Overall Commentary on Early Algebraization: Perspectives for Research and Teaching
The twenty-nine chapters of this volume on early algebraization, which include an introduction and commentary for each of the three main parts, reveal the rich diversity that characterizes the rapidly evolving field of early algebra. The volume articulates the ways in which researchers are currently conceptualizing early algebraization from curricular, cognitive, and instructional perspectives, and thus offers to researchers, teachers, curriculum developers, professional development educators, and policy makers alike some of the most recent thinking in the field. The research that is presented herein, research that is shaping both our ways of thinking about the nature and components of algebraic thinking and the routes by which its growth might be encouraged, includes the following focal themes: Thinking about the general in the particular; Thinking rule-wise about patterns; Thinking relationally about quantity, number, and numerical operations; Thinking representationally about the relations in problem situations; Thinking conceptually about the procedural; Anticipating, conjecturing, and justifying; Gesturing, visualizing, and languaging. The impact of this research will be felt not only on the way in which children come to think about their mathematics at the elementary and middle school levels, but also on the way in which high school students come to engage with algebra.
KeywordsEarly Grade Epistemic Rationality Algebraic Thinking Numerical Operation Algebraic Reasoning
Unable to display preview. Download preview PDF.
- Blanton, M. L., & Kaput, J. J. (2008). Building district capacity for teacher development in algebraic reasoning. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the Early Grades (pp. 361–388). New York: Routledge. Google Scholar
- Boero, P. (2001). Transformation and anticipation as key processes in algebraic problem solving. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on School Algebra (pp. 99–119). Dordrecht, The Netherlands: Kluwer Academic. Google Scholar
- Jeannotte, D. (2010). L’apport pour la formation et la pratique enseignante: analyse et synthèse de différents modèles de raisonnement mathématique dans la littérature scientifique [Contributing to teacher training and teaching practice: Analysis and synthesis of different models of mathematical reasoning in the scientific literature]. In V. Freiman (Ed.), Actes du congrès Groupe des Didacticiens des Mathématiques 2010. Moncton, New Brunswick, Canada: Comité scientifique GDM. Google Scholar
- Kaput, J. J. (2008). What is algebra? What is algebraic reasoning. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the Early Grades (pp. 5–17). New York: Routledge. Google Scholar
- Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Pérez (Eds.), Eighth International Congress on Mathematical Education: Selected Lectures (pp. 271–290). Seville: S.A.E.M. Thales. Google Scholar
- Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139–151. Google Scholar
- Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 707–762). Charlotte, NC: Information Age Publishing. Google Scholar
- Kieran, C. (to appear). The false dichotomy in mathematics education between conceptual understanding and procedural skills: An example from algebra. In K. Leatham (Ed.), Vital Directions in Mathematics Education Research. New York: Springer. Google Scholar
- Lagrange, J.-B. (2003). Learning techniques and concepts using CAS: A practical and theoretical reflection. In J. T. Fey (Ed.), Computer Algebra Systems in Secondary School Mathematics Education (pp. 269–283). Reston, VA: National Council of Teachers of Mathematics. Google Scholar
- Mason, J. (1996). Expressions of generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to Algebra (pp. 65–86). Dordrecht, The Netherlands: Kluwer Academic. Google Scholar
- Mason, J., with Graham, A., & Johnston-Wilder, S. (2005). Developing Thinking in Algebra. London: Sage Publications. Google Scholar
- Radford, L. (2010). Signs, gestures, meanings: Algebraic thinking from a cultural semiotic perspective. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (2009). Lyon, Fr: Institut National de Recherche Pédagogique. http://www.inrp.fr/editions/editions-electroniques/cerme6/plenary-1. Google Scholar