Abstract
A model of reading comprehension of geometric proofs (RCGP) has recently been proposed by the authors. This article further investigates students’ development of such comprehension based on this model, looking at the relationship between students’ reading comprehension and their prior knowledge and logical reasoning. The results show that (1) students’ development of RCGP may follow two different learning trajectories; (2) the effect of logical reasoning on RCGP in ninth grade is larger and more complex than in tenth grade; (3) knowledge about geometric figures is not the main factor contributing to RCGP, and geometric knowledge that includes knowledge of figures and of verbal description and translation between the two distinguishes only the level of surface comprehension from the other levels of RCGP; and (4) regression analysis yields a two-variable model that includes logical reasoning and relevant geometric knowledge, and that accounts for 54% and 22% of the variance on RCGP data from the ninth and tenth graders, respectively.
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Bowyer-Crane, C. & Snowling, J. (2005). Assessing children’s inference generation: What do tests of reading comprehension measure? British Journal of Educational Psychology, 75(13), 189–201.
Cain, K. Oakhill, J. & Bryant, P. (2004). Children’s reading comprehension ability: Concurrent prediction by working memory, verbal ability, and component skills. Journal of Educational Psychology, 96(1), 31–42.
Cindy, B. (2004). Statistical procedure for research on L2 reading comprehension: An examination of nova and regression models. Reading in a Foreign Language, 16(2), 51–69.
Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century. An International Commission on Mathematical Instruction (ICMI) Study [Chapter 2.2]. The Netherlands: Dordrecht, Kluwer.
Duval, R. (2002). Proof understanding in mathematics: What ways for students? In F.L. Lin (Ed.), Proceedings of the international conference on mathematics: Understanding proving and proving to understand (pp. 61–77). Taipei, Taiwan: National Science Council and National Taiwan Normal University.
Duval, R. (2006). A cognitive analysis of problems of comprehension in the learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.
Fincher-Kiefer, R.H. (1992). The role of prior knowledge in inferential processing. Journal of Research in Reading, 15, 12–27.
Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer.
Graesser, A.C., Singer, M. & Trabasso, T. (1994). Constructing inferences during narrative text comprehension. Psychological Review, 101(3), 371–395.
Haarmann, H.J., Davelaar, E.J. & Usher, M. (2003). Individual differences in semantic short-term memory capacity and reading comprehension. Journal of Memory and Language, 48, 320–345.
Healy, L. & Hoyles, C. (2000). A study of proof conception in algebra. Journal for Research in Mathematics Education, 31(4), 396–428.
Jansson, L.C. (1986). Logical reasoning hierarchies in mathematics. Journal for Research in Mathematics Education, 17(1), 3–20.
Kintsch, W. (1998). Comprehension: A paradigm for cognition. New York: Cambridge University Press.
Lin, F.L. & Tsao, L.C. (1999). Exam maths re-examined. In C. Hoyles, C. Morgan & G. Woodhouse (Eds.), Rethinking the mathematics curriculum (pp. 228–239). London: Falmer Press.
Lipson, M.Y. & Wixson, K.K. (1991). Assessment and instruction of reading disability: An interactive approach. New York: Harper & Collins.
Markovits, H. & Bouffard-Bouchard, T. (1992). The belief-bias effect in reasoning: The development and activation of competence. British Journal of Developmental Psychology, 10, 269–284.
Marr, M.B. & Gormley, K. (1982). Children’s recall of familiar and unfamiliar text. Reading Research Quarterly, 18, 89–104.
Michener, E.R. (1978). Understanding understanding mathematics. Cognitive Science, 2(4), 361–383.
Morris, A.K. (2002). Mathematical reasoning: Adults’ ability to make the inductive-deductive distinction. Cognition and Instruction, 20(1), 79–118.
Nation, K. & Snowling, J. (1998). Semantic processing and the development of word-recognition skills: Evidence from children with comprehension difficulties. Journal of Memory & Language, 39, 85–101.
Oakhill, J. (1982). Constructive processes in skilled and less-skilled comprehenders’ memory for sentences. British Journal of Psychology, 73, 13–20.
Oakhill, J. (1983). Instantiation in skilled and less-skilled comprehenders. Quarterly Journal of Experimental Psychology, 35a, 441–450.
Oakhill, J., Johnson-Laird, P.N. & Garnham, A. (1989). Believability and syllogistic reasoning. Cognition, 31(2), 117–140.
Organisation for Economic Co-operation and Development. (2005). PISA 2003 Technical Report. Paris: Author.
Pape, S.J. (2004). Middle school children’s problem-solving behavior: A cognitive analysis from a reading comprehension perspective. Journal for Research in Mathematics Education, 35(3), 187–219.
Pimm, D. & Wagner, D. (2003). Investigation, mathematics education and genre. Educational Studies in Mathematics, 53(2), 159–178.
Richardson, J.S. & Morgan, R.E. (1997). Reading to learn in the content areas (3rd ed.). Belmont, CA: Wadsworth.
Schmidt, C.R. & Paris, S.G. (1983). Children’s use of successive clues to generate and monitor inferences. Child Development, 54, 742–759.
Selden, J. & Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29(2), 123–151.
Skemp, R.R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Soucy McCrone, S.M. & Martin, T.S. (2004). Assessing high school students’ understanding of geometric proof. Canadian Journal of Science, Mathematics, & Technology Education, 4(2), 223–242.
van den Broek, P.W. (1994). Comprehension and memory of narrative texts: Inferences and coherence. In M.A. Gernsbacher (Ed.), Handbook of psycholinguistics (pp. 539–588). San Diego, CA: Academic Press.
van Hiele, P. (1986). Structure and Insight. Orlando, FL: Academic Press.
Wu Yu, C-Y., Chin, E-T. & Lin, C-J. (2004). Taiwanese junior high school students’ understanding about the validity of conditional statements. International Journal of Science and Mathematics Education, 2(2), 257–285.
Yang, K.L. & Lin, F.L. (2005, April). Facets of reading comprehension of geometric proofs. Paper presented at annual meeting of the American Educational Research Association, Montreal, Quebec, Canada.
Yang, K.L. & Lin, F.L. (2007). A model of reading comprehension of geometry proof [Electronic version]. Educational Studies in Mathematics Education. Retrieved May 3, 2007, from http://www.springerlink.com/content/jlr334n16161573v/.
Yore, L.D., Craig, M.T. & Maguire, T.O. (1998). Index of science reading awareness: An interactive-constructive model, test verification, and grade 4–8 results. Journal of Research in Science Teaching, 35, 27–51.
Yuill, N. & Oakhill, J. (1988). Effects of inference awareness training on poor reading comprehension. Applied Cognitive Psychology, 2, 33–45.
Yuill, N. & Oakhill, J. (1991). Children’s problems in text comprehension: An experimental investigation. New York: Cambridge University Press.
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Lin, FL., Yang, KL. The Reading Comprehension of Geometric Proofs: The Contribution of Knowledge and Reasoning. Int J of Sci and Math Educ 5, 729–754 (2007). https://doi.org/10.1007/s10763-007-9095-6
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DOI: https://doi.org/10.1007/s10763-007-9095-6