PUBLICATIONS: A SELECTION

Books and monographs

Kieran, C. (Ed.). (2018). Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice. New York: Springer.

Kieran, C., Pang, J. S., Schifter, D., & Ng, S. F. (2016). Early algebra: Research into its nature, its learning, its teaching. New York: Springer.

Fey, J.T., Cuoco, A., Kieran, C., McMullin, L., & Zbiek, R.M. (Eds.). (2003). Computer algebra systems in secondary school mathematics education. Reston, VA: National Council of Teachers of Mathematics.

Stigler, J., Hiebert, J., Kieran, C., Wearne, D., Seago, N., & Hood, G. (2003). TIMSS video studies: Explorations of algebra teaching (Course Guide). Los Angeles: Intel.

Stigler, J., Hiebert, J., Kieran, C., Wearne, D., Seago, N., Hood, G., Taylor, F., & Yost, J. (2003). TIMSS video studies: Explorations of algebra teaching (Facilitator Guide). Los Angeles: Intel.

Kieran, C., Forman, E., & Sfard, A. (Eds.). (2002). Learning discourse: Discursive approaches to research in mathematics education. Dordrecht, The Netherlands: Kluwer Academic.

Kieran, C., Forman, E., & Sfard, A. (Eds.). (2001). Bridging the individual and the social. (PME special issue of Educational Studies in Mathematics, 46(1-3)). Dordrecht, The Netherlands: Kluwer Academic.

Bednarz, N., Kieran, C., & Lee, L. (Eds.). (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht, The Netherlands: Kluwer Academic.

Kieran, C. (Ed.). (1995). New perspectives on school algebra: Papers and discussions of the ICME-7 Algebra Working Group. (Journal of Mathematical Behavior–special issue–Vol. 14, #1). Norwood, NJ: Ablex.

Robitaille, D., Wheeler, D., & Kieran, C. (Eds.). (1994). Selected lectures from the 7th International Congress on Mathematical Education. Québec: Les Presses de l'Université Laval.

Kieran, C., & Dawson, A. J. (1992). Current research on the teaching and learning of mathematics in Canada / Les recherches en cours sur l'apprentissage et l'enseignement des mathématiques au Canada (monograph of the Canadian Mathematics Education Study Group / Groupe canadien d'étude en didactique des mathématiques). Montréal: CMESG.

Wagner, S., & Kieran, C. (Eds.). (1989). Research issues in the learning and teaching of algebra. Reston, VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Lawrence Erlbaum.

Bergeron, J.C., Herscovics, N., & Kieran, C. (Eds.). (1987). Proceedings of the 11th International Conference for the Psychology of Mathematics Education (Vols. I, II, III). Montréal: Université de Montréal.

Book Chapters and Contributions to Collective Works

Kieran, C. (in preparation). Task design frameworks in mathematics education research: An example of a domain-specific frame for algebra learning with technological tools.

Kieran, C. (2018). Part V: Preface – Planning and assessment: Teachers and students as central actors. In A. Kajander, J. Holm, & E. J. Chernoff (Eds.), Teaching and learning secondary school mathematics – Canadian perspectives in an international context (pp. ). New York : Springer.

Kieran, C. (2018). Seeking, using, and expressing structure in numbers and numerical operations: A fundamental path to developing early algebraic thinking. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice (pp. 79-105). New York: Springer.

Kieran, C. (2018). Introduction. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice (pp. ix-xiii). New York: Springer.

Kieran, C. (2018). Conclusions and looking ahead. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice (pp. 427-438). New York: Springer.

Kieran, C. (2018). Algebra teaching and learning (updated and revised edition). In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp.). Dordrecht, The Netherlands: Springer Reference

Kieran, C., Pang, J. S., Ng, S. F., Schifter, D., & Steinweg, A. S. (2017). Topic Study Group No. 10 : Teaching and learning of early algebra. In G. Kaiser (Ed.), The Proceedings of the 13th International Congress on Mathematical Education (pp. ). New York: Springer.

Kieran, C., & Kilpatrick, J. (2017). ICMI awards ceremony. In G. Kaiser (Ed.), The Proceedings of the 13th International Congress on Mathematical Education (pp. ). New York: Springer.

