Opportunity to learn in Norwegian and Finnish lower secondary mathematics textbooks

Per Øystein Haavold; Ane Storaas; Marthe Johnsen; Kristoffer Strand; Carina Heimstad

doi:10.7146/nomad.v30i1.152930

Authors

Per Øystein Haavold
Ane Storaas
Marthe Johnsen
Kristoffer Strand
Carina Heimstad

DOI:

https://doi.org/10.7146/nomad.v30i1.152930

Keywords:

mathematics

Abstract

Although both Finland and Norway are part of a common Nordic education culture, Finland have consistently outperformed the other Nordic countries in PISA studies. In this study, we compare Finnish and Norwegian textbook series. The results indicate that both textbook series largely facilitate skill efficiency, and most tasks are low cognitive demand. However, the Finnish textbook series facilitate conceptual understanding to a greater degree. The Finnish textbook series also introduce and develop connections between a greater number of mathematical ideas, and there is a greater number and proportion of high cognitive demand tasks in the Finnish textbooks.

References

Afdal, H. W. (2013). Policy making processes with respect to teacher education in Finland and Norway. Higher Education, 65 (2), 167–180.

https://doi.org/10.1007/s10734-012-9527-2

Ainsworth, S. (2006). A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183–198.

https://doi.org/10.1016/j.learninstruc.2006.03.001

Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79 (2), 239–261.

https://doi.org/10.1007/s10649-011-9342-1

Bergem, O. K. (2016). Hovedresultater i matematikk. In O.K. Bergem, H. Karstein & T. Nilsen (Eds.), Vi kan lykkes i realfag (pp. 22–44). Universitetsforlaget. https://doi.org/10.18261/97882150279999-2016-03

Bergwall, A. & Hemmi, K. (2017). The state of proof in Finnish and Swedish mathematics textbooks – capturing differences in approaches to upper-secondary integral calculus. Mathematical Thinking and Learning, 19 (1), 1–18. https://doi.org/10.1080/10986065.2017.1258615

Blossing, U., Imsen, G. & Moos, L. (2014). Nordic schools in a time of change. In U. Blossing, G. Imsen & L. Moose (Eds.), The Nordic education model (pp. 1–14). Springer. https://doi.org/10.1007/978-94-007-7125-3_1

Brehmer, D., Ryve, A. & Van Steenbrugge, H. (2016). Problem solving in Swedish mathematics textbooks for upper secondary school. Scandinavian Journal of educational research, 60 (6), 577–593.

https://doi.org/10.1080/00313831.2015.1066427

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.

Carlgren, I. & Klette, K. (2008). Reconstructions of Nordic teachers: reform policies and teachers’ work during the 1990s. Scandinavian Journal of Educational Research, 52 (2), 117–133.

https://doi.org/10.1080/00313830801915754

Coalition for Psychology in Schools and Education (2015). Top 20 principles from psychology for preK–12 teaching and learning. American Psychological Association.

Charalambous, C. Y., Delaney, S., Hsu, H. Y. & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical thinking and learning, 12 (2), 117–151.

https://doi.org/10.1080/10986060903460070

Doyle, W. (1988). Work in mathematics classes: the context of students’ thinking during instruction. Educational Psychologist, 23 (2), 167–180.

https://doi.org/10.1207/s15326985ep2302_6

Fan, L. (1998). Applications of arithmetic in the United States and Chinese textbooks: a comparative study. In G. Kaiser, E. Luna & I. Huntly (Eds.), International comparison in mathematics education (pp. 151–162). Falmer Press.

Fan, L., Zhu, Y. & Miao, Z. (2013). Textbook research in mathematics education: development status and directions. ZDM, 45 (5), 633–646.

https://doi.org/10.1007/s11858-013-0539-x

Fan, L., Chen, J., Zhu, Y., Qiu, X. & Hu, Q. (2004). Textbook use within and beyond Chinese mathematics classrooms: a study of 12 secondary schools in Kunming and Fuzhou of China. In L. Fan, N. Y. Wong, J. Cai & S. Li (Eds.), How Chinese learn mathematics: perspectives from insiders (pp. 228–261). World Scientific. https://doi.org/10.1142/9789812562241_0009

Finnish National Board of Education. (2004). National core curriculum for basic education 2004. Author.

