Nick Long is an Associate Professor at Stephen F. Austin State University
As great as most things have been with my transition to using IBL in my classes, I didn’t expect that future semesters of teaching the same course would be so intensive in preparing materials. With a traditional lecture, you can crank out a set of notes and apply minor tweaks when you use them in future semesters with relative ease. With my IBL materials, I have found I work almost as hard to edit and re-adapt my own materials in future semesters. This is how you get better materials that others can use, through a near constant flow of application and revision. My efforts this summer have been to add some problems in order for us to get more done. That may not sound right but when we prime our students to think more carefully and more deeply, then they can do more in less time. That’s the idea but as most of you know, the correct balance of problems is exceedingly difficult to produce. As many good resources as I got at the IBL Workshop last summer, I have been going over C. Von Renesse’s recent paper “A Path to Designing Inquiry Activities in Mathematics” which is to appear in PRIMUS soon. I have read and re-scanned this paper several times this summer as I have been asking myself “What is it I want my students to get out of these problems?” I have had my own share of productive failure this summer, which I have not hesitated to tell my students about, namely I had to abandon about 3 weeks of work writing materials for a 100-level trig class.When I thought about what I was writing, it turned out to be exercises that don’t really further understanding but rather just asked students to do something without really going anywhere. I hope to write more later about how I am trying to be more explicit with my own productive failures and why I think #pf is valuable to us as faculty.
I have added a couple new writing assignments to my courses this summer as well. Specifically, I am opening the semester by having students write their math autobiographies. While not all of the students took this assignment very seriously, I got a lot of wonderful responses from students which showed both a wide range of experiences and somehow that ~80% of my students thought they were below average. One thing I am trying to figure out how to do is share some of these wonderful ideas with the class, but I’m not sure how to do this while respecting the anonymity of the students. The other new writing assignment I have added was shamelessly borrowed from Francis Su’s article in the June/July issue of the MAA Focus. His assignment is stated as:
One of the luxuries of the internet era is that you can look up the answer to almost any problem you want- as long as it’s been solved. Yet when you are learning a subject it can be counterproductive. In this class, I have emphasized the importance of struggling in mathematics: that it’s normal and part of the process of learning, and that when you are stuck, you should just “try something.” Describe an instance, so far in this course, where struggling and trying something was valuable to you.
I really like this assignment as an end of semester reflection that I hope will reinforce a lot of the non-mathematics things that our class has worked on this semester. I’m sure I will get to talk about the responses in the future.
As for the particulars of this summer’s course, I have a great mix of students. One superstar student can’t believe how well doing problems explains all the things she has ever done in math without someone telling her stuff. She even brought her 12 year old son to class when he didn’t have other summer activities and he was able to do a surprising amount of the work in the class because he saw how much math should make sense.There are a bunch of other students who are starting to understand that when something doesn’t make sense, you need to start working: In other words, don’t just say something on your homework and move on… think about what precisely you are stuck on and work to have it make sense. I’m at the point in the semester where they have normalized just about everything they are expected to do with homework, presentations, and respectful behavior. I barely need to be there but to be an administrator (and ask them a lot of questions to see how well they believe their own work). Two areas that I am particularly happy with the progress of this class is how they work and speak to each other effectively and respectfully as well as their persistence in problem solving. They have really been struggling with algebra and simplifying some of our work on conic sections but most students have not gotten over discouraged by the amount of effort they are putting into their work.
As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.