The objective of the proposed study is three-fold: to identify middle school student levels of estimation self-efficacy and student engagement, to address student multiplication estimation performance under differing teacher expectations and cultural learning contexts, and to understand how student levels of efficacy and engagement mediate their…

Proportional reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop proportional reasoning naturally. Research suggests that many students do not apply proportional methods appropriately and that they often erroneously…

We present the findings of a study on prospective elementary teachers' proportional reasoning. After describing some of the teachers' performance in solving multiplicative structure problems that involve ratios and relations of direct proportionality between quantities, we were able to establish classifications of their answers according to…