Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs

Angeles Dominguez; Pablo Barniol; Genaro Zavala

doi:10.12973/ejmste/78085

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Angeles Dominguez ¹ ², Pablo Barniol ¹, Genaro Zavala ¹ ² ^*

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¹ Tecnologico de Monterrey, MEXICO² Universidad Andres Bello, CHILE^* Corresponding Author

Abstract

Studies show that students, within the context of mathematics and science, have difficulties understanding the concepts of the derivative as the slope and the concept of the antiderivative as the area under the curve. In this article, we present the Test of Understanding Graphs in Calculus (TUG-C), an assessment tool that will help to evaluate students’ understanding of these two concepts by a graphical representation. Data from 144 students of introductory courses of physics and mathematics at a university was collected and analyzed. To evaluate the reliability and discriminatory power of this test, we used statistical techniques for individual items and the test as a whole, and proved that the test’s results are satisfactory within the standard requirements. We present the design process in this paper and the test in the appendix. We discuss the findings of our research, students’ understanding of the relations between these two concepts, using this new multiple-choice test. Finally, we outline specific recommendations. The analysis and recommendations can be used by mathematics or science education researchers, and by teachers that teach these concepts.

Keywords

concept of the derivative
concept of the antiderivative
context of calculus
reliable evaluation instrument
students’ graph understanding

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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

