Seite - 229 - in Intelligent Environments 2019 - Workshop Proceedings of the 15th International Conference on Intelligent Environments

“Programmed Learning” approaches in course materials and textbooks. In this methodology, theoretical concepts were introduced in conjunction with a large number of worked examples, broken down into small individual “steps” or “tasks” and arranged in a way such that students could “cover up” the latter parts of the model answer, try each task themselves, then reveal the next part of the model solution and compare that with their attempt. This approach led to several highly successful textbooks, including the very popular volumes by Ken Stroud [18] from Coventry University in the UK – Stroud’s “Engineering Mathematics” is now in its 7th edition [19] and popular as ever with students. Appropriate on-line resources and exercises should provide additional “virtual tutorial” support at any time and location, which is consistent with the expectations of modern students. Hence, the use of suitable e-materials is expected to improve the quality of student’s learning as these materials would provide a platform which will allow students instant access at anytime and anywhere. Furthermore, use of structured exercises will allow the students to develop and test their own knowledge and understanding of mathematical topics, concepts & methods. Linking the system to a Computer Algebra System (CAS) will also enable checking of the student’s answers for mathematical/algebraic consistency with, rather than requiring an exact match to, the model answer, allowing answers to be expressed in different, but equivalent and possibly equally correct, forms and still being marked as “correct”. Furthermore, use of this CAS, in conjunction with hand-crafted rules encoded in XML, allow the detection of “common errors” in solutions, and the possibility of offering constructive feedback specifically tailored to the error(s) the student has made. Although there have been previous attempts to produce on-line resources and “self- test” questions for mathematics, most of these have only either provided multiple choice or numerical questions without detailed feedback to students - e.g. Mathletics [7] – or are subscription services, in some cases tied to the purchase of particular textbooks – e.g. MapleTA [11] and MyMathLab [13]. There are a few systems which are free to use on line, allow algebraic input and provide reasonably detailed feedback to students – such as MathDox [2] or CALMAT [1, 6], although most materials for the former are only available in Dutch, and for the latter are at a rather elementary level more appropriate to pre-University studies. STACK [15, 16] is an exception in that it covers material at a higher level, makes use of a CAS and does offer useful feedback to students on their solutions, but several tutors (via personal communications at conferences) have reported that it is not straightforward to create one’s own resources for STACK. The CalculEng system [3, 4, 5] has been produced to support students with their mathematical studies, in-course assessments and improve their progression. This system offers students a set of exercises on elementary differential and integral calculus and covers material relevant to a good range of engineering topics, including problems on engineering applications. These on-line materials are designed using the Question and Test Interoperability (QTI) specification, which is widely being used to represent on-line questions and assessments. Each question is encoded using QTI XML code [12], in which the question, and the dynamic behaviour of the question, are described. The QTI framework provides a programming facility, which allows the tutor to author the mathematical exercises, encoded using XML, and writes the mathematical equations and formulae by employing MathML. These mathematical exercises developed using the existing QTIWorks system [14], hosted at the University of M.Davis etal. /Developing“Smart”TutorialTools toAssist StudentsLearnCalculus 229