Gender and strategy use in proportional situations: an Icelandic study
DOI:
https://doi.org/10.7146/nomad.v12i3.148036Abstract
This study was conducted to investigate the influence of contextual and number structures on individuals’ use of strategies in solving missing value proportion problems, and to examine gender differences in strategy use. Fifty-three eighth graders in one school in Reykjavik, Iceland, participated in this study. Twenty-seven females and twenty-six males were individually interviewed as they solved sixteen missing value proportion problems. The problems represented four contextual structures. No gender differences were identified in the overall success rate. However, girls were more successful than boys in handling associated sets and symbolic problems, and boys were more successful than girls in part-part-whole problems. Moreover, the data suggest that the contextual structures influence females’ choice of strategy more than that of males.
References
Abramowitz, S. (1975). Adolescent understanding of proportionality: the effects of task characteristics (Study undertaken as a doctoral dissertation). Palo Alto, CA: Stanford University.
Beaton, A., Mullis, I., Martin, M., Gonzalez, E., Kelly, D. et al. (1996). Mathematics achievement in the middle school years: IEA's third International mathematics and science study (TIMSS). Chestnut Hill, MA: Boston College, TIMSS International Study Center.
Behr, M., Harel, G., Post, T. & Lesh, R. (1992). Rational number, ratio, and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York: Macmillan.
Behr, M., Harel, G., Post, T. & Lesh, R. (1994). Units of quantity: a conceptual basis common to additive and multiplicative structures. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics, (pp. 121-176). Albany, NY: State University of New York Press.
Bell, A., Fischbein, E. & Greer, B. (1984). Choice of operation in verbal arithmetic problems. The effects of number size, problem structure, and context. Educational Studies in Mathematics, 15 (2), 129-148. https://doi.org/10.1007/BF00305893
Brandell, G., Nyström,P. & Sundqvist, C. (2004, July). Mathematics - a male domain. Paper presented at the quadrennial conference of the International Congress on Mathematical Education (ICME 10), Copenhagen.
Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L. & Empson, S.B. (1999). Children's mathematics: cognitively guided instruction. Portsmouth, NH: Heinemann.
Carr, M. & Jessup, D. (1997). Gender differences in first grade mathematics strategy use: social, metacognitive, and attribution influences. Journal of Educational Psychology, 89 (2), 318-328. https://doi.org/10.1037/0022-0663.89.2.318
Dienes, Z. P. (2000). The theory of the six stages of learning with integers. Mathematics in School, 29 (2), 27-33.
Dienes, Z. P. (2004). Six stages with rational numbers. New Zealand Mathematics Magazine, 41 (2), 44-53.
Fennema, E. (1995). Mathematics, gender, and research. In B. Grevholm & G. Hanna (Eds.), Gender and mathematics education: an ICMI study in stiftsgården Åkersberg, Höör, Sweden 1993 (pp. 21-38). Lund University Press.
Fennema, E., Carpenter, T. P., Jacobs, V. R. & Levi, L. (1996, April). Gender differences in mathematical thinking. Paper presented at the annual meeting of the American Educational Research Association, New York.
Forgasz, H. (2004, July). Computers for mathematics learning and gender stereotypes. Paper presented at the quadrennial conference of the International Congress on Mathematical Education (ICME 10), Copenhagen.
Gallagher, A. M. & De Lisi, R. (1994). Gender differences in scholastic aptitude test-mathematics problem solving among high-ability students. Journal of Educational Psychology, 86 (2), 204-211. https://doi.org/10.1037/0022-0663.86.2.204
Hart, K. M. (1981). Children's understanding of mathematics: 11-16. London: John Murray Ltd.
Inhelder, B. & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books. https://doi.org/10.1037/10034-000
Kaput, J. & West, M. (1994). Missing value proportional reasoning problems: factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235-287). Albany, NY: State University of New York Press.
Karplus, R., Pulos, S. & Stage, E. K. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 45-90). Orlando, FL: Academic Press.
Kieren, T. (1993). Rational and fractional numbers: from quotient fields to recursive understanding. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: an integration of research (pp. 49-84). Hillsdale, NJ: Lawrence Erlbaum.
Kimball, M. M. (1989). A new perspective on women's math achievement. Psychological Bulletin, 105 (2), 105-214. https://doi.org/10.1037/0033-2909.105.2.198
Lamon, S. (1993a). Ratio and proportion: connecting content and children's thinking. Journal for Research in Mathematics Education, 24 (1), 41-61. https://doi.org/10.5951/jresematheduc.24.1.0041
Lamon, S. (1993b). Ratio and proportion: children's cognitive and metacognitive processes. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: an integration of research (pp. 131-156). Hillsdale, NJ: Lawrence Erlbaum.
