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Derivatives, Integrals and Vectors in Introductory Mechanics: The Development of a Multi-representation Test for University Students

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Research and Innovation in Physics Education: Two Sides of the Same Coin

Part of the book series: Challenges in Physics Education ((CPE))

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Abstract

The use of mathematical concepts and formal reasoning is one of the main hurdles for students entering introductory physics courses at university. The ability to apply mathematical tools in the context of physics also relies on the use of multiple representations, i.e., the different forms in which a concept can be expressed, such as words, graphs, numbers and formal language. Based on these considerations, we have developed a multiple-choice test consisting in 34 items aimed at investigating students’ understanding of derivatives, integrals and vectors and their application in the context of introductory classical mechanics. The items were constructed using multiple representational formats and isomorphic items in mathematics, and in physics, in order to explore students’ representational fluency and their ability to transfer knowledge and skills from mathematics to physics. The test has been administered to 1252 students enrolled in introductory courses at the University of Padova in Spring 2018. The results indicate that the test is a valid and reliable instrument and it provides interesting insight into students’ difficulties in the use of mathematical concepts and methods in physics.

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References

  • Barniol P, Zavala G (2014) Test of understanding of vectors: A reliable multiple-choice vector concept test. Phys Rev ST Phys Educ Res 10:010121

    Article  Google Scholar 

  • Beichner RJ (1994) Testing student interpretation of kinematics graphs. Am J Phys 62(8):750–762

    Article  ADS  Google Scholar 

  • Bing TJ, Redish EF (2009) Analyzing problem solving using math in physics: epistemological framing via warrants. Phys Rev Spec Top Phys Educ Res 5(2):020108

    Article  ADS  Google Scholar 

  • Bollen L, De Cock M, Zuza K, Guisasola J, van Kampen P (2016) Generalizing a categorization of students’ interpretations of linear kinematics graphs. Phys Rev Phys Educ Res 12:010108

    Article  Google Scholar 

  • Britton S, New PB, Sharma MD, Yardley D (2005) A case study of the transfer of mathematics skills by university students. Int J Math Educ Sci Technol 36(1):1–13

    Article  Google Scholar 

  • Christensen WM, Thompson JR (2012) Investigating graphical representations of slope and derivative without a physics context. Phys Rev ST Phys Educ Res 8(2):023101

    Article  Google Scholar 

  • De Cock M (2012) Representation use and strategy choice in physics problem solving. Phys Rev ST Phys Educ Res 8:020117

    Article  Google Scholar 

  • Dominguez A, Barniol P, Zavala G (2017) Test of understanding graphs in calculus: test of students’ interpretation of calculus graphs. Eurasia J Math Sci Technol Educ 13:6507–6531

    Google Scholar 

  • Epstein J (2007) Development and validation of the calculus concept inventory. Paper presented at the ninth international conference on mathematics education in a global community. Charlotte, NC

    Google Scholar 

  • Epstein J (2013) The calculus concept inventory—measurement of the effect of teaching methodology in mathematics. Not Am Math Soc 60(8):1018–1026

    Article  Google Scholar 

  • Etkina E, Van Heuvelen A, White-Brahmia S, Brookes DT, Gentile M, Murthy S, Rosengrant D, Warren A (2006) Scientific abilities and their assessment. Phys Rev ST Phys Educ Res 2:020103

    Article  Google Scholar 

  • Flores S, Kanim SE, Kautz CH (2004) Student use of vectors in introductory mechanics. Am J Phys 72(4):460–468

    Article  ADS  Google Scholar 

  • Ivanjek L, Susac A, Planinic M, Andrasevic A, Milin-Sipus Z (2016) Student reasoning about graphs in different contexts. Phys Rev Phys Educ Res 12:010106

    Article  Google Scholar 

  • Klein P, Müller A, Kuhn J (2017) Assessment of representational competence in kinematics. Phys Rev Phys Educ Res 13:010132

    Article  Google Scholar 

  • Knight RD (1995) The vector knowledge of beginning physics students. Phys Teach 33(2):74–77

    Article  ADS  Google Scholar 

  • Kohl PB, Finkelstein ND (2005) Student representational competence and self-assessment when solving physics problems. Phys Rev ST Phys Educ Res 1:010104

    Article  Google Scholar 

  • McDermott LC, Rosenquist ML, van Zee EH (1987) Student difficulties in connecting graphs and physics: examples from kinematics. Am J Phys 55:503–513

    Article  ADS  Google Scholar 

  • Meltzer D (2005) Relation between students’ problem-solving performance and representational format. Am J Phys 73(5):463–478

    Article  ADS  Google Scholar 

  • Nguyen N, Meltzer DE (2003) Initial understanding of vector concepts among students in introductory physics course. Am J Phys 71(6):630–638

    Article  ADS  Google Scholar 

  • Nguyen D-H, Rebello NS (2011) Students’ understanding and application of the area under the curve concept in physics problems. Phys Rev ST Phys Educ Res 7:010112

