Journal ArticleDOI
Do third‐year mathematics undergraduates know what they are supposed to know?
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In this paper, the authors describe a test, covering 155 third-year undergraduates in 15 different institutions, to examine the extent to which certain core first-year material is retained and understood.Abstract:
The paper describes a test, covering 155 third‐year undergraduates in 15 different institutions, to examine the extent to which certain core first‐year material is retained and understood. The topics considered explore ideas such as the definition of differentiability, the principle of mathematical induction, understanding of basis and dimension, and perceptions about the real numbers. Also included are a question in mechanics and one on elementary aspects of group theory. As well as recording the students’ results (according to the criteria set out below), the paper includes an; lysis of the answers given by the students to each question and also some of their comments, as recorded on their scripts. Their misconceptions indicate that the foundations laid in the first year, on which their subsequent knowledge is built, is often very flimsy. Data collected include information on the final degree award of most of the test group. It is found that even among those students who subsequently achieved good degre...read more
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Changing patterns of transition from school to university mathematics
TL;DR: In this paper, the antecedents of this changed profile in the general shift across all subjects to a more utilitarian higher education, alongside the more specific changes in A-level mathematics provision have been largely market driven.
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Mathematical modelling: transitions between the real world and the mathematical model
TL;DR: In this paper, a study is presented which goes some way to demonstrate and explain the problems faced by students in linking mathematical models to real-world applications in engineering, science and technology within undergraduate programs.
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The student experience of mathematical proof at university level
TL;DR: This paper reviewed what is known of the student experience of mathematical proof at university level and found that some students may complete their degrees with an incomplete picture of what constitutes a proof and how proofs are developed.
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Conceptual Mis(understandings) of Beginning Undergraduates.
TL;DR: In this article, a taxonomy of mathematical skills of some importance to beginning undergraduates in engineering and mathematics is proposed, focusing on the distributions of the distractors chosen by the students.
Journal ArticleDOI
A Questionnaire To Elicit the Mathematical Concept Images of Engineering Students
Wendy Maull,John Berry +1 more
TL;DR: In this paper, a questionnaire has been developed which seeks to elicit from students their concept images attached to key mathematical concepts, and the questionnaire seeks to address both the level of understanding of the students and the mode in which the students hold the concept image.
References
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On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin
TL;DR: In this article, a theoretical framework for investigating the role of algorithms in mathematical thinking is presented, and it is shown that the processes of learning and of problem-solving consist in an intricate interplay between operational and structural conceptions of the same notions.
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Advanced Mathematical Thinking
TL;DR: In this article, the authors discuss the role of concepts in the teaching and learning of Advanced Mathematical Thinking at an Advanced Level and present ISETL, a computer language for advanced mathematical thinking.
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Fundamentals of learning and memory
TL;DR: Bargaining with reading habit is no need as what will be given by this fundamentals of learning and memory, how can you bargain with the thing that has many benefits for you?