Friday, February 19th, 10 -11 AM on ZOOM. Meeting link shared on mailing list.
This month we will discuss DNR-Based Instruction. Here DNR stands for the three principles described by Hately as follows:
Duality
Students develop ways of thinking through the production of ways of understanding, and, conversely, the ways of understanding they produce are impacted by the ways of thinking they possess.
Necessity
For students to learn the mathematics we intend to teach them, they must have a need for it, where ‘need’ here refers to intellectual need.
Repeated Reasoning
Students must practice reasoning in order to internalize desirable ways of understanding and ways of thinking.
Our primary source is a book chapter written by the frameworks developer Hatel. We will focus on the example lesson (pg 346-352) and the analysis of that lesson (pg 360-363).
For more examples of this pedagogy in practice see the Calculus Video Project (calcvids.org) or the October 27th talk about that project (sited below). If you are interested in how this framework applies to teaching proof writing a good starting point is the commentary in the second half of the chapter.
Harel, Guershon. 2010. "DNR-Based Instruction in Mathematics as a Conceptual Framework." In Theories of Mathematics Education: Seeking New Frontiers, edited by Bharath Sriraman and Lyn English, 343-367. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-00742-2_34.
Martin, Jason, Jason Martin, Michael Tallman and Aaron Weinberg "Quantitative Reasoning and Intellectual Need as Design Principles for Instructional Materials" (presentation, Electronic Seminar on Mathematics Education, online, October 27, 2020) math.mit.edu/seminars/esme/pastseminars.html
Friday, March 12th, 10 -11 AM on ZOOM. Meeting shared on mailing list.
This month, we will discuss best practices for creating instructional videos. Our focus will be two articles that discuss the practical implications of educational research on videos in teaching. The article by Cynthia Brame discusses design practices informed by cognitive load theory. The article by Kien discusses both when and how to embed questions directly in instructional videos. The supplementary readings are research articles showing some of the evidence that supports the recommendations in the primary readings.
Brame, Cynthia J. 2016. "Effective Educational Videos: Principles and Guidelines for Maximizing Student Learning from Video Content." Lse 15 (4): es6. doi:10.1187/cbe.16-03-0125. https://doi.org/10.1187/cbe.16-03-0125.
Kien H. Lim, and Ashley D. Wilson. "Flipped Learning: Embedding Questions in Videos." Mathematics Teaching in the Middle School 23, no. 7 (2018): 378-85. Accessed March 6, 2021. http://www.jstor.org/stable/10.5951/mathteacmiddscho.23.7.0378.
Guo, Philip J., Juho Kim, and Rob Rubin. 2014. "How Video Production Affects Student Engagement: An Empirical Study of MOOC Videos." Atlanta, Georgia, USA, Association for Computing Machinery. https://doi.org/10.1145/2556325.2566239.
Ibrahim, Mohamed, Pavlo D. Antonenko, Carmen M. Greenwood, and Denna Wheeler. 2012. "Effects of Segmenting, Signalling, and Weeding on Learning from Educational Video." Null 37 (3): 220-235. https://doi.org/10.1080/17439884.2011.585993.
Friday, Abril 9th 10 -11 AM on ZOOM. Meeting link shared on mailing list.
The MAA's College Mathematics Journal (NYU Bobcat) includes classroom capsules. These are 1-3 page articles describing teaching strategies or tools that can be introduced into a college classroom. Our exploration of these classroom capsules has two goals. The fist is to discover ideas to bring into our own classrooms. The second is develop an understanding of the scope and style of these articles with an eye towards publishing our own.
The suggested readings are three examples of classroom capsules. This sampling is a good starting point, but there are many more to explore. You are encouraged to use the topic index to find capsules that are relevant to your teaching and read those instead. Ideally, we will all read different articles and pool our knowledge.
Any three classroom capsules that interest you. Here are three examples.
Jonathan Hoseana (2018) On Zero-Over-Zero Form Limits of a Special Type, The College Mathematics Journal, 49:3, 219-221, DOI: 10.1080/07468342.2018.1445916
Donald L. Muench (2020) The Last Two Days in Elementary Linear Algebra, The College Mathematics Journal, 51:3, 222-224, DOI: 10.1080/07468342.2020.1740540
Robert W. Vallin (2015) A Magic Trick Leads to an Identity: Some Induction Fun, The College Mathematics Journal, 46:4, 295-298, DOI: 10.4169/college.math.j.46.4.295
Friday, April 30th 10 -11 AM on ZOOM. Meeting link shared on mailing list.
This month our text is a chapter from the MAA National Study of College Calculus which discusses coordinating graduate student instructors. We will discuss best practices in course coordination for courses of all levels and instructors of all experience levels. Questions to discuss include: What are the goals of course coordination? How does one foster a community of practice? How do you balance instructor independence with the constraints of coordination?
Rasmussen, Chris and Jessica Ellis. "Calculus Coordination at PhD-granting Universities: More than Just Using the Same Syllabus, Textbook, and Final Exam" In Insights and Recommendations from the MAA National Study of College Calculus, edited by David Bressoud, Vilma Mesa, Chris Rasmussen, 107 - 116. MAA Press, 2015.
---
1. If you are having trouble accessing the readings, contact Corrin Clarkson for assistance.