Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students

References

• Al-Hroub, A. (2011). Developing assessment profiles for mathematically gifted children with learning difficulties at three schools in Cambridgeshire, England. Journal for the Education of the Gifted, 34(1), 7–44. doi:10.1177/016235321003400102
   Google Scholar
• Andrews, P. (in press). Is the “telling case” a methodological myth? International Journal of Social Research Methodology. doi10.1080/13645579.2016.1198165
   Web of Science ®Google Scholar
• Andrews, P., & Sayers, J. (2012). Teaching linear equations: Case studies from Finland, Flanders, and Hungary. Journal of Mathematical Behavior, 31(4), 476–488. doi:10.1016/j.jmathb.2012.07.002
   Google Scholar
• Andrews, P., & Xenofontos, C. (2015). Analysing the relationship between problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers. Journal of Mathematics Teacher Education, 18(4), 299–325. doi:10.1007/s10857-014-9287-2
   Web of Science ®Google Scholar
• Applebaum, M., Freiman, V., & Leikin, R. (2011). Prospective teachers’ conceptions about teaching mathematically talented students: Comparative examples from Canada and Israel. Mathematics Enthusiast, 8(1), 225–289.
   Google Scholar
• Bassock, M. (2001). Semantic alignments in mathematical word problems. In D. Gentner, K. Holyoak, & B. Kokinov (Eds.), The analogical mind (pp. 401–433). Cambridge, MA: MIT Press.
   Google Scholar
• Boaler, J. (1997). Setting, social class, and the survival of the quickest. British Educational Research Journal, 23(5), 575–595. doi:10.1080/0141192970230503
   Google Scholar
• Boaler, J., Wiliam, D., & Brown, M. (2000). Students’ experiences of ability grouping: Disaffection, polarization, and the construction of failure. British Educational Research Journal, 26(5), 631–648. doi:10.1080/713651583
   Web of Science ®Google Scholar
• Brandl, M. (2011). High attaining versus (highly) gifted pupils in mathematics: A theoretical concept and an empirical survey. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 1044–1055). Rzeszow, Poland: University of Rzeszow.
   Google Scholar
• 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. doi:10.1080/00313831.2015.1066427.
   Web of Science ®Google Scholar
• Butler, R. (2008). Ego-involving and frame of reference effects of tracking on elementary school students’ motivational orientations and help seeking in math class. Social Psychology of Education, 11(1), 5–23. doi:10.1007/s11218-007-9032-0
   Google Scholar
• Cai, J., & Lester, F. A. (2005). Solution representations and pedagogical representations in Chinese and US mathematics classrooms. Journal of Mathematical Behavior, 24(3–4), 221–237. doi:10.1016/j.jmathb.2005.09.003
   Google Scholar
• Calkins, M. (1894). A study of the mathematical consciousness. Educational Review, 8, 269–283.
   Google Scholar
• Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45–75. doi:10.1007/s10649-005-0808-x
   Google Scholar
• Christou, C., & Philippou, G. (1999). Role of schemas in one-step word problems. Educational Research and Evaluation, 5(3), 269–289. doi:10.1076/edre.5.3.269.3884
   Google Scholar
• Coxbill, E., Chamberlin, S., & Weatherford, J. (2013). Using model-eliciting activities as a tool to identify and develop mathematically creative students. Journal for the Education of the Gifted, 36(2), 176–197. doi:10.1177/0162353213480433
   Google Scholar
• Deal, L., & Wismer, M. (2010). NCTM principles and standards for mathematically talented students. Gifted Child Today, 33(3), 55–65. doi:10.1177/107621751003300313
   Google Scholar
• Diezmann, C., & Watters, J. (2000). Catering for mathematically gifted elementary students: Learning from challenging tasks. Gifted Child Today, 23(4), 14–19, 52. doi:10.4219/gct-2000-737
   Google Scholar
• Foy, P., Arora, A., & Stanco, G. (2013a). TIMSS 2011 user guide for the international database: Released items. Boston, MA: TIMSS & PIRLS International Study Center.
   Google Scholar
• Foy, P., Arora, A., & Stanco, G. (2013b). TIMSS 2011 user guide for the international database: Percent correct statistics for the released items. Boston, MA: TIMSS & PIRLS International Study Center.
