A progression of student symbolizing: soultions to systems of linear equations
Tipo de documento
Lista de autores
Smith, Jessica, Inyoung, Lee, Zandieh, Michelle y Andrews--Larson, Christine
Resumen
Systems of linear equations (SLE) comprise a fundamental concept in linear algebra, but there is relatively little research regarding the teaching and learning of SLE, especially students’ conceptions of solutions. It has been shown that solving systems with no or infinitely many solutions tends to be less intuitive for students, pointing to the need for more research on the teaching and learning of the topic. We interviewed two mathematics majors who were also preservice teachers in a paired teaching experiment to see how they reasoned about solutions to SLE in ℝ3. We present findings focused on the progression of students’ reasoning about solutions to SLE through the lens of symbolizing. We document their progression of reasoning as an accumulation of coordinated numeric, algebraic, and graphical meanings and symbolizations for solution sets.
Fecha
2022
Tipo de fecha
Estado publicación
Términos clave
Estrategias de solución | Inicial | Otro (razonamiento) | Reflexión sobre la enseñanza | Sistemas de ecuaciones
Enfoque
Nivel educativo
Educación media, bachillerato, secundaria superior (16 a 18 años) | Educación superior, formación de pregrado, formación de grado
Idioma
Revisado por pares
Formato del archivo
Volumen
21
Rango páginas (artículo)
45-64
ISSN
22544313
Referencias
Andrews-Larson, C. J., Siefken, J., & Simha, R. (2022). Report on a US-Canadian fac- ulty survey on undergraduate linear algebra: Could linear algebra be an alternate first collegiate math course? Notices of the American Mathematical Society. Freudenthal, H. (1973). What groups mean in mathematics and what they should mean in mathematical education. In A.G. Howson (Ed.), Developments in Mathe- matical Education: Proceedings of the Second International Congress on Mathemati- cal Education (pp. 101-114). Cambridge University Press. https://doi.org/10.1017/CBO9781139013536.006 Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic. Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155-177. https://doi.org/10.1207/s15327833mtl0102_4 Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111-129. https://doi.org/10.1023/A:1003749919816 Harel, G. (2017). The learning and teaching of linear algebra: Observations and gener- alizations. Journal of Mathematical Behavior, 46, 69-95. https://doi.org/10.1016/j.jmathb.2017.02.007 Huntley, M. A., Marcus, R., Kahan, J., & Miller, J. L. (2007). Investigating high-school students’ reasoning strategies when they solve linear equations. Journal of Mathematical Behavior, 26, 115-139. https://doi.org/10.1016/j.jmathb.2007.05.005 Larson, C., & Zandieh, M. (2013). Three interpretations of the matrix equation Ax= b. For the Learning of Mathematics, 33(2), 11-17. Oktaç, A. (2018). Conceptions about system of linear equations and solution. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges and strategies in teaching linear algebra (pp. 71–101). Springer. Possani, E., Trigueros, M., Preciado, J.G., & Lozano, M. D. (2010). Use of models in the teaching of linear algebra. Linear Algebra and its Applications, 432, 2125-2140. https://doi.org/10.1016/j.laa.2009.05.004 Rasmussen, C., & Marrongelle, K. (2006). Pedagogical content tools: Integrating stu- dent reasoning and mathematics in instruction. Journal for Research in Mathe- matics Education, 37(5), 388-420. Rasmussen, C., Wawro, M. & Zandieh, M. (2015). Examining individual and collective level mathematical progress. Education Studies in Mathematics, 88(2), 259-281. https://doi.org/10.1007/s10649-014-9583-x Rasmussen, C., Zandieh, M., King, K. & Teppo, A. (2005). Advancing mathematical ac- tivity: A practice-oriented view of advanced mathematical thinking. Mathemati- cal Thinking and Learning, 7, 51-73. https://doi.org/10.1207/s15327833mtl0701_4 Saldaña, J. (2021). The coding manual for qualitative researchers. Sage. Sandoval, I. & Possani, E. (2016). An analysis of different representations for vectors and planes in R3: Learning challenges. Educational Studies in Mathematics, 92, 109-127. https://doi.org/10.1007/s10649-015-9675-2 Smith, J., Lee, I., Zandieh, M., & Andrews-Larson, C. (2021). Two students’ concep- tions of solutions to a system of linear equations. In Proceedings of the 22nd An- nual Conference on Research in Undergraduate Mathematics Education. Smith, J., & Thompson, P. W. (2007). Quantitative reasoning and the development of algebraic reasoning. In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp. 95-132). Erlbaum Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underly- ing principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research de- sign in mathematics and science education (pp. 267-307). Erlbaum. Wawro, M., Zandieh, M., Rasmussen, C., & Andrews-Larson, C. (2013). Inquiry oriented linear algebra: Course materials. http://iola.math.vt.edu Zandieh, M. & Andrews-Larson, C. (2019). Symbolizing while solving linear systems. ZDM, 51, 1183-1197. https://doi.org/10.1007/s11858-019-01083-3 Zandieh, M., Wawro, M., & Rasmussen, C. (2017). An example of inquiry in linear alge- bra: The roles of symbolizing and brokering, PRIMUS, 27(1), 96-124, https://doi.org/10.1080/10511970.2016.1199618