Multivariation and students’ multivariational reasoning
Tài liệu tham khảo
Arzarello, 2019, La covariación instrumentada: Un fenómeno de mediación semiótica y epistemológica, Cuadernos de Investigación y Formación en Educación Matemática, 14, 11
Ayers, 1988, Computer experiences in learning composition of functions, Journal for Research in Mathematics Education, 19, 246, 10.5951/jresematheduc.19.3.0246
Bakhtin, 1986, The problem of speech genres (V. W. McGee, Trans.), 60
Boudreaux, 2008, Student understanding of control of variables: Deciding whether or not a variable influences the behavior of a system, American Journal of Physics, 76, 163, 10.1119/1.2805235
Breidenbach, 1992, Development of the process conception of function, Educational Studies in Mathematics, 23, 247, 10.1007/BF02309532
Bucy, 2007, Student (mis)application of partial differentiation to material properties
Byerley, C., Boyce, S., Grabhorn, J., & Tyburski, B. (2019). Investigating STEM students' measurement schemes with a units coordination lens. In Proceedings of the 22nd annual conference on research in undergraduate mathematics education. SIGMAA on RUME.
Campbell, 2013, Coding in-depth semistructured interviews: Problems of unitization and intercoder reliability and agreement, Sociological Methods & Research, 42, 294, 10.1177/0049124113500475
Carlson, 2002, Applying covariational reasoning while modeling dynamic events: A framework and a study, Journal for Research in Mathematics Education, 33, 352, 10.2307/4149958
Carlson, M. P., Larsen, S., & Jacobs, S. (2001). An investigation of covariational reasoning and its role in learning the concept of limit and accumulation. In R. Speiser, C. Maher, & C. Walter (Eds.), Proceedings of the 23rd annual meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 145–153). PME-NA.
Castillo-Garsow, 2012, Continuous quantitative reasoning, 2, 55
Castillo-Garsow, 2013, Chunky and smooth images of change, For the Learning of Mathematics, 33, 31
Clarke, 2009, Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction, Educational Studies in Mathematics, 72, 127, 10.1007/s10649-009-9198-9
Confrey, 1994, Exponential functions, rates of change, and the multiplicative unit, Educational Studies in Mathematics, 26, 135, 10.1007/BF01273661
Confrey, 1995, Splitting, covariation, and their role in the development of exponential functions, Journal for Research in Mathematics Education, 26, 66, 10.2307/749228
Crookes, 1990, The utterance, and other basic units for second language discourse analysis, Applied Linguistics, 11, 183, 10.1093/applin/11.2.183
de Villiers, 2004, Using dynamic geometry to expand mathematics teachers’ understanding of proof, International Journal of Mathematics Education in Science and Technology, 35, 703, 10.1080/0020739042000232556
Dorko, 2014, Generalising calculus ideas from two dimensions to three: How multivariate calculus students think about domain and range, Research in Mathematics Education, 16, 269, 10.1080/14794802.2014.919873
Ellis, 2011, Algebra in the middle school: Developing functional relationships through quantitative reasoning
Ellis, 2016, An exponential growth learning trajectory: Students’ emerging understanding of exponential growth through covariation, Mathematical Thinking and Learning, 18, 151, 10.1080/10986065.2016.1183090
Garrison, 2006, Revisiting methodological issues in transcript analysis: Negotiated coding and reliability, The Internet and Higher Education, 9, 1, 10.1016/j.iheduc.2005.11.001
Hibbeler, 2012
Hibbeler, 2012
Hughes-Hallett, 2021
Jeppson, 2020, A comprehensive hypothetical learning trajectory for the chain rule, implicit differentiation, and related rates: Part I, the development of the HLT, 690
Johnson, 2012, Reasoning about variation in the intensity of change in covarying quantities involved in rate of change, The Journal of Mathematical Behavior, 33, 313, 10.1016/j.jmathb.2012.01.001
Johnson, 2015, Together yet separate: Students’ associating amounts of change in quantities involved in rate of change, Educational Studies in Mathematics, 89, 89, 10.1007/s10649-014-9590-y
Johnson, 2017, Ferris wheels and filling bottles: A case of a student’s transfer of covariational reasoning across tasks with different backgrounds and features, ZDM–The International Journal on Mathematics Education, 49, 851, 10.1007/s11858-017-0866-4
Jones, 2015, Calculus limits involving infinity: The role of students’ informal dynamic reasoning, International Journal of Mathematics Education in Science and Technology, 46, 105, 10.1080/0020739X.2014.941427
Jones, 2018, Building on covariation: Making explicit four types of “multivariation”
Jones, 2019, Students’ application of concavity and inflection points to real-world contexts, International Journal of Science and Mathematics Education, 17, 523, 10.1007/s10763-017-9876-5
