A study of creative reasoning opportunities in assessments in undergraduate calculus courses

Bhaird, Ciarán Mac an; Nolan, Brien C.; O’Shea, Ann

doi:10.1080/14794802.2017.1318084

Cited by 19 publications

(15 citation statements)

References 26 publications

(40 reference statements)

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“…For example, using this classification, Bergqvist (2007) found, in the Swedish context, that it was possible to pass an introduction to calculus closed book exam by employing only imitative reasoning while the tasks involving creative reasoning consisted mostly in asking students to create specified examples. A similar study in Ireland (Mac an Bhaird et al, 2017) found that there were more creative reasoning tasks in the assessment of mathematics for mathematics students than in the assessment of mathematics for non-mathematics specialists (e.g., engineers) and that for the latter it was possible to achieve high marks in calculus exams by just employing imitative reasoning.…”

Section: Summative Assessment Of Mathematics At University Levelmentioning

confidence: 94%

“…Since this situation is likely to be similar in many other countries, as some of the literature reviewed below indicates (see Bergqvist, 2007, for Sweden andMac an Bhaird, Nolan, O'Shea, &Pfeiffer, 2017, for Ireland), it is not surprising that much of the literature on summative assessment of mathematics at university discusses the types of reasoning assessed by closed book exam as they are currently designed. The analysis of types of reasoning elicited by current summative assessment is important for our study in the light of the link posed by Entwistle and Entwistle (1991) between perceived assessment demands and approaches to learning.…”

Section: Summative Assessment Of Mathematics At University Levelmentioning

confidence: 95%

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The impact of high stakes oral performance assessment on students’ approaches to learning: a case study

2020

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This paper presents findings from a case study on the impact of high stakes oral performance assessment on third year mathematics students' approaches to learning (Entwistle and Ramsden, Understanding student learning, 1983). We choose oral performance assessment as this mode of assessment differs substantially from written exams for its dialogic nature and because variation of assessment methods is seen to be very important in an otherwise very uniform assessment diet. We found that students perceived the assessment to require conceptual understanding over memory and were more likely to employ revision strategies conducive to deep learning (akin to conceptual understanding) when preparing for the oral performance assessment than when preparing for a written exam. Moreover, they reported to have engaged and interacted in lectures more than they would have otherwise, another characteristic conducive to deep learning approaches. We conclude by suggesting some implications for the summative assessment of mathematics at university level. Keywords Case study. Oral performance assessment. Students' approaches to learning. University mathematics Mathematics is an academic discipline that employs very few summative assessment methods at university level and researchers (Steen, 2006) have often called for a variety of its summative assessment. Amongst the methods in use, written, timed exams dominate and indeed in a recent survey of assessment methods in England and Wales, Iannone and Simpson (2011) found the written, timed exam to be the modal assessment method across their sample. At the same time, the general education literature perceives uniformity of summative assessment as problematic (Brown, Bull, & Pendlebury, 2013) and indicates that traditional written timed exams alone are not suitable to assess all the competencies that may be desirable to assess (Birenbaum et al., 2006).

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Section: Summative Assessment Of Mathematics At University Levelmentioning

confidence: 94%

Section: Summative Assessment Of Mathematics At University Levelmentioning

confidence: 95%

The impact of high stakes oral performance assessment on students’ approaches to learning: a case study

2020

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“…Indeed, several studies have shown that students are mainly given tasks that promote the use of predetermined algorithms, procedures, and/or examples of how to solve the task rather than opportunities to engage in a problem-solving struggle without instruction (Stacey and Vincent, 2009;Denisse et al, 2012;Boesen et al, 2014;Jäder et al, 2019). For example, Jäder et al (2019) examined mathematics textbooks from 12 countries and found that 79% of the textbook tasks could be solved by merely following provided procedures, 13% could be solved by minor adjustments of the procedure, and only 9% required students to create (parts of) their own methods (for similar findings, also see Pointon and Sangwin, 2003;Bergqvist, 2007;Mac an Bhaird et al, 2017). In response to these findings, Lithner (2008Lithner ( , 2017 developed a framework arguing that the use of instructions in terms of predefined algorithms has negative long-term consequences for the development of students' conceptual understanding.…”

Section: Introductionmentioning

confidence: 91%

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

2020

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In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.

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“…Such frameworks enable the study of the types of tasks assigned in university level courses (Kinnear et al, 2020a;Mac an Bhaird et al, 2017), but it seems that very little work has been done in the area of e-assessment.…”

Section: What Developments At the Forefront Of E-assessment (Such As Artificial Intelligence) Can We Apply To University Mathematics?mentioning

confidence: 99%

A collaboratively-derived research agenda for e-assessment in university mathematics

Kinnear¹,

Jones²,

Sangwin³

et al. 2021

Preprint

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This paper describes the collaborative development of an agenda for research on e-assessment in university mathematics. We adapted an established approach to develop the agenda from the contributions of 22 mathematics education researchers, university teachers and learning technologists interested in this topic. The resulting set of 55 questions are grouped into 5 broad themes: errors and feedback, students, design and implementation, affordances, and mathematical skills. This agenda gives the framework for a programme of research aligned with practical concerns, that will contribute to both theoretical and practical development.

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A study of creative reasoning opportunities in assessments in undergraduate calculus courses

Cited by 19 publications

References 26 publications

The impact of high stakes oral performance assessment on students’ approaches to learning: a case study

The impact of high stakes oral performance assessment on students’ approaches to learning: a case study

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

A collaboratively-derived research agenda for e-assessment in university mathematics

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