Page - 233 - in Intelligent Environments 2019 - Workshop Proceedings of the 15th International Conference on Intelligent Environments

4.1. The early versions of CalculEng The initial versions of CalculEng [3, 4, 5] required a lot of preparation on the part of the tutor. The tutor had to set an appropriate single part question, work out the “correct” answer, and also try to anticipate several mistakes which a less able or slightly careless student might make – for example, differentiating the given function when the question asked the student to integrate it, or forgetting to multiply by a necessary factor. The correct answer and each of the anticipated “common mistake” incorrect answers would then have to be encoded into QTI XML by hand, along with appropriate feedback comments for each response. This was a very tedious, time- consuming and potentially error prone process for tutors, and deterred many of our colleagues from using the system. An example CalculEng question, with its response to the student’s incorrect answer, is shown in Figure 3. Further examples, together with the corresponding QTI-XML code, are given in [4]. Figure 3. An example CalculEng question, including a student’s “common mistake” incorrect answer, and the system’s feedback appropriate to that particular “common mistake”. The early versions of CalculEng only permitted simple single part questions, whereas more realistic mathematical problems often consist of several related parts. For example, consider the following problem from elementary Dynamics : “An object is oscillating, undergoing simple harmonic motion, such that its displacement at time t is given by x = 3 cos (2t) + 5 sin (2t). (a) Find the velocity, v, of the object; (b) Hence find the values of t which give maximum or minimum values of the displacement; (c) Find these maximum and minimum values of the displacement.” This problem first requires the student to differentiate the function specifying x with respect to time t, to give the velocity v. He/she then has to solve the equation v = 0 for those values of t which make v zero. Finally, the student then has to substitute each of those values of t into the expression defining x to find the actual maximum and M.Davis etal. /Developing“Smart”TutorialTools toAssist StudentsLearnCalculus 233