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Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 20 No. 3 (2017): Noviembre

THE ROLE OF CONTEXT AND CONTEXT FAMILIARITY ON MATHEMATICS PROBLEMS

DOI
https://doi.org/10.12802/relime.17.2031
Submitted
June 28, 2023
Published
2017-11-30

Abstract

The mathematics education literature advocates the use of mathematics problems embedded in different contexts and therefore different mathematics curricula reflect this recommendation. A number of theoretical arguments support this, but the influence of context, and specifically the role of context familiarity, on students’ performance is an issue that is not yet fully understood. After a literature review, it is argued in this paper that ninety - odd years of research on problem context and students’ performance  suggest that nothing firm can be said about this relationship, because evidence about this relationship is undeniably sparse. Given that context takes on a number of meanings in the literature, this paper starts by clarifying and differentiating this term from others. Then, theoretical arguments and empirical research are reviewed in relation to the role of context and context familiarity on students’ performance.

References

  1. Almuna Salgado, F. (2016). Investigating the impact of context on students’ performance. In White, B., Chinnappan, M. & Trenholm, S. (Eds.), Proceedings of the 39th annual conference of the Mathematics Education Research Group of Australasia (pp.100-107). Adelaide: MERGA. ISBN 978-1-920846-29-9
  2. Almuna Salgado, F. (2010). Investigating the effect of item - context on students’ performance on Mathematics items. Master’s thesis. Available from University of Melbourne’s Catalogue (melb.b4103780)
  3. Almuna Salgado, F., & Stacey, K. (2014). Item context factors affecting students’ performance on mathematics items. In J. Anderson, M. Cavanagh & A. Prescott (Eds.), Proceedings of the the 37th annual conference of the Mathematics Education Research Group of Australasia
  4. (pp.55-62). Sydney: MERGA. ISBN: 978-1-920846-27-5
  5. Baranes, R., Perry, M., & Stigler, J. W. (1989). Activation of real - world knowledge in the solution of word problems. Cognition and Instruction, 6 (4), 287-318. doi: https://doi.org/10.1207/s1532690xci0604_1
  6. Bernardo, A. B. I. (1994). Problem - specific information and the development of problem - type schemata. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20 (2), 379-395.
  7. Bishop, A. J. (1993). Conceptualising cultural and social contexts in mathematics education. In B. Atweh, C. Kanes, M. Carss & G. Booker (Eds.), Proceedings of the Sixteenth AnnualConference of the Mathematics Education Research Group of Australasia. Brisbane: MERGA.
  8. Blum, W. (2002). ICMI Study 14: Applications and Modelling in Mathematics Education. Educational Studies in Mathematics, 51 (1), 149-171.
  9. Blum, W., Galbraith, P. L., Henn, H. W., & Niss, M. (2007). Modelling and applications in mathematics education: the 14th ICMI study. New York: Springer.
  10. Blum, W., Galbraith, P., & Niss, M. (2007). Introduction. In W. Blum, P. Galbraith, H. Henn & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (Vol. 10, pp. 3-32). New York: Springer.
  11. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects - State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 1, 37-68.
  12. Boaler, J. (1994). When Do Girls Prefer Football to Fashion? An Analysis of Female Underachievement in Relation to ’Realistic’ Mathematic Contexts. British Educational Research Journal, 20, 5, 551-564. doi: 10.2307/1500676
  13. Boaler, J. (1993). The Role of Contexts in the Mathematics Classroom: Do They Make Mathematics More ’Real’? For the Learning of Mathematics, 13, 2, 12-17. doi: 10.2307/40248079
