Page - 234 - in Intelligent Environments 2019 - Workshop Proceedings of the 15th International Conference on Intelligent Environments

minimum values of that displacement x. This type of structured question, with inter- dependencies between its sections, was not possible within the framework employed by the first versions of CalculEng, so was something we addressed in the latest version. 4.2. The latest version of CalculEng and our Question Creation and Editing Tool As noted above, the initial version of CalculEng had serious limitations, which restricted the extent to which it could be easily used and extended by colleagues. To address these points, we created a Java tool to make the creation and editing of questions much more straightforward, allowing teachers essentially to type-in questions as a combination of plain text and ASCII-Math notation for mathematical symbols, plus permitting dependencies between the answers to successive sections of questions, as in the elementary Dynamics example above, including awarding partial credit for “follow through” errors. For example, if the student has incorrectly differentiated the expression for the displacement, but then had found the appropriate values of the time t which made his/her incorrect expression for the velocity v equal to zero, our new version of CalculEng could award partial credit for those incorrect, but consistent with the earlier error, values. The essential features of the editing tool were identified as : (i) A computer software package which will enable a teacher to specify a question in relatively natural mathematical language, and the corresponding “correct” and “common error” answers, with appropriate feedback, then (ii) Convert this question (and both “correct” and “common mistake” answers) into correct QTI XML code. and the additional desirable features as : (iii) Allow multi-part questions, where subsequent parts depend on results from earlier parts, BUT such that (iv) the system can also check if (incorrect) answers to later parts were consistent with earlier errors (i.e. were “follow-through” errors). Implementing the Question Creation and Editing Tool We implemented this tool in Java using NetBeans on a Windows PC. Our system renders equations and formulae which have been converted to MathML by the free Equation to MathML encoder provided by Wiris “Maths for More” [20]. Our editing tool allows three broad types of questions : (1) simple question(s) , primarily used by students for practicing their mathematical knowledge and skills, which gives the student appropriate feedback on each of his/her answers, and can allow the student to be given hints and/or the model solution on request; (2) test question(s), allowing a single attempt by each student and primarily used for assessment. However, this can still give a student feedback appropriate to the student’s answer. Finally, (3) a complex or compound question, which can have between 2 and 4 sections, and can allow inter-dependency between answers to successive parts of the question, and award marks according to whether a student’s solution is completely correct, partially correct, or completely incorrect, including awarding partial credit for answers consistent with a “follow through” error. The complex question type can also give students feedback on their responses to each part of the question. Examples of use of the editing interface for each type of question are given in Figures 4, 5 and 7. The allowed dependencies between sections of a complex or compound question are specified by a (topological) tree structure, as shown in Figure 6. The correct path M.Davis etal. /Developing“Smart”TutorialTools toAssist StudentsLearnCalculus234