Materialisering av algebraiska uttryck i helklassdiskussioner med lärandemodeller som medierande redskap i årskurs 1 och 5
DOI:
https://doi.org/10.7146/nomad.v24i3-4.149028Abstract
Syftet med denna artikel är att beskriva och diskutera vilka funktioner lärandemodeller kan ha för att främja yngre elevers kollektiva diskussioner om algebraiska uttryck. Artikeln bygger på data från ett designforskningsprojekt baserat på Davydovs principer för lärandeverksamhet, bestående av videofilmade forskningslektioner i årskurs 1 och 5. Analysen fokuserar på vad som skapar förutsättningar för helklassdiskussioner om algebraiska uttryck, hur de drivs framåt och kvalificeras samt vilka funktioner lärandemodeller kan ha för elevernas utforskande av matematiska strukturer och relationer i algebraiska uttryck. Resultatet indikerar att lärandemodeller som medierande redskap gör det möjligt för eleverna att föra kreativa och reflekterande diskussioner om algebraiska uttryck och deras komponenter.
References
Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I. & Kim, J.-S. (2015). The development of children's algebraic thinking: the impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46, 39-87. https://doi.org/10.5951/jresematheduc.46.1.0039
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.
Bråting, K., Madej, L. & Hemmi, K. (2019). Development of algebraic thinking: opportunities offered by the Swedish curriculum and elementary mathematics textbooks. Nordic Studies in Mathematics Education, 24 (1), 27-49.
Cai, J. & Knuth, E. (red). (2011). Early algebraization: a global dialogue from multiple perspectives. New York: Springer. https://doi.org/10.1007/978-3-642-17735-4
Davydov, V. V. (2008). Problems of developmental instruction: a theoretical and experimental psychological study. New York: Nova Science Publishers.
Davydov, V. V., Gorbov, S. F., Mikulina, G. G. & Saveleva, O. V. (2012). Matematikka 1 [Matematik 1]. Moskva: VitaPress.
Davydov, V. V., Slobodchikov, V. I. & Tsuckerman, G. A. (2003). The elementary school students as an agent of learning activity. Journal of Russian and East European Psychology, 41 (5), 63-76. https://doi.org/10.2753/RPO1061-0405410563
Eriksson, H. (2015). Rationella tal som tal: algebraiska symboler och generella modeller som medierande redskap (Licentiatuppsats). Stockholms universitet.
Eriksson, I. (2017). Lärandeverksamhet som redskap i en learning study. I I. Carlgren (red), Undervisningsutvecklande forskning. Exemplet learning study (s 61-81). Malmö: Gleerups.
Eriksson, I. (2018). Lärandeverksamhet, lärandeuppgifter & lärandemodeller. I E. Insulander & S. Selander (red), Att bli lärare (s 160-165). Stockholm: Liber.
Eriksson, I. & Jansson, A. (2017). Designing algebraic tasks for 7-year-old students - a pilot project inspired by Davydov's learning activity. International Journal for Mathematics Teaching and Learning, 18 (2), 257-272. https://doi.org/10.4256/ijmtl.v18i2.67
Fermsjö, R. (2014). Rekonstruktion av logaritmer med tallinjer som medierade redskap (Licentiatuppsats). Stockholms universitet.
Godino, J. D., Neto, T., Wilhelmi, W., Aké, L., Etchegaray, S. et al. (2015). Algebraic reasoning levels in primary and secondary education. I K. Krainer & N. Vondrová (red), Proceedings of CERME 9 (s 426-432). Prag: ERME.
Gorbov, S. F. & Chudinova, E. V. (2000). The effect of modeling on the students' learning (regarding problem formulation). Psychological Science and Education, 2, 96-110.
Hodgen, J., Oldenburg, R. & Strømskag, H. (2018). Algebraic thinking. I T. Dreyfus, M. Artigue, D. Potari, S. Prediger & K. Ruthven (red), Developing research in mathematics education (s 32-45). London: Routledge. https://doi.org/10.4324/9781315113562-4
Kaput, J., Carraher, D. & Blanton, M. (red). (2008). Algebra in the early grades. Mahwah: Erlbaum.
Kieran, C. (2006). Research on the learning and teaching of algebra. I A. Gutiérrez & P. Boero (red), Handbook of research on the psychology of mathematics education: past, present and future (s 11-50). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087901127_003
Kieran, C. (2018). Introduction. I C. Kieran (red), Teaching and learning algebraic thinking with 5- to 12-year-olds: the global evolution of an emerging field of research and practice (s ix-xiii). Cham: Springer International.
Kieran, C., Pang, J., Schifter, D. & Ng, S. F. (2016). Early algebra research into its nature, its learning, its teaching. Cham: Springer International. https://doi.org/10.1007/978-3-319-32258-2
Krutetskii, V. D. (1976). The psychology of mathematical abilities in school children. The University of Chicago Press.
Larsson, M. (2015). Orchestrating mathematical whole-class discussions in the problem-solving classroom: theorizing challenges and support for teachers (Doktorsavhandling). Västerås: Mälardalens högskola.
Larsson, M. & Ryve, A. (2012). Balancing on the edge of competency-oriented versus procedural-oriented practices: orchestrating whole-class discussions of complex mathematical problems. Mathematics Education Research Journal, 42, 447-465. https://doi.org/10.1007/s13394-012-0049-0
Leontiev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs: Prentice-Hall.