  14. Brownell, W. A., & Stretch, L. B. (1931). The effect of unfamiliar settings on problem - solving. Durham, N.C: Duke University Press.
  15. Busse, A. (2011). Upper secondary students’ handling of real - world contexts. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling (Vol. 1, pp. 37-46). Dordrecht: Springer Netherlands.
  16. Busse, A., & Kaiser, G. (2003). Context in application and modelling - An empirical approach. In Q. X. Ye, W. Blum, S. Houston & Q. Y. Jiang (Eds.), Mathematical modelling in education and culture: ICTMA 10 (pp. 3-15). Chichester, UK: Albion Publishing.
  17. Carpenter, T. P., Lindquist, M. M., Matthews, W., & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary school. The Mathematics Teacher, 76 (9), 652-659. doi: 10.2307/27963780
  18. Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3 (1), 21-29. doi: 10.1111/j.2044-835X.1985.tb00951.x
  19. Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1987). Written and Oral Mathematics. Journal for Research in Mathematics Education, 18 (2), 83-97. doi: 10.2307/749244
  20. Chapman, O. (2006). Classroom Practices for Context of Mathematics Word Problems. Educational Studies in Mathematics, 62 (2), 211-230. doi: 10.1007/s10649-006-7834-1
  21. Chipman, S. F., Marshall, S. P. & Scott, P. A. (1991). Content Effects on Word Problem Performance: A Possible Source of Test Bias? American Educational Research Journal, 28(4), 897-915. doi: 10.3102/00028312028004897
  22. Civil, M. & Planas, N. (2004). Participation in the mathematics classroom: does every student have a voice? For the Learning of Mathematics, 24 (1), 7-12
  23. Clarke, D., & Helme, S. (1996). Context as Construction. In C. Keitel, U. Gellert, E. Jablonka & M. Muller (Eds.), Proceedings of the 47th meeting of the International Commision for the Study and Improvement of Mathematics Teaching in Berlin (pp. 379-389). Berlin: CIEAM.
  24. Cooper, B. & Dunne, M. (1998). Anyone for tennis? Social class differences in children’s responses to national curriculum mathematics testing. The Sociological Review, 46 (1), 115-148.
  25. De Lange, J. (2007). Large - Scale Assessment and Mathematics Education. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (pp. 1111-1142). Charlotte, NC: Information Age Publising Inc.
  26. De Lange, J. (1999). Framework for Classroom Assessment in Mathematics. Madison, WI: NICLA/ WCER.
  27. Depaepe, F., De Corte, E. & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26 (2), 152-160. doi: http://dx.doi.org/10.1016/j.tate.2009.03.016
  28. Felton, M. (2010). Is math politically neutral? Teaching Children Mathematics, 17 (2), 60-63.
  29. Fiddick, L., Cosmides, L. & Tooby, J. (2000). No interpretation without representation: the role of domain - specific representations and inferences in the Wason selection task. Cognition, 77(1), 1-79. doi: http://dx.doi.org/10.1016/S0010-0277(00)00085-8
  30. Fuchs, L. S., Fuchs, D., Hamlett, C. L. & Appleton, A. C. (2002). Explicitly Teaching for Transfer: Effects on the Mathematical Problem - Solving Performance of Students with Mathematics Disabilities. Learning Disabilities Research & Practice, 17 (2), 90.
  31. Galbraith, P., Stillman, G. & Brown, J. (2006). Identifying key transition activities for enhanced engagement in mathematical modeling. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Proceedings of the 29th annual conference of the Mathematics Education Research
  32. Group of Australasia (pp. 237-245). Adelaide: MERGA.
  33. Galbraith, P. (2012). Scoring points: Goals for real world problem solving. Australian Senior Mathematics Journal, 26 (2), 51-62.
  34. Galbraith, P. (1987). Modelling - teaching modelling. The Australian Mathematics Teacher, 43 (4), 6-9.
  35. Greatorex, J. (2014). Context in Mathematics questions. Research Matters, 17, 18-23. Retrieved from http://www.cambridgeassessment.org.uk/Images/164660-research-matters-17-january-2014.pdf
