Interpreting Derivatives

REFERENCES

• Asiala, M., J. Cottrill, E. Dubinsky, and K. E. Schwingendorf. 1997. The development of students’ graphical understanding of the derivative. Journal of Mathematical Behavior. 16: 399–431.
   Google Scholar
• Berry, J. S. and M. A. Nyman. 2003. Promoting students’ graphical understanding of the calculus. Journal of Mathematical Behavior. 22: 481–497.
   Google Scholar
• The Vector Calculus Bridge Project. 2001-2019. http://math.oregonstate.edu/bridge. Accessed 11 May 2019.
   Google Scholar
• Bucy, B. R., J. R. Thompson, and D. B. Mountcastle. 2007. Student (mis)application of partial differentiation to material properties. AIP Conference Proceedings. 883: 157–160.
   Google Scholar
• Christensen, W. M. and J. R. Thompson. 2012. Investigating graphical representations of slope and derivative without a physics context. Physics Review: Physics Education Research. 8: 023021.
   Google Scholar
• Dray, T. 2013. Using differentials to determine the derivatives of trigonometric and exponential functions. College Mathematics Journal. 44: 17–23.
   Google Scholar
• Dray, T. May 2016. Thick derivatives. AMS Blog: On teaching and learning mathematics. http://blogs.ams.org/matheducation/2016/05/31/thick-derivatives. Accessed 11 May 2019.
   Google Scholar
• Dray, T., B. Edwards, and C. A. Manogue. 2008. Bridging the gap between mathematics and physics. In M. Santos and Y. Shimizu (Eds), Proceedings of the 11th International Congress on Mathematics Education, ICME, Monterry, Mexico.
   Google Scholar
• Dray, T. and C. A. Manogue. 1999. The vector calculus gap: Mathematics ≠ physics. PRIMUS. 9: 21–28.
   Google Scholar
• Dray, T. and C. A. Manogue. 2003. Using differentials to bridge the vector calculus gap. College Mathematics Journal. 34: 283–290.
   Google Scholar
• Dray, T. and C. A. Manogue. 2004. Bridging the gap between mathematics and physics. APS Forum on Education. Spring: 13–14.
   Google Scholar
• Dray, T. and C. A. Manogue. 2005. Bridging the gap between mathematics and the physical sciences. In D. Smith and E. Swanson (Eds), Preparing Future Science and Mathematics Teachers, pp. 39–41. Bozeman, MT: Montana State University.
   Google Scholar
• Dray, T. and C. A. Manogue. 2006. The geometry of the dot and cross products. JOMA. https://www.aps.org/units/fed/newsletters/spring2004/10oregonstate.html. Accessed 11 May 2019.
   Google Scholar
• Dray, T. and C. A. Manogue. 2009–2016. The geometry of vector calculus. http://math.oregonstate.edu/BridgeBook. Accessed 11 May 2019.
   Google Scholar
• Dray, T. and C. A. Manogue. 2010. Putting differentials back into calculus. College Mathematics Journal. 41: 90–100.
   Google Scholar
• Emigh, P. J. and C. A. Manogue. 2017. Student interpretations of partial derivatives. In L. Ding, A. Traxler and Y. Cao (Eds), Proceedings of the 2017 Physics Education Research Conference. https://www.compadre.org/per/items/4761.pdf.
   Google Scholar
• Ganter, S. and W. Barker. 2004. Curriculum foundations project: Voices of the partner disciplines. http://www.maa.org/the-curriculum-foundation-project-0. Accessed 11 May 2019.
   Google Scholar
• Habre, S. and M. Abboud. 2006. Students’ conceptual understanding of a function and its derivative in an experimental calculus course. Journal of Mathematical Behavior. 25: 57–72.
   Google Scholar
• Hughes-Hallett, D., A. M. Gleason, W. G. McCallum, D. E. Flath, D. O. Lomen, D. Lovelock, J. Tecosky-Feldman, T. W. Tucker, J. Thrash, K. R. Rhea, A. Pasquale, S. P. Gordon, D. Quinney, and P. Frazer Lock. 1998. Calculus: Single Variable, 2nd edition. Hoboken, NJ: Wiley.
   Google Scholar
• Jones, S .R. 2016. Ways of understanding and ways of thinking in using the derivative concept in applied (non-kinematic) contexts. In T. Fukawa-Connelly, N. E. Infante, M. Wawro, and S. Brown (Eds), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education, pp. 917–924. Washington, DC: MAA.
   Google Scholar
• Kustusch, M. B., D. Roundy, T. Dray, and C. Manogue. 2012. An expert path through a thermo maze. AIP Conference Proceedings. 1513: 234–237.
   Google Scholar
• Kustusch, M. B., D. Roundy, T. Dray, and C. A. Manogue. 2014. Partial derivative games in thermodynamics: A cognitive task analysis. Physics Review: Physics Education Research. 10: 010101. http://journals.aps.org/prstper/abstract/10.1103/PhysRevSTPER.10.010101. Accessed 11 May 2019.
   Google Scholar
• Likwambe, B. and I. M. Christiansen. 2008. A case study of the development of in-service teachers’ concept images of the derivative. Pythagoras. 68: 22–31.
   Google Scholar
• Lithner, J. 2003. Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics. 52(1): 29–55.
   Google Scholar
• Manogue, C. and T. Dray. 2002. Functions. http://math.oregonstate.edu/bridge/ideas/functions. Accessed 11 May 2019.
