A Framework for Assessing Reading Comprehension of Geometric Construction Texts
Tóm tắt
This study investigates one issue related to reading mathematical texts by presenting a two-dimensional framework for assessing reading comprehension of geometric construction texts. The two dimensions of the framework were formulated by modifying categories of reading literacy and drawing on key elements of geometric construction texts. Three categories of reading mathematical texts were recognized and then cross-tabulated with three key elements of geometric construction texts to create a nine-category assessment framework, which was used to design an instrument. After reporting on the validation of the instrument, we conclude by discussing the implications of the framework for assessing students’ reading to learn mathematics and for improving the learning of geometric constructions by reading.
Tài liệu tham khảo
Australian Curriculum, Assessment and Reporting Authority (2012). The Australian Curriculum: Mathematics (V3.0). Retrieved from http://www.australiancurriculum.edu.au/Australian%20Curriculum.pdf?Type=0&s=M&e=ScopeAndSequence
Borasi, R., & Siegel, M. (1989). Reading to learn mathematics: A new synthesis of the traditional basics. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.
Borasi, R. & Siegel, M. (1990). Reading to learn mathematics: New connections, new questions, new challenges. For the Learning of Mathematics, 10(3), 9–16.
Common Core State Standards Initiative (2012). Common core state standards initiative: Preparing America’s students for college and career. Retrieved from http://www.corestandards.org/
Conradie, J. & Frith, J. (2000). Comprehension tests in mathematics. Educational Studies in Mathematics, 42(3), 225–235.
Department for Education (2013). National curriculum in England: Mathematics programmes of study. Retrieved from https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In R. Sutherland & F. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 142–157). Berlin, Germany: Springer.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1), 103–131.
Fang, Z. & Schleppegrell, M. J. (2010). Disciplinary literacies across content areas: Supporting secondary reading through functional language analysis. Journal of Adolescent & Adult Literacy, 53(7), 587–597.
Hanna, G. (1991). Mathematical proof. In D. Tall (Ed.), Advanced mathematical thinking (pp. 54–61). Dordrecht, The Netherlands: Kluwer.
Hölzl, R. (1995). Between drawing and figure. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 117–124). Berlin, Germany: Springer.
Inglis, M. & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358–390.
Johnston, P. (1984). Prior knowledge and reading comprehension test bias. Reading Research Quarterly, 19(2), 219–239.
Kintsch, W. (1998). Comprehension: a paradigm for cognition. New York, NY: Cambridge University Press.
Kintsch, W. (2012). Psychological models of reading comprehension and their implications for assessment. In J. P. Sabatini, E. R. Albro & T. O’Reilly (Eds.), Measuring up: Advances in how we assess reading ability (pp. 21–38). Plymouth, UK: Rowman & Littlefield.
Kirsch, I. (1995). Literacy performance on three scales: Definitions and results. In OECD & Statistics Canada (Ed.), Literacy, economy and society. Results of the first international adult literacy survey (pp. 27–53). Paris, France: OECD.
Kirsch, I., de Jong, J., LaFontaine, D., McQueen, J., Mendelovits, J. & Monseur, C. (2002). PISA reading for change: Performance and engagement across countries. Paris, France: Organisation for Economic Co-operation and Development.
Laborde, C. (1998). Relationships between the spatial and theoretical in geometry: The role of computer dynamic representations in problem solving. In D. Tinsley & D. Johnson (Eds.), Information and communications technologies in school mathematics (pp. 183–194). New York, NY: Springer.
Lissitz, R. W. & Samuelsen, K. (2007). A suggested change in terminology and emphasis regarding validity and education. Educational Researcher, 36(8), 437–448.
Mariotti, M. A. (1995). Images and concepts in geometrical reasoning. In R. Sutherland & F. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 97–116). Berlin, Germany: Springer.
Mariotti, M. A. (2000). Introduction to proof: the mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1–2), 25–53.
Mason, J. (2003). On the structure of attention in the learning of mathematics. Australian Mathematics Teacher, 59(4), 17–25.
Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K. & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3–18.
Organisation for Economic Co-operation and Development (OECD). (2004). The PISA 2003 assessment framework: mathematics, reading, science and problem solving knowledge and skills. Paris, France: Author.
Pandiscio, E. A. (2002). Alternative geometric constructions: Promoting mathematical reasoning. The Mathematics Teacher, 95(1), 32–36.
Pólya, G. (1945). How to solve it. Princeton, NJ: Princeton University.
Robertson, J. M. (1986). Geometric constructions using hinged mirrors. The Mathematics Teacher, 79(5), 380–386.
Sabatini, J., Albro, E. & O’Reilly, T. (2012). Measuring up: Advances in how we assess reading ability. Lanham, MD: R&L Education.
Sanders, C. V. (1998). Geometric constructions: Visualizing and understanding geometry. The Mathematics Teacher, 91(7), 554–556.
Schoenfeld, A. (1986). On having and using geometric knowledge. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 225–264). Hillsdale, NJ: Erlbaum.
Selden, A. & Shepherd, M. D. (2013). The Importance of and the need for research on how students read and use their mathematics textbook (technical report no. 3). Cookeville, TN: Tenessee Technological University.
Shepherd, M. D., Selden, A. & Selden, J. (2012). University students’ reading of their first-year mathematics textbooks. Mathematical Thinking and Learning, 14(3), 226–256.
Shepherd, M. D. & van de Sande, C. C. (2014). Reading mathematics for understanding—From novice to expert. The Journal of Mathematical Behavior, 35, 74–86.
Stempien, M. & Borasi, R. (1985). Students’ writing in mathematics: Some ideas and experiences. For the Learning of Mathematics, 5(3), 14–17.
Weinberg, A. & Wiesner, E. (2011). Understanding mathematics textbooks through reader-oriented theory. Educational Studies in Mathematics, 76(1), 49–63.
Yang, K.L. (2015). Study on junior high school students’ reading to learn geometry (Report No. MOST. 102-2511-S-003-022-MY3). Unpublished Technical Report. Taipei, Taiwan: Ministry of Science and Technology.
Yang, K. L. & Lin, F. L. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59–76.