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Algebra Education and Digital Resources: A Long-Distance Relationship?

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Handbook of Digital Resources in Mathematics Education

Part of the book series: Springer International Handbooks of Education ((SIHE))

Abstract

This chapter considers the general question of how technology impacts mathematical contents for the case of algebra and addresses it from the conceptual notion of instrumental distance. It first provides an overview of perspectives on the teaching and learning of algebra in primary and secondary education. Next, it presents the theoretical lens of instrumental distance, used to study how these algebraic contents are transformed by digital tools. Using three examples of digital resources that cover different school levels and different types of design, the chapter shows that this lens indeed reveals how digital technology may create distance with respect to the regular algebraic contents and procedures carried out in the paper-and-pencil environment. The results thus raise awareness not only of new potentialities, but also of the complexity generated by technology. They suggest that being aware of the instrumental distance would be beneficial while developing digital resources and professional development programs that aim to integrate digital technologies into the teaching and learning of algebra.

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Notes

  1. 1.

    Psychology of Mathematics Education

  2. 2.

    https://scratch.mit.edu

  3. 3.

    If the solving process is more complex, we may need to introduce one or several variables corresponding to important subgoals of the broader calculation.

  4. 4.

    We do not mention here the “solver” function of spreadsheets.

  5. 5.

    https://www.geogebra.org

References

  • Arcavi A, Drijvers P, Stacey K (2017) The learning and teaching of algebra. Routledge, London

    Google Scholar 

  • Artigue M (2020) Michèle Artigue Unit. (ICMI Awardees Multimedia Online Resources). https://www.mathunion.org/icmi/awards/amor/michele-artigue-unit

  • Bakos S (2022) Primary teachers implementing TouchTimes. Twelfth Congress of the European Society for Research in Mathematics Education, Bolzano. https://storage.ibrida.io/public/cerme12/TWG15/paper/Bakos_TWG15_final.pdf

  • Balacheff N (1994) Didactique et intelligence artificielle. Recherches en Didactique des Mathématiques 14(1–2):9–42

    Google Scholar 

  • Benton L, Hoyles C, Kalas I, Noss R (2017) Bridging primary programming and mathematics: some findings of design research in England. Digit Exp Math Educ 3(2):115–138

    Article  Google Scholar 

  • Bråting K, Kilhamn C (2021) Exploring the intersection of algebraic and computational thinking. Math Think Learn 23(2):170–185

    Article  Google Scholar 

  • Carpenter TP, Franke ML, Levi L (2003) Thinking mathematically: integrating arithmetic and algebra in elementary school. Heinemann, Portsmouth

    Google Scholar 

  • Carraher DW, Schliemann AD (2007) Early algebra and algebraic reasoning. In: Lester FK Jr (ed) Second handbook of research on mathematics teaching and learning. Information Age, Charlotte, NC, pp 669–705

    Google Scholar 

  • Carraher DW, Schliemann AD (2018) Cultivating early algebraic thinking. In: Kieran C (ed) Teaching and learning algebraic thinking with 5- to 12-year-olds: the global evolution of an emerging field of research and practice. Springer, Cham, Switzerland, pp 107–138

    Google Scholar 

  • Carraher DW, Schliemann AD, Schwartz JL (2008) Early algebra is not the same as algebra early. In: Kaput JJ, Carraher DW, Blanton ML (eds) Algebra in the early grades. Routledge, New York, pp 235–272

    Google Scholar 

  • Chazan D, Yerushalmy M (2003) On appreciating the cognitive complexity of school algebra: research on algebra learning and directions of curricular change. In: Kilpatrick J, Martin WG, Schifter D (eds) A research companion to principles and standards for school mathematics. NCTM, Reston, VA, pp 123–135

    Google Scholar 

  • Drijvers PHM (2003) Learning algebra in a computer algebra environment: design research on the understanding of the concept of parameter. Dissertation. CD-B Press. https://dspace.library.uu.nl/handle/1874/886

    Google Scholar 

  • Ely R, Adams AE (2012) Unknown, placeholder, or variable: what is x? Math Educ Res J 24(1):19–38

    Article  Google Scholar 

  • Ferrara F, Pratt D, Robutti O (2006) The role and uses of technologies for the teaching of algebra and calculus. In: Gutierrez A, Boero P (eds) Handbook of research on the psychology of mathematics education: past, present and future. Sense, Rotterdam, pp 237–273

    Google Scholar 

  • Fey JT (1984) Computing and mathematics: the impact on secondary school curricula. NCTM, Reston, VA

