Do students need to learn how to use their mathematics textbooks? The case of reading comprehension
DOI:
https://doi.org/10.7146/nomad.v13i3.148124Abstract
The main question discussed in this paper is whether students need to learn how to read mathematical texts. I describe and analyze the results from different types of studies about mathematical texts; studies about properties of mathematical texts, about the reading of mathematical tasks, and about the reading of mathematical expository texts. These studies show that students seem to develop special reading strategies for mathematical texts that are not desirable. It has not been possible to find clear evidence for the need of a specific ”mathematical reading ability”. However, there is still a need to focus more on reading in mathematics teaching since students seem to develop the non-desirable reading strategies.
References
Abedi, J. & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14 (3), 219-234. https://doi.org/10.1207/S15324818AME1403_2
Aiken Jr., L. R. (1972). Language factors in learning mathematics. Review of Educational Research, 42 (3), 359-385. https://doi.org/10.3102/00346543042003359
Bilsky, L. H., Blachman, S., Chi, C., Mui, A. C. & Winter, P. (1986). Comprehension strategies in math problem and story contexts. Cognition and Instruction, 3, 109-126. https://doi.org/10.1207/s1532690xci0302_2
Borasi, R. & Siegel, M. (1990). Reading to learn mathematics: new connections, new questions, new challenges. For the Learning of Mathematics, 10 (3), 9-16.
Borasi, R. & Siegel, M. (1994). Reading, writing and mathematics: rethinking the "basics" and their relationship. In F. Robitaille, D. H. Wheeler & C. Kieran (Eds.), Selected lectures from the !th International Congress on Mathematical Education: Québec, 17-23 August 1992 (pp. 35-48). Sainte-Foy [Québec]: Presses de l'Université Laval.
Brunner, R. B. (1976). Reading mathematical exposition. Educational Research, 18, 208-213. https://doi.org/10.1080/0013188760180306
Burton, L. & Morgan, C. (2000). Mathematicians writing. Journal for Research in Mathematics Education, 31, 429-453. https://doi.org/10.2307/749652
Cowen, C. C. (1991). Teaching and testing mathematics reading. American Mathematical Monthly, 98 (1), 50-53. https://doi.org/10.1080/00029890.1991.11995704
De Corte, E., Verschaffel, L. & De Win, L. (1985). Influence of rewording verbal problems on children's problem representations and solutions. Journal of Educational Psychology, 77 (4), 460-470. https://doi.org/10.1037/0022-0663.77.4.460
De Guzmán, M., Hodgson, B. R., Robert, A. & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. Documenta mathematica, extra volume ICM III, !&!-!'#. Retrieved May 21, 2008 from http://www. emis.de/journals/DMJDMV/xvol-icm/18/Hodgson.MAN.html https://doi.org/10.4171/dms/1-3/72
Draper, R. J. (2002). Every teacher a literacy teacher? An analysis of the literacy-related messages in secondary methods textbooks. Journal of Literacy Research, 34 (3), 357-384. https://doi.org/10.1207/s15548430jlr3403_5
Drouhard, J.-P. & Teppo, A. R. (2004). Symbols and language. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra: the "#th ICMI study (pp. 227-264). Boston: Kluwer Academic Publishers.
Ernest, P. (1987). A model of the cognitive meaning of mathematical expressions. The British Journal of Educational Psychology, 57, 343-370. https://doi.org/10.1111/j.2044-8279.1987.tb00862.x
Esty, W. W. & Teppo, A. R. (1994). A general-education course emphasizing mathematical language and reasoning. Focus on Learning Problems in Mathematics, 16 (1), 13-35.
Fenwick, C. (2001). Students and their learning from reading. Humanistic Mathematics Network Journal, 24, 52-58. https://doi.org/10.5642/hmnj.200101.24.18
Fuentes, P. (1998). Reading comprehension in mathematics. Clearing House, 72 (2), 81-88. https://doi.org/10.1080/00098659809599602
Gelfman, E., Lozinskaia, R. & Remezova, G. (1999). On teaching students to work with text books. In I. Schwank (Ed.), European research in mathematics education I.II: Proceedings of the first conference of the European society for research in mathematics education (vol. 2, pp. 49-52). Retrieved May 21, 2008, from http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/ cerme1-proceedings-1-vol2-v1-0.pdf
Gray, E. & Tall, D. (1994). Duality, ambiguity, and flexibility: a "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25 (2), 116-140. https://doi.org/10.5951/jresematheduc.25.2.0116
Halliday, M. A. K. (1975). Some aspects of sociolinguistics. In UNESCO, Interactions between linguistics and mathematical education (pp. 64-73). Retrieved May 21, 2008, from http://unesdoc.unesco.org/ images/0001/000149/014932eb.pdf
Harmon, J. M., Hedrick, W. B. & Wood, K. D. (2005). Research on vocabulary instruction in the content areas: implications for struggling readers. Reading & Writing Quarterly, 21, 261-280. https://doi.org/10.1080/10573560590949377
Hegarty, M., Mayer, R. E. & Monk, C. A. (1995). Comprehension of arithmetic word problems: a comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87 (1), 18-32. https://doi.org/10.1037/0022-0663.87.1.18
Hubbard, R. (1990). Teaching mathematics reading and study skills. International Journal of Mathematical Education in Science and Technology, 21, 265-269. https://doi.org/10.1080/0020739900210212
Jordan, N. C. & Hanich, L. B. (2000). Mathematical thinking in second-grade children with different forms of LD. Journal of Learning Disabilities, 33 (6), 567-578. https://doi.org/10.1177/002221940003300605
