I am currently developing active-learning curriculum for Calculus I and II. I am working under Heather Bolles, funded by a grant from the Howard Hughes Medical Institute. My colleague, Mary Vaughan, and I are collaborating to create short, meaningful activities which instructors can easily incorporate into the Calculus classroom.
Two Studies in Team Based Learning
Team-based learning is a specific active learning structure that has been implemented in select Calculus classes at Iowa State University (see work by Sibley, Ostafichuk). I have been involved in two research studies regarding this structure.
The first was a quantitative study evaluating the performance of students in TBL versus non-TBL sections of Calculus 1 in the Fall of 2016. The TBL students outperformed the non-TBL students in terms of exam grades (standardized across all sections), student retention, and conceptual understandings. We found that these results persisted even when measures of incoming student competency were taken into account (Bolles, et al. 2018).
The second project is a quantitative study regarding student engagement in the TBL structure. We conducted two intensive rounds of interviews with students in TBL Calculus II sections, then coded and analyzed the interviews according to principles of Self-Determination Theory (Ryan & Deci, 2000). We obtained preliminary results connecting student motivation in the TBL structure to the “supporting” or “thwarting” of three basic psychological needs: competence, relatedness, and autonomy.
One of my main areas of interest in education research is the impact of a fixed versus growth mindset (see work by Dweck, Boaler) on student learning.
Within the context of mathematics, a fixed mindset is the idea that one’s mathematical intelligence or ability is fixed—it cannot be significantly increased or improved (E.g., “I’m bad at math. This will always be the case and is out of my control”).
A growth mindset is the idea that we obtain mathematical ability through effort, with increased effort leading to increased results. Just like a muscle in your body, through consistent work and training, you can make your mathematical mind stronger.
Although I am interested in this concept at all levels of education, I would specifically like to investigate how the mathematical mindsets of elementary teachers towards mathematics influence both the mindsets toward and achievements of their students in mathematics. I would also like to develop and study the efficacy of possible interventions to address these connections.
Here is an assignment that I have written to help students identify growth or fixed mindsets in themselves, as well as embrace produce struggle, along with a rubric. Feel free to use this in any of your own classes—if you do, be sure to let me know how it goes! This was used as an extra credit assignment last year in multiple large lectures of Calculus I after the first exam of the semester.
Boaler, J., & Dweck, C. S. (2016). Mathematical mindsets: unleashing students' potential through creative math, inspiring messages and innovative teaching. First edition. San Francisco, CA: Jossey-Bass; a Wiley Brand.
Bolles, H., Peters, T., Johnston, E., Holme, T., Ogilvie, C., Knaub, A., Bozeman, C., Wang, S, Seitz (Aboud), A. (2018). Investigating student success in team-based learning calculus I and in subsequent courses. Paper presented at the 21st Annual Conference on Research in Undergraduate Mathematics Education, San Diego, CA.
Ryan, R. & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 69-78.
Sibley, J., & Ostafichuk, P. (2014). Getting started with team-based learning. Sterling, VA: Stylus Publishing.