   Google Scholar
• Manogue, C. A. and K. S. Krane. 2003. The Oregon State University Paradigms Project: Re-envisioning the upper level. Physics Today. 56: 53–58.
   Google Scholar
• Manogue, C. A., P. J. Siemens, J. Tate, K. Browne, M. L. Niess, and A. J. Wolfer. 2001. Paradigms in physics: A new upper-division curriculum. American Journal of Physics. 69: 978–990.
   Web of Science ®Google Scholar
• Marrongelle, K. A. 2004. How students use physics to reason about calculus tasks. School Science and Mathematics. 104: 258–272.
   Google Scholar
• McCallum, W. G., D. Hughes-Hallett, D. E. Flath, B. G. Osgood, A. M. Gleason, D. Quinney, P. Frazer Lock, J. Tecosky-Feldman, D. Mumford, T. W. Tucker, S. P. Gordon, A. Iovita, W. Raskind, and and J. B. Thrash. 2005. Calculus: Multivariable, 4th edition.. Hoboken, NJ: Wiley.
   Google Scholar
• Musgrave, S. and P. W. Thompson. 2014. Function notation as an idiom. In P. Liljedahl, S. Oesterle, C. Nicol, and D. Allan (Eds), Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education, volume 4, pp. 281–288. Vancouver, BC: PME.
   Google Scholar
• Orton, A. 1983. Students’ understanding of differentiation. Educational Studies in Mathematics, 14: 235–250.
   Google Scholar
• Planinic, M., Z. Milin-Sipus, H. Katic, A. Susac, and L. Ivanjek. 2012. Comparison of student understanding of line graph slope in physics and mathematics. International Journal of Science and Mathematics Education. 10: 1393–1414.
   Web of Science ®Google Scholar
• Portfolios Wiki. 2007-2019. http://physics.oregonstate.edu/portfolioswiki.
   Google Scholar
• Redish, E. and E. Kuo. 2015. Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education. 24: 561–590.
   Web of Science ®Google Scholar
• Roundy, D., T. Dray, C. A. Manogue, J. F. Wagner, and E. Weber. 2015. An extended theoretical framework for the concept of derivative. In T. Fukawa-Connelly, N. E. Infante, K. Keene, and M. Zandieh (Eds), Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education, 838–843. Washington, DC: MAA.
   Google Scholar
• Roundy, D., M. B. Kustusch, and C. Manogue. 2014. Name the experiment! Interpreting thermodynamic derivatives as thought experiments. American Journal of Physics. 82(1): 39–46.
   Web of Science ®Google Scholar
• Roundy, D., E. Weber, T. Dray, R. R. Bajaracharya, A. Dorko, E. M. Smith, and C. A. Manogue. 2015. Experts’ understanding of partial derivatives using the partial derivative machine. Physics Review: Physics Education Research. 11: 020126.
   Web of Science ®Google Scholar
• Sfard, A. 1991. On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics. 22(1): 1–36.
   Google Scholar
• Skemp, R. R. 1976. Relational understanding and instrumental understanding. Mathematics Teaching. 77: 20–26.
   Google Scholar
• Styer, D. F. 1999. A thermodynamic derivative means an experiment. American Journal of Physics. 67(12): 1094–1095.
   Web of Science ®Google Scholar
• Thompson, J. R., B. R. Bucy, and D. B. Mountcastle. 2006. Assessing student understanding of partial derivatives in thermodynamics. AIP Conference Proceedings. 818: 77–80.
   Google Scholar
• Thompson, P. W. 2013. In the absence of meaning. In K. Leatham (Ed.), Vital Directions for Research in Mathematics Education. New York, NY: Springer.
   Google Scholar
• Thompson, P. W. and M. Ashbrook. 2016. Calculus: Newton meets technology. http://patthompson.net/ThompsonCalc. Accessed 11 May 2019.
   Google Scholar
• Thompson, P. W., C. Byerley, and N. Hatfield. 2013. A conceptual approach to calculus made possible by technology. Computers in the Schools. 30: 124–147.
   Google Scholar
• Thompson, P. W. and T. Dreyfus. 2016. A coherent approach to the Fundamental Theorem of Calculus using differentials. In R. Göller, R. Biehler, and R. Hochsmith (Eds), Proceedings of the Conference on Didactics of Mathematics in Higher Education in Scientific Disciplines, pp. 355–359. Hannover, Germany: KHDM.
   Google Scholar
• Tucker, T. W. (Ed.). 1990 Priming the Calculus Pump: Innovations and Resources, Washington, DC: MAA.
   Google Scholar
• Van Zee, E, and C. Manogue. 2018. A study of the development of the Paradigms in Physics Program. http://physics.oregonstate.edu/mathbook/P20/. Accessed 11 May 2019.
   Google Scholar
• Vinner, S. 1983. Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology. 14: 293–305.
   Google Scholar
• Wangberg, A. 2012. Raising students’ calculus understandings to the surface in multivariable calculus. In S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman (Eds), Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education, volume 2, pp. 590–594. Washington, DC: MAA.
   Google Scholar
• Wangberg, A. 2013–2019. Raising Calculus to the Surface. http://raisingcalculus.winona.edu. Accessed 11 May 2019.
   Google Scholar
• Wangberg, A. and B. Johnson. 2013. Discovering calculus on the surface. PRIMUS. 23: 627–639.
   Google Scholar
• Zandieh, M. 2000. A theoretical framework for analyzing student understanding of the concept of derivative. CBMS Issues in Mathematics Education, 8: 103–122.
   Google Scholar