Learning mathematics through inquiry
DOI:
https://doi.org/10.7146/nomad.v13i3.148123Abstract
The role of inquiry in teaching and learning has been discussed for a long time and by many leading educational philosophers and analysts. The purpose of this article is to analyse the assumptions and some of the outcomes of two interrelated and extensive developmental projects in mathematics teaching and learning in Norway. The projects – referred to as the KUL projects (Knowledge, Instruction, Learning) – aimed at introducing the notion of communities of inquiry as a basis for developing mathematics teaching and learning in participating schools, and as a model for organizing developmental work in cooperation between teachers and researchers. In several respects, it seems as if the projects have been successful in the sense that they were accepted by the teachers (especially at lower levels) as a productive mode of engaging in developmental work. In the article, the interpretation of the concept of inquiry in the projects is scrutinized. It is argued that in order to develop our understanding of inquiry processes, detailed analyses of the nature of inquiry in interactional activities in mathematics learning is necessary. It is also argued that the notion of inquiry adopted by the projects is based on a conception where inquiry is seen as a means of learning mathematics better. An alternative conception is to see inquiry as a means of promoting critical thinking in which understanding of mathematics is at the core of the development of more general reasoning skills that play a central role in a democratic society.
References
Alrø, H., Blomhøj, M., Bødtkjer, H., Skovsmose, O., & Skånstrøm, M. (2003). Farlige små tal - matematikundervisning i risikosamfundet [Dangerous small numbers - mathematics teaching in the risk society]. In O. Skovsmose & M. Blomhøj, (Eds.), Kan det virkelig passe? [Does it really fit?] (pp. 39-49). Copenhagen: LR-uddannelse.
Alrø, H., Blomhøj, M., Bødtkjer, H., Skovsmose, O., & Skånstrøm, M. (2006). Farlige små tal - almendannelse i risikosamfundet [Terrible small numbers - general education in a risk society]. In O. Skovsmose & M. Blomhøj (Eds.), Kunne det tænkes? [Can we think that?] (pp. 24-39). Copenhagen: Malling Beck.
Alrø, H., & Skovsmose, O. (2002). Dialogue and learning in mathematics education: intention, reflection, critique. Dordrecht: Kluwer Academic Publishers.
Alrø, H., & Skovsmose, O. (2003). Læring gennem samtale [Learning through conversation]. In O. Skovsmose & M. Blomhøj (Eds.), Kan det virkelig passe? [Will it really fit?] (pp. 25-37). Copenhagen: LR-uddannelse.
Alrø, H., & Skovsmose, O. (2004). Dialogic learning in collaborative investigation, Nordic Studies in Mathematics Education 9 (2), 39-62.
Alrø, H., & Skovsmose, O. (2006a). Undersøgende samarbejde i matematikundervisningen: Udvikling af IC-Modellen [Inquiry-based cooperation in mathematics teaching: Development of the IC-model]. In O. Skovsmose & M. Blomhøj (Eds.), Kunne det tænkes? [Can we think that?] (pp. 110- 126). Copenhagen: Malling Beck.
Alrø, H., & Skovsmose, O. (2006b). Læring mellem dialog, intention, refleksion og kritik [Learning between dialogue, intention, reflection and critique]. In O. Skovsmose & M. Blomhøj (Eds.), Kunne det tænkes? [Can we think that?] (pp. 127-138). Copenhagen: Malling Beck.
Bjuland, R., Cestari, M. L., & Borgersen, H. E. (2008a). A Teacher's use of gestures and discourse as communicative strategies in the presentation of a mathematical task. Manuscript under preparation.
Bjuland, R., Cestari, M. L., & Borgersen, H. E. (2008b). Pupils mathematical reasoning expresses through gesture and discourse: A case study from sixth-grade lesson. Manuscript under preparation.
Christensen, O. R. (2008). Closing the gap between formalism and application: PBL and mathematical skills in engineering. Teaching mathematics and its applications, 27 (3), 131-139. https://doi.org/10.1093/teamat/hrn012
Daland, E. (2007). Mathematical tasks and community building - "early days" in the project. In B. Jaworski et al. (Eds.), Læringsfellesskap i matematikk/ Learning communities in mathematics (pp. 175-188)). Bergen: Caspar forlag.
