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A curriculum-based approach to learning trajectories in middle school algebra

  • Martinez, Mara V [1] ; Castro-Superfine, Alison [1] ; Stoelinga, Timothy [2]
    1. [1] University of Illinois-Chicago
    2. [2] Loyola University
  • Localización: REDIMAT, ISSN-e 2014-3621, Vol. 11, Nº. 1, 2022 (Ejemplar dedicado a: REDIMAT), págs. 5-32
  • Idioma: inglés
  • DOI: 10.17583/redimat.5539
  • Títulos paralelos:
    • Un enfoque basado en el plan de estudios para las trayectorias de aprendizaje en álgebra de la escuela intermedia
  • Enlaces
  • Resumen
    • español

      Nuestro objetivo es contribuir al cuerpo de investigación sobre trayectorias de aprendizaje (TA) en matemáticas al hacer visible un proceso para articular una trayectoria de aprendizaje hipotética implícita en un currículo de matemáticas de grado medio ampliamente adoptado y basado en la reforma. Al hacerlo, destacamos las consideraciones, decisiones y desafíos que enfrentamos como parte de este trabajo. Al describir nuestro proceso de articulación de TA, nuestro objetivo es resaltar las formas en que se pueden articular las TA específicas del plan de estudios para que sirvan como una herramienta más próxima e instrumental para la práctica educativa de los maestros. Además, para ilustrar, describimos cómo se usaron los productos del trabajo en experiencias de aprendizaje profesional basadas en la práctica con profesores de matemáticas de grados medios.

    • English

      Our aim is to contribute to the body of research on learning trajectories (LTs) in mathematics by making visible a process for articulating a hypothetical learning trajectory implicit in a widely adopted, reform-based, middle-grades mathematics curriculum. In doing so, we highlight considerations, decisions, and challenges we faced as part of this work. By describing our LT articulation process, our aim is to highlight ways in which curriculum-specific LTs can be articulated to serve as a more proximal and instrumental tool for teachers’ instructional practice. Furthermore, to illustrate we describe how the products of the work were used in practice-based professional learning experiences with middle-grades mathematics teachers.

