One of the most significant steps in learning algebra is understanding the change in the role of letters in mathematical expressions from unknowns to variables. We describe the historical development of this change in usage, starting with the ancient use of mathematical unknowns, detailing several important changes in practice that allowed for the…

Preparing teacher candidates for their roles in 21st century schools calls for direct experiences with inquisitive, linguistically diverse, and often technologically savvy students across global and economic contexts. This article presents the lessons learned from a practicum experience during a semester abroad in Italy, where faculty, teacher…

Three samples of 58 subjects each, selected from the students of seven eighth grade classes and matched with respect to scholastic achievement, program of study, and sex, were taught a foreign alphabet (Arabic) differently. Sample A was told the principles of the alphabet and applied it to examples; Sample B was given most examples first, then…

The value of using inductive and deductive methods in instructing a mathematical principle and foreign language alphabet are tested with sample groups of sixth and eighth grade students in two separate educational experiments. In both cases, the instructional methods used were--(1) instruction in principle before application to examples, (2)…