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RESEARCH PAPER
Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs
Angeles Dominguez 1,2
,
 
Pablo Barniol 1
,
 
Genaro Zavala 1,2
 
 
 
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1
Tecnologico de Monterrey, MEXICO
 
2
Universidad Andres Bello, CHILE
 
 
Online publication date: 2017-09-29
 
 
Publication date: 2017-09-29
 
 
Corresponding author
Genaro Zavala   

Tecnologico de Monterrey, Mexico
 
 
EURASIA J. Math., Sci Tech. Ed 2017;13(10):6507-6531
DOI: https://doi.org/10.12973/ejmste/78085
 
 
Article (PDF)
References (36)
 
KEYWORDS
concept of the derivative
concept of the antiderivative
context of calculus
reliable evaluation instrument
students’ graph understanding
 
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.
 
REFERENCES (36)
1.
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.
Google Scholar
 
 
2.
Beichner, R. (1994). Testing student interpretation of kinematic graphs. American Journal of Physics, 62(8), 750-762.
Google Scholar
 
 
3.
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.
Google Scholar
 
 
4.
Chanpichai, N., & Wattanakasiwich, P. (2010). Teaching Physics with Basketball, AIP Conference Proceedings, 1263, 212-215.
Google Scholar
 
 
5.
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.
Google Scholar
 
 
6.
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.
Google Scholar
 
 
7.
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/Reposi....
Google Scholar
 
 
8.
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.
Google Scholar
 
 
9.
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.
Google Scholar
 
 
10.
Hadjidemetriou, C., & Williams, J. (2002). Children’s graphical conceptions, Research in Mathematics Education, 4(1), 69-87.
Google Scholar
 
 
11.
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.
Google Scholar
 
 
12.
Hammer, D. (2000). Student resources for learning introductory physics, American Journal of Physics, 68, S52.
Google Scholar
 
 
13.
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.
Google Scholar
 
 
14.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60, 1–64.
Google Scholar
 
 
15.
Leonard, W., Gerace, W., & Dufresne, R. (1999). Concept-based problem solving: Making concepts the language of physics. Retrieved from http://www.srri.umass.edu/publ....
Google Scholar
 
 
16.
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.
Google Scholar
 
 
17.
McDermott, L. C. (2001). Oersted medal lecture 2001: “Physics education research - The key to student learning”. American Journal of Physics, 69(11), 1127-1137.
Google Scholar
 
 
18.
McDermott, L. C., & Shaffer, P. (2001). Tutoriales para Física Introductoria. México, D. F., México: Pearson.
Google Scholar
 
 
19.
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.
Google Scholar
 
 
20.
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.
Google Scholar
 
 
21.
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.
Google Scholar
 
 
22.
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.
Google Scholar
 
 
23.
Orton, A. (1983). Students’ understanding of integration. Educational Studies in Mathematics, 14(1), 1-18.
Google Scholar
 
 
24.
Pérez, N., Domínguez, A., & Zavala, G. (2010). Diseño de un instrumento para evaluar entendimiento de gráficas en cálculo. 24ALME.
Google Scholar
 
 
25.
Perez-Goytia, N., Dominguez, A., & Zavala, G. (2010). Understanding and interpreting calculus graphs: Refining an instrument. AIP Conference Proceedings, 1289, 249-252.
Google Scholar
 
 
26.
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.
Google Scholar
 
 
27.
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.
Google Scholar
 
 
28.
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.
Google Scholar
 
 
29.
Redish, E. (1999). Millikan Lecture 1998: Building a science of teaching physics, American Journal of Physics, 67, 562.
Google Scholar
 
 
30.
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.
Google Scholar
 
 
31.
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.
Google Scholar
 
 
32.
Serway, R. A., & Jewett, J. W. (2008). Física para ciencias e ingeniería (Vol. 1). México, D.F.: Cengage Learning.
Google Scholar
 
 
33.
Sheskin, D. J. (2007). Handbook of Parametric and Nonparametric Statistical Procedures (4th ed.). Florida, Boca Raton: Chapman and Hall/CRC.
Google Scholar
 
 
34.
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.
Google Scholar
 
 
35.
Woolnough, J. (2000). How do students learn to apply their mathematical knowledge to interpret graphs in physics? Research in Science Education, 30, 259–267.
Google Scholar
 
 
36.
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.
Google Scholar
 
 
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