We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he tried to convey these ideas in this lecture. We also interviewed 6 students to see what they understood from this lecture. The students did not comprehend the ideas that the professor cited as central to his lecture. Based on our analyses, we propose 2 factors to account for why students did not understand these ideas.
Kristen Lew, Timothy Patrick Fukawa-Connelly, Juan Pablo Mejía-Ramos and Keith Weber
Timothy Fukawa-Connelly, Keith Weber and Juan Pablo Mejía-Ramos
This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not record the informal content that is only stated orally but do if it is written on the board. The authors found that (a) informal content was common (with, on average, 32 instances per lecture), (b) most informal content was presented orally, and (c) typically students recorded written content while not recording oral content in their notes.
Sandra L. Laursen, Marja-Liisa Hassi, Marina Kogan and Timothy J. Weston
Slow faculty uptake of research-based, student-centered teaching and learning approaches limits the advancement of U.S. undergraduate mathematics education. A study of inquiry-based learning (IBL) as implemented in over 100 course sections at 4 universities provides an example of such multicourse, multi-institution uptake. The study suggests the real-world promise of broad uptake of student-centered teaching methods that improve learning outcomes and, ultimately, student retention in college mathematics.
Estrella Johnson, Christine Andrews-Larson, Karen Keene, Kathleen Melhuish, Rachel Keller and Nicholas Fortune
in college mathematics . International Journal of Research in Undergraduate Mathematics Education , 2 ( 1 ), 59 – 82. https://doi.org/10.1007/s40753-015-0021-y 13. Hill , C. , Corbett , C. , & St. Rose , A. ( 2010 ). Why so
Rebecca Vinsonhaler and Alison G. Lynch
Undergraduate Mathematics Education 2 , no. 2 (July): 165 – 96 . National Council of Teachers of Mathematics (NCTM) . 2014 . Principles to Actions: Ensuring Mathematical Success for All. Reston, VA : NCTM . National Governors Association Center for
Jason Knight Belnap and Amy Parrott
Fuglestad , pp. 17 – 24 , vol. 2 . Bergen, Norway : Bergen University College . Belnap , Jason , and Amy Parrott . 2013 . “Understanding Mathematical Conjecturing.” In Proceedings of the 16th SIGMAA on Research in Undergraduate Mathematics
Debasmita Basu, Nicole Panorkou, Michelle Zhu, Pankaj Lal and Bharath K. Samanthula
–11, 2010 . Moore , Kevin C. , and Patrick W. Thompson . 2015 . “ Shape Thinking and Students' Graphing Activity .” In Proceedings of the 18th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education , edited by
Theresa J. Grant and Mariana Levin
. Wawro , & S. Brown (Eds.), Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education , San Diego, CA . 22. Saxe , G. B. , Shaughnessy , M. M. , Shannon , A. , Langer-Osuna , J. M
Lara Alcock, Paul Hernandez-Martinez, Arun Godwin Patel and David Sirl
undergraduate mathematics education, such studies have often been based in small specialist classes, and reports have focused on teacher and student activity ( Johnson, Caughman, Fredericks, & Gibson, 2013 ), on guided reinvention task sequences ( Larsen, 2013
Emilie Wiesner, Aaron Weinberg, Ellie Fitts Fulmer and John Barr
: Research and teaching in undergraduate mathematics education (pp. 43 – 52 ). Washington, DC: Mathematical Association of America . doi: 10.5948/UPO9780883859759.005 40. Weber , K. , & Mejia-Ramos , J. P. ( 2011 ). Why and