Kieran, C. (2017). Cognitive neuroscience and algebra: Challenging some traditional beliefs. In S. Stewart (Ed.), And the rest is just algebra (pp. 157-172). New York: Springer.

Kieran, C. (2016). Task design in mathematics education: Frameworks and exemplars. In S. Oesterle, D. Allan, & J. Holm (Eds.), Proceedings of the 2016 Annual Meeting of the Canadian Mathematics Education Study Group (40th anniversary meeting, invited plenary, pp. 45-66). Burnaby, BC: CMESG.

Kieran, C., & Drijvers, P. (2016). Digital technology and mathematics education: Core ideas and key dimensions of Michèle Artigue’s theoretical work on digital tools and its impact on mathematics education research. In B. R. Hodgson, A. Kuzniak, & J.-B. Lagrange (Eds.), The didactics of mathematics: Approaches and issues. A homage to Michèle Artigue (pp. 123-142). New York: Springer.

Kieran, C. (2016). A historical perspective on mathematics education research in Canada : The emergence of a community. In P. Liljedahl et al. (Ed.), 40 Years of Canadian Mathematics Education Study Group (pp. 255-278). Burnaby, BC: CMESG.

Kieran, C., & Towers, J. (2016). From theory to observational data (and back again). In P. Liljedahl et al. (Ed.), 40 Years of Canadian Mathematics Education Study Group (pp. 161-167). Burnaby, BC: CMESG.

Kieran, C., Doorman, L.M., & Ohtani, M. (2015). Frameworks and principles for task design. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education (pp. 19-81). New York: Springer.

Kieran, C. (2015). ICMI Awards Report. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 13-15). New York: Springer.

Kieran, C. (2014). Algebra teaching and learning. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 27-32). Dordrecht, The Netherlands: Springer Reference.

Martinez, C., Guzman, J., & Kieran, C. (2014). El papel de CAS en la promoción del razonimiento algebraico y en el surgimiento de teoría. In L. López Vera (Ed.), Tecnologia computacional en la enseñanza de las matemáticas (libro electrónico, pp. 49-56). Nuevo Léon, México: Publicaciones UANL (ISBN: 978-607-27-0301-8).

Kieran, C., Krainer, K., Shaugnessy, J.M. (2013). Linking research and practice: Teachers as key stakeholders in mathematics education research. In M.A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Third international handbook of mathematics education (pp. 361-392). Dordrecht, The Netherlands: Springer.

Kieran, C. (2013). 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 (pp. 153-171). New York: Springer.

Kieran, C. (2013). Entretien avec Carolyn Kieran. In J. Proulx (Ed.), De la didactique des mathématiques: Entretiens avec ses batisseurs (pp. 145-169). Québec, QC: Presses de l’Université du Québec.

Kieran, C. (2012). Algebra teaching and learning. Encyclopedia of Mathematics Education. Springer: SpringerReference. http://www.springerreference.com/docs/html/chapterdbid/313185.html

Kieran, C., Tanguay, D., & Solares, A. (2012). Researcher-designed resources and their adaptation within classroom teaching practice: Shaping both the implicit and the explicit. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), : From text to ‘lived’ resources: Mathematics curriculum material and teacher development (pp. 189-213). New York: Springer.

Kieran, C. (2011). Overall commentary on early algebraization: Perspectives for research and teaching. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 579-593). New York: Springer.

Kieran, C., & Guzman, J. (2010). Role of task and technology in provoking teacher change: A case of proofs and proving in high school algebra. In R. Leikin & R. Zazkis (Eds.), Learning through teaching mathematics: Development of teachers’ knowledge and expertise in practice (pp. 127-152). New York: Springer.

Drijvers, P., Kieran, C., & Mariotti, M.-A. (2009). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology: Rethinking the terrain (pp. 89-132). New York: Springer.

Kieran, C., & Saldanha, L. (2008). Designing tasks for the co-development of conceptual and technical knowledge in CAS activity: An example from factoring. In K. Heid & G.W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Syntheses, cases, and perspectives (Vol. 2, pp. 393-414). Greenwich, CT: Information Age Publishing.

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). Greenwich, CT: Information Age Publishing.

