By: Becca Thomases, Associate Professor of Mathematics

Origins of a Math Community 

As a college student, I spent a lot of time in the math department lounge. In my first year I went during drop-in tutoring hours hosted by the more advanced students. It was also a great place to study for exams and finish homework assignments because there was invariably a classmate hanging about to talk about difficult problems with. For an introverted and socially awkward young person, the math lounge was an entryway to a social group, but it grew into so much more. I began to volunteer tutor, and by my final year I was one of the “older students” talking about math.

Why use LAs in Math?

Several years ago I was contemplating how our undergraduate math students could get more experience talking about math in groups, and how I, as faculty, could facilitate that. I thought back to when I started to understand mathematics in college. I was a good student in high school, but not an especially math-y student. I didn’t do extra-curricular math activities or contests; I didn’t even really like puzzles. I realized that it was in the community of my college’s math lounge, talking and tutoring, that I began my mathematical journey. I realized that having a place for conversations about math amongst students of a range of ages had been crucial to my own path.

Piloting Learning Assistants in Math

I decided to implement a peer-led tutoring environment in my calculus discussion sections for Math 17 (MAT17). At UC Davis such peers are called Learning Assistants (LAs): advanced undergraduates who assist in discussion sections and labs on campus. I had no idea this was already taking place on campus, but a colleague told me that it was happening in various STEM lab courses, and that the CalTeach/Math and Science Teaching Program (CalTeach/MAST) ran a 1-unit weekly Learning-Assistants seminar.

Calculus students benefit from an active learning environment, but high TA-to- student ratios make this difficult to achieve. Putting LAs into the discussion sections makes small group work practical. The LAs benefit in turn from building community, vertical integration, and reinforcing knowledge.  They learn to explain difficult concepts, and to see the material from the instructor’s perspective. They become a branch communicating between the lower division students - often in language the calculus students can relate to more – and the graduate student TAs and instructors. The LA seminar run by CalTeach/MAST is the hub of all the STEM LAs, creating a wider community of LAs across campus. 

While I was designing my pilot program, my colleagues Tim Lewis and Sam Walcott were developing a series of project-based worksheets to incorporate into the math-for-biology calculus curriculum (MAT 17). These calculus classes can be as large as 275 students, with 7 discussion sections of around 40 students each. It is very difficult to manage group work as a single TA with sections this large.  Tim, Sam, and I decided that starting the Math LA program in the bio calculus series (MAT 17) was a perfect pairing. The worksheets were ideal for group work, and each TA would be assisted by 2 undergraduate LAs to make the large number of groups feasible. 

We have been using LAs and project worksheets in the Math 17 series for four years averaging 20 LAs per quarter.  

Strategies for using LAs

Developing a pilot to include LAs in one of your own classes is not difficult. If you decide LAs might be right for one of your classes, here are some of the issues you will want to consider: 

• The content of the discussion section must be amenable to students working in groups. We have found that open-ended problems are better, but it can be hard to maintain motivation if the problems are too hard. The material ideally will inspire some discussion or cooperation. 
   
• You need TA buy-in. The TAs are on the ground working with the undergraduates and LAs and this may change their job significantly. For example, we are now asking our TAs to mentor the LAs. I found many TAs eager to try this, but certainly not every TA so it should be optional at least in the beginning. 
   
• You need to meet with the TAs and LAs to go over content and classroom dynamics as well as to help troubleshoot issues in time to make meaningful changes. We have a weekly meeting (typically one hour) with all the instructors, TAs, and LAs working on a particular course. 
   
• You need to recruit undergraduate LAs. The math department staff helps us by providing lists of students who have been successful in our Calculus series, both the math major series as well as the Calc for Bio series. We find that many students are looking for ways to be more actively involved with the department, and to get to know faculty. This program provides career development for our future teachers as well as students preparing for graduate school. We also incentivize the students by providing 1 unit of credit, which they earn by working in 2 discussion sections per week as well as attending a 1-hour content meeting.
   
• We suggest that the LAs attend the 1 unit LA seminar course (GEL 186) the first quarter they work as an LA. The course provides training on active learning teaching, provides the LA’s with transferable skills and an academic connection for their future careers.
   

Positive Experiences for LAs

The feedback from LA’s and TA’s has been very positive. Many LA’s volunteer for two or three quarters. We are now often recruiting LAs who have taken MAT17 with discussion sections led by LA’s and TA’s. One LA said “I was able to contribute frequently, which made it an even better experience as I knew I was helping others discover math.”  Another of my LAs in Spring 2019, who has worked in the program since the Fall 2018 said “Being an LA has definitely allowed me to gain insight into what a potential future may be in the teaching profession while getting hands-on experience working with students. It also gave me the opportunity to interact with graduate students as well. I have worked with a different TA every quarter and every quarter I always learn something from them whether it be about math, life as a graduate student, job opportunities, or life in general. I was lucky enough to get to take something away from this program, and I have been a LA for the entire 2018-2019 school year and it honestly was such a rewarding, introspective, and interesting experience that I would recommend to anyone interest in teaching or mathematics in general.”

Acknowledgements

Tim Lewis, Sam Walcott, and I were supported for this project in part by the Provost’s Fellowship for Innovation of Teaching Award.  We worked with Marco Molinaro and 
Chris Pagliarulo from the Center for Educational Effectiveness. Thanks also to Mary-Betty Stevenson from CalTeach/MAST, Malina Gillies-Doherty and Tina Denena in the math department office and Korana Burke who have helped with LA recruitment.  Graduate student Will Wright and former graduate student Jamie Haddock helped develop the worksheets. There are also many other math department instructors, and TA’s who have contributed to this project. 

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