D'Ambrosio, U. (1994). Cultural framing of mathematics teaching and learning. In R. Biehler, R. W. Scholz, R. Strässer & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 443-455). Dordrecht: Kluwer Academic Publishers.
Dewey, J. (1966). Democracy and education. New York, NY: The Free Press. (Original work published 1916)
Dewey, J., & Bently, A. (1949). Knowing and the known. Boston, MA: Beacon Press.
Eriksen, S. (2007). In B. Jaworski et al. (Eds.), Læringsfellesskap i matematikk/ Learning communities in mathematics (pp. 161-174). Bergen: Caspar forlag.
Fuglestad, A. B. (2007a). IKT som støtte for "inquiry" i matematikkundervisningen. In B. Jaworski et al. (Eds.), Læringsfellesskap i matematikk/Learning communities in mathematics (pp. 27-38).). Bergen: Caspar forlag.
Fuglestad, A. B. (2007b) Developing tasks and teaching with ICT in mathematics in an inquiry community. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth Congress of the European Society for Research in Mathematics Education (p. 1409-1418). Retrieved October 2, 2008 from http://ermeweb.free.fr/CERME5b/WG9.pdf
Fuglestad, A. B., & Jaworski, B. (2005). Læringsfellesskap i matematikk - utvikling og forskning i samarbeid [Communities of learning in mathematics - development and research in cooperation]. Tangenten 16 (3), 54-59.
Goodchild, S. (2007). Inside the outside: Seeking evidence of didacticians' learning by expansion. In B. Jaworski et al. (Eds.), Læringsfellesskap i matematikk/Learning communities in mathematics (pp. 189-203). Bergen: Caspar forlag.
Grevholm, B. (2007). Å undersøke forbedret læring i matematikk. In B. Jaworski et al. (Eds.), Læringsfellesskap i matematikk/Learning communities in mathematics (pp. 39-49). Bergen: Caspar forlag.
Hundeland, P. S., Erfjord, I., Grevholm, B., & Breiteig, T. (2008). Teachers and researchers inquiring into mathematics teaching and learning: A case of linear functions. Manuscript under preparation.
Jakobsson, A., Mäkitalo, Å., & Säljö, R. (in press). Learning to reason in the context of socioscientific problems: Exploring the demands on students in 'new' classroom activities. In K. Kumpulainen & M. César (Eds.), Investigating classroom interaction: methodological choices and challenges. London: Sense.
Jaworski, B. (2004b). Grappling with complexity: co-learning in inquiry communities in mathematics teaching development (Invited Plenary Lecture). In M. Johnsen Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol 1). (pp. 17-36). Bergen University College.
Jaworski B. (2005). Learning communities in mathematics: Creating an inquiry community between teachers and didacticians. In R. Barwell & A. Noyes (Eds.), Papers of the British Society for Research into Learning Mathematics, Research in Mathematics Education (Volume 7) (pp. 101-120). London: BSRLM. https://doi.org/10.1080/14794800008520148
Jaworski B. (2006), Theory and practice in mathematics teaching development: critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9 (2), 187-211. https://doi.org/10.1007/s10857-005-1223-z
Jaworski B. (2007a). Learning Communities in mathematics: research and development in mathematics teaching and learning. In C. Bergsten, B. Grevholm, H. S. Måsøval & F. Rønning (Eds.), Relating practice and research in mathematics education. Proceedings of NORMA 05, Fourth Nordic Conference of Mathematics Education (pp 71-96). Trondheim: Tapir Academic Press.
Jaworski, B. (2007b). Introducing LCM - Learning communities in mathematics. In B. Jaworski et al. (Eds.), Læringsfellesskap i matematikk/ Learning communities in mathematics (pp. 13-25). Bergen: Caspar forlag.
Jaworski, B., Fuglestad, B., Bjuland, R., Breiteig, T., Goodchild, et al. (Eds.) (2007). Læringsfellesskap i matematikk/Learning communities in mathematics. Bergen: Caspar forlag.
