Page - 230 - in Intelligent Environments 2019 - Workshop Proceedings of the 15th International Conference on Intelligent Environments

Edinburgh, U.K., which allows the questions to be linked to the freely available Maxima Computer Algebra System [17], to check the questions and student’s responses for mathematical consistency with the correct solutions. The CalculEng system provides a set of structured exercises, which allow the students to enter their answers in a window (provided especially for their responses) in ASCII- based mathematical format, rather than just making a selection from a list of choices or entering a numerical value. Some of the aspects of these questions, such as specific parameters and coefficients in the equations and formulae, are written to be generated randomly and, by so doing, enable students to develop the ability to recognise the same problems when expressed in different forms. Moreover, the basis of the system is that each question can identify a student’s error via a set of rules, which are encoded in XML [12]. The system allows the student’s answer to be checked against a list of perceived “common errors” for that type of problem and then provide feedback, tailored to the particular type of mistake made. Therefore, the system provides readily available support, informs students of their mistakes and includes the facility whereby they can request a hint and/or the full solution. Students are able to use multiple-section structured questions on the application of calculus to engineering problems, with detailed feedback on each step being provided. In these multi-section questions, feedback is revealed to the student in a step-by-step process. Further technical details of how the questions are encoded can be found in [3, 4, 5]. However, as noted in section 1 above, the first version of CalculEng required the questions, correct answers and “common mistake” answers all to be encoded into QTI XML by hand – a time-consuming, tedious and error-prone job which deterred many tutors from creating resources for it. Furthermore, this first version of CalculEng only permitted relatively simple single part questions, in contrast to typical multi-section questions, developing a theme, with inter-dependencies between the answers to successive sections, common in many mathematical problems. Recently, we have developed a more sophisticated editing tool to address many of these issues, which will be described in section 4 below. 3. How do Current Students Prefer to Study Mathematics ? Our team for this project consists of an interesting balance – two of us (MD and GH) are highly experienced teachers of Mathematics and its applications, but completed our own mathematical studies many years ago. Whilst we have a lot of experience of teaching mathematical topics, and are very familiar with misapprehensions and common mistakes students make when solving mathematical exercises and problems, our studies pre-date computers being on every desk or the World Wide Web being available everywhere. Our own studies followed a format of formal lectures (in large groups), and tutorials/problems classes (in smaller groups), plus self-study using our lecture notes and textbooks, plus working through exercises set by our teachers. However, the other three members of our team are current students – one of undergraduate Mathematics (AW-O) and two Masters level students of Engineering (VTB and LT), both of whom had had to study a substantial range of mathematical topics during their Engineering degrees. 3.1. Methodology for our Study As a group, we devised a set of questions which would be put to student volunteer participants – all of whom study a substantial amount of Mathematics, including M.Davis etal. /Developing“Smart”TutorialTools toAssist StudentsLearnCalculus230