Echoes of the Instructor’s Reasoning: Exemplars of Modeling for Homework

REFERENCES

• Atkinson, R. K., S. J. Derry, A. Renkl, and D. Wortham. 2000. Learning from examples: Instructional principles from the worked examples research. Review of Educational Research. 70(2): 181–214.
   Web of Science ®Google Scholar
• Baker, G. 2016. Differential Equations as Models in Science and Engineering. Singapore: B & Jo Enterprise Pte Ltd.
   Google Scholar
• Bliss, K., K. Fowler, B. Galluzzo, S. Garfunkel, F. Giordano, L. Godbold, … and R. Zbiek. 2016. Guidelines for Assessment & Instruction in Mathematical Modeling Education. Philadelphia, PA: Society for Industrial and Applied Mathematics.
   Google Scholar
• Blomhöj, M. and T. H. Jensen. 2003. Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications. 22(3): 123–140.
   Google Scholar
• Braun, V, and V. Clarke. 2006. Using thematic analysis in psychology. Qualitative Research in Psychology. 3: 77–101.
   Google Scholar
• Camacho, M., J. Perdomo, and M. Santos-Trigo. 2008. Revisiting university students knowledge that involves basic differential equation questions. NAP: Journal of Research in Teaching of Mathematics. 3(3): 123–133.
   Google Scholar
• Cyril, J. and V. Mudaly. 2007. Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. L. Galbraith, H.-W. Henn, and M. Niss (Eds), Modelling and Applicatins in Mathematics Education: The 14 ICMI Study, pp. 503–510. New York, NY: Springer.
   Google Scholar
• Czocher, J. A. 2017. How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course? Journal of Mathematical Behavior. 45: 78–94.
   Web of Science ®Google Scholar
• Czocher, J. A. and G. Baker. 2011. Contextual learning in math education for engineers. In W. Aung, V. Ilic, J. Moscinski, and J. Uhomoibhi (Eds), World Innovations in Engineering Education and Research, pp. 309–326. Potomac, MD: iNEER.
   Google Scholar
• Czocher, J. A., J. Tague, and G. Baker. 2013. Where does the calculus go? An investigation of how calculus ideas are used in later coursework. The International Journal of Mathematical Education in Science and Technology. 44(5): .
   Google Scholar
• Czocher, J. A., J. Tague, G. Baker, and A. Roble. 2013. Successful collaboration among engineering, education, and mathematics. In American Society for Engineering Education, North Central Chapter.
   Google Scholar
• Freudenthal, H. 1968. Why to teach mathematics so as to be useful. Educational Studies in Mathematics. 1(1–2): 3–8.
   Google Scholar
• Hammons, J. L.and A. White. 2014. The effects of smart pen narrated solution sets on student study routines and their perceptions of the solution sets as a help resource. Doctoral Dissertation. Texas State University.
   Google Scholar
• Lesh, R. and J. Zawojewski. 2007. Problem solving and modeling. In F. K. Lester Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning, pp. 763–804. Charlotte, NC: Information Age Publishing Inc.
   Google Scholar
• Orange, A., W. Heinecke, E. Berger, C. Krousgrill, B. Mikic, and D. Quinn. 2012. Technologies in undergraduate mechanical engineering courses. Advances in Engineering Education. 3: 1–29.
   Google Scholar
• Raman, M. 2004. Epistemological messages conveyed by three high-school and college mathematics textbooks. The Journal of Mathematical Behavior. 23(4): 389–404.
   Google Scholar
• Rasmussen, C. and O. N. Kwon. 2007. An inquiry-oriented approach to undergraduate mathematics. Journal of Mathematical Behavior. 26: 189–194.
   Google Scholar
• Redish, E. F. and K. A. Smith. 2008. Looking beyond content: Skill development for engineers. Journal of Engineering Education. 97(3): 295–307.
   Web of Science ®Google Scholar
• Renkl, A., R. K. Atkinson, and C. S. Groß. 2004. How fading worked solution steps works - A cognitive load perspective. Instructional Science. 32(1/2): 59–82.
   Web of Science ®Google Scholar
• Rowland, D. R. 2006. Student difficulties with units in differential equations in modelling contexts. International Journal of Mathematical Education in Science and Technology. 37(5): 553–558.
   Google Scholar
• Rowland, D. R. and Z. Jovanoski. 2004. Student interpretations of the terms in first-order ordinary differential equations in modelling contexts. International Journal of Mathematics Education in Science and Technology. 35(4): 503–516.
   Google Scholar
• Schukajlow, S., J. Kolter, and W. Blum. 2015. Scaffolding mathematical modelling with a solution plan. ZDM - Mathematics Education. 47(7): 1241–1254.
   Google Scholar
• SIMIODE. 2017. Starter kit. https://www.simiode.org/starterkit. Accessed 27 October 2017.
   Google Scholar
• Star, J. R. 2005. Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education. 36(5): 404–411.
   Web of Science ®Google Scholar
• Tague, J. and J. A. Czocher. 2016. A theoretical approach to ensuring instructional and curricular coherence in the flipped classroom model of a differential equations course. International Journal for Research in Undergraduate Mathematics Education. 2(2): 223–245.
   Google Scholar
• Tague, J., J. A. Czocher, G. Baker, K. Harper, D. Grzybowski, and R. Freuler. 2013. Choosing and adapting technology in a mathematics course for engineers. In Proceedings of the 120th Annual Meeting of the American Society of Engineering Education. https://www.asee.org/public/conferences/20/papers/7445/view. Accessed 14 December 2018.
   Google Scholar
• Tague, J., J. A. Czocher, G. Baker, K. Harper, D. Grzybowski, and R. Freuler. 2013. Engineering faculty perspectives on mathematical preparation of students. In Proceedings of the International Conference on Engineering Education.
   Google Scholar
• Weinberg, A. and E. Wiesner. 2011. Understanding mathematics textbooks through reader-oriented theory. Educational Studies in Mathematics. 76(1): 49–63.
   Web of Science ®Google Scholar
• Zbiek, R. M. and A. Conner. 2006. Beyond motivation: Exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics. Educational Studies in Mathematics. 63(1): 89–112.
   Google Scholar
• Zhu, X. and H. A. Simon. 1987. Learning mathematics from examples and by doing. Cognition and Instruction. 4(3): 137–166.
   Google Scholar