Prospective mathematics teachers' quantitative reasoning on the development of decimal representation of real numbers and its effect on their comprehension of a related proof

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. The proof comprehension can be assessed according to seven dimensions developed by Mejia-Ramos and his colleagues (2012). Embedded experimental design was adopted in the study. Considering proof comprehension dimensions, a proof comprehension test about the proof of a statement on decimal representation of real numbers was formed. 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. Also, one hour long post clinical interviews were conducted with six of them. Results from Wilcoxon Signed Rank test showed that there was a significant difference between pre and post proof comprehension test performances of prospective teachers. The results were also supported with the data from the post-interviews. Prospective teachers' thinking processes through quantitative reasoning during instruction and during the interviews are shared. 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.