Hunter, Gordon, Davis, Mastaneh and Ruvinga, Stenford (2018) Facilitating the creation and editing of on-line resources for the teaching and learning of calculus within the QTI Framework. In: CETL-MSOR 2018 : Evidencing Excellence in the Mathematical Sciences; 05 - 06 Sep 2018, Glasgow, U.K.. (Unpublished)

Abstract

Development of competence in mathematics is an essential aspect of most higher education programmes of study in science and technology, including specialist courses in mathematics and many other disciplines, including engineering and most natural sciences. Students’ knowledge of and expertise in mathematics (or lack thereof), at least at an elementary level, can have a major impact on other aspects of their studies and their subsequent career prospects. However, mathematics is a subject which many students find difficult, they often do not realise its relevance and importance to their other courses, they may not devote as much time or effort to it as they ideally should, and face to face tutorial support is often limited. Although there have been previous attempts to develop on-line tutorial exercises, with automated marking and feedback, to assist students with their mathematical studies, most of these have either been restricted to multiple choice or numerical answer questions, or have only addressed the most elementary of topics – notably simple algebra, functions & graphs and trigonometry. In a previous paper (Davis & Hunter 2016), we described our efforts to remedy this situation through the production of a set of on-line tutorial resources, called CalculEng, which included a variety of exercises on single variable differential and integral calculus, with applications, which could be delivered on-line or using a Virtual Learning Environment such as Blackboard or Moodle. These exercises, in the form of structured questions developed using the QTI framework, allow algebraic input from the student, which is checked for consistency with the “correct” solution, and with the outcomes of anticipated “common errors”, using the MAXIMA computer algebra engine. The students’ responses were automatically marked, with the aid of the Computer Algebra System, and intelligent, relevant feedback - based on the mistakes made by the student - provided. However, as we noted at that time, the creation and editing of those resources was not a trivial task for tutors, since it required “hard coding” of both the correct and “common mistake” answers in MathML/XML using the QTI framework. Most tutors would tend to find this rather tedious and very time-consuming, which limited the prospects for the range of materials being widely adopted or extended. Since that previous paper, we have developed a Java desktop question editor application, which allows tutors to type-in questions and both the correct and “common mistake” answers (using ASCII Math notation for equations and formulae) in a straightforward way, and which will automatically generate the required QTI MathML/XML code to render the question and allow the student’s responses to interact with MAXIMA. The application allows the production of multi-part structured questions, where the answers to later parts of a question depend on the answers to earlier parts. For example, a structured question on differentiation could ask the student to differentiate a specified function, and then find the points where the derivative was zero in order to locate the stationary points of the function. This application will greatly simplify the task of creating and editing additional resources, facilitating making them useful to a wider range of students and for a more comprehensive set of topics. In addition to providing details on the new editor application, we discuss the design and implementation of resources we have produced, their relevance to various degree curricula, and their evaluation when used on a number of first year mathematical modules both for specialist mathematics students and those studying calculus within other undergraduate science, engineering, economics or business degrees.

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