The development of the proportional representation of the conception of actual infinity is non-decreasing, at least in the view into the distance, in both contexts with respect to age. It can safely be maintained that the development of the proportional representation of the earliest conception comprehension of the concept of infinity, the so-called natural infinity, is not concurrent with the students’ age. We monitor the proportional representation of these conceptions in four combinations of views (into the distance and in depth) and contexts (arithmetical and geometrical). These conceptions are built on the intuitive phenomenon of the horizon. The aim of the research was to describe the development of students’ conceptions of infinity. The questionnaire survey was taken by 861 students ranging from grades 7 to 13. The paper is the result of extensive research carried out among Czech students and focuses on a conception of infinity. Results from both the proof comprehension test and the interviews suggest that once prospective teachers engage in quantitative reasoning during instruction, their proof comprehension might develop. Prospective teachers' thinking processes through quantitative reasoning during instruction and during the interviews are shared. The results were also supported with the data from the post-interviews. Results from Wilcoxon Signed Rank test showed that there was a significant difference between pre and post proof comprehension test performances of prospective teachers. Also, one hour long post clinical interviews were conducted with six of them. The proof comprehension test was used as both the pre-test prior to and the post-test upon completion of an instruction given to 19 prospective mathematics teachers to determine the effect of their quantitative reasoning on their performance of proof comprehension. Considering proof comprehension dimensions, a proof comprehension test about the proof of a statement on decimal representation of real numbers was formed. Embedded experimental design was adopted in the study. The proof comprehension can be assessed according to seven dimensions developed by Mejia-Ramos and his colleagues (2012). This study investigated prospective mathematics teachers' quantitative reasoning on the development of decimal representation of real numbers and its effect on their comprehension of a related proof.
0 kommentar(er)
