Expanding mathematical creativity by understanding student actions

Although there have been calls for secondary mathematics education in the U.S. to incorporate problem-solving and creativity, the lion’s share of instruction is designed to train students to accurately use procedures or understand concepts made by mathematicians in the past (National Research Council, 1999; Watson, 2008). This disconnect highlights a need to know more about student mathematical creativity. The goal of the study was to examine the nature of student mathematical creativity and identify how it can be influenced by social and aesthetic factors. Therefore, I performed a qualitative analysis of video and audio recordings of student and teacher interactions from eight high school mathematics lessons taught in the Northeast in the United States. To demonstrate the range of creativity of which students are capable, I identified and categorized potentially creative actions. I also developed episodes of creative action, explaining how some created new mathematical possibilities, and others were blocked in doing so. From these episodes, I identified a set of key moments in their development: taking the action, the reception by others, advocacy for the action, and an additional creative action by other members of the student group or class. Finally, from comparing multiple episodes, I found that experiencing mystery or mathematical discomfort motivated students to take actions with creative potential, and that positive relationships and strong group participation contributed to interactive discussions between group members that enabled the actions’ creative potential to be realized. Findings from this process could support educators in giving more students the opportunity to create new ways of doing mathematics