Mathematical tasks, study approaches, and course grades in undergraduate mathematics: a year-by-year analysis

Maciejewski, Wes; Merchant, Sandra M.

doi:10.1080/0020739x.2015.1072881

Cited by 31 publications

(25 citation statements)

References 36 publications

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“…In addition, Murphy (2017) associates a deep approach to learning with higher mathematical performance. By contrast, Maciejewski and Merchant (2016) find a strong negative correlation between a surface approach and course grades, implying that a surface approach leads to lower achievement. Therefore, deep and surface approaches to learning play a significant role in the quality of learning in university mathematics.…”

Section: Theoretical Frameworkmentioning

confidence: 59%

“…As a result, a deep approach is the most valued of the three approaches to learning. In the context of undergraduate mathematics education, Maciejewski and Merchant (2016) argue that proof-based mathematics courses require a deep approach to learning. In addition, Murphy (2017) associates a deep approach to learning with higher mathematical performance.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

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Supporting Quality of Learning in University Mathematics: a Comparison of Two Instructional Designs

Lahdenperä

Postareff

Rämö

2018

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

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Prior research acknowledges the need to further develop undergraduate mathematics instruction. The aim of this study is to investigate the relationship between instructional design and quality of learning. This quantitative study approaches the learning environment by comparing students' approaches to learning, self-efficacy, and experiences of the teachinglearning environment in two undergraduate mathematics courses using different pedagogical approaches. The first course functioned within a traditional lecture-based framework with the inclusion of student-centred elements, and the second course was implemented with Extreme Apprenticeship, a novel student-centred teaching method. The analysis is based on the same cohort of students in these two contexts (N = 91). Students were clustered based on their deep and surface approaches to learning and three clusters were identified: students applying a deep approach, students applying a surface approach, and students applying a context-sensitive surface approach. The results show that the more student-centred course design succeeded in supporting more favourable approaches to learning, higher self-efficacy levels, and more positive experiences of the teaching-learning environment. In addition, all three clusters benefited from the more student-centred course design, with students applying a context-sensitive surface approach benefiting the most. Overall, the results suggest that it is possible to promote the quality of university mathematics learning with instructional designs that, besides content, take a holistic approach to the learning environment. Keywords Student-centred. Instructional design. Approaches to learning. Experiences of the teaching-learning environment. Self-efficacy. Quantitative research

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Section: Theoretical Frameworkmentioning

confidence: 59%

Section: Theoretical Frameworkmentioning

confidence: 99%

Supporting Quality of Learning in University Mathematics: a Comparison of Two Instructional Designs

Lahdenperä

Postareff

Rämö

2018

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

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“…Empirical evidence has shown that students' learning approaches contribute significantly to their academic success in higher education (e.g., [1,2]). Learning approaches could be conceived as an individual's adopted predispositions when dealing with tasks and strategies used to process learning materials which can be deep or surface in nature [3,4].…”

Section: Introductionmentioning

confidence: 99%

Study Approaches in Higher Education Mathematics: Investigating the Statistical Behaviour of an Instrument Translated into Norwegian

Zakariya

2019

Education Sciences

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The revised two-factor study process questionnaire (R-SPQ-2F) has widely been considered valid and reliable in many contexts for measuring students’ learning approaches. However, its cultural specificity has generated considerable discussion, with inconclusive results when translated to different languages. This paper provides more insights into the construct validity of a Norwegian version of this instrument. The R-SPQ-2F is composed of ten items designed to expose deep learning approaches and 10 items designed to expose surface learning approaches. A survey research design involving a sample of 253 first year university students in a mathematics course was adopted. Ten hypothesized models were compared using a series of confirmatory factor analyses following the model proposals reported in the literature. A weighted least square mean and variance adjusted (WLSMV) estimator was used to enhance model parameter estimations under multiple violations of assumptions inherent in ordinal data. The results favored a two first-order factor model with ten items measuring the deep approach and nine items measuring the surface approach including a deletion of one item from this instrument. The findings of this study provide empirical evidence for the cultural specificity of the instrument that is consistent with the literature. The R-SPQ-2F is therefore recommended to assess students’ approaches to learning, and further studies into its cultural specificity are recommended.

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“…An analysis of tasks from different modules across the four years of an undergraduate mathematics degree is offered by Maciejewski and Merchant (2016). They analyse the tasks using Bloom's taxonomy (1956) aiming to find the relationship between study approaches and module grades in undergraduate mathematics modules in all four years of the undergraduate mathematics course.…”

Section: Examination Tasks and Lecturer Perspectivesmentioning

confidence: 99%

“…The content of the first-year examination papers is seen as highlighting what lecturers consider important (Smith et al 1996; Van de Watering et al 2008) and students' ways of approaching those examination tasks can demonstrate how the students experience this transition and where their enculturating difficulties may lie. Researchers have studied assessment tasks using different theoretical frameworks and focusing on different aspects of the tasks (Bergqvist 2007;Darlington 2014;Maciejewski and Merchant 2016;Tallman et al 2016). Some researchers also propose characterisations of examination tasks (Tallman et al 2016) or examine what mathematical reasoning lecturers prioritise when they design tasks (Bergqvist 2012).…”

Section: Introductionmentioning

confidence: 99%

Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students’ Examination Scripts

Thoma

Nardi

2017

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

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We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the tasks and the lecturers' (also exam setters') assessment practices, and focuses on manifestations of unresolved commognitive conflict in students' engagement with the tasks. Here we note four such manifestations concerning the students' identification of and consistent work with: the appropriate numerical context of the examination tasks; the visual mediators and the rules of school algebra and Set Theory discourses; the visual mediators of the Probability and Set Theory discourses; and, with the visual mediators and rules of the Probability Theory discourse. Our analysis suggests that, despite lecturers' attempts to assist students towards a smooth transition to the different discourses of university mathematics, students' errors at the final examination reveal unresolved commognitive conflicts. A pedagogical implication of our analysis is that a more explicit and systematic presentation of the distinctive differences between these discourses, along with facilitation of the flexible moves between them, is needed.

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Mathematical tasks, study approaches, and course grades in undergraduate mathematics: a year-by-year analysis

Cited by 31 publications

References 36 publications

Supporting Quality of Learning in University Mathematics: a Comparison of Two Instructional Designs

Supporting Quality of Learning in University Mathematics: a Comparison of Two Instructional Designs

Study Approaches in Higher Education Mathematics: Investigating the Statistical Behaviour of an Instrument Translated into Norwegian

Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students’ Examination Scripts

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