first task administration, and (2) 19% of the 16 US participants and 89% of the 27 Chinese participants correctly solved the given problem during the second task administration. In their problem posing, Chinese participants posed a much higher percentage of solvable mathematical problems in the Comprehending and Selecting processes compared to their US counterparts, while their US counterparts were challenged most by these two processes. Additionally, both US and Chinese participants’ best performance in problem posing did not occur during problem posing after the problem solving process.

In qualitative analysis, US and Chinese participants’ problem-posing performance shared some similar patterns regarding (1) features of posed problems, (2) capability of posing problems with creative ideas, and (3) progression of problem-posing performance throughout all five problem-posing processes. The US and Chinese participants also showed some differences during the problem-posing process as follows: (1) figure visualization; (2) calculation interpretation; (3) habitual preference of posing a sequence of problems; (4) perception of a given answer based on previously posed or solved problems; and (5) problem-posing strategy selection for integrating given information. This study further examined the features of the relationship between problem posing and problem solving. Different types of problem-posing tasks needed different amounts of problem-solving effort and they had different impacts on problem-solving performance. In addition, problem solving before problem posing had a positive influence on participants’ subsequent problem-posing performance.

This study suggests recommendations for future research to understand other forms of interactions between problem posing and problem solving, explore specific impacts of cultural or academic background on problem-posing performance, and develop models or frameworks that could help problem posers overcome the difficulties involved in posed problems that were ill-structured, unsolvable, or not mathematical problems. For teacher preparation, this study advocates that prospective elementary teachers need more exposure to multiple types of problem-posing tasks, practices involving interactions between problem posing and problem solving, opportunities to work with ill-structured mathematical problems, as well as opportunities to recognize and analyze different types of mathematical problems before posing their own problems.

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