    Google Scholar 

  • Freudenthal H (1982) Variables and functions. In: van Barneveld G, Krabbendam H (eds) Proceedings of conference on functions. National Institute for Curriculum Development, Enschede, pp 7–20

    Google Scholar 

  • Freudenthal H (1983) Didactical phenomenology of mathematical structures. Reidel, Dordrecht

    Google Scholar 

  • Guin D, Trouche L (1998) The complex process of converting tools into mathematical instruments. The case of calculators. Int J Comput Math Learn 3(3):195–227

    Article  Google Scholar 

  • Guin D, Ruthven K, Trouche L (eds) (2004) The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument. Springer, New York

    Google Scholar 

  • Haspekian M (2005) An “instrumental approach” to study the integration of a computer tool into mathematics teaching: the case of spreadsheets. Int J Comput Math Learn 10(2):109–141

    Article  Google Scholar 

  • Haspekian M (2014) Teachers’ instrumental geneses when integrating spreadsheet software. In: Clark-Wilson A, Robutti O, Sinclair N (eds) The mathematics teacher in the digital era. An international perspective. Springer, Dordrecht, pp 241–276

    Google Scholar 

  • Hohenwarter M (2006) GeoGebra – didaktische Materialien und Anwendungen für den Mathematikunterricht. Universität Salzburg. https://archive.geogebra.org/static/publications/mhohen_diss.pdf

    Google Scholar 

  • Hoyles C, Kieran C, Rojano T, Sacristan AI, Trigueros M (2020) Reflections on digital technologies in mathematics education across cultures. In: Sacristan AI, Cortés-Zavala JC, Ruiz-Arias PM (eds) Proceedings of the 42nd meeting of the North American chapter of PME. PME-NA, pp 69–92

    Google Scholar 

  • Kaput JJ (2008) What is algebra? What is algebraic reasoning? In: Kaput JJ, Carraher DW, Blanton ML (eds) Algebra in the early grades. Lawrence Erlbaum, New York, pp 5–17

    Google Scholar 

  • Kaput JJ, Carraher DW, Blanton ML (eds) (2008) Algebra in the early grades. Lawrence Erlbaum, New York

    Google Scholar 

  • Kieran C (1981) Concepts associated with the equality symbol. Educ Stud Math 12(3):317–326

    Article  Google Scholar 

  • Kieran C (1992) The learning and teaching of school algebra. In: Grouws DA (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 390–419

    Google Scholar 

  • Kieran C (2004) Algebraic thinking in the early grades: what is it? Math Educ 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: Lester FK Jr (ed) Second handbook of research on mathematics teaching and learning. Information Age, Charlotte, NC, pp 707–762

    Google Scholar 

  • Kieran C (2018) Seeking, using, and expressing structure in numbers and numerical operations: a fundamental path to developing early algebraic thinking. In: Kieran C (ed) Teaching and learning algebraic thinking with 5- to 12-year-olds: the global evolution of an emerging field of research and practice. Springer, Cham, Switzerland, pp 79–105

    Google Scholar 

  • Kieran C (ed) (2022) Early algebraic thinking: a multi-dimensional and ever-expanding global vision (special issue). ZDM, 54(6):1131–1406

    Google Scholar 

  • Kieran C, Martínez-Hernández C (2022) Structure sense at early ages: the case of equivalence of numerical expressions and equalities. In: Rojano T (ed) Algebra structure sense development amongst diverse learners. Routledge, New York, pp 35–66

    Google Scholar 

  • Kieran C, Pang J, Schifter D, Ng SF (2016) Early algebra: research into its nature, its learning, its teaching. Springer, Cham, Switzerland

    Google Scholar 

  • Kilhamn C, Bråting K, Helenius O, Mason J (2022) Variables in early algebra: exploring didactic potentials in programming activities. ZDM 54(6):1273–1288

    Article  Google Scholar 

  • Kilpatrick J, Izsák A (2008) A history of algebra in the school curriculum. In: Greenes CE, Rubenstein R (eds) Algebra and algebraic thinking. 70th yearbook of the National Council of teachers of mathematics. NCTM, Reston, VA, pp 3–18

    Google Scholar 

  • Lagrange J-B, Artigue M, Laborde C, Trouche L (2003) Technology and mathematics education: a multidimensional study of the evolution of research and innovation. In: Bishop AJ, Clements MA, Keitel C, Kilpatrick J, Leung FKS (eds) Second international handbook of mathematics education. Springer, Dordrecht

    Google Scholar 

  • Mason J, Graham A, Pimm D, Gowar N (1985) Routes to/roots of algebra. The Open University, Milton Keynes, UK