Flanders, J. R. (1987). How much of the content in mathematics textbooks is new? Arithmetic Teacher, 35 (1), 18–23. https://doi.org/10.5951/AT.35.1.0018

Freeman, D. J. & Porter, A. C. (1989). Do textbooks dictate the content of mathematics instruction in elementary schools? American Educational Research Journal, 26 (3), 403–421. https://doi.org/10.3102/00028312026003403

Fuson, K. C., Stigler, J. W. & Bartsch, K. (1988). Grade placement of addition and subtraction topics in Japan, mainland China, the Soviet Union, Taiwan, and the United States. Journal for Research in Mathematics Education, 19, 449–456. https://doi.org/10.5951/jresematheduc.19.5.0449

Gray, E. & Tall, D. (1994). Duality, ambiguity, and flexibility: a "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25/2, 116–140. https://doi.org/10.5951/jresematheduc.25.2.0116

Grønmo, L.S. & T. Onstad (2013). The Significance of TIMSS and TIMSS Advanced. Mathematics Education in Norway, Slovenia and Sweden. Akademika publishing.

Hong, D. S. & Choi, K. M. (2014). A comparison of Korean and American secondary school textbooks: the case of quadratic equations. Educational Studies in Mathematics, 85 (2), 241–263.

https://doi.org/10.1007/s10649-013-9512-4

Hiebert, J. & Wearne, D. (1997). Instructional tasks, classroom discourse and student learning in second grade arithmetic. American Educational Research Journal, 30 (2), 393–425. https://doi.org/10.3102/00028312030002393

Hiebert, J. C. & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Information Age.

Husén, T. (Ed.). (1967). International study of achievement in mathematics: a comparison of twelve countries (Vol. 2). John Wiley & Sons.

Jensen, F., Pettersen, A. Frønes, T. S., Kjærnsli, M., Rohatgi, A. et al. (2019). PISA 2018. Norske elevers kompetanse i lesing, matematikk og naturfag. Universitetsforlaget.

Kilhamn, C. & Säljö, R. (2019). Encountering algebra: a comparative study of classrooms in Finland, Norway, Sweden, and the USA. Springer.

https://doi.org/10.1007/978-3-030-17577-1

Kjærnsli, M., Nortvedt, G. A. & Jensen, F. (2014). Norske elevers kompetanse i problemløsing i PISA 2012. Oslo University.

Klette, K., Bergem, O. K. & Roe, A. (Eds.). (2016). Teaching and learning in lower secondary schools in the era of PISA and TIMSS. Springer.

https://doi.org/10.1007/978-3-319-17302-3

Klette, K. (2018). Individualism and collectivism in Nordic schools. A comparative approach. In N. Witoszek, D. S. Wilson & A. Midttun (Eds.), Reneweing the Nordic model (pp. 59–78). Routledge.

https://doi.org/10.4324/9781315195964-4

Krzywacki, H., Pehkonen, L. & Laine, A. (2016). Promoting mathematical thinking in Finnish mathematics education. In H. Niemi, A. Toom & A. Kallioniemi (Eds.), Miracles of education: the principles and practices of teaching and learning in Finnish schools (pp. 109–123). Sense.

https://doi.org/10.1007/978-94-6300-776-4_8

Kunnskapsdepartementet. (2013). På rett vei. Kvalitet og mangfold i fellesskolen. Stortingsmelding 20.

Landis, J. R. & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 159–174. https://doi.org/10.2307/2529310

Lepik, M., Grevholm, B. & Viholainen, A. (2015). Using textbooks in the mathematics classroom – the teachers’ view. Nordic Studies in Mathematics Education, 20 (3-4), 129–156.

Lester, F. (2013). Thoughts about research on mathematical problem solving instruction. The Mathematics Enthusiast, 10 (1), 245–278.

https://doi.org/10.54870/1551-3440.1267

Leung, S. S. & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9 (1), 5–24. https://doi.org/10.1007/BF03217299

Leung, C. (2005). Mathematical vocabulary: fixers of knowledge or points of exploration? Language and Education, 19 (2), 127-135.

https://doi.org/10.1080/09500780508668668

Li, Y., Chen, X. & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: the case of fraction division. ZDM, 41 (6), 809-826.

https://doi.org/10.1007/s11858-009-0177-5

Luoto, J. M., Klette, K. & Blikstad-Balas, M. (2022). Patterns of instruction in Finnish and Norwegian lower secondary mathematics classrooms. Research in Comparative and International Education, 17 (3), 399–423.

