pp. 503-520 | Article Number: iejme.2017.026
Published Online: July 19, 2017
Article Views: 157 | Article Download: 249
There is a variety of classroom assessment techniques we can use in the college classroom (Angelo and Cross, 1993). In an effort to diagnose and identify gaps between students’ learning and classroom teaching, we implemented weekly short assessments in a calculus I classroom at an urban community college in the United States. The goals of these assessments were to identify misconceptions, and address them using an appropriate intervention. In this paper, we share these assessments, how they can be used to cement students’ conceptual learning, and how it can help the instructor develop insights into students’ misunderstandings. We also share students’ feedback, challenges and implications for practitioners.
Keywords: Assessment, calculus, community college
Angelo, T. A., & Cross, K. P. (1993). Classroom Assessment Techniques: A Handbook for College Teachers.Second Edition (2nd ed.). San Fransisco, CA: Jossey-Bass.
Attorps, I., Björk, K., Radic, M., & Tossavainen, T. (2013). Varied Ways to Teach the Definite Integral Concept. SOURCE International Electronic Journal of Mathematics Education, 8(2-3), 81-99.
Bailey, T., Jeong, D. W., & Cho, S. (2010). Referral, enrollment, and completion in developmental education sequences in community colleges. Economics of Education Review, 29(2), 255-270. doi:10.1016/j.econedurev.2009.09.002
Bean, J. C. (2011). Engaging ideas: The professor's guide to integrating writing, critical thinking, and active learning in the classroom. San Francisco: Jossey-Bass.
Bonwell, C. C., &Eison, J. A. (1991). Active learning: Creating excitement in the classroom. ASHE-Eric Higher Education Report No. 1. Washington, DC.: George Washington University.
Bolte, L. A. (1999). Using Concept Maps and Interpretive Essays for Assessment in Mathematics. School Science and Mathematics, 99(1), 19-30. doi:10.1111/j.1949-8594.1999.tb17442.x
Cross, K. P. (2003). Techniques for Promoting Active Learning. League for Innovation in the Community College Educational Testing Service, AZ: The Cross Papers #7.
Cullinane, M. J. (2011). Helping Mathematics Students Survive the Post-Calculus Transition. PRIMUS, 21(8), 669-684. doi:10.1080/10511971003692830
Dawkins, P. C., & Epperson, J. A. (2014). The development and nature of problem-solving among first-semester calculus students. International Journal of Mathematical Education in Science and Technology, 45(6), 839-862. doi:10.1080/0020739x.2014.884645
Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics (2013), 82, 439–453.
Idris, N. 2009. Enhancing Students' Understanding in Calculus Through Writing. International Electronic Journal of Mathematics Education. 4(1): 36-55.
Iannone, P., & Simpson, A. (2015). Students' preferences in undergraduate mathematics assessment. Studies in Higher Education, 40(6), 1046-1067. Retrieved from http://dx.doi.org/10.1080/03075079.2013.858683
Jaafar, R. (2016). Writing-to-Learn Activities to Provoke Deeper Learning in Calculus. PRIMUS, 26(1), 67-82. doi:10.1080/10511970.2015.1053642
Kinley, (2016). Grade Twelve Students Establishing the Relationship Between Differentiation and Integration in Calculus Using graphs. IEJME-Mathematics Education, 11(9), 3371-3385.
Maharaj, A., & Wagh, V. (2014). An outline of possible pre-course diagnostics for differential calculus. South African Journal of Science, 110(7/8), 1-7. doi:10.1590/sajs.2014/20130244
Meyers, C., & Jones, T. B. (1993). Promoting active learning: Strategies for the college classroom. San Francisco, CA: Jossey-Bass.
National Research Council, & Bass, H. (1993). Measuring what counts: Conceptual guide for mathematics assessment. Washington, DC: National Academy Press.
Porter, M. K., & Masingila, J. O. (2000). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics, 42(2), 165–177.
Pugalee, D. K. (2001). Writing, Mathematics, and Metacognition: Looking for Connections Through Students' Work in Mathematical Problem Solving. School Science and Mathematics, 101(5), 236-245. doi:10.1111/j.1949-8594.2001.tb18026.x
Robert, A., & Speer, N. (2001). Research on the teaching and learning of calculus/elementary analysis. In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study (Vol. 7, pp. 283–299). Dordrecht & Boston: Kluwer Academic Publishers.
Rybolt, W., & Recck, G. (2012). Conceptual versus Computational Formulae in Calculus and Statistics Courses. The International Journal of Technology, Knowledge, and Society: Annual Review, 8(2), 1-6. doi:10.18848/1832-3669/cgp/v08i02/56287.
Scheja, M., & Pettersson, K. (2009). Transformation and contextualization: conceptualizing students’ conceptual understandings of threshold concepts in calculus. Higher Education, 59(2), 221-241. doi:10.1007/s10734-009-9244-7
Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(2-3), 229-274. doi:10.1007/bf01273664
Vincent, B., LaRue, R., Sealey, V., & Engelke, N. (2015). Calculus students' early concept images of tangent lines. International Journal of Mathematical Education in Science and Technology, 46(5), 641-657. doi:10.1080/0020739x.2015.1005700.
Yoder, J., & Hochevar, C. (2005). Encouraging Active Learning Can Improve Students' Performance on Examinations. Teaching of Psychology, 32(2), 91-95. doi:10.1207/s15328023top3202_2