In their collegiate studies, students are given a wide range of concepts, theories, and equations to assist them in their future endeavors. However, students have not been sufficiently exposed to practical critical thinking methodologies that will benefit them as they encounter open-ended problems. A course developed at the University of Michigan…

The goal of this study is to identify the characteristics of pre-service primary teachers' configural reasoning, understood as the relationships between concepts and figures set to solve geometrical proof problems. Ninety-seven primary teachers were asked to solve two geometrical proof problems in which a geometrical figure was provided. The…

Pattern blocks are inexpensive wooden, foam, or plastic manipulatives developed in the 1960s to help students build an understanding of shapes, proportions, equivalence, and fractions (EDC 1968). The colorful collection of basic shapes in classic pattern block kits affords opportunities for amazing puzzle-like problem-solving tasks and for…

This article describes how a sixth-grade teacher's "missing word" task uncovered higher-level thinking and engaged her students in the Standards for Mathematical Practice. The role and selection of the task promotes higher-level thinking and connects to the Common Core State Standards for Mathematics. The task required students to apply…

Base-rate neglect refers to the tendency for people to underweight base-rate probabilities in favor of diagnostic information. It is commonly held that base-rate neglect occurs because effortful (Type 2) reasoning is required to process base-rate information, whereas diagnostic information is accessible to fast, intuitive (Type 1) processing…

"Resilience" has become a popular goal in research, social policy, intervention design and implementation. Reinforced by its conceptual and political slipperiness, resilience has become a key construct in school-based, universal interventions that aim to develop it as part of social and emotional competence or emotional well-being.…

This article examines pre-service secondary school teachers' responses to a learning situation that presented a student's struggle with determining the area of an irregular hexagon. Responses were analyzed in terms of participants' evoked concept images as related to their knowledge at the mathematical horizon, with attention paid…

Encouraging students to develop multiple solutions for given problems is an important way to improve mathematical knowledge. However, the influence of this teaching element on students' interest-related motivational orientations is an open question. In this article, we report the results of an experimental study (N = 145) that was carried out to…

In supporting students toward literacy, teachers must provide experiences that support the formation of informed understandings of the nature of science (NOS), as well as a structure for developing evidence-based explanations. In this article the authors describe how they guided their students through this learning cycle to answer the essential…

To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…

This interdisciplinary study sketches the ways in which proportional reasoning is involved in the solution of chemistry problems, more specifically, problems involving quantities in chemical reactions (commonly referred to as stoichiometry problems). By building on the expertise of both mathematics and chemistry education research, the present…

Philosophy and schools, children and dynamite, elephants and postage stamps: each has a place, but not necessarily in any natural combination with the other. Whether schools and philosophy belong together depends largely on what we mean by both. To the extent that schools are instruments of government regulation and a mechanism for production of…

This article explores the use of protocol-structured dialogue in promoting reflective practices and shared theories of action within a district leadership team. Protocols have been used to make individuals' theories of action visible and subject to evaluation. This is important for leaders trying to establish coherence across a system; in…

Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…

The Beat the Flood challenge involves designing and building a model flood-proof home, which is then tested in "flood" conditions. It is set on the fictitious Watu Island. The children form teams, with each team member being assigned a responsibility for the duration of the task--team leader, chief recorder, and resource manager. This…