Robert Talbert is an educator affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan, who also writes the Casting Out Nines blog on the Chronicle of Higher Education web site. He’s been writing a wonderful series on inverting his MTH 210: Communicating in Mathematics classroom that is well worth the time to read.
In his first post on the series, he states his goals:
Force the issue about students taking initiative over their learning. Where the acculturation issue really comes to a head in MTH 210 is in the changing role of the student versus host of the professor. Students are used to being passive recipients of information, lectured to by their teachers and asked to do things that people who listen to lectures are cognitively ready to do – which is to say, very simple things. In MTH 210, as in mathematics generally, students are required to be active learners: building examples of terms, seeking out the meanings of theorem statements, making conjectures of their own, asking questions and seeking knowledge. The students who end up in the bottom end of the course or withdraw tend to be the ones who hold on to their passive ways even if it kills them. And it usually does in the end – although in a traditional course design, they can hold on for a long time. I wanted to make passivity practically impossible.
Provide a robust social network of peers. For many students, MTH 210 is already stressful, even more so if I want to really make students active from day 1. The key in life to not cracking under stress is to have a strong network of people who want you to do well. This happens for some students but not for others. I wanted to change that so when students are asked to go places their mathematical training has never taken them before, they will have live people who have their backs – in class, online, at all times of the day and especially on the formative stages of learning the content and mastering the processes.
Be maximally available at the point of greatest need. One of those people in the social network is me, and if I am going to ask a lot of students – and I do – then I have to extend myself proportionally and be there when students need help the most. When is that time? It’s when students are applying basic concepts to actually solve complex problems (= writing proofs). Learning terminology and encountering material for the first time can be difficult, but not nearly as difficult in my experience as applying content to constructing a proof. So does it make sense to focus class time on the tasks that are the least difficult and then outsource the most difficult stuff to the students to work out when I’m not around? Or would it work better to switch this, and focus class time on the stuff where they are most likely to get stuck and need their social network and a professor to help?
Robert has also made extensive use of MIT OpenCourseWare in designing his courses, efforts we profiled a while back. Here’s part of that profile:
Initially, OCW was helpful to Talbert personally in updating his own programming skills. “I had actually not programmed in three to four years, and so my programming skills were rusty to say the least. The OCW course was actually my re-training course in programming in general, and then I adapted what I was learning generally about programming to the particulars of my course. I wish I had had a course like the OCW course when I was an undergrad!”
Professor Talbert’s class was not a direct equivalent of courses offered at MIT—his was MATLAB®-based—but OCW was nonetheless the perfect resource for designing and supporting the course. Talbert planned to teach using an “inverted classroom” approach, in which students acquire the bulk of the course information outside of class, through print and media resources, do preparatory homework assignments, and then put their basic knowledge to work through in-class lab activities.
He recognized that while MIT’s 6.00 Introduction to Computer Science and Programming was a Python™-based course, it was conceptually very similar to the one he planned to teach. “Of the 15 students in the course,” Talbert explains, “only two had ever had any exposure to computer programming before in any sense, and I really liked the OCW course’s way of introducing a sequence of simple yet progressively more complex examples to motivate the basic constructs of programming such as loops and branching structures.” Read more.