The Reading Comprehension of Geometric Proofs: The Contribution of Knowledge and Reasoning

摘要

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.