Abstract
Algebra is the fundamental language of mathematics, and a profound understanding of school algebra is an important prerequisite for further studies in mathematical sciences. The aim of this study is to characterize the algebraic competence of the Norwegian upper secondary school students participating in Trends in International Mathematics and Science Study (TIMSS) Advanced. Based on theoretical conceptualizations of school algebra (Kieran, 2004) and of mathematical competence (Niss & Højgaard, 2011), a set of item descriptors have here been developed. Each of the algebra items in the TIMSS Advanced mathematics test have then been evaluated with respect to these descriptors, and correlations between student performance and item descriptors have been calculated. The results show that Norwegian upper secondary school students tend to perform weakly on items that place high demands on symbol manipulation. Furthermore, these students’ strength is in tasks that are placed in an extra-mathematical (applied) context, that require text comprehension, where students are expected to generate the mathematical expressions needed to find a solution, but that place low demands on student ability to manipulate symbolic expressions. Hence, the results of this study suggests that if Norwegian upper secondary school students’ mastery of algebra is to be promoted, it seems reasonable to devote more teaching resources to the transformational aspects of algebraic activity, i.e. to developing their ability to efficiently manipulate symbolic expressions.
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Alseth, B., Breiteig, T. & Brekke, G. (2003). Endringer og utvikling ved R97 som bakgrunn for videre planlegging og justering: matematikkfaget som kasus TELEMARKSFORSKNING-NOTODDEN. Senter for pedagogisk forsking og utviklingsarbeid
Angell, C., Kjærnsli, M. & Lie, S. (1999). Hva i all verden skjer i realfagene i videregående skole? Oslo, Norway: Universitetsforlaget.
Angell, C., Lie, S. & Rohatgi, A. (2011). TIMSS Advanced 2008: Fall i fysikk-kompetanse i Norge og Sverige. NorDiNa, 7(1), 17–31.
Arora, A., Foy, P., Martin, M. O. & Mullis, I. V. S. (Eds.). (2009). TIMSS Advanced 2008 technical report. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College
Bardini, C., Pierce, R. U. & Stacey, K. (2004). Teaching linear functions in context with graphics calculators: Students’ responses and the impact of the approach on their use of algebraic symbols. International Journal of Science and Mathematics Education, 2(3), 353–376.
Bednarz, N., Kieran, C. & Lee, L. (1996). Approaches to algebra. Perspectives for research and teaching. Dordrecht, the Netherlands: Kluwer Academic.
Drijvers, P., Goddijn, A. & Kindt, M. (2010). Algebra education: Exploring topics and themes. In P. Drijvers (Ed.), Secondary algebra education (pp. 5–26). Rotterdam, the Netherlands: Sense.
Garden, R. A., Lie, S., Robitaille, D. F., Angell, C., Martin, M. O., Mullis, I. V. S. & Alka, A. (2006). TIMSS Advanced 2008 assessment frameworks. Boston: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.
Grønmo, L. S. (2010). Norway: Low achievement in mathematics in compulsory school as evidenced by TIMSS and PISA. In B. Sriraman, C. Bergsten, S. Goodchild, G. Pálsdóttir, B. Dahl & L. Haapasalo (Eds.), The first sourcebook on Nordic research in mathematics education. Charlotte, NC: Information Age.
Grønmo, L. S., Bergem, O., K., Kjærnsli, M., Lie, S. & Turmo, A. (2004). Hva i all verden har skjedd i realfagene? Norske elevers prestasjoner i matematikk og naturfag i TIMSS 2003: Acta Didactica, ILS, UiO.
Grønmo, L. S. & Olsen, R. V. (2006). TIMSS versus PISA: The case of pure and applied mathematics. The Second IEA International Research Conference: Proceedings of the IRC-2006.
Grønmo, L. S., Onstad, T. & Pedersen, I. F. (2010). Matematikk i motvind. TIMSS Advanced 2008 i videregående skole. Oslo, Norway: Unipub.
Heid, M. K. & Edwards, M. T. (2001). Computer algebra systems: Revolution or retrofit for today’s mathematics classrooms? Theory Into Practice, 40(2), 128–136.
Huntley, M. A., Rasmussen, C. L., Villarubi, R. S., Sangtong, J. & Fey, J. T. (2000). Effects of Standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra and functions strand. Journal of Research in Mathematics Education, 31(3), 328–361.
KD. (2006). Matematikk for realfag—Programfag i studiespesialiserende utdanningsprogram. Retrieved 05.05.2013 from http://www.udir.no/kl06/MAT3-01/Hele/
Kendal, M. & Stacey, K. (2004). Algebra: A world of difference. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra. The 12 th ICMI study (Vol. 8, pp. 329–346). Dordrecht, the Netherlands: Kluwer Academic.
Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde & A. Pérez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (pp. 271–290). Seville, Spain: S.A.E.M. Thales.
Kieran, C. (2004). The core of algebra: Reflections on its main activities. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra. The 12 th ICMI study (Vol. 8, pp. 21–33). Dordrecht, the Netherlands: Kluwer Academic.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. Building meaning for symbols and their manipulation. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2). Charlotte, NC: Information Age.
Kieran, C. & Drijvers, P. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11(2), 205–263.
Kjærnsli, M., Lie, S., Olsen, R. V. & Roe, A. (2007). Tid for tunge løft. Norske elevers kompetanse i naturfag, lesing og matematikk i PISA 2006. Oslo, Norway: Universitetsforlaget.
