Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning

Reem Jaafar; Yan Lin

doi:10.29333/iejme/628

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Reem Jaafar, Yan Lin

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Abstract

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

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2017, Volume 12, Issue 3, 503-520

https://doi.org/10.29333/iejme/628

Publication date: 19 Jul 2017

Article Views: 3401

Article Downloads: 5913

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References

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

How to cite this article

APA

Jaafar, R., & Lin, Y. (2017). Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning. International Electronic Journal of Mathematics Education, 12(3), 503-520. https://doi.org/10.29333/iejme/628

Vancouver

Jaafar R, Lin Y. Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning. INT ELECT J MATH ED. 2017;12(3):503-20. https://doi.org/10.29333/iejme/628

AMA

Jaafar R, Lin Y. Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning. INT ELECT J MATH ED. 2017;12(3), 503-520. https://doi.org/10.29333/iejme/628

Chicago

Jaafar, Reem, and Yan Lin. "Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning". International Electronic Journal of Mathematics Education 2017 12 no. 3 (2017): 503-520. https://doi.org/10.29333/iejme/628

Harvard

Jaafar, R., and Lin, Y. (2017). Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning. International Electronic Journal of Mathematics Education, 12(3), pp. 503-520. https://doi.org/10.29333/iejme/628

MLA

Jaafar, Reem et al. "Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning". International Electronic Journal of Mathematics Education, vol. 12, no. 3, 2017, pp. 503-520. https://doi.org/10.29333/iejme/628