Over the course of my time at Rutgers, I found and became more involved with the Active Learning Community, including going to several of their meetings and symposia. With the information I gathered at these meetings and hearing stories from other Rutgers professors who were implementing these practices into their classes with great success, I decided that I would attempt to do the same. I believe that the tenents of Active Learning are well suited to the mathematics classroom, as math is best learned by doing problems and working things out for oneself, instead of just hearing a lecture. Therefore, I started to implement various "Active Learning" activites into my summer classes. This webpage will outline the various attempts I have made to put these into my classroom.
During the Summer of 2017, I decided to run my Differential Equations class as a flipped classroom. This involved making video lectures for the entire course and desigining assignments for the students to work on in class. The video lectures took a very long time to make, even more than I had originally expected, but I thought it was a great experience. The general structure of the class was that students would watch videos and complete worksheets before class. The worksheets would be due at the start of class, and students would spend most of the class period working on problems in groups. The class period would end with either a quiz or in-class presentations, and students would need to complete one slightly longer problem for homework. This class met for 4 hours a day, Monday through Thursday, for 8 weeks. Overall, I think the class went well, but there are definitely a few takeaways and things that I would improve on in future classes.
For reference, the YouTube channel containing all of the videos for this course can be found here. In addition, here is a sample worksheet and worksheet quiz that was used during the class.
In contrast to the flipped classroom I ran the summer before, the classroom I designed for Math 252 was built around active learning without being a flipped classroom. Students were assigned sections of the textbook to read prior to showing up to class, and their knowledge of this would be tested with a Readiness Assessment at the start of class. Afterwards, I would give a brief lecture on the material, followed by a chunk of time devoted to the students completing problems in groups. After this, they would be given a practice problem to complete on this material which I would grade, and the process would repeat itself for the second half of class. As opposed to doing and turning in homework problems, students would be given problems to work on that would not be collected, and a mini-quiz (basically a homework check) at the start of the following class would make sure that they knew the material. This process would happen on Mondays and Fridays, while the Wednesday classes would consist of a quiz, followed by a more activity-centered investigation of the present material. This class met on Mondays, Wednesdays, and Fridays for 2 hours and 45 minutes for 6 weeks. Overall, I think things went well with this class as well. The ideas could have been a little more flushed out, and the accelerated pace of the class made doing activities difficult, but I think the students learned a lot and got a lot out of the class. Some of the activities will be outlined in the following sections.
My syllabus for this class can be found here.
The first activity the students did over the summer was a Gallery Walk. The class had a prerequisite exam on the second day of class to make sure that everyone was clear on what was expected for them. The main thing I was testing here was the base knowledge of linear algebra, which was a prerequisite for this class and is necessary for the last two-thirds of the course. In order to review for this, I prepared 26 problems and posted them around the room on sheets of poster paper. I brought in markers, and the plan was for every student to complete one of the problems. The problems would then be left on the walls so that the rest of the class could look over the problems and make sure they knew how to do them. Overall, I think the activity went really well. Students enjoyed it, at least at the start, but some of them got stuck with the harder problems and weren't too thrilled with it. I also think I had a few students who did not participate in the activity, so some students did multiple problems. In the end, all of them got done, and I think it gave the students a good review for the exam. I didn't end up getting all of the problems physically put up around the room during the break in class, so it was a little annoying getting the activity started, but it went well. This is something I would consider doing again in the future, but I would want to be more prepared for it and find a different way of posting the problems for the class to do.
The activity during the second week was a Jigsaw-type activity on Bifurcations. The plan was that the students would put themselves into 6 groups. The entire class would start by working on a pair of problems, which I would them cover and discuss before moving forward. After that, each group would work on a distinct problem, and I would walk around the room and make sure that the work was coming along and the groups were getting to the correct answer. Once I was content with all of the answers, I rearranged all of the groups to put one person from each group together, and they would explain their answer and how they got it. The goal would be that they would get practice not only solving the problem but explaining the solution to others, which would help them on the upcoming exam. Overall, the activity went fairly well. A few of the problems were harder than others, and those groups took longer to get to the point of being able to share their answer. This is the tricky part of designing this type of activity; if students need to work on their own and then get back into groups, there is not necessarily a good way to make sure that everyone is on the same page and ready to go after a reasonable time. The jigsaw part of the activity (talking to members of the other groups about what they learned) should also be more structured, because I saw a few good things out of a few of the groups, but for some of the groups, it felt like they were just chatting the whole time instead of discussing the problems at hand. Having a little more structure here might help to move the discussion forward. Overall, I would definitely consider doing an activity like this in the future, because I think it was helpful for the class.
The handout for this assignment can be found here.
The new piece that I added to this class was the Readiness Assessments that were used to test student understanding of the material after reading the textbook. The point of these assignments were to get students thinking what parts of the textbook were most important for that day's class. It was also my way of enforcing accountability for reading the textbook before coming to class. The students were allowed to use whatever they wanted to use for the assessment (textbook, notes), but they were not allowed to talk to other students and only had 10 minutes to complete the two-page assessment. This was met with a variety of success. Overall, I felt that the students had some idea of what was in the sections before coming to class, but didn't really see the important parts of the section. Even though these were open book and open note assignments, many of the scores were still lower than I had anticipated. Clearer expectations may have helped with this, as well as notes that accompanied the sections of the textbook, as opposed to just giving them sections to read. I also feel like having them specifically test definitions, as opposed to also expecting interpretations and use of these definitions may have been more effective. I think that these were an essential part of the class, and did their job, but they could have been carried out better.
A sample Readiness Assessment from the course can be found here.
Another concept that I tried to emphasize in this class was the importance of group work and peer teaching. The Jigsaw activity was designed to specifically force the students to teach each other what they learned, but the entire structure of the class was around doing problems in groups to help learn the material. On a few specific class days, I would encourage more peer-to-peer interaction, but it mostly took care of itself. Over the course of the class, I noticed that students eventually stopped coming to me for answers or when they got stuck, but instead turned to ask their neighbors or group members first. Eventually they would flag me down if they had an issue they couldn't resolve, but on the whole, they were self-sufficient in trying to figure out the problems and reach the correct answer. This kind of ownership of the material is something that I had not seen in the classes I had taught previously (it was present in a small amount during Summer 2017, but not nearly to this extent), and I feel like the format of the class did a lot to encourage it. I think this is one of the main reasons that my class was so successful this summer; the students who bought in to how I was trying to get them to learn the material accepted it as something they had learned themselves, not something that had just been taught with them, and could run with that knowledge to tackle problems they had not seen before.
My syllabus for this class is here and sample problem sets that was given out to be worked on in groups (and specifically encouraged peer teaching) can be found here and here.