  • Referencias bibliográficas
    • Barrett, J.E., Clements, D.H., Klanderman, D., Pennisi, S.J., & Polaki, M.V. (2006). Students' coordination of geometric reasoning...
    • Berland, L.K., & McNeill, K.L. (2010). A learning progression for scientific argumentation: Understanding student work and designing supportive...
    • Bernbaum Wilmot, D., Schoenfeld, A. H., Wilson, M., Champney, D., & Zahner, W. (2011). Validating a learning progression in mathematical...
    • Bishop, Alan J., Lamb, L. L., Phillip, R. A. , Whitacre, I., & Schappelle, B. (2014). Using order to reason about negative numbers: The...
    • Bowers, Janet, Cobb, P., & McClain, K. (1999). The evolution of mathematical practices: A case study. Cognition and Instruction, 17(1),...
    • Brown, Matthew W. (2009). The Teacher–Tool Relationship: Theorizing the Design and Use of Curriculum Materials. In J. Remillard, B. Herbel-Eisenmann...
    • Clark, D. B. (2006). Longitudinal conceptual change in students' understanding of thermal equilibrium: An examination of the process of...
    • Clements, D.H., & Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thinking & Learning, 6(2), 81-89.
    • Clements, D.H., Wilson, D. C., & Sarama, J. (2004). Young children's composition of geometric figures: A learning trajectory. Mathematical...
    • Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking & Learning,...
    • Cobb, P., & Whitenack, J. W. (1996). A method for conducting longitudinal analyses of classroom videorecordings and transcripts. Educational...
    • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational...
    • Collopy, Rachel. (2003). Curriculum Materials as a Professional Development Tool: How a Mathematics Textbook Affected Two Teachers' Learning....
    • Common Core Standards Writing Team. (2013a). Grades 3-5, numbers and operations, fractions: A progression of the Common Core State Standards...
    • Common Core Standards Writing Team. (2013b). Preface for the draft progressions. Institute for Mathematics and Education, University of Arizona.
    • Confrey, J., & Maloney, A. (2010). The construction, refinement, and early validation of the equipartitioning learning trajectory. Paper...
    • Confrey, J., Maloney, A. P., & Corley, A. K. (2014). Learning Trajectories: a Framework for connecting standards with curriculum. ZDM-The...
    • Corcoran, Tom, Mosher, Frederic A., Rogat, Aaron, & Consortium for Policy Research in, Education. (2009). Learning progressions in science:...
    • Daro, Phil, Mosher, Frederic A., Corcoran, Tom, Barrett, Jeffrey, & Consortium for Policy Research in, Education. (2011). Learning trajectories...
    • Gravemeijer, K., Bowers, Janet, & Stephan, Michelle. (2003). A hypothetical learning trajectory on measurement and flexible arithmetic....
    • Gunckel, K.L., Mohan, L., Covitt, B. A., & Anderson, C. W. (2012). Addressing challenges in developing learning progressions for environmental...
    • Hackenberg, A. J. (2014). Musings on three epistemic algebraic students. In K. C. Moore, L. P. Steffe & L. L. Hatfield (Eds.), Epistemic...
    • Hackenberg, A. J., & Tillema, E.S. (2009). Students' whole number multiplicative concepts: A critical constructive resource for fraction...
    • Jacobs, V., & Empson, S. (2015). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves....
    • Jin, H., & Anderson, C. W. (2012). A learning progression for energy in socio-ecological systems. Journal of Research in Science Teaching,...
    • Lobato, J., & Walters, C. D. (2017). A Taxonomy of Approaches to Learning Trajectories and Progressions. In J. Cai (Ed.), The Compendium...
    • Mason, J., Dreyfus, Tommy, Bills, L, Tsamir, P, Watson, A, & Zaslavsky, Orit. (2006). Exemplification in mathematics education. In J....
    • Meletiou-Mavrotheris, M, & Paparistodemou, E. (2015). Developing students' reasoning about samples and sampling in the context of...
    • Mitchelmore, Michael, & White, Paul. (2000). Development of angle concepts by progressive abstraction and generalisation. Educational...
    • Moore, K. C. (2013). Making sense by measuring arcs: A teaching experiment in angle measure. Educational Studies in Mathematics, 83(2), 225-245....
    • Nabors, W.K. (2003). From fractions to proportional reasoning: A cognitive schemes of operation approach. The Journal of Mathematical Behavior,...
    • Petty, O., & Jansson, L. (1987). Sequencing Examples and Nonexamples to Facilitate Concept Attainment. Journal for Research in Mathematics...
    • Rasmussen, Chris, & Stephan, Michelle. (2008). A methodology for documenting collective activity. In A. E. Kelly, R. Lesh & J. Y....
    • Remillard, Janine T. (2005). Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula. Review of Educational Research,...
    • Simon, M. (1995). Reconstructing Mathematics Pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26,...
    • Steffe, L., & Thompson, P. (2000). Teaching Experiment Methodology: Underlying Principles and Essential Elements. In R. Lesh & A....
    • Stephan, Michelle, & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics...
    • Sztajn, P., Confrey, J., Wilson, H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational...
    • Tillema, E.S. (2014). Students' coordination of lower and higher dimensional units in the context of constructing and evaluating sums...
    • Vermont Mathematics Partnership's Ongoing Assessment Project. (2013). OGAP proportional reasoning framework. Montpelier, VT.
    • Vermont Mathematics Partnership's Ongoing Assessment Project. (2014a). OGAP fraction framework. Montpelier, VT.
    • Vermont Mathematics Partnership's Ongoing Assessment Project. (2014b). OGAP multiplicative framework. Montpelier, VT.
    • Weber, E., & Thompson, P.W. (2014). Students' images of two-variable functions and their graphs. Educational Studies in Mathematics,...
    • Wilson, P. H., Sztajn, P., Edgington, C., & Confrey, J. (2013). Teachers' use of their mathematical knowledge for teaching in learning...
    • Wilson, P., et al. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking....

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