    Google Scholar 

  • Mason J, Stephens M, Watson A (2009) Appreciating mathematical structure for all. Math Educ Res J 21(2):10–32

    Article  Google Scholar 

  • Moss J, London McNab S (2011) An approach to geometric and numeric patterning that fosters second grade students’ reasoning and generalizing about functions and co-variation. In: Cai J, Knuth E (eds) Early algebraization. Springer, Berlin Heidelberg, pp 277–301

    Google Scholar 

  • Philipp R (1992) The many uses of algebraic variables. Math Teach 85(7):557–561

    Article  Google Scholar 

  • Rabardel P (2002) People and technology, Université Paris 8. https://hal.archives-ouvertes.fr/hal-01020705

    Google Scholar 

  • Radford L (2018) The emergence of symbolic algebraic thinking in primary school. In: Kieran C (ed) Teaching and learning algebraic thinking with 5- to 12-year-olds: the global evolution of an emerging field of research and practice. Springer, Cham, Switzerland, pp 3–25

    Google Scholar 

  • Radford L (2022) Introducing equations in early algebra. ZDM 54(6):1151–1168

    Article  Google Scholar 

  • Rivera F (2013) Teaching and learning patterns in school mathematics: psychological and pedagogical considerations. Springer, Dordrecht

    Google Scholar 

  • Sierpinska A (1992) On understanding the notion of function. In: Dubinsky E, Harel G (eds) The concept of function: aspects of epistemology and pedagogy. Mathematical Association of America, Washington, pp 25–58

    Google Scholar 

  • Stephens AC, Ellis AB, Blanton M, Brizuela BM (2017) Algebraic thinking in the elementary and middle grades. In: Cai J (ed) Compendium for research in mathematics education. National Council of Teachers of Mathematics, Reston, VA, pp 386–420

    Google Scholar 

  • Tabach M, Friedlander A (2008) Understanding equivalence of algebraic expressions in a spreadsheet-based environment. Int J Comput Math Educ 13(1):27–46

    Google Scholar 

  • Trouche L (2016) Didactics of mathematics: concepts, roots, interactions and dynamics from France. In: Monaghan J, Trouche L, Borwein JM (eds) Tools and mathematics, instruments for learning. Springer, Cham, Switzerland, pp 219–256

    Google Scholar 

  • Usiskin Z (1988) Conceptions of school algebra and uses of variables. In: Coxford AF (ed) The ideas of algebra, K-12. 1988 yearbook of the National Council of Teachers of Mathematics. NCTM, Reston, VA, pp 8–19

    Google Scholar 

  • Vergnaud G (2009) The theory of conceptual fields. Hum Dev 52:83–94

    Article  Google Scholar 

  • Verillon P, Rabardel P (1995) Cognition and artifacts: a contribution to the study of thought in relation to instrumented activity. Eur J Psychol Educ 10(1):77–101

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Université Paris Cité, EDA, Paris, France

    Mariam Haspekian

  2. Département de Mathématiques, Université du Québec à Montréal, Montreal, Canada

    Carolyn Kieran

  3. Freudenthal Institute, Utrecht University, Utrecht, The Netherlands

    Paul Drijvers

  4. Department of Education, Uppsala University, Uppsala, Sweden

    Kajsa Bråting

  5. Tel-Aviv University, Tel-Aviv, Israel

    Michal Tabach

Authors
  1. Mariam Haspekian
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  2. Carolyn Kieran
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  3. Paul Drijvers
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  4. Kajsa Bråting
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  5. Michal Tabach
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Corresponding author

Correspondence to Mariam Haspekian .

Editor information

Editors and Affiliations

  1. Eindhoven School of Education, Eindhoven University of Technology, Eindhoven, The Netherlands

    Birgit Pepin

  2. University of Paris-Saclay, Orsay, France

    Ghislaine Gueudet

  3. University of Rochester, Rochester, NY, USA

    Jeff Choppin

Section Editor information

  1. Tel-Aviv University, Tel-Aviv, Israel

    Michal Tabach

  2. S2HEP (UR4148), INSPE, Claude Bernard University, Lyon, France

    Jana Trgalova

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Haspekian, M., Kieran, C., Drijvers, P., Bråting, K., Tabach, M. (2023). Algebra Education and Digital Resources: A Long-Distance Relationship?. In: Pepin, B., Gueudet, G., Choppin, J. (eds) Handbook of Digital Resources in Mathematics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-030-95060-6_16-1

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  • DOI: https://doi.org/10.1007/978-3-030-95060-6_16-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-95060-6

  • Online ISBN: 978-3-030-95060-6

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