Abstract
Students, when answering a mathematical question, may make a mistake in their answer for a variety of reasons. For example, not reading the question properly, making a mistake due to carelessness or due to a mathematical misconception. It is this latter category, which is of particular interest to us in this paper. When such mistakes occur in handwritten work then, in general, the teacher is able to identify the mistake(s) during the marking process and give written detailed feedback on the student’s script. The disadvantage of this approach is the time and effort it takes to mark and to get feedback back to the student. As a result, e-assessment is becoming a standard means of providing formative and summative assessment of mathematical techniques. The research problem that we have identified is how to detect mathematical misconceptions when students answer e-assessment questions incorrectly, and how to improve the feedback provided to the student in such cases. By analyzing students’ rough paper-based workings for an e-examination, we have captured mathematical misconceptions made by first year engineering students. This has enabled us to catalogue common student errors made by students. By amending the e-assessment feedback code, students who make these errors will subsequently benefit from enhanced, tailored feedback, highlighting the mathematical misconception/error made. In addition, detailed guidance on how to improve their knowledge related to the topic will be given. The aim of our work is to improve the e-assessment experience for students as well as addressing and tackling misconceptions in a timely fashion.
Highlights
An understandable but incorrect implementation of a process resulting from a student’s misconception is called a mal-rule [1]
We found several of the questions to have more than one common student errors (CSEs) associated with them and we catalogued 40 CSEs in total
The height of the rectangle represents the number of students, aggregated over the two sittings, who answered the question incorrectly whilst the height of the shaded rectangle represents the number of students who triggered the principal CSE for that question
Summary
An understandable but incorrect implementation of a process resulting from a student’s misconception is called a mal-rule [1]. We focus on mal-rules or, in other words, common student errors (CSEs) in Engineering Mathematics - a subject in which students tend to make CSEs due to misconceptions in mathematics. States that “Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject.”. This is the case in Engineering, which is a subject that requires a strong mathematics foundation. Mathematics Education research; see for example [4]-[6], has explored possible causes and effects of certain mathematical misconceptions and the impact that they have on students’ future learning. Khiat [11] looked at the mathematics learning of engineering students at undergraduate level and the focus of the work was on conceptions of understanding using grounded theory methodology
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