Methodological issues when studying the relationship between reading and solving mathematical tasks
DOI:
https://doi.org/10.7146/nomad.v17i1.148413Abstract
In this paper we examine four statistical methods used for characterizing mathematical test items regarding their demands of reading ability. These methods rely on data of students’ performance on test items regarding mathematics and reading and include the use of regression analysis, principal component analysis, and different uses of correlation coefficients. Our investigation of these methods focuses on aspects of validity and reliability, using data from PISA 2003 and 2006. The results show that the method using principal component analysis has the best properties when taking into account aspects of both validity and reliability.
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, L. R. (1972). Language factors in learning mathematics. Review of Educational Research, 42, 359-385. https://doi.org/10.3102/00346543042003359
Ansley, T. N. & Forsyth, R. A. (1990). An investigation of the nature of the interaction of reading and computational abilities in solving mathematics word problems. Applied Measurement in Education, 3 (4), 319-329. https://doi.org/10.1207/s15324818ame0304_2
Bergqvist, E. (2009). A verbal factor in the PISA 2003 mathematics items: tentative analyses. In M. Tzekaki, M. Kaldrimidou & C. Sakonidis (Eds.), Proceedings of the ((rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 145-152). Thessaloniki: PME.
Bergqvist, E., Dyrvold, A. & Österholm, M. (in press). Relating vocabulary in mathematical tasks to aspects of reading and solving. In Proceedings of the Eighth Swedish Mathematics Education Research Seminar, Madif *.
Bergqvist, E. & Österholm, M. (2010). A theoretical model of the connection between the process of reading and the process of solving mathematical tasks. In C. Bergsten, E. Jablonka & T. Wedege (Eds.), Mathematics and mathematics education: Cultural and social dimensions (Proceedings of MADIF 7) (pp. 47-57). Linköping: SMDF. Retrieved December 14, 2010, from http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-31890
Bernardo, A. B. I. (1999). Overcoming obstacles to understanding and solving word problems in mathematics. Educational Psychology, 19 (2), 149-163. https://doi.org/10.1080/0144341990190203
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
Fuentes, P. (1998). Reading comprehension in mathematics. Clearing House, 72 (2), 81-88. https://doi.org/10.1080/00098659809599602
Hambleton, R. K., Swaminathan, H. & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park: Sage Publications.
Homan, S., Hewitt, M. & Linder, J. (1994). The development and validation of a formula for measuring single-sentence test item readability. Journal of Educational Measurement, 31 (4), 349-358. https://doi.org/10.1111/j.1745-3984.1994.tb00452.x
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
Lager, C. A. (2006). Types of mathematics-language reading interactions that unnecessarily hinder algebra learning and assessment. Reading Psychology, 27, 165-204. https://doi.org/10.1080/02702710600642475
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67, 255-276. https://doi.org/10.1007/s10649-007-9104-2
McNamara, D. S., Kintsch, E., Songer, N. B. & Kintsch, W. (1996). Are good texts always better? Interactions of text coherence, background knowledge, and levels of understanding in learning from text. Cognition and Instruction, 14, 1-43. https://doi.org/10.1207/s1532690xci1401_1
Muth, K. D. (1984). Solving arithmetic word problems: Role of reading and computational skills. Journal of Educational Psychology, 76 (2), 205-210. https://doi.org/10.1037/0022-0663.76.2.205
Möllehed, E. (2001). Problemlösning i matematik: en studie av påverkansfaktorer i årskurserna %-+. Malmö: Institutionen för pedagogik, Lärarhögskolan.
NCTM. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
Niss, M. & Jensen, T. H. (Eds.). (2002). Kompetencer og matematiklæring - idéer og inspiration til udvikling af matematikundervisning i Danmark. København: Undervisningsministeriets forlag. Retrieved August 6, 2008, from http:// pub.uvm.dk/2002/kom/hel.pdf
Nortvedt, G. A. (2009). The relationship between reading comprehension and numeracy among Norwegian grade 8 students. In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), Proceedings of the ((rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 233-240). Thessaloniki, Greece: PME.
Nyström, P. (2008). Identification and analysis of text-structure and wording in TIMSS-items. Paper presented at the 3rd IEA International Research Conference. Retrieved August 23, 2009, from http://www.iea.nl/fileadmin/user_upload/IRC2008/Papers/TIMSS_Mathematics/Nystrom.pdf
Oakland, T. & Lane, H. B. (2004). Language, reading, and readability formulas: Implications for developing and adapting tests. International Journal of Testing, 4 (3), 239-252. https://doi.org/10.1207/s15327574ijt0403_3
OECD. (2003). The PISA )''( assessment framework - mathematics, reading, science and problem solving knowlegde and skills. Paris: Author.
OECD. (2006). Assessing scientific, reading and mathematical literacy: a framework for PISA )'',. Paris: Author. https://doi.org/10.1787/9789264026407-en
Paul, D. J., Nibbelink, W. H. & Hoover, H. D. (1986). The effects of adjusting readability on the difficulty of mathematics story problems. Journal for Research in Mathematics Education, 17, 163-171. https://doi.org/10.2307/749299
Roe, A. & Taube, K. (2006). How can reading abilities explain differences in maths performance? In J. Mejding & A. Roe (Eds.), Northern lights on PISA )''( - a reflection from the Nordic countries (pp. 129-141). Copenhagen: Nordic Council of Ministers. Retrieved August 6, 2008, from http://www.norden.org/pub/uddannelse/uddannelse/sk/TN2006523.pdf
Sato, E., Rabinowitz, S., Gallagher, C. & Huang, C.-W. (2010). Accommodations for English language learner students: the effect of linguistic modification of math test item sets. Washington: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved October 13, 2011, from http://ies.ed.gov/ncee/edlabs/regions/west/pdf/REL_20094079.pdf
Shanahan, T. & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: rethinking content-area literacy. Harvard Educational Review, 78(1), 40-59. https://doi.org/10.17763/haer.78.1.v62444321p602101
Søvik, N., Frostad, P. & Heggberget, M. (1999). The relation between reading comprehension and task-specific strategies used in arithmetical word problems. Scandinavian Journal of Educational Research, 43 (4), 371-398. https://doi.org/10.1080/0031383990430403
Tabachnick, B. G. & Fidell, L. S. (2006). Using multivariate statistics (5th ed.). Boston: Allyn and Bacon.
Walker, C. M., Zhang, B. & Surber, J. (2008). Using a multidimensional differential item functioning framework to determine if reading ability affects student performance in mathematics. Applied Measurement in Education, 21, 162-181. https://doi.org/10.1080/08957340801926201
Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational Studies in Mathematics, 34, 97-129. https://doi.org/10.1023/A:1002998529016
Wu, M. (2005). The role of plausible values in large-scale surveys. Studies in Educational Evaluation, 31, 114-128. https://doi.org/10.1016/j.stueduc.2005.05.005
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 5) (pp. 136-145). Linköping: SMDF. Retrieved June 7, 2012, from http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-14116
Österholm, M. & Bergqvist, E. (in press). What mathematical task properties can cause an unnecessary demand of reading ability? In G. H. Gunnarsdóttir, F. Hreinsdóttir, G. Pálsdóttir, M. Hannula, M. Hannula- Sormunen, et al. (Eds.), Proceedings of Norma 11, The sixth Nordic conference on mathematics education in Reykjavík, May 11-14, 2011 (pp. 661-670). Reykjavík: University of Iceland Press.
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