Abstract:

The Moodle platform, when combined with the STACK plugin, becomes a powerful tool for education. This system enables students to respond to mathematical questions using expressions, providing personalised feedback and optimising Computer-assisted assessment. The STACK offers several advantages, including the ability to generate random questions, create variants of base question models, evaluate complex answers, and provide detailed feedback using decision trees.

In addition, it seamlessly integrates with computer algebra systems (CAS) like Maxima, thereby enabling the thorough assessment and analysis of complex mathematical expressions. Another notable advantage of employing CAS lies in its capability to establish dependencies between the outcomes of preceding and subsequent sections within multi-part questions. This functionality empowers instructors to evaluate the correctness or partial correctness of subsequent sections based on the input values specified in earlier sections, even if initial responses contain errors.

In this study, we present our findings regarding the utilisation of the STACK plugin across three different courses in three engineering degrees: MAT1, LMAT2, and MENUM. In MAT1, the STACK questions are focused on functions, differential calculus, and integration. Immediate feedback was provided during formative sessions, while deferred feedback occurred during summative assessments. In LMAT2, Python/Sympy was used for solving individual and group problems. The STACK facilitated the creation of complex questions that interconnected multiple topics, such as Fourier series and differential equations in electrical circuits. Students submitted their answers, generated using Sympy, which were evaluated by the STACK, streamlining the assessment process for the teaching team. In MENUM, summative assessments included both closed-response and open-response questions (STACK vs. CLOZE). The results of a survey indicated that there were no significant differences between the two types of questions from the perspective of the students.

The integration of the STACK with computer algebra systems proved essential for evaluating complex mathematical expressions. This integration demonstrated that automated assessment extends beyond simple calculations, demanding exact results with varying degrees of complexity or approximate results obtained through numerical methods, each with different levels of precision. The STACK-Moodle integration empowers instructors to create complex questions and objectively evaluate student responses. Immediate and personalised feedback during formative assessments helps students to identify areas for improvement. Overall, the STACK serves as an excellent support tool for teaching teams, enhancing assessment practices across diverse subjects and alleviating the tedium of manual grading.

The STACK system is an effective tool for assessment, automating grading and providing personalised feedback. Although it requires initial training, its versatility allows educators to focus more on pedagogical strategies and student engagement, creating a more enriching learning environment. By overcoming initial challenges through comprehensive training, STACK can bring substantial long-term benefits, empowering educators to deliver more effective instruction and enabling students to achieve better learning outcomes in mathematics and other science subjects.

Keywords:

Moodle STACK, Computer Algebra System, Computer-Assisted Assessment, Feedback.