Kieran, C., & Guzman, J. (2007). Interaction entre calculatrice technique et théorie : Émergence de structures numériques chez des élèves de 12 à 15 ans dans un environnement calculatrice. In R. Floris & F. Conne (Eds.), Environnements informatiques, enjeux pour l’enseignement des mathématiques (pp. 61-74). Genève: deBoeck.

Kieran, C. (2006). Research on the learning and teaching of algebra. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 11-50). Rotterdam: Sense.

Kieran, C., & Guzman, J. (2006). The number-theoretic experience of 12- to 15-year-olds in a calculator environment: The intertwining co-emergence of technique and theory. In R. Zazkis & S. R. Campbell (Eds.), Number theory in mathematics education (pp. 173-200). Mahwah, NJ: Lawrence Erlbaum.

Kieran, C., & Guzman, J. (2005). Five steps to zero: Students developing elementary number theory concepts when using calculators. In Wm.J. Masalski (Ed.), Technology-supported mathematics learning environments (Sixty-seventh Yearbook of the National Council of Teachers of Mathematics, pp. 35-50). Reston, VA: The Council.

Kieran, C. (2004). The core of algebra: Reflections on its main activities. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 21-34). Dordrecht, The Netherlands: Kluwer.

Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 99-152). Dordrecht, The Netherlands: Kluwer.

Kieran, C. (2003). The twentieth century emergence of the Canadian mathematics education research community. In G. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (pp. 1701-1778). Reston, VA: National Council of Teachers of Mathematics.

Cedillo, T., & Kieran, C. (2003). Initiating students into algebra with symbol-manipulating calculators. In J.T. Fey et al. (Eds.), Computer algebra systems in secondary school mathematics education (pp. 219-239). Reston, VA: National Council of Teachers of Mathematics.

Kieran, C. (2003). The transition from arithmetic to algebra: A model for conceptualizing school algebra and the role of computer technology in supporting the development of algebraic thinking. In E. Filloy (Ed.), Matemática educativa: Aspectos de la investigación actual (pp. 121-142). Mexico City: Fondo de Cultura Económica.

Kieran, C. (2002). Exploring the mathematical discourse of 13-year-old partnered problem solving and its relationship to the mathematics that emerges. In C. Kieran, E. Forman, & A. Sfard (Eds.), Learning discourse: Discursive approaches to research in mathematics education (pp. 187-228). Dordrecht, The Netherlands: Kluwer Academic.

Kieran, C. (2002). A historical perspective on mathematics education research in Canada: The emergence of a community. In E. Simmt & B. Davis (Eds.), The 25^th anniversary conference of the Canadian Mathematics Education Study Group (pp. 165-186). Kingston, ON: CMESG Program Committee.

Sfard, A., & Kieran, C. (2001). Preparing teachers for handling students' mathematical communication: Gathering knowledge and building tools. In F. L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 187-205). Dordrecht, The Netherlands: Kluwer.

Kieran, C. (1998). Models in mathematics education research: A broader view of research results. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (Vol 1, pp. 213-225). Dordrecht, The Netherlands: Kluwer Academic.

Kieran, C. (1997). Mathematical concepts at the secondary school level: The learning of algebra and functions. In T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 133-158). East Sussex, UK: Psychology Press.

Bednarz, N., Kieran, C., & Lee, L. (1996). Approaches to algebra: Perspectives for research and teaching. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 3-14). Dordrecht, The Netherlands: Kluwer.

Kieran, C., Boileau, A., & Garançon, M. (1996). Introducing algebra by means of a technology-supported, functional approach. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 257-293). Dordrecht, The Netherlands: Kluwer.

Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Perez (Eds.), 8th International Congress on Mathematical Education, Selected Lectures (pp. 271-290). Sevilla, Spain: S.A.E.M. Thales.

Kieran, C., & Chalouh, L. (1993). The transition from arithmetic to algebra. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 179-198). New York: Macmillan.

Kieran, C. (1993). Functions, graphing, and technology: Integrating research on learning and instruction. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.), Integrating research on the graphical representation of functions (pp. 189-237). Hillsdale, NJ: Lawrence Erlbaum.

Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan (this chapter has been translated into Spanish, French, and Japanese).

Kieran, C. (1990). Cognitive processes involved in learning school algebra. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 96-112). Cambridge, UK: Cambridge University Press.

Kieran, C. (1990). Perspectives on mathematical literacy. In S. P. Norris & L. M. Phillips (Eds.), Foundations of literacy policy in Canada (pp. 109-126). Calgary, AB: Detselig.

Wagner, S., & Kieran, C. (1989). An agenda for research on the learning and teaching of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 220-237). Reston, VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Lawrence Erlbaum.

Kieran, C., & Wagner, S. (1989). The Research Agenda Conference on Algebra: Background and issues. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 1-10). Reston, VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Lawrence Erlbaum.

Kieran, C. (1989). The early learning of algebra: A structural perspective. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 35-56). Reston, VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Lawrence Erlbaum.

Kieran, C. (1988). Two different approaches among algebra learners. In A.F. Coxford (Ed.), The ideas of algebra, K-12 (Yearbook of the National Council of Teachers of Mathematics, pp. 91-96). Reston, VA: NCTM.

Groen, G., & Kieran, C. (1983). In search of Piagetian mathematics. In H. Ginsburg (Ed.), The development of mathematical thinking (pp. 351-375). New York: Academic Press.

Peer-reviewed Articles in Journals

Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96, 1-16.

Kieran, C. (2014). What Does Research Tell Us About Fostering Algebraic Reasoning in School Algebra? Research brief published on the web site of the National Council of Teachers of Mathematics; retrieved on September 5, 2014, from http://www.nctm.org/news/content.aspx?id=42323

Kieran, C. (2014). What Does Research Tell Us About Fostering Algebraic Thinking in Arithmetic? Research brief published on the web site of the National Council of Teachers of Mathematics; retrieved on September 5, 2014, from http://www.nctm.org/news/content.aspx?id=42315

Solares, A., & Kieran, C. (2013). Articulating syntactic and numeric perspectives on equivalence: The case of rational expressions. Educational Studies in Mathematics, 84(1), 115-148. DOI: 10.1007/s10649-013-9473-7.

Kieran, C., Boileau, A., Tanguay, D., & Drijvers, P. (2013). Design researchers’ documentational genesis in a study on equivalence of algebraic expressions. ZDM, The International Journal on Mathematics Education, 45, 1045-1056. DOI: 10.1007/s11858-013-0516-4.

Guzman, J., & Kieran, C. (2013). Becoming aware of mathematical gaps in new curricular materials: A resource-based analysis of teaching practice. The Mathematics Enthusiast, 10(1&2), 163-190.

Kieran, C. (2012). Commentary: Characterizing meta-level mathematical discourse and accounting theoretically for its development – The instructional and the spontaneous. International Journal of Educational Research, 51–52, 146–150.

Kieran, C. (2011). Note de lecture à propos de « Ressources vives - le travail documentaire des professeurs en mathématiques ». Recherches en Didactique des Mathématiques, 31(1), 131-134.

Hitt, F., & Kieran, C. (2009). Constructing knowledge via a peer interaction in a CAS environment with tasks designed from a Task-Technique-Theory perspective. International Journal of Computers for Mathematical Learning, 14, 121-152. (available from Springer On-line at: http://dx.doi.org/10.1007/s10758-009-9151-0)

Kieran, C. (2007). Developing algebraic reasoning: The role of sequenced tasks and teacher questions from the primary to the early secondary school levels. Quadrante, XVI(1), 5-26.

Kieran, C. (2007). Interpreting and assessing the answers given by the CAS expert. The International Journal for Technology in Mathematics Education, 14, 103-107 (CAME 4 Special Issue, edited by M.K. Heid).

Kieran, C., & Drijvers, P., with Boileau, A., Hitt, F., Tanguay, D., Saldanha, L., & Guzmán, J. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11, 205-263.

Proulx, J., Descamps-Bednarz, N., & Kieran, C. (2006). Caractéristiques des explications orales en classe de mathématiques. Canadian Journal of Science, Mathematics and Technology Education, 6, 267-292.

Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139-151.

