Proving is the essence of mathematics, yet many students do not feel the need for proofs and do not even understand the concept of proving. The master's thesis deals with reading comprehension of geometric proofs, which is an important and, in school mathematics, often overlooked aspect of understanding proofs.
In the theoretical part of the master's thesis we consider the role of proving in school mathematics and how proofs are viewed from students’ and from teachers’ perspective. We focus on geometric proofs and present in great detail three forms of presenting them: the paragraph form, the two-column form and the flow-chart form. We connect the concept of understanding proof with reading ability and present aspects that indicate the levels of reading comprehension of geometric proofs. These aspects are: basic knowledge, logical status, summarization, generalization and application. Aspects are structurally placed among the levels of reading comprehension defined by Yang and Lin in their model of reading comprehension of geometric proofs.
With the empirical part of the master's thesis, which contains a pilot quantitative study on students of the 2nd year of grammar school, we researched the differences in the achieved level of reading comprehension among students, who read different forms of geometric proofs. We also research the influence of students' previous knowledge on achieving the level of reading comprehension regarding different forms of geometric proof.
The research has shown that, overall, there are no significant differences between the different forms of geometric proof in terms of achieving reading comprehension levels among students. Despite the fact that students had only learned the paragraph form of proof in class, they were equally successful in reading and understanding the two-column form of proof and the flow chart form. However, at different stages of reasoning processes, certain forms have been shown to be more effective than others. In the examination of basic knowledge, students demonstrated the best results by reading the flowchart proof form and two-column form of proof. Logical status and summarization, which are more demanding aspects, were understood best by the students who read the paragraph form. The highest mental processes, generalization and application, were achieved best by students who read a two-column form of proof. In the case of reading the paragraph proof form we noticed that students with better knowledge achieved higher levels of reading comprehension, while students with lesser previous knowledge achieved lower levels of reading comprehension. All this suggests that it is important to practice reading proofs in mathematics classes and to consider different forms of presenting proofs in order to enable students to reach, in the most appropriate way, different levels of understanding of proofs.
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