A model of reading comprehension of geometry proof

Abstract

This study aims to investigate a construct of reading comprehension of geometry proof (RCGP). The research aims to investigate (a) the facets composing RCGP, and (b) the structure of these facets. Firstly, we conceptualize this construct with relevant literature and on the basis of the discrimination between the logical and the epistemic meanings of an argument, then assemble the content of RCGP from literature and propose a hypothetical model of RCGP. Secondly, mathematicians and mathematics teachers are interviewed for their ideas on reading mathematical proof in order to enrich the content of RCGP. Adapting the phases of reading comprehension in language, the content of RCGP is classified into six facets. Lastly, these facets are structured using the hypothetical model and then justified by students' performance in the facets of RCGP using the multidimensional scaling method. The results sustain that the structure of facets can be characterized by this conceptualized model.

Students’ understanding of the structure of deductive proof

“…This level has echoes of the BRecognizing elements^level of the RCGP (Yang & Lin, 2008) and the first processes of Heinze et al (2008)). However, just recognising elements of proofs is not enough to construct valid proofs; a student at this level still needs to recognise some logical chaining relationships between the components of a proof from premises to conclusions (c.f.…”

“…In proof and proving, a model that reflects a local developmental perspective is the Reading Comprehension of Geometry Proofs (RCGP) model (Lin & Yang, 2007;Yang & Lin, 2008). This model hypothesises four levels of reading comprehension of geometric proofs; these levels are Bcomprehension of surface (epistemic value)^, Bcomprehension of recognising elements (micro level, logical value)^, Bcomprehension of chaining elements (local level, logical value)^, and Bcomprehension of encapsulation (global level, logical and epistemic values)^ (Yang & Lin, 2008, p. 63).…”

Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs

“…Yet questions remain about the process they would undergo in order to develop their understanding of proofs with highly symbolic complex structures. In the context of students reading formal proofs found in textbooks, Lin and Yang (2008) propose the model of Reading Comprehension of Geometry Proofs (RCGP). This model hypothesizes four levels of reading comprehension of geometric proofs (Yang and Lin, 2008, p. 63).…”

Investigating and Improving Undergraduate Proof Comprehension

“…The students were randomly assigned to either an experimental group who studied an e-Proof or a control group who studied the same theorem and proof on paper for the same fixed amount of time. All students then took a comprehension test designed according to the principles outlined in [3]: there were questions testing basic knowledge of algebra and differentiation, understanding of the logical reasoning used in the proof, application of ideas in the proof to examples, and ability to summarize the argument. This immediate post-test was followed two weeks later by an identical delayed post-test that was not announced in advance.…”

“…This analysis revealed a betweengroups difference: regardless of the order in which the participants experienced the proofs, those who received the self-explanation training subsequently concentrated harder. 3 Second, we looked as before at between-line saccades (see Figure 10). We compared the numbers of between-line saccades for students in the experimental and control groups on the proofs they read second, this time controlling for both the time taken to read this proof (we were effectively interested in between-line saccades per minute, not total saccades) and the number of between-line saccades for the proof read first (again to account for individual differences in reading behavior).…”