Collegiate mathematics teaching: An unexamined practice

Speer, Natasha M.; Smith, John P.; Horvath, Aladar

doi:10.1016/j.jmathb.2010.02.001

Cited by 100 publications

(62 citation statements)

References 55 publications

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“…[54,56,[59][60][61] However, reflecting the general state of undergraduate mathematics research and the nascent state of FAO instruction, little is known about undergraduate mathematics F2F feedback practices in general and FAO practices in particular [62]: In F2F undergraduate mathematics instruction, there is an emphasis on summative assessment, [8,20,29,[63][64][65][66] and assessment feedout (rather than feedback) processes are expected to dominate. In FAO mathematics instruction, of what very little is known, feedback practices appear much more complex [67] and many claim an extended purpose for the use of feedback.…”

Section: Fao Mathematics Feedback Practicesmentioning

confidence: 99%

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

Trenholm

Alcock

Robinson

2015

International Journal of Mathematical Education in Science and

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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 US, 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. 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 CAA 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.

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Section: Fao Mathematics Feedback Practicesmentioning

confidence: 99%

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

Trenholm

Alcock

Robinson

2015

International Journal of Mathematical Education in Science and

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“…Our principal research question derives from Speer et al 2010, who refer to Bwhat teachers do and think daily, in class and out, as they perform their teaching work^(p. 99). Thus our research addresses:…”

Section: Research Focus Aims and Questionsmentioning

confidence: 99%

“…While not underestimating the value of such accounts in providing insights to practices and their use of pedagogy, our main focus here is on the research literature which accounts for what is observed, offering theoretical perspectives to explain and justify outcomes. We have cited the paper by Speer et al (2010) from which we quoted above: Bvery little research has focused directly on teaching practice [at university level]-what teachers do and think daily, in class and out, as they perform their teaching work^(p. 99). Since this is precisely our area of research focus it seemed important to seek out the 'little' that has been done before 2010 and relevant research since then.…”

Section: Associated Literaturementioning

confidence: 99%

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Critical Theorising from Studies of Undergraduate Mathematics Teaching for Students’ Meaning Making in Mathematics

Jaworski

Mali

Πετροπούλου

2016

Int. J. Res. Undergrad. Math. Ed.

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This paper focuses directly on mathematics teaching practice at university level, exploring Bwhat teachers do and think daily, in class and out, as they perform their teaching work^ (Speer et al. in The Journal of Mathematical Behavior, 29, 99-114, 2010, p. 99). It is based on a small corpus of research conducted from sociocultural perspectives with qualitative and interpretative studies into mathematics teaching and the meanings it promotes for students learning mathematics. Two settings of teaching are explored: lectures and small group tutorials in which teachers are research mathematicians or mathematics educators. Analyses make use of a range of theoretical perspectives to interpret the complexities of teaching based on observations of teaching activity and interviews with teachers. Critical Theorising is seen through critical use of existing theory and construction of new theory: through the analytical process it provides insights into teaching and ways in which teaching does or can develop to promote students' meaning making in mathematics. The paper draws attention to the finer details of teaching practice and teachers' thinking that lie behind judgments such as 'traditional' or 'transmissionist'.

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“…Many studies have focused on the use of exemplification and examples when students learn a new mathematical concept and corresponding proofs [4,5]; however, very few studies have investigated the selection of examples by university teachers in teaching classes on differentiation and derivatives. Given that researching teaching processes is challenging, even though the need to study the teaching processes of collegiate mathematics has been repeatedly emphasized [6,7], empirical studies that demonstrate and analyze the actual practice of collegiate mathematics teachers are limited [8]. The focus, research questions, methods, and analyses of existing studies are not directly based upon what teachers say, do, and think about in collegiate classrooms from an extensive and detailed perspective [7].…”

Section: Introductionmentioning

confidence: 99%

Teachers’ Choice and Use of Examples in Teaching Derivatives

Huang¹

2017

EDUCATION

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Students' understanding of a mathematical idea depends upon the examples used by their teachers. Thus, the key responsibility of a math teacher is to select examples that provide the best learning opportunities for students, as well as present the examples in the way most suitable to promote learning. The study reported here is part of a larger research program addressing the role and nature of examples in mathematical thinking, learning, and teaching. The main goal of this part of the study is to characterize mathematics teachers' choice and use of examples in teaching derivatives. This study provided evidence of the application of instructional examples to teach derivatives in calculus courses.

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Collegiate mathematics teaching: An unexamined practice

Cited by 100 publications

References 55 publications

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

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

Critical Theorising from Studies of Undergraduate Mathematics Teaching for Students’ Meaning Making in Mathematics

Teachers’ Choice and Use of Examples in Teaching Derivatives

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