Klieme, E. & Baumert, J. (2001). Identifying national cultures of mathematics education: Analysis of cognitive demands and differential item functioning in TIMSS. European Journal of Psychology of Education, 16(3), 385–402.
KUF. (2000). Læreplan for videre opplæring Matematikk.Studieretningsfag i studieretning for allmenne, økonomiske og administrative fag. Retrieved 05.05.2013 from http://www.udir.no/Lareplaner/Finn-lareplan/Lareplanverket-for-videregaende-opplaring-R94/#Felles allmenne fag
KUF (1999). Læreplan for videregående opplæring Matematikk. Felles allment fag i alle studieretninger. Retrieved 05.05.2013 from http://www.udir.no/Lareplaner/Finn-lareplan/Lareplanverket-for-videregaende-opplaring-R94/#Felles allmenne fag
Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231–258.
Lee, L. (1996). An initiation into algebraic culture through generalization activities. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra. Perspectives for research and teaching. Dordrecht, the Netherlands: Kluwer Academic.
Lie, S., Angell, C. & Rohatgi, A. (2010). Fysikk i fritt fall? TIMSS Advanced 2008 i videregående skole. Oslo, Norway: Unipub.
Llinares, S. & Roig, A. (2008). Secondary school students’ construction and use of mathematical models in solving word problems. International Journal of Science and Mathematics Education, 6(3), 505–532.
MacGregor, M. (2004). Goals and content of an algebra curriculum for the compulsory years of schooling. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra. The 12 th ICMI study (Vol. 8, pp. 311–328). Dordrecht, the Netherlands: Kluwer Academic.
MacGregor, M. & Stacey, K. (1994). Progress in learning algebra: Temporary and persistent difficulties. In B. W. G. Bell, N. Leeson, & J. Geake (Ed.), Proceedings of the Seventeenth Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 403–410).
Mullis, I. V. S. Martin, M. O., Robitaille, D. F. & Foy, P. (2009). TIMSS Advanced international report. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis & S. Papastavridis (Eds.), 3 rd Mediterranean conference on mathematical education (pp. 115–124). Athens, Greece: Hellenic Mathematical Society and Cyprus Mathematical Society.
Niss, M. & Højgaard, T. (Eds.). (2011). Competencies and mathematical learning. Ideas and inspiration for the development of mathematics teaching and learning in Denmark. Roskilde, Denmark: Roskilde University.
Olsen, R. V. (2005). Achievement tests from an item perspective: an exploration of single item data from the PISA and TIMSS studies, and how such data can inform us about students’ knowledge and thinking in science. Ph.D., University of Oslo, Oslo.
Olsen, R. V. (2006). A Nordic profile of mathematics achievement: Myth or reality? In J. Mejding & A. Roe (Eds.), Northern Lights on PISA 2003—a reflection from the Nordic countries. Copenhagen, Denmark: Nordic Council of Ministers.
Olsen, R. V. & Grønmo, L. S. (2006). What are the characteristics of the Nordic profile in mathematical literacy? In J. Mejding & A. Roe (Eds.), Northern lights on PISA 2003—a reflection from the Nordic countries. Copenhagen, Denmark: Nordic Council of Ministers.
Pedersen, I. F. (2013). Is TIMSS Advanced an appropriate instrument for evaluating mathematical performance at the advanced level of Norwegian upper secondary school? An analysis of curriculum documents and assessment items. Acta Didactica Norge, 7(1), Art-5.
Pierce, R. & Stacey, K. (2004). Monitoring progress in algebra in a CAS active context: Symbol sense, algebraic insight and algebraic expectation. International Journal of Technology in Mathematics Education, 11(1), 3–11.
Rittle-Johnson, B. & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561–574.
Rutkowski, L. & Rutkowski, D. (2009). Trends in TIMSS responses over time: evidence of global forces in education? Educational Research and Evaluation, 15(2), 137–152.
Schoenfeld, A. H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55–80.
Schoenfeld, A. H. (2004). The math wars. Educational Policy, 18, 253–286.
Schoenfeld, A. H. (2007). Issues and tensions in the assessment of mathematical proficiency. In A. H. Schoenfeld (Ed.), Assessing mathematical proficiency (Vol. 53). Berkeley, CA: Mathematical Sciences Research Institute Publications.
Stacey, K. & Chick, H. (2004). Solving the problem with algebra. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra. The 12 th ICMI study (Vol. 8, pp. 1–20). Dordrecht, the Netherlands: Kluwer Academic.
Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411.
Star, J. R. & Rittle-Johnson, B. (2009). Making algebra work: Instructional strategies that deepen student understanding, within and between representations. ERS Spectrum, 27(2), 11–18.
Stein, M. K., Grover, B. W. & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.
Stemler, S. E. (2004). A comparison of consensus, consistency, and measurement approaches to estimating interrater reliability. Practical Assessment, Research and Evaluation, 9(4).
Thompson, D. R. & Senk, S. L. (2001). The effects of curriculum on achievement in second-year algebra: The example of the University of Chicago School Mathematics Project. Journal for Research in Mathematics Education, 32(1), 58–84.
Yerushalmy, M. (2000). Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra. Educational Studies in Mathematics, 43(2), 125–147.
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Pedersen, I.F. WHAT CHARACTERIZES THE ALGEBRAIC COMPETENCE OF NORWEGIAN UPPER SECONDARY SCHOOL STUDENTS? EVIDENCE FROM TIMSS ADVANCED. Int J of Sci and Math Educ 13 (Suppl 1), 71–96 (2015). https://doi.org/10.1007/s10763-013-9468-y
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DOI: https://doi.org/10.1007/s10763-013-9468-y