Exercise design in mathematics textbooks: the case of subtraction

Authors

  • Malin Norberg

DOI:

https://doi.org/10.7146/nomad.v26i1.149147

Abstract

Mathematics textbooks are teaching tools used by most students studying mathematicsworldwide.Inthisdescriptivetextbookanalysis,allSwedishmathematics textbooks for year 1, both digital and printed, were mapped out according to the resources used for communication. For delimitation, a focus on subtraction as an arithmetic operation was chosen. The result shows large differences between the 17 textbook series, concerning both the type of subtraction exercises offered and the use of different resources for communication and learning, such as writing, images, and mathematical symbols. Digital textbooks were largely similar to the printed textbooks, except for one tablet-based textbook. Altogether, the study shows that the choice of mathematics textbooks affects how subtraction is presented to students and, by extension, the learning situations students encounter when working with mathematics textbooks.

References

Alshwaikh, J. (2016). Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse. Research in Mathematics Education, 18 (2), 165-181. https://doi.org/10.1080/14794802.2016.1177580

Bartolini Bussi, M. G., Canalini, R. & Ferri, F. (2011). Towards cultural analysis of content: problems with variation in primary school. In J. Novotna & H. Moraova (Eds.), Proceedings of SEMT'11, international symposium elementary math teaching: the mathematical knowledge needed for teaching elementary school (pp. 9-20). Charles University.

Carpenter, T. P. & Moser, J. M. (1983). The acquisition of addition and subtraction concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics: concepts and processes (pp. 7-44). Academic Press.

Carter, J., Li, Y. & Ferrucci, B. J. (1997). A comparison of how textbooks present integer addition and subtraction in PRC and USA. The Mathematics Educator, 2 (2), 197-209.

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

Despina, D. & Harikleia, L. (2014). Addition and subtraction word problems in Greek grade A and grade B mathematics textbooks: distribution and children's understanding. International Journal for Mathematics Teaching and Learning, July 2014, web.

Dyrvold, A. (2016). The role of semiotic resources when reading and solving mathematics tasks. Nordic Studies in Mathematics Education, 21 (3), 51-72.

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

Foxman, D. & Beishuizen, M. (2002). Mental calculation methods used by 11-year-olds in different attainment bands: a reanalysis of data from the 1987 APU survey in the UK. Educational Studies in Mathematics, 51 (1-2), 41-69. https://doi.org/10.1023/A:1022416021640

Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243-275). Macmillan.

Fuson, K., Stigler, J. & 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 (5), 449-456. https://doi.org/10.2307/749177

Grönlund, Å., Wiklund, M. & Böö, R. (2017). No name, no game: challenges to use of collaborative digital textbooks. Education and Information Technologies, 23 (3), 1359-1375. https://doi.org/10.1007/s10639-017-9669-z

Hiebert, J. & Grouws, D. A. (2002). The effects of classroom mathematics teaching on students learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). NCTM.

Mayer, R. E., Sims, V. & Tajika, H. (1995). A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32 (2), 443-60. https://doi.org/10.2307/1163438

Morgan, C. (2006). What does social semiotics have to offer mathematics education research? Educational Studies in Mathematics, 61 (1/2), 219-245. https://doi.org/10.1007/s10649-006-5477-x

Mullis, I. V., Martin, M. O., Foy, P. & Arora, A. (2012). TIMSS 2011 international results in mathematics. IEA.

Norberg, M. (2019). Potential for meaning making in mathematics textbooks. Designs for Learning, 11 (1), 52-62. https://doi.org/10.16993/dfl.123

Norberg, M. (2020). Från design till meningsskapande - en multimodal studie om elevers arbete med matematikläroböcker i årskurs 1 [From design to meaning-making - a multimodal study on students' work with mathematics textbooks in grade 1] (PhD thesis). Mittuniversitetet.

O'Halloran, K. L. (2005). Mathematical discourse: language, symbolism and visual images. Continuum.

Österholm, M. & Bergqvist, E. (2013). What is so special about mathematical texts? Analyses of common claims in research literature and of properties of textbooks. ZDM, 45 (5), 751-763. https://doi.org/10.1007/s11858-013-0522-6

Österholm, M., Bergqvist, T., Liljekvist, Y. & Bommel, J. van (2016). Utvärdering av Matematiklyftets resultat [Evaluation of the Mathematics Lift result]. Umeå University.

Remillard, J. T. Harris, B. & Agodini, R. (2014). The influence of curriculum material design on opportunities for student learning. ZDM, 46 (5), 735-749. https://doi.org/10.1007/s11858-014-0585-z

Reys, B., Reys, R. & Koyama, M. (1996). The development of computation in three Japanese primary-grade textbooks. The Elementary School Journal, 96 (4), 423-437. https://doi.org/10.1086/461837

Riley, M. S., Greeno, J. G. & Heller, J. I. (1983). Development of children's problem-solving ability in arithmetic. In H. Ginsburg (Ed.), The development of mathematical thinking (pp. 153-196). Academic Press.

Ristola, K., Tapaninaho, T. & Tirronen, L. (2012). Favoritmatematik 1A [Favourite mathematics]. Studentlitteratur. (Illustrator: M. Rajamäki)

Segerby, C. (2017). Supporting mathematical reasoning through reading and writing in mathematics: making the implicit explicit [PhD thesis]. Malmö University.

Skolverket. (2006). Läromedlens roll i undervisningen - grundskollärares val, användning och bedömning av läromedel i bild, engelska och samhällskunskap [The role of teaching materials in teaching - the choice, use and assessment of teaching materials in Arts, English and Social Studies by compulsory schoolteachers]. Skolverket.

Skolverket. (2010). Ämnesproven i grundskolans årskurs 5 [National tests in year 5]. Skolverket.

Skolverket. (2011). Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011 [Curriculum for compulsory school, pre-school class and leisure centre 2011]. Skolverket.

Skolverket. (2019). Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011. Reviderad 2019 [Curriculum for compulsory school, pre-school class and leisure centre 2011. Revised 2019]. Skolverket.

Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H. & Houang, R. T. (2002). According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks. Kluwer Academic. https://doi.org/10.1007/978-94-007-0844-0_8

Zhou, Z. & Peverly, S. (2005). Teaching addition and subtraction to first graders: a Chinese perspective. Psychology in the Schools, 42 (3), 259-272. https://doi.org/10.1002/pits.20077

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Published

2021-03-01

How to Cite

Norberg, M. (2021). Exercise design in mathematics textbooks: the case of subtraction. NOMAD Nordic Studies in Mathematics Education, 26(1), 5–29. https://doi.org/10.7146/nomad.v26i1.149147

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