Measuring conceptual understanding quickly and reliably
Developing conceptual understanding is a key goal of mathematics education at all levels. Unfortunately, compared to procedural understanding, it is much harder to reliably assess. Most efforts to measure students’ conceptual understanding involve the time-consuming development of a domain-specific concept inventory (e.g. Epstein, 2005) or the use of detailed clinical interviews (e.g. Piaget, 1959). Both of these methods are highly time-intensive, either in terms of development work or researcher time. These costs present a serious barrier to rigorously evaluating educational interventions that are designed to improve students’ conceptual understanding.
In this talk I discuss an alternative approach to assessing conceptual understanding, based on Thurstone’s Law of Comparative Judgement from the psychophysics literature. I will explain the theoretical basis of the approach, and report a number of studies where my colleagues and I have employed it. These studies include assessing children’s understanding of fractions, assessing undergraduate students’ understanding of statistics, and the comparison of high-stakes examination standards over time.
The Challenges of Spreading and Sustaining Research-Based Instruction in Undergraduate STEM
There have been many calls for the reform of introductory Science, Technology, Engineering and Mathematics (STEM) courses. These calls have resulted in a cadre of researchers who study the teaching and learning of undergraduate STEM and have developed instructional methods that improve student learning. There currently exists a substantial gap between research-based knowledge of ‘best practice’ instructional methods and the teaching practices of typical STEM faculty. This talk will connect data about the spread of research-based instructional strategies in college-level STEM to ideas from the change literature. Recommendations will be made for how to decrease the knowledge-practice gap.
Understanding and alleviating children's difficulties with mathematical equivalence
Why do children sometimes fail to learn new information, even after substantial amounts of experience or instruction? Several prevailing accounts suggest that learning difficulties are caused by something that children lack (e.g., working-memory resources or proficiency with prerequisite skills). In contrast, others argue that difficulties are caused, at least in part, by something that children have--existing knowledge. In this talk, I will focus on children's difficulties with mathematical equivalence (i.e., the concept that the two sides of an equation are equal and interchangeable), and I will present evidence that children's existing knowledge of arithmetic contributes to these difficulties. I will discuss how this evidence informs our understanding of theoretical issues related to the nature of children's difficulties with math equivalence, as well as practical issues related to the malleable factors that can be changed to improve children's understanding of this fundamental concept.
The SIGMAA on Research in Undergraduate Mathematics Education presents its Eighteenth Annual
February 19 - 21, 2015 | Pittsburgh, PA