Undergraduate Students’ Quantitative Reasoning in Economic Contexts

References

• Ärlebäck, J. B., Doerr, H. M., & O’Neil, A. H. (2013). A modeling perspective on interpreting rates of change in context. Mathematical Thinking and Learning, 15(4), 314–336. doi:10.1080/10986065.2013.834405
   Web of Science ®Google Scholar
• Beichner, R. (1994). Testing student interpretation of kinematics graphs. American Journal of Physics, 62(8), 750–755. doi:10.1119/1.17449
   Web of Science ®Google Scholar
• Bingolbali, E., & Monaghan, J. (2008). Concept image revisited. Educational Studies in Mathematics, 68(1), 19–35. doi:10.1007/s10649-007-9112-2
   Google Scholar
• Borasi, R. (1986). On the nature of problems. Educational Studies in Mathematics, 17(2), 125–141. doi:10.1007/BF00311517
   Google Scholar
• Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352–378. doi:10.2307/4149958
   Web of Science ®Google Scholar
• Carlson, M. P. (1998). A cross-sectional investigation of the development of the function concept. CBMS Issues in Mathematics Education, 7, 114–162.
   Google Scholar
• Davis, J. D. (2007). Real-world contexts, multiple representations, student-invented terminology, and y-intercept. Mathematical Thinking and Learning, 9(4), 387–418. doi:10.1080/10986060701533839
   Google Scholar
• Ellis, A. B., Ozgur, Z., Kulow, T., Dogan, M. F., & Amidon, J. (2016). An exponential growth learning trajectory: Students’ emerging understanding of exponential growth through covariation. Mathematical Thinking and Learning, 18(3), 151–181. doi:10.1080/10986065.2016.1183090
   Web of Science ®Google Scholar
• Freudenthal, H. (1993). Thoughts in teaching mechanics didactical phenomenology of the concept of force. Educational Studies in Mathematics, 25(1), 71–87. doi:10.1007/BF01274103
   Google Scholar
• Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517–545). Mahwah, NJ: Laurence Erlbaum Associates.
   Google Scholar
• Gordon, S. P. (2008). What’s wrong with college algebra? Problems, Resources, and Issues in Mathematics Undergraduate Studies, 18(6), 516–541.
   Google Scholar
• Haeussler, E. F., Paul, R. S., & Wood, R. J. (2011). Introductory mathematical analysis for business, economics, and the life and social sciences (13th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.
   Google Scholar
• Hughes-Hallett, D., Lock, P. F., Gleason, A. M., Flath, D. E., Lovelock, D., Quinney, D., & Osgood, B. G. (2002). Applied calculus (2nd ed.). Hoboken, NJ: Wiley.
   Google Scholar
• Ibrahim, B., & Rebello, N. S. (2012). Representational task formats and problem solving strategies in kinematics and work. Physical Review Special Topics-Physics Education Research, 8(1), 010126 (1–19). doi:10.1103/PhysRevSTPER.8.010126
   Google Scholar
• Johnson, H. L. (2012b). Reasoning about variation in the intensity of change in covarying quantities involved in rate of change. The Journal of Mathematical Behavior, 31(3), 313–330. doi:10.1016/j.jmathb.2012.01.001
   Google Scholar
• Johnson, H. L. (2015). Secondary students’ quantification of ratio and rate: A framework for reasoning about change in covarying quantities. Mathematical Thinking and Learning, 17(1), 64–90. doi:10.1080/10986065.2015.981946
   Web of Science ®Google Scholar
• Lobato, J., Hohensee, C., Rhodehamel, B., & Diamond, J. (2012). Using student reasoning to inform the development of conceptual learning goals: The case of quadratic functions. Mathematical Thinking and Learning, 14(2), 85–119. doi:10.1080/10986065.2012.656362
   Web of Science ®Google Scholar
• Lobato, J., & Siebert, D. (2002). Quantitative reasoning in a reconceived view of transfer. The Journal of Mathematical Behavior, 21(1), 87–116. doi:10.1016/S0732-3123(02)00105-0
   Google Scholar
• Michelsen, C. (2006). Functions: A modelling tool in mathematics and science. Zentralblatt Für Didaktik Der Mathematik, 38(3), 269–280. doi:10.1007/BF02652810
   Google Scholar
• Mkhatshwa, T. P. (2016). Business calculus students’ reasoning about optimization problems: A study of quantitative reasoning in an economic context ( Doctoral dissertation). New York, NY: Syracuse University.
