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Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA

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Abstract

In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in mathematics by analyzing their problem-posing abilities in geometric scenarios. The participants in this study were from one location in the USA and two locations in China. All participants were enrolled in advanced mathematical courses in the local high school. Differences in the problems posed by the three groups are discussed in terms of quality (novelty/elaboration) as well as quantity (fluency). The analysis of the data indicated that even mathematically advanced high school students had trouble posing good quality and/or novel mathematical problems. We discuss our findings in terms of the culture and curricula of the respective school systems and suggest implications for future directions in problem-posing research within mathematics education.

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Notes

  1. There were 117 studies included in this meta-analysis that most of them support the existence of incubation effects on problem solving.

  2. Cross-national studies of temperamental styles are typically based on the Myers and Briggs theory of temperament and the associated psychometric test called Myers–Briggs Type Indicator (MBTI).

    Oakland, Glutting, and Horton (1996) adapted the MBTI to detect cross-national differences in children aged 8 to17 years old on four bipolar temperament style dimensions, namely extroversion–introversion, practical–imaginative (MBTI's judging–perceiving), thinking–feeling, and organized–flexible (MBTI's judging–perceiving). The adapted test is called the Student Styles Questionnaire (see Oakland et al., 1996).

  3. We do not enter into a discussion of the definition of mathematical giftedness in this paper. This is a well-defined term in the research literature in gifted education. In this paper, the participants by virtue of their enrollment in the advanced mathematical courses were among the high achievers in their respective schools and included students of varying mathematical abilities.

  4. The reader may be surprised to learn that the term “normal” schools for teachers colleges comes from the first such school in Normal, Illinois.

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Acknowledgments

The first author would like to thank her dissertation committee members for their patience and expert guidance. They are Dr. Norma Presmeg (the committee chair), Dr. Nerida Ellerton, Dr. McKenzie Clements, Dr. Bharath Sriraman, and Dr. John Rugutt.

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Authors and Affiliations

  1. Illinois State University, Normal, IL, USA

    **anwei Y. Van Harpen

  2. The University of Montana, Missoula, MT, USA

    Bharath Sriraman

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Correspondence to **anwei Y. Van Harpen.

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Van Harpen, X.Y., Sriraman, B. Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA. Educ Stud Math 82, 201–221 (2013). https://doi.org/10.1007/s10649-012-9419-5

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