The University of Montana

Department of Mathematical Sciences

Technical report #11/2011

Creativity and Mathematical Problem Posing: An Analysis of High School Students' Mathematical Problem Posing in China and the United States

**Xianwei Yuan Van Harpen**, Illinois State University

**Bharath Sriraman**, The University of Montana

**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 United States and China. This study was aimed at exploring high school students' creativity in mathematics by analyzing their abilities in posing problems in geometric scenarios. The participants in this study were from one location in the United States 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 as well as quantity. 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 directions in problem posing research within mathematics education.

**Keywords:** advanced high school students; cross cultural thinking; geometry; mathematical creativity;
novelty; problem posing; problem solving; U.S and Chinese students; rural and urban Chinese students

**AMS Subject Classification:** 97

Preprint of paper submitted to *Educational Studies in Mathematics* Pdf (660 KB)