1. Defining and tracking learning goals

Andrea is a fourth year graduate student in the Math department. This semester, she is teaching Calculus I. She has a class size of 20 students. Her class is lecture-based and meets twice weekly for an hour and fifteen minutes per session. She taught an accelerated version of the same course last summer.

Observed assignment
Andrea would like to use Grace's observation as an opportunity to try a brand new type of in-class assignment. She would like to experiment with transferring from a lecture style to a peer-led team learning approach. There are a set of four topics related to differentiation rules (product rule, quotient rule, trig differentiation, and chain rule) that she thinks would work well for this. Andrea will assign each student one of the four rules to learn on their own. She will email the students ahead of time with their topics and a detailed description of what she thinks that they should learn and some sample problems to work through. Then, in class, she will have students work in groups of four so that each group has all four topics represented. The focus of the session will mostly be on problem solving: Andrea will give the students a worksheet of problems that they must rely on each other's knowledge to complete. Each problem on the worksheet will also come with a list of the rules needed to solve it, so that it is clear for each student when their expertise is needed. Interspersed with the problem solving will be breaks where each student gets about five minutes to "lecture" or go over the basics of their topic for their teammates.

Andrea's vision of the assignment
In designing this assignment, I had the following learning goals in mind:
  1. Students will take responsibility for their own learning by independently learning a new topic from a guided worksheet
  2. Students will improve their ability to communicate math concepts in a rigorous manner
  3. Students will gain confidence by learning from a peer group rather than an instructor

I hope that by assigning students to learn these topics on their own, they will begin to relinquish their reliance on learning from an in-class lecture and instead apply the skills they've learned already to acquire new knowledge in an independent setting. Because each student in a group will be learning a different topic, I hope that they will use the responsibility they have to their classmates as incentive to learn the material, as opposed to a lecture-based class where no one is relying on them to have done the reading ahead of time. Because each student will only have partial knowledge of what they need to complete a common task, I expect them transfer their knowledge to one another and ask questions of one another, pressing each one to solidify their own understanding and communication skills. I hope that with the instructor in the background during the activity they will feel less pressure to not be wrong, which will open up communication dramatically.

Grace's understanding of what she is tracking and how
Three main factors will be tracked in this observation: whether students effectively learned the material (to be measured primarily in a quiz graded by Andrea and discussed with Grace), whether students thought the assignment was effective and engaging (to be measured in a survey yet to be formulated in consultation with Nisa), and finally to what degree students actually engaged with each other during the assignment (to be tracked by Grace during the observed class). When students are working in groups, Grace will observe the general classroom atmosphere, and perhaps sit in on individual groups, to get a sense of what kinds of collaboration are being practiced. Andrea will leave the room for some period of time when students begin this assignment, so that students can adjust to the new collaborative learning dynamic. Grace will keep detailed notes on how often students are speaking to one another and during which parts of the assignment, as well as monitoring overall student engagement through qualitative factors like body language, tone, and classroom environment. The goal is for students to work together rather than do problems individually, so close observation of the learning process is just as important as the learning outcome.


With the assistance of Nisa Bakkalbasi, Assessment Coordinator at Columbia University Libraries, Andrea developed a survey that will be distributed at the end of class. We considered doing a focus group rather than a survey, but after consulting with Nisa we decided that a focus group would require an imposition on students' time that we did not want to make, since it was not necessary for the kind of data we want to gather. An in-class survey virtually guarantees a 100% response rate, the assignment will still be very fresh in students' minds, and the simplicity of its design will give us concrete and easily interpretable data. The survey we will be using is appended below.

2. Timeline

1/23 Andrea and Grace meet to discuss first draft of observation plan
2/10 Draft of observation plan posted online
2/12 Observation plan workshop
2/13 Andrea and Grace meet to revise observation plan
2/16 Andrea and Grace meet with Nisa to formulate survey
2/18 Andrea emails students with a description of the assignment, their assigned topics, and guiding worksheets
2/25 Day of observation
4:00 Grace meets Andrea before class to discuss any logistics4:10 to 5:25 Class meets:

  • 4:10-4:15: Students break up into their pre-assigned groups of four
  • 4:15-5:15: Activity takes place- students work through worksheets in their groups, with Grace observing as described above.
  • 5:15-5:25: Students individually take short quiz to measure whether they learned all four topics
  • Immediately following class: Survey administered

TBD (soon after observation) Andrea and Grace meet to debrief observation, discuss quiz and survey