   Google Scholar
• Gamoran, A., Porter, A., Smithson, J., & White, P. (1997). Upgrading high school mathematics instruction: Improving learning opportunities for low-achieving, low-income youth. Educational Evaluation and Policy Analysis, 19(4), 325–338. doi: 10.3102/01623737019004325
   Web of Science ®Google Scholar
• Garofalo, J. (1993). Mathematical problems preferences of meaning-oriented and number-oriented problem solvers. Journal for the Education of the Gifted, 17(1), 26–39. doi: 10.1177/016235329301700104
   Web of Science ®Google Scholar
• Garofalo, J., & Lester, F. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176. doi:10.1177/016235329301700104
   Google Scholar
• Gavin, M., Casa, T., Adelson, J., Carroll, S., Sheffield, L., & Spinelli, A. (2007). Project M3: Mentoring mathematical minds: A research-based curriculum for talented elementary students. Journal of Advanced Academics, 18(4), 566–585. doi:10.4219/jaa-2007-552
   Google Scholar
• Gavin, M., Casa, T., Adelson, J., Carroll, S., & Sheffield, L. (2009). The impact of advanced curriculum on the achievement of mathematically promising elementary students. Gifted Child Quarterly, 53(3), 188–202. doi:10.1177/0016986209334964
   Web of Science ®Google Scholar
• Ginsburg, H. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(3), 4–11.
   Google Scholar
• Graneheim, U., & Lundman, B. (2004). Qualitative content analysis in nursing research: Concepts, procedures and measures to achieve trustworthiness. Nurse Education Today, 24(2), 105–112. doi:10.1016/j.nedt.2003.10.001
   PubMed Web of Science ®Google Scholar
• Greer, B., Verschaffel, L., Van Dooren, M. & Mukhopadhyay, S. (2009). Introduction: Making sense of word problems: past, present, and future. In L. Verschaffel, B. Greer, W. Van Dooren & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. xi–xxviii). Rotterdam, Netherlands: Sense.
   Google Scholar
• Hattie, J. (2002). Classroom composition and peer effects. International Journal of Educational Research, 37(5), 449–481. doi:10.1016/S0883-0355(03)00015-6
   Google Scholar
• Heinze, A. (2005). Differences in problem solving strategies of mathematically gifted and nongifted elementary students. International Education Journal, 6(2), 175–183.
   Google Scholar
• Hensberry, K., & Jacobbe, T. (2012). The effects of Polya’s heuristic and diary writing on children’s problem solving. Mathematics Education Research Journal, 24(1), 59–85. doi:10.1007/s13394-012-0034-7
   Google Scholar
• Hsieh, H.-F., & Shannon, S. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15(9), 1277–1288. doi:10.1177/1049732305276687
   PubMed Web of Science ®Google Scholar
• Juter, K., & Sriraman, B. (2011). Does high achieving in mathematics = gifted and/or creative in mathematics? In B. Sriraman & K. H. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 45–66). Rotterdam, Netherlands: Sense.
   Google Scholar
• Kapa, E. (2001). A metacognitive support during the process of problem solving in a computerized environment. Educational Studies in Mathematics, 47(3), 317–336. doi:10.1023/a:1015124013119
   Google Scholar
• Karp, A. (2011). Toward a history of teaching the mathematically gifted: Three possible directions for research. Canadian Journal of Science, Mathematics and Technology Education, 11(1), 8–18. doi:10.1080/14926156.2011.548898
   Google Scholar
• Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM, 45(2), 167–181. doi:10.1007/s11858-012-0467-1
   Google Scholar
• Koshy, V., & Casey, R. (2005). Actualizing mathematical promise: Possible contributing factors. Gifted Education International, 20(3), 293–305. doi:10.1177/026142940502000305
   Google Scholar
• Krutetskii, V. (1976). The psychology of mathematical abilities in schoolchildren. Chicago, IL: University of Chicago Press.
   Google Scholar
• Kvale, S., and Brinkmann, S. (2009). Interviews: Learning the craft of qualitative research interviewing. London, UK: Sage.
   Google Scholar
• Leikin, R. (2010). Teaching the mathematically gifted. Gifted Education International, 27(2), 161–175. doi:10.1177/026142941002700206
   Google Scholar
• Leikin, R. (2014). Giftedness and high ability in mathematics. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 247–251). Dordrecht, Netherlands: Springer.
   Google Scholar
• Lithner, J. (2011). University mathematics students’ learning difficulties. Education Inquiry, 2(2), 289–303. doi: 10.3402/edui.v2i2.21981
   Google Scholar
• Mann, E. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236–260. doi:10.4219/jeg-2006-264
   Google Scholar
• Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. Wokingham, UK: Addison-Wesley.
   Google Scholar
• McClure, L. (2001). Supporting the able mathematician. Support for Learning, 16(1), 41–45. doi:10.1111/1467-9604.00184
   Google Scholar
• Mitchell, J. (1984). Typicality and the case study. In R. Ellen (Ed.), Ethnographic research: A guide to general conduct (pp. 237–241). London, UK: Academic Press.