EURASIA J Math Sci Tech Ed, 2017, Volume 13, Issue 10, 6507-6531

https://doi.org/10.12973/ejmste/78085

Publication date: 29 Sep 2017

Article Views: 2736

Article Downloads: 1318

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References

Bajracharya, R. R., Wemyss, T. M., & Thompson, J. R. (2012). Student interpretation of the signs of definite integrals using graphical representations. AIP Conference Proceedings, 1413, 111-114.
Beichner, R. (1994). Testing student interpretation of kinematic graphs. American Journal of Physics, 62(8), 750-762.
Bektasli, B., & White, A. L. (2012). The relationships between logical thinking, gender, and kinematics graph interpretation skills. Egitim Arastirmalari - Eurasian Journal of Educational Research, 12(48), 1-19.
Chanpichai, N., & Wattanakasiwich, P. (2010). Teaching Physics with Basketball, AIP Conference Proceedings, 1263, 212-215.
Christensen, W. M., & Thompson, J. R. (2012). Investigating graphical representations of slope and derivative without a physics context. Physical Review Special Topics - Physics Education Research, 8, 023101.
Ding, L., Chabay, R., Sherwood, B., & Beichner R. (2006). Evaluating an electricity and magnetism assessment tool: Brief electricity and magnetism assessment. Physical Review Special Topics - Physics Education Research, 2(1), 010105.
Engelhardt, P. (2009). An Introduction to Classical Test Theory as Applied to Conceptual Multiple-Choice Tests in Getting Started in PER, Vol. 2. Retrieved from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=8807&DocID=1148.
Epstein, J. (2013). The calculus concept inventory-measurement of the effect of teaching methodology in mathematics. Notices of the American Mathematical Society, 60(8), 1018-1026.
Gurel, D. K., Eryilmaz, A., & McDermott, L. C. (2015). A review and comparison of diagnostic instruments to identify students’ misconceptions in science. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 989-1008.
Hadjidemetriou, C., & Williams, J. (2002). Children’s graphical conceptions, Research in Mathematics Education, 4(1), 69-87.
Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses, American Journal of Physics, 66, 64.
Hammer, D. (2000). Student resources for learning introductory physics, American Journal of Physics, 68, S52.
Hill, M., & Sharma, M. D. (2015). Students’ representational fluency at university: A cross-sectional measure of how multiple representations are used by physics students using the representational fluency survey. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1633-1655.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60, 1–64.
Leonard, W., Gerace, W., & Dufresne, R. (1999). Concept-based problem solving: Making concepts the language of physics. Retrieved from http://www.srri.umass.edu/publications/gerace-1999cbp.
Maries, A., & Singh, C. (2013). Exploring one aspect of pedagogical content knowledge of teaching assistants using the test of understanding graphs in kinematics. Physical Review Special Topics - Physics Education Research, 9, 020120.
McDermott, L. C. (2001). Oersted medal lecture 2001: “Physics education research - The key to student learning”. American Journal of Physics, 69(11), 1127-1137.
McDermott, L. C., & Shaffer, P. (2001). Tutoriales para Física Introductoria. México, D. F., México: Pearson.
McDermott, L. C., Rosenquist, M. L., & van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal of Physics, 55, 503–513.
Meltzer, D. E. (2004). Investigation of students’ reasoning regarding heat, work, and the first law of thermodynamics in an introductory calculus-based general physics course. American Journal of Physics, 72(11), 1432-1446.
Mesic, V., Dervic, D., Gazibegovic-Busuladzic, A., Salibasic, D., & Erceg, N. (2015). Comparing the impact of dynamic and static media on students’ learning of one-dimensional kinematics. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 1119-1140.
Nguyen, D., & Rebello, N. S. (2011). Students’ understanding and application of the area under the curve concept in physics problems. Physical Review Special Topics - Physics Education Research, 7, 010112.
Orton, A. (1983). Students’ understanding of integration. Educational Studies in Mathematics, 14(1), 1-18.
Pérez, N., Domínguez, A., & Zavala, G. (2010). Diseño de un instrumento para evaluar entendimiento de gráficas en cálculo. 24ALME.
Perez-Goytia, N., Dominguez, A., & Zavala, G. (2010). Understanding and interpreting calculus graphs: Refining an instrument. AIP Conference Proceedings, 1289, 249-252.
Planinic, M., Ivanjek, L., Susac, A., & Milin-Sipus, Z. (2013). Comparison of university students’ understanding of graphs in different contexts. Physical Review Special Topics - Physics Education Research, 9.
Planinic, M., Milin-Sipus, Z., Katic, H., Susac, A., & Ivanjek, L. (2012). Comparison of student understanding of line graph slope in physics and mathematics. International Journal of Science and Mathematics Education, 10(6), 1393-1414.
Pollock, E. B., Thompson, J. R., & Mountcastle, D. B. (2007). Student understanding of the physics and mathematics of process variables in P-V diagrams. AIP Conference Proceedings, 951, 168-171.
Redish, E. (1999). Millikan Lecture 1998: Building a science of teaching physics, American Journal of Physics, 67, 562.
Salinas, N. P., Alanís, J. A., Garza, J. L., Pulido, R., Santos, F. X., & Escobedo, J. C. (2000). Elementos del Cálculo: Reconstrucción Conceptual para el Aprendizaje y la Enseñanza, 1. México: Trillas.
Salinas, N. P., Alanís, J. A., Garza, J. L., Pulido, R., Santos, F. X., & Escobedo, J. C. (2012). Cálculo Aplicado: Competencias matemáticas a través de contextos, 1. México: Cengage Learning.
Serway, R. A., & Jewett, J. W. (2008). Física para ciencias e ingeniería (Vol. 1). México, D.F.: Cengage Learning.
Sheskin, D. J. (2007). Handbook of Parametric and Nonparametric Statistical Procedures (4th ed.). Florida, Boca Raton: Chapman and Hall/CRC.
Tejada Torres, S. E., & Alarcon, H. (2012). A tutorial-type activity to overcome learning difficulties in understanding graphics in kinematics. Latin American Journal of Physics Education, 6, Suppl. I, 285-289.
Woolnough, J. (2000). How do students learn to apply their mathematical knowledge to interpret graphs in physics? Research in Science Education, 30, 259–267.
Zavala, G., Tejeda, S., Barniol, P., & Beichner, R. J. (2017). Modifying the test of understanding graphs in kinematics. Physical Review Physics Education Research, 13, 020111.

How to cite this article

APA

Dominguez, A., Barniol, P., & Zavala, G. (2017). Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs. Eurasia Journal of Mathematics, Science and Technology Education, 13(10), 6507-6531. https://doi.org/10.12973/ejmste/78085

Vancouver

Dominguez A, Barniol P, Zavala G. Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs. EURASIA J Math Sci Tech Ed. 2017;13(10):6507-31. https://doi.org/10.12973/ejmste/78085

AMA

Dominguez A, Barniol P, Zavala G. Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs. EURASIA J Math Sci Tech Ed. 2017;13(10), 6507-6531. https://doi.org/10.12973/ejmste/78085

Chicago

Dominguez, Angeles, Pablo Barniol, and Genaro Zavala. "Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs". Eurasia Journal of Mathematics, Science and Technology Education 2017 13 no. 10 (2017): 6507-6531. https://doi.org/10.12973/ejmste/78085

Harvard

Dominguez, A., Barniol, P., and Zavala, G. (2017). Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs. Eurasia Journal of Mathematics, Science and Technology Education, 13(10), pp. 6507-6531. https://doi.org/10.12973/ejmste/78085

MLA

Dominguez, Angeles et al. "Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs". Eurasia Journal of Mathematics, Science and Technology Education, vol. 13, no. 10, 2017, pp. 6507-6531. https://doi.org/10.12973/ejmste/78085