Lesh, R., Post, T. & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Reston, VA: National Council of the Teachers of Mathematics.
Linn, M. C. & Pulos, S. (1983). Aptitude and experience influences on proportional reasoning during adolescence: focus on male-female differences. Journal of Research in Mathematics Education, 14 (1), 30-46. https://doi.org/10.2307/748795
Lubienski, S. T. & Bowen, A. (2000). Who's counting? A survey of mathematics education research 1982-1998. Journal for Research in Mathematics Education, 31 (5), 626-633. https://doi.org/10.2307/749890
Mahlomaholo, S. & Sematly, M. (2004, July). Gender differences and black learners' attitudes towards mathematics in selected high schools in South Africa. Paper presented at the quadrennial conference of the International Congress on Mathematical Education (ICME 10), Copenhagen, Denmark.
Marshall, S.P. & Smith, J. D. (1987). Sex differences in learning mathematics: a longitudinal study with item and error analyses. Journal of Educational Psychology, 79 (4), 372-383. https://doi.org/10.1037/0022-0663.79.4.372
Noelting, G. (1980a). The development of proportional reasoning and the ratio concept. Part 1 - Differentiation of stages. Educational Studies in Mathematics, 11 (2), 217-253. https://doi.org/10.1007/BF00304357
Noelting, G. (1980b). The development of proportional reasoning and the ratio concept. Part 2 - Problem-structure at successive stages; Problem solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11 (3), 331-363. https://doi.org/10.1007/BF00697744
OECD (2004). PISA Learning for tomorrow's world: first results from PISA 2003. Paris: OECD. https://doi.org/10.1787/9789264006416-en
Olafsson, R. F., Halldorsson, A. M. & Bjornsson, J. K. (2006). Gender and the urban-rural differences in mathematics and reading: an overview of PISA 2003 results in Iceland. In J. Mejding & A. Roe (Eds.), Northern lights on PISA 2003 - a reflection from Nordic countries, (185-198). Copenhagen: Nordic Council of Ministers.
Pourkazemi, M. H. (2004, July). In the name of God. Gender and mathematics. Paper presented at the quadrennial conference of the International Congress on Mathematical Education (ICME 10), Copenhagen.
Pulos, S., Karplus, R. & Stage, E. K. (1981). Generality of proportional reasoning in early adolescence: content effects and individual differences. Journal of Early Adolescence, 1 (3), 257-264. https://doi.org/10.1177/027243168100100304
Resnick, L. B. & Singer, J. A. (1993). Protoquantitative origins of ratio reasoning. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: an integration of research (pp. 107-130). Hillsdale, NJ: Lawrence Erlbaum.
Soro, R. (2004, July). Teachers' beliefs about girls and boys equity in mathematics. Paper presented at the quadrennial conference of the International Congress on Mathematical Education (ICME 10), Copenhagen.
Sriraman, B. & English, L. (2004). Combinatorial mathematics: research into practice. Connecting research into teaching. The Mathematics Teacher, 98 (3), 182-191. https://doi.org/10.5951/MT.98.3.0182
Sriraman, B. & Lesh, R. (2006). Modeling conceptions revisited. Zentralblatt für Didaktik der Mathematik, 38 (3), 248-254. https://doi.org/10.1007/BF02652808
Sriraman, B. & Lesh, R. (2007). A conversation with Zoltan P. Dienes. Mathematical Thinking and Learning, 9 (1), 59-75. https://doi.org/10.1080/10986060709336606
Steinthorsdottir, O &, Sriraman, B. (2007). Iceland and rural/urban girls - PISA 2003 examined from an emancipatory viewpoint. In B. Sriraman (Ed.), International perspectives on social justice in mathematics education. The Montana Mathematics Enthusiast (Monograph 1), 169-178.
Steinthorsdottir,O. & Sriraman, B. (2007b). Icelandic 5th grade girls developmental trajectories in proportional reasoning. Paper submitted for publication.
Tourniaire. (1986). Proportion in elementary school. Educational Studies in Mathematics, 17 (4), 401-412. https://doi.org/10.1007/BF00311327
Tourniaire, F. & Pulos, S. (1985). Proportional reasoning: a review of the literature. Educational Studies in Mathematics, 16 (2), 181-204. https://doi.org/10.1007/PL00020739
Vergnaud, G. (1994). Multiplicative conceptual field: what and why? In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 41-59). Albany, NY: State University of New York Press.
Wiest. L. R. (2004, July). The critical role of an informal mathematics program for girls. Paper presented at the quadrennial conference of the International Congress on Mathematical Education (ICME 10), Copenhagen, Denmark.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