Guzman, J., Kieran, C., & Squalli, H. (2003). La calculadora con pantalla multilinea y el surgimento de estrategias numéricas en alumnus de primero, segundo y tercer año de secundaria. Revista Educación Matemática, 15(2). 105-128.

Hershkowitz, R., & Kieran, C. (2002). Fusionner des représentations mathématiques machinalement ou en réfléchissant : expériences d’utilisation de calculatrices graphiques. Sciences et techniques éducatives, 9(1-2), 201-218.

Kieran, C. (2001). Exploring the mathematical discourse of 13-year-old partnered problem solving and its relationship to the mathematics that emerges. Educational Studies in Mathematics, 46(1-3), 187-228.

Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions. Mind, Culture, and Activity, 8(1), 42-76.

Kieran, C., & Sfard, A. (1999). Seeing through symbols: The case of equivalent expressions. Focus on learning problems in mathematics, 21(1), 1-17.

Kieran, C. (1995). A new look at school algebra – past, present, and future. Journal of Mathematical Behavior, 14, 7-12.

Dugdale, S., Thompson, P.W., Harvey, W., Demana, F., Waits, B.K., Kieran, C., McConnell, J.W., & Christmas, P. (1995). Technology and algebra curriculum reform: Current issues, potential directions, and research questions. Journal of Computers in Mathematics and Science Teaching, 14, 325-357.

Kieran, C. (1994). Doing and seeing things differently: A 25-year retrospective of mathematics education research on learning. Journal for Research in Mathematics Education, 25, 583-607.

Kieran, C., & Hillel, J. (1990). "It's tough when you have to make the triangles angle": Insights from a computer-based geometry environment. Journal of Mathematical Behavior, 9, 99-127.

Kieran, C., & Filloy, E. (1989). El aprendizaje del algebra escolar desde una perspectiva psicologia. Ensenanza de las Ciencias, 7, 229-240.

Hillel, J., Kieran, C., & Gurtner, J.-L. (1989). Solving structured geometric tasks on the computer: The role of feedback in generating strategies. Educational Studies in Mathematics, 20(1), 1-39.

Hillel, J., & Kieran, C. (1987). Schemas used by 12-year-olds in solving selected turtle geometry tasks. Recherches en Didactique des Mathématiques, 8(1.2), 61-102.

Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317-326.

Herscovics, N., & Kieran, C. (1980). Constructing meaning for the concept of equation. Mathematics Teacher, 73(8), 572-580.

Peer-reviewed Scientific Papers in Conference Proceedings (a selection of conference papers from 2001 onward)

Martinez, C., & Kieran, C. (2018). Strategies used by Mexican students in seeking structure on equivalence tasks. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), Proceedings of the 40^th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp.). Greenville, NC: PME-NA.

Reid, D.A., Anderson, A., Thom, J., Suurtamm, C., Mamolo, A., Kieran, C., et al. (2014). Mathematics education in Canada: PME 2014 National Presentation. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the 38th PME and 36th PME-NA (Vol. 1, pp. 263-273). Vancouver, BC: PME et PME-NA.

Martinez, C., Guzman, J., & Kieran, C. (2013). El papel de CAS en la promoción del razonimiento algebraico y en el surgimiento de teoría. In L. López Vera (Ed.), La Memoria del VI Seminario Nacionl de Tecnologia Computacional en la Enseñanza y el Aprendizaje de la Matemática. Nuevo Léon, México : Comité cientifico AMIUTEM.

Kieran, C., & Drijvers, P. (2012). The didactical triad of theoretical framework, mathematical topic, and digital tool in research on learning and teaching. In Les Actes du Colloque Hommage à Michèle Artigue (Atelier 6: Technologies numériques pour l’enseignement des mathématiques, pp. 5-24). Paris: Comité Scientifique. https://sites.google.com/site/colloqueartigue/short-proceedings

Martínez, C., Kieran, C., & Guzmán, J. (2012). The use of CAS in the simplification of rational expressions and emerging paper-and-pencil techniques. In L.R. Van Zoest, J.-J. Lo, & J.L. Kratky (Eds.), Proceedings of the 34^th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1089-1096). Kalamazoo, MI: PME-NA.

