Mathematical Literacy from the Perspective of Solving Contextual Problems
The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA.
- Pub. date: January 15, 2021
- Pages: 467-483
- 1498 Downloads
- 964 Views
- 17 Citations
The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA POTI, which aims to develop mathematical literacy at the national level, from kindergarten to secondary education. All of the topics treated represent starting points for our research, in which we were interested in how sixth-grade primary school students solve non-contextual and contextual problems involving the same mathematical content (in the contextual problems this content still needs to be recognised, whereas in the non-contextual problems it is obvious). The main guideline in the research was to discover the relationship between mathematical knowledge, which is the starting point for solving problems from mathematical literacy (contextual problems), and mathematical literacy. The empirical study was based on the descriptive, causal and non-experimental methods of pedagogical research. We used both quantitative and qualitative research based on the grounded theory method to process the data gathered from how the participants solved the problems. The results were quantitatively analysed in order to compare the success at solving problems from different perspectives. Analysis of the students’ success in solving the contextual and non-contextual tasks, as well as the strategies used, showed that the relationship between mathematical knowledge and mathematical literacy is complex: in most cases, students solve non-contextual tasks more successfully; in solving contextual tasks, students can use completely different strategies from those used in solving non-contextual tasks; and students who recognise the mathematical content in contextual tasks and apply mathematical knowledge and procedures are more successful in solving such tasks. Our research opens up new issues that need to be considered when developing mathematical literacy competencies: which contexts to choose, how to empower students to identify mathematical content in contextual problems, and how to systematically ensure – including through projects such as NA-MA POTI – that changes to the mathematics curriculum are introduced thoughtfully, with regard to which appropriate teacher training is crucial.
Keywords: Contextual problem, mathematical literacy, NA-MA POTI project, non-contextual problem, sixth-grade students, mathematical knowledge.
References
Afgani, M. W., Suryadi, D., & Dahlan, J. A. (2019). The enhancement of pre-service mathematics teachers’ mathematical understanding ability through ACE teaching cyclic. Journal of Technology and Science Education, 9(2), 153–167. https://doi.org/10.3926/jotse.441
Alsina, C. (2002). Too much is not enough. Teaching math through useful applications with local and global perspectives. Educational Studies in Mathematics, 50, 239-250. https://doi.org/10.1023/A:1021114525054
Amit, M., & Portnov-Neeman, Y. (2017). Explicit teaching’ as an effective method of acquiring problem solving strategies - the case of ’working backwards. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10). DCU Institute of Education and ERME. https://hal.archives-ouvertes.fr/hal-01950528
Baiduri, , Utami, O.R., & Alfani, P.I. (2020). Mathematical connection process of students with high mathematics ability in solving PISA problems. European Journal of Educational Research, 9(4), 1527-1537. https://doi.org/10.12973/eu-jer.9.4.1527
Calado, F. M., & Bogner, F. X. (2013). A Reflection on distorted views of science and technology in science textbooks as obstacles to the improvement of students’ scientific literacy. European Journal of Educational Research, 2(2), 51-68. https://doi.org/10.12973/eu-jer.2.2.51
Cañadas, M. C., & Castro, E. (2007). A proposal of categorisation for analysing inductive reasoning. PNA, 1(2), 67-78.
Celik, H. C. (2019). Investigating the visual mathematics literacy self-efficacy (VMLSE) perceptions of eighth grade students and their views on this issue. International Journal of Educational Methodology, 5(1), 165-176. https://doi.org/10.12973/ijem.5.1.177
Creswell, J. W. (2003). Research design: Qualitative, quantitative, and mixed methods approach (2nd ed.). Sage Publications, Inc.
Dubinsky, E. (2001). Using a theory of learning in college mathematics courses. University of Warwick.
Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2013). Mathematical connections and their relationship to mathematics knowledge for teaching geometry. School Science and Mathematics, 113(3), 120–134. https://doi.org/10.1111/ssm.12009
Geraniou, E. & Jankvist, U.T. (2019). Towards a definition of “mathematical digital competency”. Educational Studies in Mathematics, 102, 29–45. https://doi.org/10.1007/s10649-019-09893-8
Glasnović Gracin, D. (2014). Mathematics textbook as an object of research. Croatian Journal of Education,16(3), 211-237.
Goos, M., & Kaya, S. (2019). Understanding and promoting students’ mathematical thinking: a review of research published in ESM. Educational Studies in Mathematics, 103, 7-25. https://doi.org/10.1007/s10649-019-09921-7
Hackenberg, A. (2007). Units coordination and construction of improper fractions: A revision of the splitting hypothesis. Journal of Mathematical Behaviour, 26(1), 27–47. https://doi.org/10.1016/j.jmathb.2007.03.002
Hannula, M. S. (2003). Location fractions on number line. In N. A. Pateman, B. J. Dougherty, & J. T. Zillox (Eds.), Proceedings of the 27th conference of the international group for the psychology of mathematics education (pp. 17-24). PME.
Hartas, D. (2010). Educational research and inquiry, qualitative and quantitative approaches. Continuum International Publishing Group.
Hiebert, J. (Ed.). (1986). Conceptual and procedural knowledge: The case of mathematics. Lawrence Erlbaum.
Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). Macmillan.