Jones, 2020, Scalar and vector line integrals: A conceptual analysis and an initial investigation of student understanding, Journal of Mathematical Behavior, 59, 10.1016/j.jmathb.2020.100801
Jones, 2015, Students’ understandings of multivariate integrals and how they may be generalized from single integral conceptions, The Journal of Mathematical Behavior, 40, 154, 10.1016/j.jmathb.2015.09.001
Jones, 2021, Examining students’ variational reasoning in differential equations, Journal of Mathematical Behavior, 64, 10.1016/j.jmathb.2021.100899
Kertil, 2020, Covariational reasoning of prospective mathematics teachers: How do dynamic animations affect?, Turkish Journal of Computer and Mathematics Education, 11, 312
Kuhn, 2007, Reasoning about multiple variables: Control of variables is not the only challenge, Science Education, 91, 710, 10.1002/sce.20214
Martinez-Planell, 2012, Students’ understanding of the general notion of a function of two variables, Educational Studies in Mathematics, 81, 365, 10.1007/s10649-012-9408-8
Martinez-Planell, 2014, On students’ understanding of partial derivatives and tangent planes, 6, 170
Martinez-Planell, 2020, Students’ understanding of Riemann sums for integrals of functions of two variables, Journal of Mathematical Behavior, 59
Moore, 2016, Graphing as figurative and operative thought, 3, 323
Moore, 2016, Putting the unit in pre-service secondary teachers’ unit circle, Educational Studies in Mathematics, 92, 221, 10.1007/s10649-015-9671-6
Moore, 2013, Covariational reasoning and invariance among coordinate systems, The Journal of Mathematical Behavior, 32, 461, 10.1016/j.jmathb.2013.05.002
Moore, 2014, Complexities in students’ construction of the polar coordinate system, The Journal of Mathematical Behavior, 36, 135, 10.1016/j.jmathb.2014.10.001
Moore, 2016, Graphing habits: “I just don’t like that”, 16
Moore, 2015, Shape thinking and students’ graphing activity
Oehrtman, 2008, Foundational reasoning abilities that promote coherence in students' understandings of function, 27
Panorkou, 2020, Examining students’ reasoning about multiple quantities, 291
Paoletti, 2017, The parametric nature of two students’ covariational reasoning, The Journal of Mathematical Behavior, 48, 137, 10.1016/j.jmathb.2017.08.003
Paoletti, 2018, A covariational understanding of function: Putting a horse before the cart, For the Learning of Mathematics, 38, 37
Rodriguez, 2019, Covariational reasoning and mathematical narratives: Investigating students’ understanding of graphs in chemical kinetics, Chemistry Education Research and Practice, 20, 107, 10.1039/C8RP00156A
Roundy, 2014, Name the experiment! Interpreting thermodynamic derivatives as thought experiments, American Journal of Physics, 82, 39, 10.1119/1.4824548
Roundy, 2015, Experts’ understanding of partial derivatives using the partial derivative machine, Physical Review Special Topics: Physics Education Research, 11
Saldanha, 1998, Re-thinking covariation from a quantitative perspective: Simultaneous continuous variation, 298
Serway, 2008
Smith, 1995, Semi-structured interviewing and qualitative analysis, 10
Stafylidou, 2004, The development of students’ understanding of the numerical value of fractions, Learning and Instruction, 14, 503, 10.1016/j.learninstruc.2004.06.015
Stevens, 2019, The role of multiplicative objects in a formula, 273
Stewart, 2016
Talmon, 2004, Understanding dynamic behavior: Parent-child relations in dynamic geometry environments, Educational Studies in Mathematics, 57, 91, 10.1023/B:EDUC.0000047052.57084.d8
Thompson, 1994, The development of the concept of speed and its relationship to concepts of rate, 179
Thompson, 1994, Images of rate and operational understanding of the fundamental theorem of Calculus, Educational Studies in Mathematics, 26, 229, 10.1007/BF01273664
Thompson, 1994, Students, functions, and the undergraduate curriculum, 21
Thompson, 2008, Conceptual analysis of mathematical ideas: Some spadework at the foundation of mathematics education, 1, 31
Thompson, 2011, Quantitative reasoning and mathematical modeling, 1, 33
Thompson, 2017, Variation, covariation, and functions: Foundational ways of thinking mathematically, 421
Thompson, 2008, The concept of accumulation in calculus, 43
Tipler, 2008
Trigueros, 2010, Geometrical representations in the learning of two-variable functions, Educational Studies in Mathematics, 73, 3, 10.1007/s10649-009-9201-5
Weber, 2014, Students’ images of two-variable functions and their graphs, Educational Studies in Mathematics, 87, 67, 10.1007/s10649-014-9548-0
Yerushalmy, 1997, Designing representations: Reasoning about functions of two variables, Journal for Research in Mathematics Education, 28, 431, 10.2307/749682