  36. Griggs, R. A. & Cox, J. R. (1982). The elusive thematic - materials effect in Wason’s selection task. British Journal of Psychology, 73 (3), 407-420.
  37. Helme, S. (1994). Mathematics Embedded in Context: The Role of Task Context in Performance, Task Perceptions and the Solution Methods of Adult Women Students. Master of Education, Australian Catholic University, Melbourne.
  38. Hembree, R. (1992). Experiments and Relational Studies in Problem Solving: A Meta - Analysis. Journal for Research in Mathematics Education, 23 (3), 242-273. doi: 10.2307/749120
  39. Huang, H. (2004). The impact of context on children’s performance in solving everyday mathematical problems with real - world settings. Journal of Research in Childhood Education, 18 (4), 278-292.
  40. Inhelder, B. & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence: An essay on the construction of formal operational structures (Vol. 22). New York: Routledge & Kegan Paul PLC.
  41. Johnson - Laird, Legrenzi, P. & Legrenzi, M. S. (1972). Reasoning and a sense of reality. British Journal of Psychology, 63 (3), 395-400.
  42. Johnson - Laird, P. & Wason, P. (1970). A theoretical analysis of insight into a reasoning task. Cognitive Psychology, 1 (2), 134-148.
  43. Lave, J. (1988). Cognition in Practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press.
  44. Leighton, J., & Gokiert, R. (2005). The Cognitive Effects of Test Item Features: Informing Item Generation by Identifying Construct Irrelevant Variance. Paper presented at the Annual Meeting of the National Council on Measurement in Education (NCME), Quebec, Canada.
  45. Lewis, A. B. & Mayer, R. E. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79 (4), 363-371.
  46. Lyda, W. J. & Franzén, C. G. (1945). A Study of Grade Placement of Socially Significant Arithmetic Problems in the High - School Curriculum. The Journal of Educational Research, 39 (4), 292-295. doi: https://doi.org/10.1080/00220671.1945.10881432
  47. Manktelow, K., & Evans, J. (1979). Facilitation of reasoning by realism: Effect or non - effect? British Journal of Psychology, 70 (4), 477-488.
  48. McNeil, N. M., Uttal, D. H., Jarvin, L. & Sternberg, R. J. (2009). Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, 19 (2), 171-184. doi: http://dx.doi.org/10.1016/j.learninstruc.2008.03.005
  49. Marsh, B., Tood, P. M. & Gigerenzer, G. (2004). Cognitive heuristics: Reasoning the fast and frugal way. In J. P. Leighton & R. J. Sternberg (Eds.), The Nature of Reasoning (pp. 273-290). New York: University Cambridge Press.
  50. National Council of Teachers of Mathematics. (2011). Focus in high school mathematics : fostering reasoning and sense making for all students: Reston, VA : National Council of Teachers of Mathematics.
  51. Niss, M., Bruder, R., Planas, N., Turner, R. & Villa - Ochoa, J. A. (2016). Survey team on: conceptualisation of the role of competencies, knowing and knowledge in mathematics education research. ZDM, 48 (5), 611-632. doi: https://doi.org/10.1007/s11858-016-0799-3
  52. Organisation for Economic Co-Operation and Development. (2013). PISA 2015 Draft mathematics framework. Retrieved January 6, 2015, from https://goo.gl/HdttDk
  53. Organisation for Economic Co-Operation and Development. (2006). PISA released items -Mathematics Retrieved May 22, 2013, from http://www.oecd.org/pisa/38709418.pdf
  54. Pierce, R. & Stacey, K. (2006). Enhancing the image of mathematics by association with simple pleasures from real world contexts. ZDM, 38 (3), 214-225. doi:https://doi.org/10.1007/BF02652806
  55. Pollard, P. & Evans, J. (1987). Content and Context Effects in Reasoning. The American Journal of Psychology, 100 (1), 41-60. doi: 10.2307/1422641