Hodnik Čadež, T, & Manfreda Kolar, V. (2015). Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem. Educational Studies in Mathematics, 89(2), 283-306. https://doi.org/10.1007/s10649-015-9598-y
Ic, U., & Tutak, T. (2017). Correlation between computer and mathematical literacy levels of 6th grade students. European Journal of Educational Research 7(1), 63 - 70. https://doi.org/10.12973/eu-jer.7.1.63
Islami, M. D., Sunardi, S., & Slamin, S. (2018). The mathematical connections process of junior high school students with high and low logical mathematical intelligence in solving geometry problems. International Journal of Advanced Engineering Research and Science, 5(4), 10–18. https://doi.org/10.22161/ijaers.5.4.3
Jablonka E. (2003) Mathematical Literacy. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education. Springer international handbooks of education (pp. 75-102). Springer. https://doi.org/10.1007/978-94-010-0273-8_4
Kieren, T. E. (1976). On the mathematical, cognitive and instructional foundations of rational numbers. In R. A. Lesh (Ed.), Number and measurement: papers from a research workshop (pp.101–144). ERIC/SMEAC.
Kilpatrick, J. (2002). Understanding mathematical literacy: The contribution of research. Educational Studies in Mathematics, 47, 101-116.
Krek, J. (2015). Two principles of early moral education: a condition for the law, reflection and autonomy. Studies in Philosophy & Education, 34(1), 9-29.
Krek, J., Klopčič, L. (2019). Teacher authority and the educational role of the class teacher in the era of permissiveness. Didactica Slovenica, 34(3/4), 122-140.
Kula Unver, S., Hidiroglu, C. N., Tekin Dede, A., & Bukova Guzel, E. (2018). Factors revealed while posing mathematical modelling problems by Mathematics student teachers. European Journal of Educational Research, 7(4), 941-952. https://doi.org/10.12973/eu-jer.7.4.941
Kyriakides, L. Campbell, R. J., & Christofidou, E. (2002). Generating criteria for measuring teacher effectiveness through a self-evaluation approach: a complementary way of measuring teacher effectiveness. School Effectiveness and School Improvement, 11, 501-529.
Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowldege to explain the gap between theory-based recommendations and school practice in the use of connection task. Educational Studies in Mathematics, 66, 349-371. https://doi.org/10.1007/s10649-006-9071-z
Manfreda Kolar, V., Slapar, M., & Hodnik Čadež, T. (2012). Comparison of competences in inductive reasoning between primary teacher students and mathematics teacher students. In B. Maj-Tatsis & K. Tatsis (Eds.), Generalization in mathematics at all educational levels (pp. 299-311). Wydawnictwo Uniwersytetu Rzeszowskiego.
Mason, J., Burton, L., & Stacey, K. (2010). Thinking Mathematically. Pearson Education Limited.
Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26, 400-417.
Niss, M., Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102, 9-28. https://doi.10.1007/s10469-019-09903-9
North, M., & Christiansen, I. M. (2015). Problematizing current forms of legitimized participation in the examination papers for mathematical literacy. Pythagoras, Journal of the Association for Mathematics Education of South Africa, 36(1), 1-11. https://doi.10.4102/pythagoras.v36i1.285
Organisation for Economic Co-operation and Development. (2003). The PISA 2003 assessment framework. Mathematics, reading, science and problem solving knowledge and skills. OECD.
Pólya, G. (1945). How to Solve It. University Press.
Radford, L. (2008). Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM Mathematics Education, 40, 83-96.
Reid, D. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, 33(1), 5-29.
Rittle-Johnson, B., & Koedinger, K. R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23(3), 313-349. https://doi.10.1207/s1532690xci2303_1
Sáenz, C. (2009). The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA). Educational Studies in Mathematics, 71, 123-143. https://www.jstor.org/stable/40284590
Sagadin, J. (1991). Razprave iz pedagoške metodologije [Discussions on pedagogical methodology]. Znanstveni inštitut Filozofske fakultete Univerze v Ljubljani.
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press, Inc.
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), 1–36. https://doi.org/10.1007/BF00302715
Spangenberg, E. D. (2012). Thinking styles of mathematics and mathematical literacy learners: Implications for subject choice. Pythagoras, 33(3), 1-12. https://doi.10.4102/pythagoras.v33i3.179.
Stacey, K., & Turner, R. (2015). The evolution and key concepts of the PISA mathematics frameworks. In K. Stacey & R. Turner (Eds.), Assessing mathematical literacy (pp. 5-33). Springer international Publishing.
Steen, L. A. (Ed.) (2001). Mathematics and democracy: The case for quantitative literacy. National Council on Education and the Disciplines.
Suciati, Munadi, S., Sugiman, & Febriyanti, R. W. D. (2020). Design and Validation of Mathematical Literacy Instruments for Assessment for Learning in Indonesia. European Journal of Educational Research, 9(2), 865 - 875. https://doi.org/10.12973/eu-jer.9.2.865
Sullivan, P. (2011). Teaching mathematics: Using research informed strategies. Australian Council for Educational Research.
Tohir, M., Maswar, M., Atikurrahman, M., Saiful, S., & Pradita, D. A. R. (2020). Prospective teachers' expectations of students' mathematical thinking processes in solving problems. European Journal of Educational Research, 9(4), 1735-1748. https://doi.org/10.12973/eu-jer.9.4.1735
Tunç-Pekkan, Z. (2015). An analysis of elementary school children’s fractional knowledge depicted with circle, rectangle, and number line representations. Educational Studies in Mathematics, 89, 419–441.
Umbara, U., & Suryadi, D. (2019). Re-Interpretation of Mathematical Literacy Based on the Teacher's Perspective. International Journal of Instruction, 12(4), 789-806. https://doi.org/10.29333/iji.2019.12450a
Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9–35.
Yin, R. K. (2017). Case study research and applications: Design and methods. Sage publications.