Teaching methods comparison in a large calculus class
 Warren Code,
 Costanza Piccolo,
 David Kohler,
 Mark MacLean
 … show all 4 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
We report findings from a classroom experiment in which each of two sections of the same Calculus 1 course at a North American researchfocused university were subject to an “intervention” week, each for a different topic, during which a lessexperienced instructor encouraged a much higher level of student engagement, promoted active learning (answering “clicker” questions, smallgroup discussions, worksheets) during a significant portion of class time and built on assigned preclass tasks. The lesson content and analysis of the assessments were informed by existing research on student learning of mathematics and student interviews, though the interventions and assessments were also intended to be compatible with typical course practices in an attempt to appeal to practitioners less familiar with the literature. Our study provides an example of active learning pedagogy (including materials and assessment used) for students at this level of mathematics in a classroom of over one hundred students, and we report improved student performance—on conceptual items in particular—with a switching replication in that each section outperformed the other on the topic for which it received the intervention.
 blah 11858_2014_582_MOESM1_ESM.pdf (3283KB)
 Adair, JG, Sharpe, D, Huynh, CL (1989) Hawthorne control procedures in educational experiments: A reconsideration of their use and effectiveness. Review of Educational Research 59: pp. 215228 CrossRef
 Ambrose, SA, Bridges, MW, DiPietro, M, Lovett, MC, Norman, MK (2010) How learning works: Seven researchbased principles for smart teaching. JosseyBass, San Francisco, CA
 Andrews, TM, Leonard, MJ, Colgrove, CA, Kalinowski, ST (2011) Active learning not associated with student learning in a random sample of college biology courses. CBE Life Sciences Education 10: pp. 394405 CrossRef
 Asiala, M, Cottrill, JF, Dubinsky, E, Schwingendorf, KE (1997) The development of students’ graphical understanding of the derivative. The Journal of Mathematical Behavior 16: pp. 399431 CrossRef
 Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.) (2003). How People Learn: Brain, Mind, Experience, and School. Psychology (Expanded.). Washington D.C.: National Academy Press.
 Bressoud, DM, Carlson, MP, Mesa, V, Rasmussen, C (2013) The calculus student: insights from the Mathematical Association of America national study. International Journal of Mathematical Education in Science and Technology 44: pp. 685698 CrossRef
 Carlson, M, Jacobs, S, Coe, E, Larsen, S, Hsu, E (2002) Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education 33: pp. 352378 CrossRef
 Crouch, CH, Mazur, E (2001) Peer Instruction: Ten years of experience and results. American Journal of Physics 69: pp. 970 CrossRef
 Deslauriers, L, Schelew, E, Wieman, C (2011) Improved learning in a largeenrollment physics class. Science (New York, N.Y.) 332: pp. 862864 CrossRef
 Dubinsky, ED, McDonald, MA APOS: A constructivist theory of learning in undergraduate mathematics education research. In: Holton, D, Artigue, M, Kirchgräber, U, Hillel, J, Niss, M, Schoenfeld, A eds. (2002) The teaching and learning of mathematics at university level. Springer, The Netherlands, pp. 275282 CrossRef
 Engelke, N. (2007). Students’ understanding of related rates problems in calculus. Arizona State University.
 Epstein, J (2013) The calculus concept inventory—measurement of the effect of teaching methodology in mathematics. Notices of the AMS 60: pp. 10181026 CrossRef
 Hake, RR (1998) Interactiveengagement versus traditional methods: A sixthousandstudent survey of mechanics test data for introductory physics courses. American Journal of Physics 66: pp. 6474 CrossRef
 Hora, M, Ferrare, J (2009) Structured observation protocol for instruction in Institutions of Higher Education (IHEs). Madison, WI
 Klymchuk, S, Zverkova, T, Gruenwald, N, Sauerbier, G (2010) University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal 22: pp. 10332170 CrossRef
 Kogan, M, Laursen, SL (2013) Assessing longterm effects of inquirybased learning: A case study from college mathematics. Innovative Higher Education 39: pp. 117
 Kwon, ON, Rasmussen, C, Allen, K (2005) Students’ retention of mathematical knowledge and skills in differential equations. School Science and Mathematics 105: pp. 227239 CrossRef
 Martin, T (2000) Calculus students’ ability to solve geometric relatedrates problems. Mathematics Education Research Journal 12: pp. 7491 CrossRef
 McGivneyBurelle, J. & Xue, F. (2013). Flipping Calculus. PRIMUS, 23(5).
 Michael, J (2006) Where’s the evidence that active learning works?. Advances in Physiology Education 30: pp. 159167 CrossRef
 RuizPrimo, MA, Briggs, D, Iverson, H, Talbot, R, Shepard, LA (2011) Impact of undergraduate science course innovations on learning. Science (New York, N.Y.) 331: pp. 12691270 CrossRef
 Schoenfeld, AH (2004) The Math Wars. Educational Policy 18: pp. 253286 CrossRef
 Shadish, WR, Cook, TD, Campbell, DT (2001) Experimental and quasiexperimental designs for generalized causal inference. Houghton Mifflin, Boston
 Speer, NM, Smith, JP, Horvath, A (2010) Collegiate mathematics teaching: An unexamined practice. The Journal of Mathematical Behavior 29: pp. 99114 CrossRef
 Star, JR (2005) Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education 36: pp. 404411
 Stylianides, AJ, Stylianides, GJ (2013) Seeking researchgrounded solutions to problems of practice: Classroombased interventions in mathematics education. ZDM—The International Journal on Mathematics Education 45: pp. 333341 CrossRef
 Tallman, M., & Carlson, M. P. (2012). A characterization of calculus I final exams in U.S. colleges and universities. Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education (p. 217–226). Portland, OR: Portland State University.
 Tsai, F. S., Natarajan, K., Ahipasaoglu, S. D., Yuen, C., Lee, H., Cheung, N.M., Magnanti, T. L. (2013). From boxes to bees: Active learning in freshmen calculus. In 2013 IEEE Global Engineering Education Conference (EDUCON) (pp. 59–68).
 Tziritas, M. (2011). APOS Theory as a Framework to Study the Conceptual Stages of Related Rates Problems. Analysis. Concordia University.
 Weller, K, Clark, J, Dubinsky, E, Loch, S, McDonald, M, Merkovsky, R Student performance and attitudes in courses based on APOS Theory and the ACE Teaching Cycle. In: Selden, A, Dubinsky, E, Harel, G, Hitt, F eds. (2003) Research in Collegiate Mathematics Education V. American Mathematical Society, Providence, pp. 97131
 Title
 Teaching methods comparison in a large calculus class
 Journal

ZDM
Volume 46, Issue 4 , pp 589601
 Cover Date
 20140801
 DOI
 10.1007/s1185801405822
 Print ISSN
 18639690
 Online ISSN
 18639704
 Publisher
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Calculus
 Teaching experiment
 Authors

 Warren Code ^{(1)}
 Costanza Piccolo ^{(1)}
 David Kohler ^{(1)}
 Mark MacLean ^{(1)}
 Author Affiliations

 1. University of British Columbia, Vancouver, Canada
