Active Learning in Calculus, CTL Mini-grant Fall 2015

Instructor: Janet Bower, Mathematics

Summary:To bring social interaction and real-life applications into lectures of the 700-student Math 141 course, Professor Janet Bowers added weekly active learning labs.  Instead of sitting in lectures for three hours per week, students now meet in smaller groups once per week to engage in data collection and explore novel solutions to problems related to material covered in earlier lectures. These collaborative breakout sessions facilitate the Course Learning Goals for students to engage in exploration, work on questions with others, and share solution strategies using precise mathematical language.

Final report

What I Did

The active learning innovation was actually carried out on two levels: a course level, and a classroom level.

Class level pedagogy: At the class level, all students (over 700) attended two weekly lectures taught by one of six instructors, and a weekly “lab” class run by an undergraduate ISA. As one of the lecture instructors, I used active learning innovations such as group work and cell phone questions to encourage active learning.

The pedagogy during the lecture section involved having students (145 in total in my class) listen to a maximum of about 15 minutes of lecture followed by an invitation to try a problem or example. Students were always encouraged to work with a friend. During this time, I was able to have 6 undergraduate ISAs walking around the classroom making sure that the students were working and answering any questions they had. Then we would debrief and finish the lecture. The remaining 20 mins of class were then devoted to a longer more active learning activity such as giving them a series of functions in graphical, algebraic, and translation forms.

Course level pedagogy: The course-level intervention involved developing the “lab” activities to engage the students in real-world modeling in hopes that they would see applications of the mathematical functions they were studying in the lectures. Students were broken into lab groups with 27 or fewer students. The pedagogy involved developing activities that illustrated real life examples of the math topics they were studying in lecture.

These activities were designed to:

  • Involve a social component of teamwork (e.g., team collects data measurements, students walk around and interact to collect data)
  • Involve a real-life application (not just studying for a test)
  • Be finished in one sitting, and not take too long or need too much explanation
  • Be an obvious link to lecture

The learning goals for both the class and break course were for students to:

  1. Engage in exploration by figuring out a solution pathway based on recognizing patterns
  2. Use various tools (e.g., graphs, notes, words, data charts, etc.) to represent ideas
  3. Use time to work on questions with others
  4. Talk with each other about their strategies for solving problems
  5. Persevere in problem solving by overcoming road blocks and using creative solutions
  6. Build conceptual understanding by constructing links to main ideas and concepts
  7. Create mathematical models based on the functions studied in class
  8. Use precise mathematical terms/language
How It Went

The original intention for evaluation was to use the MCOP2 (Mathematics Classroom Observation Practices Protocol) to evaluate both the lectures and the break out sections. I worked with another professor, Dr. Susan Nickerson, two graduate students and one undergraduate student to calibrate our observations for the scale. It became obvious, however, that the undergraduate was overwhelmed with the task and that the faculty and grad students did not have time to observe all of the lectures and break outs.  Therefore, we have data on their observations of my class, but no others.  Instead, I converted the protocol into a student survey and asked all of the students to answer the anonymous survey during the final weeks of the semester. This “conversion” process was vetted by conducting a confirmatory factor analysis which revealed that the items aligned with the original observation protocol with a .77 correlation.  This means that we can assume that the validity and reliability of the items from the original was preserved in the survey.

The classroom level results indicate that students in my section of the course rated all aspects of the learning goals higher than the other class sections. In particular, they rated their opportunities to explore and discuss strategies with their neighbors as significantly greater than students in the other sections.

I attribute this to the use of Learning Catalytics, a cell-phone based app that allows students to input answers in novel ways. For example, they are able to draw a graph with their fingers on the screen based on certain given criteria. The program automatically overlays each graph on the display so that students can see, overall, how their graphs lined up and what differences some students incorporated.

At the course level, I used the survey to measure the mean scores of each of the learning outcomes based on student responses. The results indicate that both lecture and lab were most effective in achieving the goals of engaging students in novel exploration of patterns, constructing conceptual links, and modeling. The largest differences between the lab and lecture occurred in having students explore novel solutions and discuss their answers with others, which seems reasonable given that we would hope that they would discuss their answers and explore new ideas in the labs over the lectures.

What I Learned

Although I won’t be teaching this course again in the near future, others will, so I plan to share the survey (and results) with both the instructors and the break out leaders so that they are aware of the criteria we are using and the learning goals we are setting. I believe I can improve teaching by sharing these results and talking with the break out leaders about how to modify both the topics of some of the lessons (e.g. the discussion questions that are difficult to get students talking) and helping them develop better class management skills to engage students earlier and more frequently.

Overall, 70% of the students indicated they felt that they wanted either the same, or even more active breakout sessions. In quickly perusing the same data from this semester, it is once again clear that this approach does not appeal to all learners, especially for whom this type of learning is new. One idea moving forward is to offer some labs that are “quiet” labs where students work on parallel material, but do it quietly in the room without being asked to talk with others or collect data.