Abstract:

This work explains the design of nine multiple-choice quizzes used as formative e-assessment for teaching multivariable differential calculus, they included GeoGebra and problem solving tools as well. It was a preliminary experiment conducted inside a second course of calculus for about 200 students in Managerial and Electronic Engineering at University of Udine.

One advantage of regular quizzes is that they encourage students to keep up with the course content as it is presented, to provide immediate feedback to students about their level of learning and help the tutor identify parts of the course content that students are struggling with and that require further explanation in class. Six batteries of quizzes were administered online, every two or three weeks, one for each chapter of the course. The students did not have a time limit to answer the questions, but it was mandatory for them to reach a certain level to enter the midterm test. Quiz questions were not randomly generated, so all students got the same questions and naturally, students shared the solutions with each other.

The quizzes were designed following MATH taxonomy (Mathematical Assessment Task Hierarchy). We used eight different descriptors: Factual knowledge (quiz 4); Comprehension (recognition of formulas and situations) (quiz 3); Routine use of procedure or algorithms (quiz 7); Information transfer (classification of math objects) (quiz 2); Application in new situations (planning work, selection of methods) (quiz 9); Justifying, proof, reasoning and interpreting (quiz 5); Implications, making conjectures, comparisons and finding patterns (quiz 1); Evaluation (quiz 6).

From the Psychometric Analysis, the quizzes were well chosen, and they discriminated adequately between higher and lower student subject knowledge. For the students the most difficult question was quiz 5, where to answer correctly is necessary to have a good conceptual knowledge of the subject, followed by quiz 9, which requires a capacity for problem solving and modelling, and 8 that becomes simple if the graphic interpretation of the problem is used. The question with the lowest discrimination index, but acceptable, was quiz 7 followed by quiz 9 and 3 this means that they help less than the others to discern between the good and the bad performances.

A survey was also administered to evaluate the appreciation of the students about the quizzes and GeoGebra. 148 out of 168 students answers the survey. The results show that the students have appreciated the use of the quizzes: they have considered them useful to highlight their gaps and to keep up with the study of the course. In addition, many students have preferred to deal with colleagues, for fear of making mistakes and lost so the possibility to participate to the midterm test. The comparison with the colleagues has been also widely used by students to resolve their doubts, followed by consulting online material and then the use of books. Nonetheless asking to professors has been the least chosen alternative (there have been frequent requests for clarification especially at the end of the lessons principally about the subject of the lesson just taught). The 68% of the students has thought that the use of GeoGebra has allowed them to better understand the theoretical notions of the course Very or Little enough. Just the 29% has Never used the applets made available on Moodle.

Keywords:

Formative e-assesment, multiple-choice quizzes, multivariable differential calculus, GeoGebra, MATH taxonomy, Psychometric Analysis, survey.