Leung, A. & Bolite-Frant, J. (2015). Designing mathematics tasks: the role of tools. I A. Watson & M. Ohtani (red), Task design in mathematics education (ICMI study 22) (s 191-225). Cham: Springer International. https://doi.org/10.1007/978-3-319-09629-2_6
Lindberg, V. (2010). Skolans kunskapsinnehåll i ljuset av elevers uppgifter - exemplet matematik. I I. Eriksson, V. Lindberg & E. Österlind (red), Uppdrag undervisning - kunskap och lärande! (s 109-123). Lund: Studentlitteratur.
Lins, R. & Kaput, J. (2004). The early development of algebraic reasoning: the current state of the field. I H. Chick & K. Stacy (red), The future of the teaching and learning of algebra (ICMI study 12) (s 45-70). New York: Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-8131-6_4
Lithner, J. (2008). Research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67, 255-276. https://doi.org/10.1007/s10649-007-9104-2
Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM, 49, 937-949. https://doi.org/10.1007/s11858-017-0867-3
Marton, F. (2015). Necessary conditions of learning. London: Routledge. https://doi.org/10.4324/9781315816876
Newman, D., Griffin, P. & Cole, M. (1989). The construction zone: working for cognitive change in school. Cambridge University Press.
Radford, L. (2010). Signs, gestures, meanings: algebraic thinking from a cultural semiotic perspective. I V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (red), Proceedings of CERME 6 (s XXXIII-LIII). Lyon: Institut National de Recherche Pédagogique.
Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. I C. Kieran (red), Teaching and learning algebraic thinking with 5- to 12-year-olds: the global evolution of an emerging field of research and practice (s 3-25). Cham: Springer International. https://doi.org/10.1007/978-3-319-68351-5_1
Radford, L. & Barwell, R. (2016). Language in mathematics education research. I A. Gutiérrez, G. Leder & P. Boero (red), The second handbook of research on the psychology of mathematics education. The journey continues (s 275-313). Rotterdam: Sense Publishers. https://doi.org/10.1007/978-94-6300-561-6_8
Repkin, V. V. (2003). Developmental teaching and learning activity. Journal of Russian & East European Psychology, 41 (5), 10-33. https://doi.org/10.2753/RPO1061-0405410510
Roth, W. M. & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam: Sense Publishers. https://doi.org/10.1007/978-94-6091-564-2
Ryve, A., Larsson, M. & Nilsson. P. (2011). Analyzing content and participation in classroom discourse: dimensions of variation, mediating tools and conceptual accountability. Scandinavian Journal of Educational Research, 57, 101-114. https://doi.org/10.1080/00313831.2011.628689
Ryve, A., Nilsson, P. & Pettersson, K. (2013). Analyzing effective communication in mathematics group work: the role of visual mediators and technical terms. Educational Studies in Mathematics, 82, 497-514. https://doi.org/10.1007/s10649-012-9442-6
Schmittau, J. (2004). Vygotskian theory and mathematics education: resolving the conceptual procedural dichotomy. European Journal of Psychology of Education, XIX (1), 19-43. https://doi.org/10.1007/BF03173235
Schmittau, J. (2005). The development of algebraic thinking. A Vygotskian perspective. ZDM, 37(1), 16-22. https://doi.org/10.1007/BF02655893
Schmittau, J. & Morris, A. (2004). The development of algebra in the elementary mathematics curriculum of V. V. Davydov. The Mathematics Educator, 8 (1), 60-87.
Schön, D. A. (1983). The reflective practitioner: how professionals think in action. New York: Basic Books.
Sfard, A. (2008). Thinking as communicating: human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Stacey, K. & Chick, H. (2004). Solving the problem with algebra. I K. Stacey, H. Chick & M. Kendal (red), The future of the teaching and learning of algebra (ICMI study 12) (s 1-20). New York: Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-8131-6_1
Stacey, K. & MacGregor, M. (1999). Ideas about symbolism that students bring to algebra. I B. Moses (red), Algebraic thinking grades K-12 (s 308-312). Reston: NCTM.
Strømskag, H. (2017). A methodology for instructional design in mathematics - with the generic and epistemic student at the centre. ZDM, 49, 909-921. https://doi.org/10.1007/s11858-017-0882-4
Veneciano, L. & Dougherty, B. (2014). Addressing priorities for elementary school mathematics. For the Learning of Mathematics, 34 (1), 18-24.
Vygotskij, L. S. (1963). Learning and mental development at school age. I B. Simon & J. Simon (red), Educational psychology in the U.S.S.R. London: Routledge & Kegan Paul (arbete i original publicerat 1934).
Vygotskij, L. S. (2001). Tänkande och språk. Göteborg: Daidalos.
Warren, E., Trigueros, M. & Ursini, S. (2016). Research on the learning and teaching of algebra. I Á. Gutiérrez, G. C. Leder & P. Boero (red), The second handbook of research on the psychology of mathematics education. The journey continues (s 73-108). Rotterdam: Sense Publishers. https://doi.org/10.1007/978-94-6300-561-6_3
Wickman, P. O. (2014). Teaching learning progressions: an international perspective. I N. G. Lederman & S. K. Abell (red) Handbook of research on science education (volume II, s 159-178). London: Routledge. https://doi.org/10.4324/9780203097267-16
Zuckerman, G. (2003). The learning activity in the first years of schooling. I A. Kozulin, B. Gindis, V. S. Ageyev & S. M. Miller (red), Vygotsky's educational theory in cultural context (s 39-64). Cambridge University Press. https://doi.org/10.1017/CBO9780511840975.011
Zuckerman, G. (2004). Development of reflection through learning activity. European Journal of Psychology of Education, XIX (1), 9-18. https://doi.org/10.1007/BF03173234
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.