Supporting students with learning disabilities to explore linear relationships using online learning objects
DOI:
https://doi.org/10.30827/pna.v7i1.6132Palabras clave:
Comprensión algebraica, Dificultades de aprendizaje y matemáticas, Instrucción basada en ordenadoresResumen
The study of linear relationships is foundational for mathematics teaching and learning. However, students’ abilities to connect different representations of linear relationships have proven to be challenging. In response, a computer-based instructional sequence was designed to support students’ understanding of the connections among representations. In this paper we report on the affordances of this dynamic mode of representation specifically for students with learning disabilities. We outline four results identified by teachers as they implemented the online lessons.
Apoyo a estudiantes con problemas de aprendizaje para explorar relaciones lineales mediante el uso de objetos de aprendizaje en línea
El estudio de las relaciones lineales es fundamental en la enseñanza y el aprendizaje de las matemáticas. Sin embargo, las habilidades de los estudiantes para conectar distintas representaciones de las relaciones lineales han demostrado ser un reto. Ante esto, hemos diseñado una secuencia de enseñanza basada en ordenadores para fomentar en los estudiantes la comprensión de las conexiones entre estas representaciones.Presentamos las potencialidades de este tipo de representación dinámica para estudiantes con dificultades de aprendizaje, destacando cuatro resultados identificados por maestros al implementar las lecciones en línea.
Descargas
Citas
Anderson-Inman, L., Knox-Quinn, C., & Horney, M. A. (1996). Computer-based study strategies for students with learning disabilities: individual differences associated with adoption level. Journal of Learning Disabilities, 29(5), 461-484.
Bardini, C., & Stacey, K. (2006). Students' conceptions of m and c: How to tune a linear function. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 113-120). Prague, Czech Republic: Charles University.
Beatty, R. (2007). Young students' understanding of linear functions: Using geometric growing patterns to mediate the link between symbolic notation and graphs. In T. Lamberg (Ed.), Proceedings of the 29th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Lake Tahoe, NV: University of Nevada.
Beatty, R., & Bruce, C. (2008, July). Assessing a research/pd model in patterning and algebra. Paper presented at the 11th International Congress on Mathematical Education. Monterrey, Mexico.
Bloch, I. (2003). Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove? Educational Studies in Mathematics, 52(1), 3-28.
Brassel, H. M., & Rowe, M. B. (1993). Graphing skills among high school physics students. School Science and Mathematics, 93(2), 63-71.
Cawley, J. F., & Parmar, R. S. (1992). Arithmetic programming for students with disabilities: an alternative. Remedial and Special Education, 13, 6-18.
Evan, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105-121.
Foegen, A. (2008). Algebra progress monitoring and interventions for students with learning disabilities. Learning Disabilities Quarterly, 31(1), 65-78.
Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97(3), 493-513.
Fuchs, L. S., Fuchs, D., & Hamlett, C. L. (1989). Effects of instrumental use of curriculum-based measurement to enhance instructional programs. Remedial and Special Education, 10(2), 43-52.
Fuchs, L. S., Fuchs, D., & Hollenbeck, K. N. (2007). Extending responsiveness to intervention to mathematics at first and third grades. Learning Disabilities Research and Practice, 22(1), 13-24.
Fuchs, L. S., Fuchs, D., Powell, S. R., Seethaler, P. M., Cirino, P. T., & Fletcher, J. M. (2008). Intensive intervention for students with mathematics disabilities: seven principles of effective practice. Learning Disabilities Quarterly, 31(1), 79-92.
Geary, D. C. (1993). Mathematical disabilities: cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345-362.
Geary, D. C. (2007). An evolutionary perspective on learning disability in mathematics. Developmental Neurophysiology, 32(1), 471-519.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293-304.
Green, J. C., Caracelli, V. J., & Graham, W. F. (1989). Toward a conceptual framework for mixed-method evaluation designs. Educational Evaluation and Policy Analysis, 11(3), 255-274.
Gross-Tsur, V., Manor, O., & Shalev, R. S. (1996). Developmental dyscalculia: prevalence and demographic features. Developmental Medicine and Child Neurology, 38(1), 25-33.
Guskey, T. R., & Gates, S. L. (1989). Synthesis of research on the effects of mastery learning in elementary and secondary classrooms. Educational Leadership, 33(8), 73-80.
Mason, J. (2008). Making use of children's powers to produce algebraic thinking. In J. Kaput, D., Carraher, & M. Blanton (Eds.), Algebra in the Early Grades (pp. 57-94). Hillsdale, NJ: Lawrence Erlbaum Associates.
Mason, J., & Johnston-Wilder, S. (2004). Designing and Using Mathematical Tasks. London, United Kingdom: Tarquin Books.
Montague, M. (2007). Self-regulation and mathematics instruction. Learning Disabilities Research and Practice, 22(1), 75-83.
Moschkovich, J. (1996). Moving up and getting steeper: Negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, 5(3), 239-277.
Moschkovich, J. (1998). Resources for refining conceptions: case studies in the domain of linear functions. The Journal of the Learning Sciences, 7(2), 209-237.
Moschkovich, J. (1999). Students' use of the x-intercept as an instance of a transitional conception. Educational Studies in Mathematics, 37(2), 169-197.
Moschkovich, J., Schoenfeld, A., & Arcavi, A. (1993). Aspects of understanding: on multiple perspectives and representations of linear relations, and connections among them. In T. A. Romberg, E. Fennema, & T. Carpenter (Eds.), Integrating research on the graphical representation of function (pp. 69-100). Hillsdale, NJ: Erlbaum.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Ostad, S. A. (1997). Developmental differences in addition strategies: a comparison of mathematically disables and mathematically normal children. British Journal of Educational Psychology, 67(3), 345-357.
Pedrotty-Bryant, D. (2005). Commentary on early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 340-345.
Rico, L. (2009). Sobre las nociones de representación y comprensión en la investigación en Educación Matemática. PNA, 4(1), 1-14.
Shalev, R., Auerbach, O. M., & Gross-Tsur, V. (2000). Developmental dyscalculia: prevalence and prognosis. European Adolescent Psychiatry, 9(Supplement 2), 58-64.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematical Teaching, 77(3), 20-26.
Skemp, R. (1979). Intelligence, learning, and action: a foundation for theory and practice in education. New York, NY: Wiley.
Swanson, H. L., & Hoskyn, M. (1999). Definition x treatment interactions for students with learning disabilities. School Psychology Review, 28(4), 644-658.
Yerushalmy, M. (1991). Students perceptions of aspects of algebraic function using multiple representation software. Journal of Computer Assisted Learning, 7(1), 42-57.