Adaptation of tertiary mathematics instruction to the virtual medium: approaches to assessment practice

Mathematics has been singled out as a challenging discipline to teach fully online (FO). Yet both the demand for and development of FO mathematics courses is increasing with little known about the quality of these courses and many calling for research. Whereas most research has investigated the nature of these courses by examining instructional outputs such as student grades this research seeks the same insight but by examining instructional inputs. Specifically, it seeks to investigate the nature of current assessment practice in FO mathematics courses. To conduct this investigation, deep learning (Marton & Säljö, 1976a, 1976b) is used as the principle theoretical framework. From the growing body of literature associated with deep learning, two studies are selected to investigate current FO mathematics instructors assessment practices. An additional framework based on empirical findings related to the use of different kinds of feedback is also used. In total, six study measures are used to conduct a mixed methods study in two parts. The target demographic and course context are tertiary instructors from Western nations that teach introductory level mathematics (particularly statistics and calculus). The first study explores current FO mathematics assessment practices using an online survey (n=70) where the majority of participants originate from US higher education institutions. In the second study six of the US survey participants are interviewed about how their assessment practices and approaches used in their FO mathematics courses differ from those used in their face-to-face (F2F) mathematics courses. This study represents the first known attempt to investigate the nature of tertiary FO mathematics instructors assessment practices using appropriate theoretical frameworks. In particular, it investigates mathematics instructors experiences of the affordances and constraints of the FO course context when adapting their F2F practice to this new environment. Findings suggest the FO course context is a challenging environment for instructors to orient their teaching and assessment practice in a way that helps develop students understanding of mathematics. Analysis of interview responses suggests the problem lies with the nature of interactivity provided in the FO course context

An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses

Research suggests it is difficult to learn mathematics in the fully asynchronous online (FAO) instructional modality, yet little is known about associated teaching and assessment practices. In this study, we investigate FAO mathematics assessment and feedback practices in particular consideration of both claims and findings that these practices have a powerful influence on learning. A survey questionnaire was constructed and completed by 70 FAO undergraduate mathematics instructors, mostly from the USA, who were each asked to detail their assessment and feedback practices in a single FAO mathematics course. Alongside these questions, participants also answered the 16-item version of the Approaches to Teaching Inventory. In addition, a novel feedback framework was also created and used to examine how feedback practices may be related to participants' approaches to teaching. Results show that assessment and feedback practices are varied and complex: in particular, we found there was not a simple emphasis on summative assessment instruments, nor a concomitant expectation these would always be invigilated. Though richer assessment feedback appears to be emphasized, evidence suggests this feedback may not be primarily directed at advancing student learning. Moreover, we found evidence of a reliance on computer--human interactions (e.g. via computer-assisted assessment systems) and further evidence of a decline in human interactions, suggesting a dynamic that is both consistent with current online learning theory and claims FAO mathematics courses are becoming commodified. Several avenues for further research are suggested

Mathematics lecturing in the digital age

In this article, we consider the transformation of tertiary mathematics lecture practice. We undertake a focused examination of the related research with two goals in mind. First, we document this research, reviewing the findings of key studies and noting that reflective pieces on individual practice as well as surveys are more prevalent than empirical studies. Second, we investigate issues related to the transformation of lecture practice by the emergence of e-lectures. We discuss the latter in terms of claims about the efficiencies offered by new technologies and contrast these with possible disadvantages in terms of student engagement in a learning community. Overall findings indicate that while survey results appear to trumpet the value of e-lecture provision, empirical study results appear to call that value into question. Two explanatory theoretical frameworks are presented. Issues concerning the instructional context (e.g. the nature of mathematical thinking), inherent complexities and recommendations for implementation are discussed

Investigating undergraduate mathematics learners’ cognitive engagement with recorded lecture videos

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, though it is unclear whether this is because regular users are generally weaker mathematics students or because RLV use is somehow depressing student learning. Through the lens of cognitive engagement, a quasi-experimental pre- and post-test design study was conducted to investigate the latter possibility. Cognitive engagement was operationalised using the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F), which measures learning approaches on two major scales: surface and deep. In two mathematics courses at two universities, in Australia and the UK, participants were administered the questionnaire near the course start and finish. Overall findings were similar in both contexts: a reduction in live lecture attendance coupled with a dependence on RLVs was associated with an increase in surface approaches to learning. This study has important implications for future pedagogical development and adds to the sense of urgency regarding research into best practices using RLVs in mathematics

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

An investigation of assessment in fully asynchronous online math courses

This study is based on a voluntary survey of all listed Fall 2006 State University of New York (SUNY) Learning Network (SLN) mathematics faculty. The survey focuses on assessment in SLN math e-learning. Based on survey data, the study attempts to answer the following questions: What percentage of math e-learning courses overall, by course category and by institution (two year or four year) are proctored? In proctored and unproctored math e-learning courses, which assessment instruments are utilised and how? Comparing the two approaches, how does the practice of assessment in proctored math e-learning courses compare to the practice of assessment in unproctored math e-learning courses? Finally, what are the ten most popular strategies for assessing math e-learning courses? The paper concludes with questions, suggestions for further research and implications regarding the academic integrity of math e-learning courses

The instructor experience of fully online tertiary mathematics: a challenge and an opportunity

As part of a dramatic recent shift in tertiary education, many undergraduate students now learn mathematics via fully online courses. At present, the mathematics education research community knows very little about this shift, and in this report, we consider implications of an investigation into the instructor experience of fully online undergraduate mathematics courses. We explored assessment schemes, feedback practices, and approaches to teaching and used semistructured interviews to compare instructor experiences of fully online and face-to-face discussion, assessment, and feedback. The main emergent theme was instructor concern about the loss of short-cycle face-to-face human interaction. We argue that this concern is serious but should be seen as an opportunity for education researchers to leverage knowledge about effective mathematics teaching to simultaneously alleviate instructors’ difficulties and promote and study pedagogical development

Tertiary mathematics education

Mathematical and Statistical Education Research relevant to students in tertiary is reviewed. This is an expanding field and is evolving as researchers shift their attention from the reporting of innovations in lecturing practice and course design, to include a deeper consideration of the experiences of educators and learners in this space. The purposeful inclusion of group work and discussion, focus on concepts, authentic problem solving, interactions in lectures with student response systems and online learning are all changing the way mathematics and statistics are taught at this level. The authors note that traditional measures of achievement in the form of exam marks are still relied upon, and call for theory-based and theory-building research including investigations of depth of understanding, and of transfer of knowledge and skills to new situations. An emphasis on the learner’s experience and the employment of cross-disciplinary teams of researchers are further suggestions

Teaching and learning mathematics with digital technologies

This chapter provides a critical synthesis of research on technology related classroom practice from the early years of schooling through to tertiary and initial teacher mathematics education. The synthesis considers ways in which research has explored the use of digital technologies through the three dimensions identified by Pierce and Stacey’s map of pedagogical opportunity: mathematics content (subject), in classroom interactions (classroom), and through task design (task) (2010). The chapter also provides a synthesis of the research methodologies undertaken within the included studies. The review concludes with a discussion of emerging themes and a range of future directions for research into technology-related mathematics education