The effects of implementing recitation activities on success rates in a college calculus course
Main Article Content
Abstract
Over a period of six years, three different types of recitation sessions were implemented into the large enrollment section of a college calculus course. During the fall semesters, the results on the departmental final examination, the DFW rates, and the one-year retention rates of students as STEM majors were examined by the type of recitation session used with the large enrollment section. The three types of recitation sessions studied were: (1) optional mentoring sessions at the Math Assistance Center conducted by undergraduate students (peer mentors), (2) required mentoring sessions conducted by graduate students, and (3) required VGNA (Verbal, Graphical or Geometric, Numeric, and Algebraic) Concept activities, which were also coupled with mentoring sessions conducted by graduate students. The success of the students in the large enrollment section of the course, which included one of the three different types of recitation sessions, was compared to the success of students in the small enrollment sections of the course (enrollments less than 50 students). The effects of using each type of recitation session on raising departmental final examination scores, lowering DFW rates, and raising one-year retention rates is presented. The results of this study demonstrate methods of raising student success rates in large enrollment (lecture-format) courses.
Downloads
Article Details
- Authors retain copyright and grant the Journal of the Scholarship of Teaching and Learning (JoSoTL) right of first publication with the work simultaneously licensed under a Creative Commons Attribution License, (CC-BY) 4.0 International, allowing others to share the work with proper acknowledgement and citation of the work's authorship and initial publication in the Journal of the Scholarship of Teaching and Learning.
- Authors are able to enter separate, additional contractual agreements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in the Journal of the Scholarship of Teaching and Learning.
- In pursuit of manuscripts of the highest quality, multiple opportunities for mentoring, and greater reach and citation of JoSoTL publications, JoSoTL encourages authors to share their drafts to seek feedback from relevant communities unless the manuscript is already under review or in the publication queue after being accepted. In other words, to be eligible for publication in JoSoTL, manuscripts should not be shared publicly (e.g., online), while under review (after being initially submitted, or after being revised and resubmitted for reconsideration), or upon notice of acceptance and before publication. Once published, authors are strongly encouraged to share the published version widely, with an acknowledgement of its initial publication in the Journal of the Scholarship of Teaching and Learning.
References
Beidleman, J., Jones, D., & Wells, P. (1995). Increasing students' conceptual understanding of first semester calculus through writing. Primus, 5(4), 297-316. doi: 10.1080/10511979508965795
Bonsangue, M. (1994). An efficacy study of the calculus workshop model. In Dubinsky, A. Schoenfeld, & J. Kapuut (Ed.), CBMS Issues in Mathematics Education Volume 4: Research in Collegiate Mathematics Education I (pp. 117-137). Providence: AMS.
Britton, J., Burgess, T., Martin, N., McLeod, A., & Rosen, H. (1975). The development of writing abilities (11-18). London: MacMillan Educational for the Schools Council.
Bruffee, K. A. (1984). Collaborative learning and the 'Conversation of Mankind'. College English, 46(7), 635-652. doi: 10.2307/376924
Budny, D., LeBold, W., & Bjedov, G. (1998). Assessment of the impact of freshman engineering courses. Journal of Engineering Education, 87(4), 405-411. doi: 10.1002/j.21689830.1998.tb00372.x
Cooley, L. (2002). Writing in calculus and reflective abstraction. Journal of Mathematical Behavior, 21(3), 255-282. doi: 10.1016/S0732-3123(02)00129-3
Douglas, R. G. (1986). Toward a lean and lively calculus (Vol. 6). Washington, DC: Mathematical Association of America.
Ganter, S. L., & Jiroutek, M. R. (2000). The need for evaluation in the calculus reform movement: A comparison of two calculus teaching methods. In E. Dubinsky, A. H. Schoenfeld & J. Kaput (Eds.), CBMS Issues in Mathematics Education Volume 8: Research in Collegiate Mathematics Education IV (pp. 42-62). Providence: AMS.
Gehrke, M., & Pengelley, D. (1996). Towards active processes for teaching and learning. In A. W. Roberts (Ed.), Calculus: The dynamics of change (Vol. 39, pp. 20-23). Washington, DC: Mathematical Association of America.
