Investigation of the effect of computer-supported instruction on students’ achievement on optimization problems

References

• Altıparmak, K. (2014). Impact of computer animations in cognitive learning: Differentiation. International Journal of Mathematical Education in Science and Technology, 45(8), 1146–1166. https://doi.org/10.1080/0020739X.2014.914256
   Google Scholar
• Arcavi, A. (2008). Modelling with graphical representations. For the Learning of Mathematics, 28(2), 2–10.
   Google Scholar
• Baker, B., Cooley, L., & Trigueros, M. (2000). A calculus graphing schema. Journal for Research in Mathematics Education, 31(5), 557–578. https://doi.org/10.2307/749887
   Google Scholar
• Berry, J. S., & Nyman, M. A. (2003). Promoting students’ graphical understanding of the calculus. The Journal of Mathematical Behavior, 22(4), 479–495. https://doi.org/10.1016/j.jmathb.2003.09.006
   Google Scholar
• Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning mathematical modelling (pp. 15–30). Springer.
   Google Scholar
• Büyüköztürk, Ş. (2009). Sosyal bilimler için veri analizi el kitabı [Handbook of data analysis in social sciences]. Pegem Akademi.
   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. https://doi.org/10.2307/4149958
   Web of Science ®Google Scholar
• Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45–75. https://doi.org/10.1007/s10649-005-0808-x
   Google Scholar
• Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159. https://doi.org/10.1037/0033-2909.112.1.155
   PubMed Web of Science ®Google Scholar
• Crouch, R., & Haines, C. (2004). Mathematical modelling: Transitions between the real world and the mathematical model. International Journal of Mathematical Education in Science and Technology, 35(2), 197–206. https://doi.org/10.1080/00207390310001638322
   Google Scholar
• Çekmez, E., & Baki, A. (2016). Examining students’ generalizations of the tangent concept: A theoretical perspective. PRIMUS, 26(5), 466–484. https://doi.org/10.1080/10511970.2015.1104765
   Google Scholar
• Dominguez, A. (2010). Single solution, multiple perspectives. In R. Lesh, C. R. Haines, P. L. Galbraith, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 223–233). Springer.
   Google Scholar
• Fuentealba, C., Sánchez-Matamoros, G., Badillo, E., & Trigueros, M. (2017). Thematization of derivative schema in university students: Nuances in constructing relations between a function's successive derivatives. International Journal of Mathematical Education in Science and Technology, 48(3), 374–392. https://doi.org/10.1080/0020739X.2016.1248508
   Web of Science ®Google Scholar
• Habre, S., & Abboud, M. (2006). Students’ conceptual understanding of a function and its derivative in an experimental calculus course. The Journal of Mathematical Behavior, 25(1), 57–72. https://doi.org/10.1016/j.jmathb.2005.11.004
   Google Scholar
• Haines, C. (2011). Drivers for mathematical modelling: Pragmatism in practice. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 349–365). Springer.
   Google Scholar
• Jukić, L., & Dahl, B. (2012). University students’ retention of derivative concepts 14 months after the course: Influence of ‘met-befores’ and ‘met-afters’. International Journal of Mathematical Education in Science and Technology, 43(6), 749–764. https://doi.org/10.1080/0020739X.2012.662300
   Google Scholar
• Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(2), 81–91. https://doi.org/10.1007/BF03217567
   Google Scholar
• Larsen, S., Marrongelle, K., Bressoud, D., & Graham, K. (2017). Understanding the concepts of calculus: Frameworks and roadmaps emerging from educational research. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 526–550). National Council of Teachers of Mathematics.
   Google Scholar
• LaRue, R. (2016). An analysis of student approaches to solving optimization problems in first semester calculus (Doctoral Dissertation). ProQuest Dissertations & Theses Global. (1830447913). https://search.proquest.com/docview/1830447913?accountid=7412.
   Google Scholar
• Mkhatshwa, T. P. (2019). Students’ quantitative reasoning about an absolute extrema optimization problem in a profit maximization context. International Journal of Mathematical Education in Science and Technology, 50(8), 1105–1127. https://doi.org/10.1080/0020739X.2018.1562116
   Web of Science ®Google Scholar
• Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 43–59). Springer.
   Google Scholar
• Pallant, J. (2001). SPSS survival manual. Open University Press.
   Google Scholar
• Park, J. (2013). Is the derivative a function? If so, how do students talk about it? International Journal of Mathematical Education in Science and Technology, 44(5), 624–640. https://doi.org/10.1080/0020739X.2013.795248
   Google Scholar
• Speer, N., & Kung, D. (2016). The complement of RUME: What’s missing from our research? Conference on research in undergraduate mathematics education. MAA.
   Google Scholar
• Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25(3), 165–208. https://doi.org/10.1007/BF01273861
   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 monographs, Vol. 1 (pp. 33–57). University of Wyoming.
   Google Scholar
• Ubuz, B., & Ersoy, Y. (1997). The effect of problem-solving method with handout material on achievement in solving max-min word problems. The Journal of Mathematical Behavior, 16(1), 75–85. https://doi.org/10.1016/S0732-3123(97)90009-2
   Google Scholar
• White, P., & Mitchelmore, M. (1996). Conceptual knowledge in introductory calculus. Journal for Research in Mathematics Education, 27(1), 79–95. https://doi.org/10.2307/749199
   Web of Science ®Google Scholar
• Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in collegiate mathematics education, IV, Vol. 8 (pp. 103–127). American Mathematical Society.
   Google Scholar
• Zeytun, A. S., Cetinkaya, B., & Erbas, A. K. (2010). Mathematics teachers’ covariational reasoning levels and predictions about students’ covariational reasoning abilities. Educational Sciences: Theory and Practice, 10(3), 1601–1612.
   Google Scholar