Active Learning in Sophomore Mathematics: A Cautionary Tale

Math 245: Multivariate Calculus, Linear Algebra, and Differential Equations with Computer I is the first half of a year-long sophomore sequence that emphasizes the subjects\u27 interconnections and grounding in real-world applications. The sequence is aimed primarily at students from physical and mathematical sciences and engineering. In Fall, 1998, as a result of my affiliation with the Science, Technology, Engineering, and Mathematics Teacher Education Collaborative (STEMTEC), I continued and extended previously-introduced reforms in Math 245, including: motivating mathematical ideas with real-world phenomena; student use of computer technology; and, learning by discovery and experimentation. I also introduced additional pedagogical strategies for more actively involving the students in their own learning—a collaborative exam component and in-class problem-solving exercises. The in-class exercises were well received and usually productive; two were especially effective at revealing normally unarticulated thinking. The collaborative exam component was of questionable benefit and was subsequently abandoned. Overall student performance, as measured by traditional means, was disappointing. Among the plausible reasons for this result is that too much material was covered in too short a time. Experience here suggests that active-learning strategies can be useful, but are unlikely to succeed unless one sets realistic limits to content coverage

Coming Out of the Dungeon: Mathematics and Role-Playing Games

After hiding it for many years, I have a confession to make. Throughout middle school and high school my friends and I would gather almost every weekend, spending hours using numbers, probability, and optimization to build models that we could use to simulate almost anything. That’s right. My big secret is simple. I was a high school mathematical modeler. Of course, our weekend mathematical models didn’t bear any direct relationship to the models we explored in our mathematics and science classes. You would probably not even recognize our regular gatherings as mathematical exercises. If you looked into the room, you’d see a group of us gathered around a table, scribbling on sheets of paper, rolling dice, eating pizza, and talking about dragons, magical spells, and sword fighting. So while I claim we were engaged in mathematical modeling, I suspect that very few math classes built models like ours. After all, how many math teachers have constructed or had their students construct a mathematical representation of a dragon, a magical spell, or a swordfight? And yet, our role-playing games (RPGs) were very much mathematical models of reality — certainly not the reality of our everyday experience, but a reality nonetheless, one intended to simulate a particular kind of world. Most often for us this was the medieval, high-fantasy world of Dungeons & Dragons (D&D), but we also played games with science fiction or modern-day espionage settings. We learned a lot about math, mythology, medieval history, teamwork, storytelling, and imagination in the process. And, when existing games were inadequate vehicles for our imagination, we modified them or created new ones. In doing so, we learned even more about math. Now that I am a mathematics professor, I find myself reflecting on those days as a “fantasy modeler” and considering various questions. What is the relationship between my two interests of fantasy games and mathematics? Does having been a gamer make me a better mathematician or modeler? Does my mathematical experience make me a better gamer? These different aspects of my life may seem mostly unconnected; indeed, the “nerd” stereotype is associated with both activities, but despite public perception, the community of role-players includes many people who are not scientifically-minded. So we cannot say that role-players like math, or math-lovers role-play, because “that is simply what nerds do.” To get at the deeper question of how mathematics and role-playing are related, we first need to look at the processes of gaming, game designing, and modeling

Detailed and GlobalAnalysis of a Remedial Course's Impact on Incoming Students' Marks

Engineering incoming students are facing great difficulties to overcome first course subjects. To tackle that situation and increase the students’ success a Remedial course in Mathematics was offered to Informatics Engineering freshmen. This study presents a statistical analysis of their results comparing the marks obtained by those joining the course (studio group) versus those who did not participate (control group). ANOVA tests are performed over the students’ marks averages as well as over each subject students marks. These tests show statistically significant differences between both groups, with the studio group consistently outperforming the control group at 99% confidence level in most cases and at more than 92% confidence level in every case