https://doi.org/10.1177/17454999221077848

Lucariello, J. M., Nastasi, B. K., Dwyer, C., Skiba, R., DeMarie, D. & Anderman, E. M. (2016). Top 20 psychological principles for PK-12 education. Theory Into Practice, 55 (2), 86-93. https://doi.org/10.1080/00405841.2016.1152107

Mayring, P. (2015). Qualitative content analysis: theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds), Approaches to qualitative research in mathematics education (pp. 365–380). Springer. https://doi.org/10.1007/978-94-017-9181-6_13

Merrienboer, J. J. G. van, Kirschner, P. A. & Kester, L. (2003). Taking the load off a learner’s mind: instructional design for complex learning. Educational Psychologist, 38, 5-13. https://doi.org/10.1207/S15326985EP3801_2

Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: an empirical approach. Educational Studies in Mathematics, 56 (2-3), 255–286. https://doi.org/10.1023/B:EDUC.0000040409.63571.56

Mullis, I. V. S., Martin, M. O., Foy, P. & Arora, A. (2012). TIMSS 2011 international results in mathematics. TIMSS & PIRLS International Study Center.

Mølstad, C. E. & Karseth, B. (2016). National curricula in Norway and Finland: the role of learning outcomes. European Educational Research Journal, 15 (3), 329–344. https://doi.org/10.1177/1474904116639311

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author.

OECD (2013). PISA 2012 assessment and analytical framework: mathematics, reading, science, problem solving and financial literacy. OECD Publishing.

Palm, T., Boesen, J. & Lithner, J. (2011) Mathematical reasoning requirements in Swedish upper secondary level assessments. Mathematical Thinking and Learning, 13 (3), 221–246. https://doi.org/10.1080/10986065.2011.564994

Pepin, B. & Haggarty, L. (2001). Mathematics textbooks and their use in English, French and German classrooms. ZDM, 33 (5), 158–175.

https://doi.org/10.1007/BF02656616

Pepin, B., Gueudet, G. & Trouche, L. (2013). Investigating textbooks as crucial interfaces between culture, policy, and teacher curricular practice: two contrasted case studies in France and Norway. ZDM, 45 (5), 685–698.

https://doi.org/10.1007/s11858-013-0526-2

Presmeg, N. (2014). Visualization and learning in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 636–640). Springer. https://doi.org/10.1007/978-94-007-4978-8_161

Robitaille, D. F. & Travers, K. J. (1992). International studies of achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 687–709). Macmillan.

Rocard, M. (2007). EUR22845-Science education now: a renewed pedagogy for the future of Europe. European Commision. Directorate-General for Research.

Rohrer, D. & Pashler, H. (2007). Increasing retention without increasing study time. Current Directions in Psychological Science, 16 (4), 183-186.

https://doi.org/10.1111/j.1467-8721.2007.00500.x

Schoenfeld, A. H. (2012). Problematizing the didactic triangle. ZDM, 44 (5), 587–599. https://doi.org/10.1007/s11858-012-0395-0

Schmidt, W. H., McKnight, C. C., Valverde, G., Houang, R. T. & Wiley, D. E. (1997). Many visions, many aims: a cross-national investigation of curricular intentions in school mathematics. Kluwer.

https://doi.org/10.1007/978-94-011-5786-5

Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H. A., Wiley, D. E. et al. (2001). Why schools matter: a cross-national comparison of curriculum and learning. Jossey-Bass.

Schmidt, W., Gueudet, G., Pepin, B. & Trouche, L. (2012). Measuring content through textbooks: the cumulative effect of middle-school tracking. In G. Gueudet, B. Pepin & L. Trouche (Eds.), From text to "lived" resources: mathematics curriculum materials and teacher development (pp. 143–160). Springer. https://doi.org/10.1007/978-94-007-1966-8

Sfard, A. (1991), On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36. https://doi.org/10.1007/BF00302715

Simola, H., Kauko, J., Varjo, J., Kalalahti, M. & Sahlstrom, F. (2017). Dynamics in education politics. Routledge. https://doi.org/10.4324/9780203068793

Skovsmose, O. (2001). Landscapes of investigation. ZDM, 33 (4), 123–132.

