Abstract
What do you do when a change in enrollment policies leaves you with more than 600 students in a first-term university calculus class, three-quarters of those students had a failing mark in mathematics in the pre-enrollment test, you planned a series of remedial activities for the second term, and the COVID-19 pandemic shuts the university down with a two-day notice? The pandemic hit instruction with might, forcing schools and universities that were timidly experimenting with digital tools to reinvent themselves in days. The pandemic also offered incentives for creative solutions that, in normal times, would have been considered fit for submission to the committee for recursive committee submissions at best. This paper narrates a teaching experience of how we proposed and managed an at-distance remedial course in August that not only catered to more than twice the number of students expected by our best forecasts, but was a very good success once its effectiveness was compared to the outcomes predicted by the pre-enrollment test scores. We expose the design of the course and link its measured effectiveness with both its design and student engagement; in particular, we show that a different approach to the examination of cognitive load and to fostering student–teacher and student–student communication thanks to digital mediation could be effective in countermanding the math-induced drop-out phenomenon in STEM.
Highlights
A busy examination schedule in June, July, and September made it nigh impossible to envision a remedial course, even supposing that it would have been possible to hold it face to face; the lack of time urged against creating an MOOC
The COVID-19 pandemic made at-distance teaching the only viable possibility, but one should take notice of its effects on teachers’ praxeologies ([23]) and evaluate the advantages in assessments—such as the greater flexibility in test-taking and faster scoring—towards the importance “that mathematics education should be for all students, including those who have special needs, who live in poverty” ([24])
“[b]etween the start and the end of the students’ college calculus class, their confidence and enjoyment of mathematics dropped sharply, with confidence falling by half a standard deviation and enjoyment of mathematics by a third”; even among students that do well in such a class, many lose any interest in taking further mathematics classes, and some even leave the STEM track
Summary
Istituzioni di matematiche for Natural Sciences students at the University of Milan is a standard first-term 8 ETCS credit introductory course in calculus. Since the threeyear bachelor program removed limits on admissions in the 2018/2019 academic year, enrollment has been skyrocketing, and the level of incoming students, as measured by the non-selective national standardized test, TOLC-C ([1]), has been dropping. In 2019, students enrolled, of whom 72.3% had a failing mark in mathematics (defined as a score less than 10 out of 20); some of them even had a negative score ([2]). Academic regulations stipulate that students can take every exam at least seven times per year at their discretion. Rizzo ([2]) showed a good correlation between the mathematics marks in the TOLC-C and the number of times that a student had to take an exam before passing it (if ever). A busy examination schedule in June, July, and September made it nigh impossible to envision a remedial course, even supposing that it would have been possible to hold it face to face; the lack of time urged against creating an MOOC (even supposing that an MOOC would be effective, a hypothesis that is not necessarily supported by the literature [4])
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