| The purpose of this study was to investigate students' conceptions of between ratios and within ratios and make distinctions with respect to those conceptions. The study included two one and one-half hour written sessions and a follow up one-hour interview session in which prospective elementary and secondary mathematics teachers reasoned about different tasks/problems in the context of ratio. The study showed that a student may have a fairly sophisticated ability to make sense of between ratios although not even having a per-one meaning for within ratios.; The study also showed that students with an understanding of within ratios may not have meaning for the ratio representing quantities coming from the same measure space, between ratios. That is, they might not have abstracted that between ratios represent the change factor from one ratio situation to the other. These results suggest that an understanding of between ratios may develop to some degree independently from the understanding of within ratios, and vice versa.; In this study, I go on to discuss implications, derived from the data, for further understanding the development of within ratios. |