https://doi.org/10.1007/BF02652747

Son, J. & Diletti, J. (2017). What can we learn from textbook analysis? In J. Son, T. Watanabe & J. J. Lo (Eds.), What matters? Research trends in international comparative studies in mathematics education (pp. 3–32). Springer. https://doi.org/10.1007/978-3-319-51187-0_1

Sousa, D. A. (2011). How the brain learns (4th ed.). Corwin.

https://doi.org/10.4135/9781452219684

Stein, M. K. & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: an analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2, 50–80.

https://doi.org/10.1080/1380361960020103

Stein, M. K. & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: from research to practice. Mathematics teaching in the middle school, 3 (4), 268–275. https://doi.org/10.5951/MTMS.3.4.0268

Stein, M. K., Smith, M., Henningsen, M. & Silver, E. (2000). Implementing Standards-based mathematics instruction. A casebook for professional development. Columbia University.

Stein, M., Remillard, J. & Smith, M. (2007). How curriculum influences students’ learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Information Age.

Stein, M. K. & Smith, M. S. (2010). The influence of curriculum on students’ learning. In B. J. Reys, R. E., Reys & R. Rubenstein (Eds.), Mathematics curriculum: issues, trends, and future directions (pp. 351–362). NCTM.

Stigler, J. W. & Hiebert, J. (1999). The teaching gap. Free Press.

Sweller, J. & Cooper, G. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2 (1), 59–89.

https://doi.org/10.1207/s1532690xci0201_3

Sweller, J., Merrienboer, J. J. van & Paas, F. G. (1998). Cognitive architecture and instructional design. Educational psychology review, 10 (3), 251–296.

https://doi.org/10.1023/A:1022193728205

Tall, D. (1988). Concept image and concept definition. In J. de Lange & M. Doorman (Eds.), Senior secondary mathematics education (pp. 37–41). OW & OC.

Taajamo, M., Puhakka, E. & Välijärvi, J. (2014). Opetuksen ja oppimisen kansainvälinen tutkimus TALIS 2013: yläkoulun ensituloksia. Valtioneuvosto.

Telhaug, A., Asbjørn Mediås, O. & Aasen, P. (2006). The Nordic model in education: education as part of the political system in the last 50 years. Scandinavian journal of educational research, 50 (3), 245-283.

https://doi.org/10.1080/00313830600743274

Toppino, T. C. & Gerbier, E. (2014). About practice: repetition, spacing, and abstraction. The Psychology of Learning and Motivation, 60, 113–189.

https://doi.org/10.1016/B978-0-12-800090-8.00004-4

Utdanningsdirektoratet (2016). Læreplan i matematikk. Author.

Van Steenbrugge, H., Valcke, M. & Desoete, A. (2013). Teachers’ views of mathematics textbook series in Flanders: Does it (not) matter which mathematics textbook series schools choose? Journal of Curriculum Studies, 45 (3), 322-353. https://doi.org/10.1080/00220272.2012.713995

Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H. & Houng, R. T. (2002). According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks. Kluwer.

https://doi.org/10.1007/978-94-007-0844-0

Viholainen, A., Partanen, M., Piiroinen, J., Asikainen, M. & Hirvonen, P. E. (2015). The role of textbooks in Finnish upper secondary school mathematics: theory, examples and exercises. Nordic Studies in Mathematics Education, 20 (3-4), 157-178.

Vincent, J. & Stacey, K. (2008). Do mathematics textbooks cultivate shallow teaching? Applying the TIMSS video study criteria to Australian eighth-grade mathematics textbooks. Mathematics Education Research Journal, 20 (1), 82-107. https://doi.org/10.1007/BF03217470

Wertsch, J. V. (1998). Mind as action. Oxford University Press.

https://doi.org/10.1093/acprof:oso/9780195117530.001.0001

Wijaya, A., Heuvel-Panhuizen, M. van den & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89 (1), 41–65.

https://doi.org/10.1007/s10649-015-9595-1

Yang, D. C., Tseng, Y. K. & Wang, T. L. (2017). A comparison of geometry problems in middle-grade mathematics textbooks from Taiwan, Singapore, Finland, and the United States. Eurasia Journal of Mathematics, Science and Technology Education, 13 (7), 2841-2857.

https://doi.org/10.12973/eurasia.2017.00721a

Yang, D. C. (2018). Study of fractions in elementary mathematics textbooks from Finland and Taiwan. Educational Studies, 44 (2), 190-211.

https://doi.org/10.1080/03055698.2017.1347493