Solares, A., & Kieran, C. (2012). Equivalence of rational expressions: Articulating syntactic and numeric perspectives. In T. Y. Tso (Ed.), Proceedings of 36th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp 99-106). Taipei, Taiwan: PME.

Jeannotte, D., Kieran, C., & Cyr, S. (2012). Composantes d’un modèle du raisonnement mathématique : un aperçu. In F. Hitt & C. Cortés (Eds.), Formation à la recherche en didactique des mathématiques (pp. 72-79). Longueuil, QC : Loze-Dion.

Kieran, C., Tanguay, D., & Solares, A. (2011). Teachers participating in a research project on learning: The spontaneous shaping of researcher-designed resources within classroom teaching practice. In B. Ubuz (Ed.), Proceedings of 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 81-88). Ankara, Turkey: PME Program Committee.

Guzmán, J., Kieran, C., & Martínez, C. (2011). Simplification of rational algebraic expressions in a CAS environment: A technical-theoretical approach. In B. Ubuz (Ed.), Proceedings of 35th Conference of the International Grooup for the Psychology of Mathematics Education (Vol. 2, pp. 481-488). Ankara, Turkey: PME Program Committee.

Guzmán, J., Kieran, C., & Martínez, C. (2010). The role of Computer Algebra Systems (CAS) and a task on the simplification of rational expressions designed with a technical-theoretical approach. In P. Brosnan, D.B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd PME-NA Conference (pp. 1497-1505). Columbus, OH: PME-NA Program Committee.

Kieran, C. & Guzmán, J. (2009). Developing teacher awareness of the roles of technology and novel tasks: An example involving proofs and proving in high school algebra. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (PME) (Vol. 3, pp. 321-328). Thessaloniki, Greece: PME Program Committee.

Kieran, C., Guzmán, J., Boileau, A., Tanguay, D., & Drijvers, P. (2008). Orchestrating whole-class discussions in algebra with CAS technology. In O. Figueras, J.-L. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the joint 32nd PME Conference and 30th PME-NA Conference (Vol. 3, pp. 249-256). Morelia, Mexico: PME et PME-NA.

Kieran, C., & Damboise, C. (2007). “How can we describe the relation between the factored form and the expanded form of these trinomials? – We don’t even know if our paper-and-pencil factorizations are right”: The case for Computer Algebra Systems (CAS) with weaker algebra students. In J.H. Woo, H.C. Lew, K.S. Park, & D.Y. Seo (Eds.), Proceedings of the 31^st PME (Vol. 3, pp. 105-112). Seoul, Korea: PME.

Bartlo, J., Saldanha, L., & Kieran, C. (2007). Attending to structure and form in algebra: Challenges in designing CAS-centered instruction that supports construing patterns and relationships among algebraic expressions. In T. Lamberg, & L.R. Wiest (Eds.), Proceedings of the 29^th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (CD version). Lake Tahoe, NV: PME-NA.

Kieran, C., & Drijvers, P., with Boileau, A., Hitt, F., Tanguay, D., Saldanha, L., & Guzmán, J. (2006). Learning about equivalence, equality and equation in a CAS environment: The interaction of machine techniques, paper-and-pencil techniques, and theorizing. In C. Hoyles, J.-B. Lagrange, & N. Sinclair (Eds.), Proceedings of the 17^th ICMI Study, “Digital technologies and mathematics teaching and learning.” [CD-ROM]. Hanoi, Viet-Nam: 17th ICMI Study. Available on line:

http://icmistudy17.didirem.math.jussieu.fr/doku.php#proceedings_of_the_study_conference

Kieran, C. (2006). A response to ‘algebraic thinking and the generalization of patterns.’ In S. Alatorre, J.L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of 28th Annual Meeting of PME-NA (invited plenary conference; CD version). Mérida, Mexico: PME-NA Program Committee.

Drijvers, P., & Kieran, C., with Boileau, A., Hitt, F., Tanguay, D., Saldanha, L., Guzmán, J. (2006). Reconciling factorizations made with CAS and with paper-and-pencil: The power of confronting two media. In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30^th PME (Vol. 2, pp. 473-480). Prague, Czech Republic: PME.

