Teaching Basic Vector Concepts: A Worksheet for the Recovery of Students’ Vector Understanding
Keywords:Vector, Vector addition, Vector subtraction, Resultant vectors, Worksheet
The investigation of high-school students’ qualitative understanding of graphical vector addition in one and two dimensions has revealed that students did not grasp the important basic concepts about vectors. Based on their misunderstanding, we had designed a worksheet in order to help them learn such topics in class more effectively. The content in the worksheet includes vector directions, magnitude, addition and subtraction. A 2-page worksheet was constructed and distributed to 3 classes of high-school students in a large public school (n=103). Students took approximately 30-40 minutes to complete the worksheet. A seven-item diagnostic quiz was applied as a pre/post-test in order to evaluate the effectiveness of the worksheet. Using paired-sample t-test, results from the diagnostic quiz showed that the students’ average post-test scores for all classes were significantly higher than their average pre-test scores (p<0.000). In addition, the class average normalized gains ranged from 0.69-0.76 which was considered as high gains that might be rarely reached by conducting classes even with active learning activities.
Aguirre, J.M. (1988). Student Preconceptions about Vector Kinematics. The Physics Teacher, 26 (4), 212-216.
Aguirre, J.M., & Rankin, G. (1989). College students’ conceptions about vector kinematics. Physics Education, 24 (5), 290-294.
Bao, L. (2006). Theoretical comparisons of average normalized gain calculations. American Journal of Physics, 74 (10), 917-922.
Barniol, P. & Zavala, G. (2009). Investigation of Students’ Preconceptions and Difficulties with the Vector Direction Concept at a Mexican University. AIP Conference Proceedings, 1179, 85-88.
Barniol, P. & Zavala, G. (2010). Vector Addition: Effect of the Context and Position of the Vectors. AIP Conference Proceedings, 1289, 73-76.
Barniol, P. & Zavala, G. (2012). Students' difficulties with unit vectors and scalar multiplication of a vector. AIP Conference Proceedings, 1413, 115-118.
Barniol, P. & Zavala, G. (2014). Test of understanding of vectors: A reliable multiple-choice vector concept test. Physical Review Special Topics-Physics Education Research, 10(1), 010121-1 - 010121-14.
Barniol, P. & Zavala, G. (2015). Force, velocity, and work: The effects of different contexts on students’ understanding of vector concepts using isomorphic problems. Physical Review Special Topics-Physics Education Research, 11 (1), 020115-1 - 020115-15.
Barniol, P., Zavala, G. & Hinojosa, C. (2013). Investigation of Students’ Preconceptions and Difficulties with the Vector Direction Concept at a Mexican University. AIP Conference Proceedings, 1513, 58-61.
Celleta, V. P. & Phillipss, J. (2005). Interpreting FCI scores: Normalized gain, preinstruction scores, and scientific reasoning ability. American Journal of Physics, 73 (12), 341-344.
Celleta, V.P., Phillipss, J., Jeffery, A., & Jeff, S. (2011). FCI normalized gain, scientific reasoning ability, thinking in physics, and gender effects. AIP Conference Proceedings, 1413, 23-26.
Flores, S., Kanim, S.E., & Kautz, C.H. (2004). Student use of vectors in introductory mechanics. American Journal of Physics, 72 (4), 460-468.
Flores-Garc´ıa, S., Alfaro-Avena, L.L. & Dena-Ornelas, O. (2008). Students’ understanding of vectors in the context of forces. Revista Mexicana De Fi´Sica E, 54(1), 7–14.
Hake, R.R. (1998). Interactive-engagement versus traditional methods: A six-thousand student survey of mechanics test for introductory physics course. American Journal of Physics, 66 (1), 64-74.
Heckler, A.F. & Scaife, T.M. (2015). Adding and subtracting vectors: The problem with the arrow representation. Physical Review Special Topics-Physics Education Research, 11(1), 010101-1 - 010101-17.
Knight, R. D. (1995). The Vector Knowledge of Beginning Physics Students. The Physics Teacher, 33 (2), 74-77.
Marx, J.D. & Cummings, K. (2006). Normalized change. American Journal of Physics, 75(1), 87-91.
Nguyen, N. & Meltzer, D.E. (2003). Initial understanding of vector concepts among students in introductory physics course. American Journal of Physics, 71 (6), 630-638.
Shaffer, P.S. & McDermott, L.C. (2005). A research-based approach to improving student understanding of the vector nature of kinematical concepts. American Journal of Physics, 73 (10), 921-931.
Sheets, H.D. (1998). Communicating with Vectors. The Physics Teacher, 33 (2), 74-77.
Stewart, J. & Stewart, G. (2010). Correcting the Normalized Gain for Guessing. The Physics Teacher, 48 (3), 194-196.
Wutchana, U. & Emarat, N. (2011). Students’ Understanding of Graphical Vector Addition in One and Two Dimensions. Eurasian Journal of Physics and Chemistry, 3 (2), 102-111.
Wutchana, U. & Emarat, N. (2014). Finding resultant vectors using a rubber band. Physics Education, 49 (2), 141-143.
Zavala, G. & Barniol, P. (2010). Students’ understanding of the concepts of vector components and vector products. AIP Conference Proceedings, 1289, 341-344.
Zavala, G. & Barniol, P. (2013). Students’ understanding of dot product as a projection in nocontext, work and electric flux problems. AIP Conference Proceedings, 1513, 438-441.
How to Cite
Copyright © Authors