Kieras, D. E. (1985). Thematic processes in the comprehension of technical prose. In B. K. Britton & J. B. Black (Eds.), Understanding expository text: a theoretical and practical handbook for analyzing explanatory text (pp. 89-107). Hillsdale, N.J.: Lawrence Erlbaum Associates. https://doi.org/10.4324/9781315099958-4
Knifong, J. D. & Holtan, B. D. (1977). A search for reading difficulties among erred word problems. Journal for Research in Mathematics Education, 8 (3), 227-230. https://doi.org/10.2307/748525
Konior, J. (1993). Research into the construction of mathematical texts. Educational Studies in Mathematics, 24, 251-256. https://doi.org/10.1007/BF01275425
Krygowska, Z. (1969). Le texte mathématique dans l'enseignement. Educational Studies in Mathematics, 2, 360-370. https://doi.org/10.1007/BF00303469
Laborde, C. (1990). Language and mathematics. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: a research synthesis by the International Group for the Psychology of Mathematics Education (pp. 53-69). Cambridge University Press. https://doi.org/10.1017/CBO9781139013499.005
Langer, J. A. (1984). Examining background knowledge and text comprehension. Reading Research Quarterly, 19, 468-481. https://doi.org/10.2307/747918
Lerkkanen, M.-K., Raska-Puttonen, H., Aunola, K. & Nurmi, J.-E. (2005). Mathematical performance predicts progress in reading comprehension among 7-year olds. European Journal of Psychology of Education, 20 (2), 121-137. https://doi.org/10.1007/BF03173503
Love, E. & Pimm, D. (1996). 'This is so': a text on texts. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds.), International handbook of mathematics education (part -, pp. 371-409). Dordrecht: Kluwer.
McKenna, M. C. & Robinson, R. D. (1990). Content literacy: a definition and implications. Journal of Reading, 34, 184-186
Metsisto, D. (2005). Reading in the mathematics classroom. In J. M. Kenney (Ed.), Literacy strategies for improving mathematics instruction (pp. 9-23). Alexandria, VA, USA: Association for Supervision & Curriculum Development.
Nesher, P. & Teubal, E. (1975). Verbal cues as an interfering factor in verbal problem solving. Educational Studies in Mathematics, 6, 41-51. https://doi.org/10.1007/BF00590023
Pimm, D. (1989). Speaking mathematically: communication in mathematics classrooms (paperback edition). London: Routledge.
Roe, A. & Taube, K. (2006). How can reading abilities explain differences in maths performances? In J. Mejding & A. Roe (Eds.), Northern lights on PISA #(($ - a reflection from the Nordic countries (pp. 145-157). Copenhagen: Nordic Council of Ministers. Retrieved May 21, 2008, from http://www. norden.org/pub/uddannelse/uddannelse/sk/TN2006523.pdf
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, 1-36. https://doi.org/10.1007/BF00302715
Siegel, M. & Borasi, R. (1992). Toward a new integration of reading in mathe- matics instruction. Focus on Learning Problems in Mathematics, 14 (2), 18-36.
Sierpinska, A. (1998). Whither mathematics education? In C. Alsina, J. M. Alvarez, M. Niss, A. Pérez, L. Rico et al. (Eds.), Proceedings of the )th international congress on mathematical education, Sevilla "&-#" July "%%' (pp. 21-46). Sevilla: S.A.E.M. Thales.
Stephens, L. J. & Sloan, B. F. (1981). Important sources used for doing homework and preparing for exams in undergraduate mathematics courses. International Journal of Mathematical Education in Science and Technology, 12, 135-138. https://doi.org/10.1080/0020739810120201
Tall, D. (1991). The psychology of advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 3-21). Dordrecht: Kluwer academic press. https://doi.org/10.1007/0-306-47203-1
Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H. & Houang, R. T. (2002). According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-94-007-0844-0
Watkins, A. E. (1979). The symbols and grammatical structures of mathematical English and the reading comprehension of college students. Journal for Research in Mathematics Education, 10, 216-218. https://doi.org/10.2307/748810
Woodrow, D. (1982). Mathematical symbolism. Visible Language, 16 (3), 289-302.
Wyndhamn, J. & Säljö, R. (1997). Word problems and mathematical reasoning - a study of children's mastery of reference and meaning in textual realities. Learning and Instruction, 7, 361-382. https://doi.org/10.1016/S0959-4752(97)00009-1
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, 329-338. https://doi.org/10.1016/S0959-4752(97)00007-8
Österholm, M. (2006a). Characterizing reading comprehension of mathematical texts. Educational Studies in Mathematics, 63, 325-346 https://doi.org/10.1007/s10649-005-9016-y
Österholm, M. (2006b). Kognitiva och metakognitiva perspektiv på läsförståelse inom matematik [Cognitive and metacognitive perspectives on reading comprehension in mathematics] (Doctoral Dissertation). Department of Mathematics, Linköping University. Retrieved May 21, 2008 from http:// urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7674
Österholm, M. (2006c). Metacognition and reading - criteria for comprehension of mathematics texts. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings $(th conference of the international group for the psychology of mathematics education (vol. 4, pp. 289-296). Prague: PME. Retrieved May 21, 2008 from http://www.mai.liu.se/~maost/pme30.pdf
Österholm, M. (2007). A reading comprehension perspective on problem solving. In C. Bergsten & B. Grevholm (Eds.), Developing and Researching Quality in Mathematics Teaching and Learning. Proceedings of MADIF *, the *th Swedish Mathematics Education Research Seminar, Malmö, January #&-#*, #((' (pp. 136-145). Linköping: SMDF.
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