   Google Scholar
• Monk, S. (1992). Students’ understanding of a function given by a physical model. In G. Harel, & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA Notes (Vol. 25, pp. 175–193). Washington, DC: Mathematical Association of America.
   Google Scholar
• Monk, S., & Nemirovsky, R. (1994). The case of Dan: Student construction of a functional situation through visual attributes. CBMS Issues in Mathematics Education, 4, 139–168.
   Google Scholar
• Moore, K. C. (2014). Quantitative reasoning and the sine function: The case of Zac. Journal for Research in Mathematics Education, 45(1), 102–138. doi:10.5951/jresematheduc.45.1.0102
   Web of Science ®Google Scholar
• Moore, K. C., & Carlson, M. P. (2012). Students’ images of problem contexts when solving applied problems. The Journal of Mathematical Behavior, 31(1), 48–59. doi:10.1016/j.jmathb.2011.09.001
   Google Scholar
• Oehrtman, M. C., Carlson, M. P., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ understandings of function. In M. P. Carlson, & C. Rasmussen (Eds.), Making the connection: Research and practice in undergraduate mathematics (pp. 27–42). Washington, DC: Mathematical Association of America.
   Google Scholar
• Prince, M., Vigeant, M., & Nottis, K. (2012). Development of the heat and energy concept inventory: Preliminary results on the prevalence and persistence of engineering students’ misconceptions. Journal of Engineering Education, 101(3), 412–438. doi:10.1002/j.2168-9830.2012.tb00056.x
   Web of Science ®Google Scholar
• Rasmussen, C. L., & King, K. D. (2000). Locating starting points in differential equations: A realistic mathematics education approach. International Journal of Mathematical Education in Science and Technology, 31(2), 161–172. doi:10.1080/002073900287219
   Google Scholar
• Rasmussen, C., & Marrongelle, K. (2006). Pedagogical content tools: Integrating student reasoning and mathematics in instruction. Journal for Research in Mathematics Education, 37, 388–420.
   Web of Science ®Google Scholar
• Thompson, P. W. (1990). A theoretical model of quantity-based reasoning in arithmetic and algebraic Unpublished manuscript.Center for Research in Mathematics & Science Education, San Diego State University, San Diego, USA.
   Google Scholar
• Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25(3), 165–208. doi:10.1007/BF01273861
   Google Scholar
• Thompson, P. W. (1994b). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(2), 229–274. doi:10.1007/BF01273664
   Google Scholar
• Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education WISDOMe Mongraphs (Vol. 1, pp. 33–57). Laramie, WY: University of Wyoming.
   Google Scholar
• van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–9.
   Google Scholar
• White, P., & Mitchelmore, M. (1996). Conceptual knowledge in introductory calculus. Journal for Research in Mathematics Education, 27, 79–95. doi:10.2307/749199
   Web of Science ®Google Scholar
• Wilhelm, J. A., & Confrey, J. (2003). Projecting rate of change in the context of motion onto the context of money. International Journal of Mathematical Education in Science and Technology, 34(6), 887–904. doi:10.1080/00207390310001606660
   Google Scholar
• Yoon, C., Dreyfus, T., & Thomas, M. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, 22(2), 141–157. doi:10.1007/BF03217571
   Google Scholar
• Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. CBMS Issues in Mathematics Education, 8, 103–127.
   Google Scholar