  56. Post, R. (1958). A study of certain factors affecting the understanding of verbal problems in arithmetic. Doctoral dissertation, Columbia University, New York.
  57. Ross, S. M. McCormick, D., & Krisak, N. (1986). Adapting the Thematic Context of Mathematical Problems to Student Interests: Individualized versus Group - Based Strategies. Journal of Educational Research, 79 (4), 45-252 doi: https://doi.org/10.1080/00220671.1986.10885685
  58. Roth, W. M. (1996). Where Is the Context in Contextual Word Problems?: Mathematical Practices and Products in Grade 8 Students’ Answers to Story Problems. Cognition and Instruction, 14 (4), 487-527. doi: https://doi.org/10.1207/s1532690xci1404_3
  59. Shannon, A. (2007). Task Context and Assessment. In A. Schoenfeld (Ed.), Assessing Mathematical Proficiency (pp. 177-191). New York: MSRI Publications.
  60. Silver, E. A. (1981). Recall of Mathematical Problem Information: Solving Related Problems. Journal for Research in Mathematics Education, 12 (1), 54-64. doi: 10.2307/748658
  61. Stacey, K. (2015). The Real World and the Mathematical World. In K. Stacey & R. Turner (Eds.), Assessing Mathematical Literacy. The PISA Experience (pp. 57-84). Cham: Springer International Publishing.
  62. 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.
  63. Stillman, G. (2002). Assessing higher order mathematical thinking through applications. Doctoral dissertation, The University of Queensland, Brisbane.
  64. Stillman, G., & Galbraith, P. (1998). Applying mathematics with real world connections: metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36 (2), 157-194. doi:10.1023/a:1003246329257
  65. Sutherland, J. (1942). An investigation into some aspects of problem solving in arithmetic. British Journal of Educational Psychology, 12 (1), 35-46. doi:10.1111/j.2044-8279.1942.tb02178.x
  66. The Florida Legislature Service Bureau, 1980. Summary of General Legislation Act of 1980. Retrieved from http://archive.law.fsu.edu/library/collection/FlSumGenLeg/FlSumGenLeg1980.pdf
  67. Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics instruction. The Netherlands, Dordrecht: Reidel.
  68. Turner, R. (2011). Exploring mathematical competencies. Research Developments, 24 (5), 2-7.
  69. Van den Heuvel - Panhuizen, M. (2005). The Role of Contexts in Assessment Problems in Mathematics. For the Learning of Mathematics, 25 (2), 2-23.
  70. 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. doi:10.1023/B:EDUC.0000005212.03219.dc
  71. Van den Heuvel - Panhuizen, M. (1999). Context problems and assessment: Ideas from the Netherlands. In I. Thompson (Ed.), Issues in teaching numeracy in primary schools (pp. 130-142). Buckingham, UK: Open University Press.
  72. Verschaffel, L., De Corte, E., & Greer, B. (2000). Making sense of word problems. Exton, PA: Swets & Zeitlinger Publishers.
  73. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4 (4), 273-294. doi: http://dx.doi.org/10.1016/0959-4752(94)90002-7
  74. Washburne, C. W. & Osborne, R. (1926a). Solving Arithmetic Problems. I. The Elementary School Journal, 27 (3), 219-226. doi: https://doi.org/10.1086/461989
  75. Washburne, C. W. & Osborne, R. (1926b). Solving Arithmetic Problems. II. The Elementary School Journal, 27 (4), 296-304. doi:https://doi.org/10.1086/462005
  76. Watson, R. & Yip, P. (2011). How many were there when it mattered? Significance, 8 (3), 104-107. doi: 10.1111/j.1740-9713.2011.00502.x
  77. Wedege, T. (1999). To know or not to know – Mathematics, that is a question of context. Educational Studies in Mathematics, 39 (1-3), 205-227. https://doi.org/10.1023/A:1003871930181
  78. Yoshida, H., Verschaffel, L. & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? Learning and Instruction, 7 (4), 329-338. doi: http://dx.doi.org/10.1016/S0959-4752(97)00007-8

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