In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers' learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning…

Learning to teach is a complex intellectual and adaptive performance act. Student engagement is the cornerstone of effective instruction. Current education reform policies, such as Common Core State Standards (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) and Teacher Effectiveness…

In his last book, "Toward a Logic of Meanings" (Piaget & Garcia, 1991), Jean Piaget describes how thought can be categorized into a form of propositional logic, a logic of meanings. The intent of this article is to offer this analysis by Piaget as a means to understand the language and teaching of science. Using binary propositions, conjunctions,…

Martial arts have recently gained the attention of physical educators as a viable activity in their physical education curriculum. However, physical education teachers may have difficulty teaching martial arts because they have little pedagogical content knowledge and no experience, and because they perceive martial arts to be dangerous and…

This case study report provides information that can be useful in implementing rational changes in mathematics teacher education. Considering teachers' thinking about a specific mathematical topic, such as functions, allows one to better understand the broader domain of teachers' mathematical thinking and its influence on teaching and learning.…