Lave, J., & Wenger, E. (1991). Situated learning: legitimate peripheral participation. Cambridge, MA: Cambridge University Press. https://doi.org/10.1017/CBO9780511815355
Linell, P. (1998). Approaching dialogue. Talk, interaction and contexts in dialogical perspectives. Amsterdam: John Benjamins. https://doi.org/10.1075/impact.3
Piaget, J. (1970). Piaget's theory. In P. H. Mussen (Ed.), Manual of child psychology (pp. 703-732). London: Wiley.
Rommetveit, R. (1974). On message structure. London: Academic Press.
Säljö, R. (2004). Epilogue: notes on classroom practices, dialogicality and the transformation of learning. I J. van der Linden & P. Renshaw (Ed.), Dialogic learning (pp.251-260). Dordrecht:Kluwer,2004. https://doi.org/10.1007/1-4020-1931-9_13
Säljö, R. (2005). Lärande och kulturella redskap. Om lärprocesser och det kollektiva minnet [Learning and cultural tools. On processes of learning and the collective memory]. Stockholm: Norstedts Akademiska Förlag.
Säljö, R., & Wyndhamn, J. (1993). Solving everyday problems in the formal setting: an empirical study of the school as a context for thought. In S. Chaiklin & J. Lave (Eds.), Understanding practice. Perspectives on activity and context (pp. 327-342). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511625510.013
Skovsmose, O. (2001). Landscapes of investigation. Zentralblatt für Didaktik der Mathematik, 33 (4), 123-132. https://doi.org/10.1007/BF02652747
Skovsmose, O. (2003a). Undersøgelseslandskaber [Landscapes of investigation]. In O. Skovsmose & M. Blomhøj (Eds.), Kan det virkelig passe? [Will it really fit?] (pp. 143-157). Copenhagen: LR-uddannelse.
Skovsmose O. (2003b). Matematikken er hverken god eller dårlig - og da slet ikke neutral [Mathematics is neither good nor bad - and definitely not neutral]. In O. Skovsmose & M. Blomhøj (Eds.), Kan det virkelig passe? [Will it really fit?]. (pp. 229-236). Copenhagen: LR-uddannelse.
Skovsmose, O. (2005). Travelling through education: uncertainty, mathematics, responsibility. Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087903626
Skovsmose, O. (2006a). Challenges for mathematics education research. In J. Maasz & W. Schloegelmann (Eds.), New mathematics education research and practice (pp. 33-50). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087903510_006
Skovsmose, O. (2007). Doubtful rationality. ZDM The International Journal on Mathematics Education, 39 (3), 215-224. https://doi.org/10.1007/s11858-007-0024-5
Skovsmose, O. & Blomhøj, M. (Eds.) (2003). Kan det virkelig passe? [Will it really fit?] Copenhagen: LR-uddannelse.
Skovsmose, O. & Blomhøj, M. (Eds.) (2006). Kunne det tænkes? - om matematiklæring [Can we think that? - on mathematics learning]. Copenhagen: Malling Beck.
Skovsmose, O. & Säljö, R. (2007). Report on the KUL-projects: Learning Communities in Mathematics and ICT in Mathematics Learning. Retrieved October 2, 2008 from http://fag.hia.no/lcm/papers/Report-KULfinal_OSK_RS_ okt07.pdf
Skovsmose, O., & Valero, P. (2005). Mathematics education and social justice: Facing the paradoxes of the informational society. Utbildning & Demokrati, 14 (2), 57-71. https://doi.org/10.48059/uod.v14i2.799
Vithal, R. (2003). In search of a pedagogy of conflict and dialogue for mathematics education. Dordrecht: Kluwer. https://doi.org/10.1007/978-94-010-0086-4
Vithal, R., Christiansen, I. M., & Skovsmose, O. (1995). Project work in univeristy mathematics education: a Danish experience: Aalborg University. Educational Studies in Mathematics, 29 (2), 199-223. https://doi.org/10.1007/BF01274213
Wenger, E. (1998). Communities of practice: learning, meaning, and identity. Cambridge, MA: Cambridge University Press. https://doi.org/10.1017/CBO9780511803932
Wyndhamn, J., & Säljö, R. (1997). Word problems and mathematical reasoning - a study of children's mastery of reference and meaning in textual realities. Learning and Instruction, 7 (4), 361-382. https://doi.org/10.1016/S0959-4752(97)00009-1
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
