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.

In this study, we explored the structural relationship between the students' perceived use of cognitive and metacognitive reading strategies (CMRS) and their reading comprehension of geometry proof (RCGP), and we also examined the differences in students' perceived use of reading strategies among the poor, moderate and good comprehenders. A sample of ninth graders (N=533) completed a RCGP test and then the CMRS questionnaire. In the exploratory factor analysis with one subsample (n=150), principal component analysis was used to extract factors of CMRS use for improving the CMRS instrument. Another subsample of students (n=370) participated in the study on the confirmatory factor analysis with structural equation modelling method. Results revealed that the use of metacognitive reading strategies exerts an executive function over that of cognitive reading strategies, which directly influenced students' RCGP. Our interesting findings were that good comprehenders tended to employ more metacognitive reading strategies for planning and monitoring comprehension and more cognitive reading strategies for elaborating proof compared with the moderate comprehenders, who in turn employed these strategies more often compared with the poor comprehenders.

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To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students’ situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students’ interest in modelling improved more in Germany. An in-depth quantitative analysis of students’ responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.

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.