Goerdt, S. (2007). The effect of emphasizing multiple representations on calculus students' understanding of the derivative concept. Ph.D., University of Minnesota, United States – Minnesota. Retrieved from http://0-proquest.umi.com.catalog.library.colostate.edu/pqdweb?did=1500055151&Fmt=7&clientId=14436&RQT=309&VName=PQD
Gosser, D. K., & Roth, V. (1998). The Workshop Chemistry Project: Peer-led team learning. Journal of Chemical Education, 75, 185-187. doi: 10.1021/ed075p185
Harel, G. (1997). The linear algebra curriculum study group recommendations: Moving beyond concept definition. In Carlson D., Johnson, C, Lay, D., Porter, D., Watkins, A, & Watkins, W. (Eds.). Resources for Teaching Linear Algebra, MAA Notes, Vol. 42, 107-126.
Harel, G. (2004). A perspective on "concept image and concept definition in mathematics with particular reference to limits and continuity." In T. Carpenter, J. Dossey, & L. Koehler (Eds.), Classics in mathematics education research (pp. 98-108). Reston: The National Council of Teachers of Mathematics.
Herzig, A., & Kung, D. T. (2003). Cooperative learning in calculus reform: What have we learned? In A. Selden, E. Dubinsky, G. Harel & F. Hitt (Eds.), CBMS Issues in mathematics education Vol 12: Research in collegiate mathematics education V (pp. 30-55). Providence: American Mathematical Society.
Hillocks, G. (1986). Research on written composition: New directions for teaching. Urbana: NCRE/ERIC Clearinghouse on Reading and Communication Skills.
McDermott, L. C., Shaffer, P. S., & Somers, M. D. (1994). Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood's machine. Am. J. Phys., 62, 46-55. doi: 10.1119/1.17740
Monk, S., & Nemirovsky, R. (1994). The case of Dan: Student construction of a functional situation through visual attributes. In E. Dubinsky, A. H. Schoenfeld, & J. Kaput (Eds.), CBMS Issues in mathematics education volume 4: Research in collegiate mathematics education I (pp. 139-168). Providence: American Mathematical Society.
Norwood, K. (1995). The effects of the use of problem solving and cooperative learning on the mathematics achievement of underprepared college freshmen. Primus, 5, 229–252. Doi: 10.1080/10511979508965789
Pilgrim, M. E. (2010). A concepts for calculus intervention: Measuring student attitudes toward mathematics and achievement in calculus. Unpublished doctoral dissertation, Colorado State University, Fort Collins.
Ross, S. C. (1996). Visions of calculus. In A. W. Roberts (Ed.), Calculus: The dynamics of change (Vol. 39, pp. 8-15). Washington, DC: Mathematical Association of America.
Smith, D. (1994). Trends in calculus reform. In A. E. Solow (Ed.), Preparing for a new calculus (Vol. 36, pp. 3-13). Washington, DC: Mathematical Association of America.
Smith, D. (1996). Thinking about learning, learning about thinking. In A. W. Roberts (Ed.), Calculus: The dynamics of change (Vol. 39, pp. 31-37). Washington, DC: Mathematical Association of America.
Springer, L., Stanne, M. E., & Donovan, S. S. (1999). Effects of small-group learning on undergraduates in science, mathematics, engineering, and technology: A meta-analysis. Review of Educational Research, 69, 21–51. doi: 10.3102/00346543069001021
Stewart, J. (2012). Calculus, 7th Edition. Belmont, CA: Brooks/Cole.
Shaw, D. (2012). Instructor's guide for calculus, 7th Edition. Belmont, CA: Brooks/Cole.
Steen, L. (Ed.). (1988). Calculus for a new century: A pump, not a filter. MAA Notes No. 8. Washington, DC: Mathematical Association of America.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151– 169. doi: 10.1007/BF00305619
Treisman, P. M. (1985). A study of the mathematics performance of black students at the University of California, Berkeley. Unpublished doctoral dissertation, University of California, Berkeley.
Tucker, T. (1996). Nonalgebraic approaches to calculus. In A. W. Roberts (Ed.), Calculus: The dynamics of change (Vol. 39, pp. 16-19). Washington, DC: Mathematical Association of America.
Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. In The concept of function: Aspects of epistemology and pedagogy, edited by Guershon Harel and Ed Dubinsky, pp. 195–214. Washington, D.C.: Mathematical Association of America.
Watt, J. X. (2013). CI-STEP: Transforming the calculus course to increase STEM graduates. Proceedings of the 2013 International Conference on Mathematics Education (2013. 11. 1-2) 635-645.
Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M., & Merkovsky, R. (2003). Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle. In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (Eds.), CBMS Issues in mathematics education Vol 12: Research in collegiate mathematics education V (pp. 97-131). Providence: American Mathematical Society.
Wieschenberg, A. A. (1994). Overcoming conditioned helplessness in mathematics. College Teaching, 42(2), 51–54. doi: 10.1080/87567555.1994.9926820