STACK question database for engineering analysis courses

Formative quizzes, multiple choice platforms, interactive scripts, videos and web applets have enabled students to work more and more independently while still receiving valuable feedback on their progress. However, all these tools are only able to give feedback in the sense of right/wrong with no room for partial solutions, individual problems per student, or insights why a student made a mistake.
Every previously available solution with the required features depended on a vast amount of manual grading work. Resources for manual grading are scarce, both in formative assessment and exams. Over the past few years, the heavily rising number of students made the grading hours available per student decrease dramatically. A larger amount of multiple choice (MC) questions is now being used in service lectures taught by D-MATH, resulting in a slightly lower exam quality.
This project aimed at improving on all aspects of this situation using STACK. STACK is a free online assessment package for mathematics using a computer algebra kernel. Available as a Moodle question type, STACK is suitable for evaluating both numeric and algebraic expressions. Hence the questions can be more sophisticated and mimic better mathematical thinking.
A solid STACK question database allows students to work independently and to get detailed and personalised feedback on their solutions. In this project we addressed mainly engineering students and their analysis courses, resulting in several hundred STACK tasks for this audience. They are now used in formative assessment and for a grade bonus, as well as in an online training module on integration techniques available for all ETH students. We also made an effort to establish and document best practices for writing STACK questions in order to help others getting started working with STACK.

To build the question database for the formative assessment and the grade bonus during the semester we designed new problems and converted previously existing open questions from our exercises into STACK on a weekly basis. While the main question design was done by the leaders of this project (Meike Akveld and Andreas Steiger), they were implemented, tested and deployed by the project employee (George Ionita). The results of the students consistenly analysed and evaluated in order to further improve the questions› quality in terms of potential feedback options. Finally, the now field-tested and polished questions were put in a separate Moodle course which serves as a repository for future years.
During teaching, these questions were used in different manners: Some were used as diagnostic tests for common misconceptions or as entry-level practice sets in weekly online quizzes or during a blended learning session (flipped classroom), while others were part of a grade bonus which could be achieved by solving these problems correctly.
We spent the summer break to design a self-paced, lecture-independent training module on integration techniques. Integration is one of the key competencies taught in a first year analysis course, and from previous evaluations we know that it is also something where students struggle a lot. The result of our effort is a new Moodle course with more than one hundred integration tasks, organized in roughly a dozen quizzes. Students can choose which technique they want to practice and several levels of difficulty are available. Furthermore there is also a step-by-step quiz on learning how to do integration of rational functions. This Moodle course is intended to accompany a lecture covering the theory of integration and is available to all ETH students.

In our project proposal we aimed at building more than just the one training module on integration techniques. The work needed to get that training module into a well designed, usable and useful state was much higher than we anticipated. We thus ended up with a question base which is slightly shallower in some parts of our courses, but it is also much deeper when it comes to problems on integration. However, the massive effort to get the Integral-Trainer up and raining paid off: The students in our courses expressed their gratitude and the trainer’s usefulness in various oral and written feedback opportunities. The numbers speak for themselves, too: In the first three months after the release in November 2022, over 1,400 students have taken more than 30,000 attempts at solving an integral in this module. We aim to expand the Trainer further and also on making it available outside of ETH. Education specialists from other universities have already expressed their interest.
For us this shows that sometimes changing goals and focusing on one central and important project can be the right move. Providing a self-learning platform for just a part of the course was the right decision.

• Innovation Learning & Teaching Fair 2022
• Moodle-Kurs: Integral-Trainer