    Article  Google Scholar 

  • Nieminen P, Savinainen A, Viiri J (2010) Force concept Inventory-based multiple-choice test for investigating students’ representational consistency. Phys Rev ST Phys Educ Res 6:020109

    Article  Google Scholar 

  • Pantano O, Cornet F (eds) (2018) Tuning guidelines and reference points for the design and delivery of degree programmes in physics. University of Groningen. Published in the framework of the CALOHEE Project 2016–2018 (Agreement number: 562148-EPP-1-2015-1-NL-EPPKA3-PIFORWARD) funded with support from the European Commission, https://www.calohee.eu

  • Planinic M, Milin-Sipus Z, Katic H, Susac A, Ivanjek L (2012) Comparison of student understanding of line graph slope in physics and mathematics. Int J Sci Math Educ 10:1393–1414

    Article  Google Scholar 

  • Planinic M, Ivanjek L, Susac A, Milin-Sipus Z (2013) Comparison of university students’ understanding of graphs in different contexts. Phys Rev ST Phys Educ Res 9:020103

    Article  Google Scholar 

  • Redish EF (2003) Teaching physics with the physics suite. Wiley Inc., Somerset

    Google Scholar 

  • Redish E (2005) Problem solving and the use of math in physics courses. Paper presented at world view on physics education of focusing on change, Delhi, pp 1–10

    Google Scholar 

  • Redish EF, Kuo E (2015) Language of physics, language of math: disciplinary culture and dynamic epistemology. Sci Educ 24:561–590

    Article  Google Scholar 

  • Roberts AL, Sharma MD, Britton S, New PB (2007) An index to measure the ability of first year science students to transfer mathematics. Int J Math Educ Sci Technol 38(4):429–448

    Article  Google Scholar 

  • Shaffer PS, McDermott LC (2005) A research-based approach to improving student understanding of the vector nature of kinematical concepts. Am J Phys 73(10):921–931

    Article  ADS  Google Scholar 

  • Van Deventer J (2008) Comparing student performance on isomorphic math and physics vector representations. Electronic Theses and Dissertations 1348

    Google Scholar 

  • Van Deventer J, Wittmann M (2007) Comparing student use of mathematical and physical vector representations. Paper presented at the physics education research conference, Greensboro, NC, vol 951, pp 208–211

    Google Scholar 

  • Van Heuvelen A (1991) Learning to think like a physicist: a review of research-based instructional strategies. Am J Phys 59(10):891–897

    Article  ADS  Google Scholar 

  • Wemyss T, van Kampen P (2013) Categorization of first-year university students’ interpretations of numerical linear distance-time graphs. Phys Rev ST Phys Educ Res 9:010107

    Article  Google Scholar 

  • Zavala G, Tejeda S, Barniol P, Beichner RJ (2017) Modifying the test of understanding graphs in kinematics. Phys Rev Phys Educ Res 13:020111

    Article  Google Scholar 

Download references

Acknowledgements

This work is part of the FisicaMente project, jointly funded by the University of Padova and the PLS—Piano Lauree Scientifiche (Scientific Degrees Plan) of the Italian Ministry of Education, University and Research (MIUR). We acknowledge the School of Science and the School of Engineering of the University of Padova for both financial and motivational support. We also thank all the students and instructors who volunteered to take or administer the test, and all the colleagues who provided helpful comments. A special thanks goes to Dott. Francesca Zanandrea for her help with data processing.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Padova, Via Marzolo 8, 35131, Padua, Italy

    Marta Carli, Ornella Pantano & Giuseppe Tormen

  2. Liceo Scientifico ‘J. Da Ponte’, Via S. Tommaso d’Aquino 12, 36061, Bassano del Grappa (VI), Italy

    Stefania Lippiello

  3. IIS ‘C. Marchesi’, Viale Codalunga 1, 35138, Padua, Italy

    Mario Perona

Authors
  1. Marta Carli
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  2. Stefania Lippiello
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  3. Ornella Pantano
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  4. Mario Perona
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  5. Giuseppe Tormen
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Correspondence to Marta Carli .

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Editors and Affiliations

  1. Donostia Physics Education Research Group (DoPER), Department of Physics Applied, Gipuzkoa School of Engineering, University of the Basque Country (UPV/EHU), Donostia-San Sebastian, Spain

    Jenaro Guisasola

  2. Donostia Physics Education Research Group (DoPER), Department of Physics Applied, Gipuzkoa School of Engineering, University of the Basque Country (UPV/EHU), Donostia-San Sebastian, Spain

    Kristina Zuza

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Carli, M., Lippiello, S., Pantano, O., Perona, M., Tormen, G. (2020). Derivatives, Integrals and Vectors in Introductory Mechanics: The Development of a Multi-representation Test for University Students. In: Guisasola, J., Zuza, K. (eds) Research and Innovation in Physics Education: Two Sides of the Same Coin. Challenges in Physics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-51182-1_13

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  • DOI: https://doi.org/10.1007/978-3-030-51182-1_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-51181-4

  • Online ISBN: 978-3-030-51182-1

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