Sacristan, A. I., & Kieran, C. (2006). Bryan’s story: Classroom miscommunication about general symbolic notation and the emergence of a conjecture during CAS-based algebra activity. In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30^th PME (Vol. 5, pp. 1-8). Prague, Czech Republic: PME.

Kieran, C., Boileau, A., Saldanha, L., Hitt, F., Tanguay, D., & Guzmán, J. (2006). Le rôle des calculatrices symboliques dans l’émergence de la pensée algébrique : le cas des expressions équivalentes. Actes du colloque EMF2006 (Espace Mathématique Francophone, mai 2006). Sherbrooke, QC : EMF.

(retrieved on 6 October, 2006, from http://ermeweb.free.fr/definitif/)

Kieran, C. (2005). Some results from the PISA 2003 international assessment of mathematics learning: What makes items difficult for students? In H. L. Chick & J. L. Vincent (Eds.), Proceedings of 29^th PME (plenary panel contribution, Vol. 1, pp. 83-86). Melbourne, Australia: PME.

Kieran, C., & Saldanha, L. (2005). Computer algebra systems (CAS) as a tool for coaxing the emergence of reasoning about equivalence of algebraic expressions. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of 29^th PME (Vol. 3, pp. 193-200). Melbourne, Australia: PME.

Saldanha, L., & Kieran. C. (2005). A slippery slope between equivalence and equality: Exploring students’ reasoning in the context of algebraic instruction involving a computer algebra system. In Proceedings of the 27^th Annual Meeting of PME-NA (CD version). Roanoke, VA: PME-NA.

Kieran, C. (2004). The equation / inequality connection in constructing meaning for inequality situations. In M. Johnsen Høines & A. Berit Fuglestad (Eds.), Proceedings of 28th PME (Vol. 1, pp. 143-148). Bergen, Norway: PME.

Kieran, C., & Guzman, J. (2004). Tâche, technique et théorie : Une recherche sur l’instrumentation de la calculatrice à affichage graphique et la co-émergence de la pensée numérique chez des élèves de 12 à 15 ans. In J.B. Lagrange, M. Artigue, D. Guin, C. Laborde, D. Lenne et L. Trouche (Eds.), Intégration des technologies dans l’enseignement des mathématiques (Proceedings on-line of the Colloque Européen ITEM, Reims, June 2003). (http://www.reims.iufm.fr/Recherche/Cadre_recherche.htm).

Proulx, J., Kieran, C., & Bednarz, N. (2004). Case studies of future secondary level mathematics teachers’ mode of explaining. In D.E. McDougall & J.A. Ross (Eds.), Proceedings of the 26th PME-NA (pp. 1253-1264). Toronto, ON: PME-NA.

Kieran, C., & Guzman, J. (2003). The spontaneous emergence of elementary number-theoretic concepts and techniques in interaction with computing technology. In N.A. Pateman, B.J. Dougherty, & J. Zilliox (Eds.), Proceedings of 27^th PME (Vol. 3, pp. 141-148). Honolulu, HI: PME.

Guzman, J., & Kieran, C. (2002). The role of calculators in instrumental genesis: The case of Nicolas and factors and divisors. In A.D. Cockburn & E. Nardi (Eds.), Proceedings of 26th PME (Vol. 3, pp. 41-48). Norwich, UK: PME.

Kieran, C. (2001). Looking at the role of technology in facilitating the transition from arithmetic to algebraic thinking through the lens of a model of algebraic activity. In K. Stacey, H. Chick, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12^th ICMI Study Conference on the future of the teaching and learning of algebra (Vol. 3, pp. 713-720; this article has been translated into Spanish in 2007 and republished in the journal Revista EMA). Melbourne, Australia: ICMI-12 Program Committee.

Hershkowitz, R., & Kieran, C. (2001). Algorithmic and meaningful ways of joining together representatives within the same mathematical activity: An experience with graphing calculators. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of 25th International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 96-107). Utrecht, The Netherlands: PME.

Guzman, J., Kieran, C., & Squalli, H. (2001). The multi-line-screen calculator and the emergence of numerical strategies in secondary 1, 2, and 3 students. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th International Conference for the Psychology of Mathematics Education (Vol. 1, p. 312). Utrecht, The Netherlands: PME.