   Google Scholar
• Nesher, P., Hershkovitz, S., & Novotna, J. (2003). Situation model, text base and what else? Factors affecting problem solving. Educational Studies in Mathematics, 52(2), 151–176. doi:10.1023/a:1024028430965
   Google Scholar
• Nogueira de Lima, R., & Tall, D. (2008). Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, 67(3), 3–18. doi:10.1007/s10649-007-9086-0
   Google Scholar
• Nunokawa, K. (2005). Mathematical problem solving and learning mathematics: What we expect students to obtain. Journal of Mathematical Behavior, 24(3-4), 325–340. doi:10.1016/j.jmathb.2005.09.002
   Google Scholar
• Organisation for Economic Cooperation and Development (2013). PISA 2012 results: What students know and can do - Student performance in mathematics, reading and science (Vol. I). Paris, France: OECD.
   Google Scholar
• Öystein, H. (2011). What characterizes high achieving studentś mathematical reasoning? In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 193–216). Rotterdam, Netherlands: Sense.
   Google Scholar
• Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67(1), 37–58. doi:10.1007/s10649-007-9083-3
   Google Scholar
• Pólya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.
   Google Scholar
• Reed, C. (2004). Mathematically gifted in the heterogeneously grouped mathematics classroom: What is a teacher to do? Journal of Secondary Gifted Education, 15(3), 89–95. doi: 10.4219/jsge-2004-453
   Google Scholar
• Roberts, S., & Tayeh, C. (2007). It’s the thought that counts: Reflecting on problem solving. Mathematics Teaching in the Middle School, 12(5), 232–237.
   Google Scholar
• Roediger, H. (1990). Implicit memory: Retention without remembering. American Psychologist, 45(9), 1043–1056. doi:10.1037/0003-066X.45.9.1043
   PubMed Web of Science ®Google Scholar
• Ruthven, K. (1987). Ability stereotyping in mathematics. Educational Studies in Mathematics, 18(3), 243–253. doi:10.1007/bf00386197
   Google Scholar
• Schoenfeld, A. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
   Google Scholar
• Sheffield, L. (2003). Extending the challenge in mathematics: Developing mathematical promise in K-8 students. Thousand Oaks, CA: Corwin Press.
   Google Scholar
• Sheffield, L. (2006). Mathematically promising students from the space age to the information age. Montana Mathematics Enthusiast, 3(1), 104–109.
   Google Scholar
• Singer, F., & Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational Studies in Mathematics, 83(1), 9–26. doi:10.1007/s10649-012-9422-x
   Web of Science ®Google Scholar
• Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: The problem-solving experiences of four gifted students. Journal of Advance Academics, 14(3), 151–165. doi:10.4219/jsge-2003-425
   Google Scholar
• Stake, R. (2005). Qualitative case studies. In N. Denzin & Y. Lincoln (Eds.), The Sage handbook of qualitative research. (3rd ed., pp. 443–466). Thousand Oaks, CA: Sage.
   Google Scholar
• Tulving, E., & Schacter, D. (1990). Priming and human memory systems. Science, 247(4940), 301–306. doi:10.1126/science.2296719
   PubMed Web of Science ®Google Scholar
• van Leeuwen, T. (2005). Introducing social semiotics. London, UK: Routhledge.
   Google Scholar
• Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 7(4), 339–359. doi:10.1016/S0959-4752(97)00008-X
   Web of Science ®Google Scholar
• Vilenius-Tuohimaa, P., Aunola, K., & Nurmi, J.-E. (2008). The association between mathematical word problems and reading comprehension. Educational Psychology: An International Journal of Experimental Educational Psychology, 28(4), 409–426. doi:10.1080/01443410701708228
   Web of Science ®Google Scholar
• Vilkomir, T., & O’Donoghue, J. (2009). Using components of mathematical ability for initial development and identification of mathematically promising students. International Journal of Mathematical Education in Science and Technology, 40(2), 183–199. doi:10.1080/00207390802276200
   Google Scholar
• Wiliam, D., & Bartholomew, H. (2004). It’s not which school but which set you're in that matters: The influence of ability grouping practices on student progress in mathematics. British Educational Research Journal, 30(2), 279–293. doi:10.1080/0141192042000195245
   Web of Science ®Google Scholar
• Xenofontos, C., & Andrews, P. (2012). Prospective teachers’ beliefs about problem solving: Cypriot and English cultural constructions. Research in Mathematics Education, 14(1), 69–85. doi:10.1080/14794802.2012.657439
   Google Scholar
• Yin, R. (2009). Case study research: Design and methods (4th ed.). London, UK: Sage.
   Google Scholar
• Zevenbergen, R. (2005). The construction of a mathematical habitus: Implications of ability grouping in the middle years. Journal of Curriculum Studies, 37(5), 607–619. doi:10.1080/00220270500038495
   Web of Science ®Google Scholar