Identifying mathematics teachers' competency to look at elementary mathematics from an advanced standpoint: a pilot study

This study evaluates the impact of "the ability to look at elementary mathematics from an advanced standpoint (EMFAS)," which was originally proposed by Felix Klein, in mathematics education. By strengthening the connection between elementary and tertiary mathematics, mathematics teachers are expected to have advanced knowledge to offer students higher mathematical insights. Thus, EMFAS serves as a great indicator for measuring teaching effectiveness. By investigating newly qualified and pre-service teachers' ability to apply EMFAS techniques, we analyze the logic involved in solving some specially constructed problems and how teachers could deliver mathematical knowledge to students at the elementary level with the advanced knowledge they possess. We explain the importance of the EMFAS course, in terms of pedagogy and content knowledge. This course prepares pre-service mathematics teachers by equipping them with advanced knowledge for their future profession. This study evaluates mathematics teachers' proficiency in applying EMFAS techniques via a problem set and interviews. We summarize the hierarchical nature of how teachers perceive EMFAS, which could play an important role in guiding pedagogy in mathematics education.