Quantitative Reasoning: Exploring Troublesome Thresholds

Conversations about teaching and student learning with faculty across many of the science disciplines will invariably lead to a number of shared concerns. One such concern typically revolves around quantitative reasoning (QR). This paper presents the results of a pilot study in which instructors and students were interviewed with a view to identifying key QR obstacles in earth, ocean, and environmental sciences courses at one Canadian university. The instructor point of view was obtained by interviewing faculty and graduate student teaching assistants, while the student perspective came from a focus group of undergraduate students from across these disciplines. In both cases, participants were asked about specific quantitative aspects of their courses where students struggle and strategies they were already using in these cases. We examine the possible role of threshold concepts in QR within the earth, ocean, and environmental sciences. Threshold concepts are transformative, often troublesome concepts that are key to developing true expertise in a discipline; once mastered, they are irreversible and can serve to bring together different aspects of the subject. As such, their possible role in QR holds potential for enhancing the learning. Meyer and Land (2005) suggest that in crossing these thresholds into new ways of viewing the discipline, or indeed, the world, the journey is somewhat akin to travelling through a portal, or liminal space, where uncertainty is common and developing understanding is not necessarily linear. We further explore a number of strategies that can be used to help students overcome the challenges that were identified. The results revealed a range of themes considered troublesome that crossed all disciplines including applying math across changing contexts, a fear of math, the lack of student’s ability to reflect on their answers and therefore correct where necessary, and working with conversions and scale. Additionally, both faculty and students identified the difficulty many students have when working with data, in particular, plotting data, manipulating data and interpreting results, with and without the use of computer software packages. We note in particular that students’ difficulty in articulating or identifying threshold concepts may reflect their incomplete journey through the liminal stage. We need other strategies, such as looking at their work, in order to assess this more completely. Although no group specifically articulated concepts, they considered transformative amongst the troublesome concepts they identified. We suggest that there are learning thresholds within QR, and that these span all the sciences. Two such thresholds we propose based on our study are: (a) the ability to apply QR across a range of contexts and use it as a tool or a form of language for scientific problem solving, and (b) fluency in data literacy which enables a student to work through the scientific process. We conclude by presenting a set of strategies to help instructors guide students as they develop QR skills while working through these troublesome areas. These strategies include those suggested by faculty and students in this study, and others identified from evidence-based best practices in the literature