Assessing mathematical reasoning: analyzing imitative and creative reasoning by students

Abstract The ability to reason mathematically is considered one of the key purposes of mathematics education in schools. In this paper, we investigate students’ success in mathematical reasoning on a nationally administered upper secondary school exam in Norway. The exam is analyzed both qualitatively and quantitatively. Each task is categorized by six teachers based on the type of reasoning required: either imitative reasoning or creatively-founded mathematical reasoning. Additionally, we analyze the point scores from 2112 student assessment forms using Item Response Theory. Our findings show that 32% of the exam points are awarded for tasks requiring creative mathematical reasoning. These tasks provide more information about both lower- and higher-achieving students compared to other tasks; however, we do not find creative reasoning to be an underlying trait that explains the variance in point scores. Instead, factor analysis suggests that mathematical content (e.g., functions) is more important. We conclude that tasks requiring creative reasoning are well suited for assessing students across all performance levels.