This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic…

Central to ambitious teaching is a constellation of practices we have come to call "leveraging student thinking." In leveraging, teachers position students' understanding and reasoning as a central means to drive learning forward. While leveraging typically is described as a feature of mature practice, in this article we examine…

A characterization of the modelling process in science is proposed for science education, based on Mario Bunge's ideas about the construction of models in science. Galileo's "Dialogues" are analysed as a potentially fruitful starting point to implement strategies aimed at modelling in the classroom in the light of that proposal. It is…

In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area…

This is a position paper in the field of Engineering Education, which is at the very beginning in Europe. It relates challenges in the new field to the emerging technology of (Computer) Theorem Proving (TP). Experience shows, that "teaching" abstract models, for instance the wave equation in mechanical engineering and in electrical…

This concluding commentary takes the perspective of research on practicing scientists and engineers to consider what open areas and future directions on relational thinking and learning should be considered beyond the impressive research presented in the special issue. Areas for more work include (a) a need to examine educational applications of…

This case study demonstrates the ability of high school chemistry students, with varying levels of math preparation, to experience learning-gains on state and district assessments as it relates to chemical reactions, thermodynamics, and kinetics. These advances were predicated on the use of a teaching style rooted in abstract reasoning. The…

The "no-excuses" model of education has become one of the most prominent educational alternatives for urban youth. Recently, notable no-excuses charter schools have begun a concerted effort to develop students' character strengths, striving to increase their chances of future success. In this article, we situate the no-excuses approach…

This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Research in physics education has contributed substantively to improvements in the learning and teaching of university physics by informing the development of research-based instructional materials for physics courses. Reports on the design of these…

This research study explored robotics as the catalyst for computational thinking (CT) by sixth-grade students as they are engaged in a science lesson. The interactions, understandings, and applications are discussed, along with the participants' connections and implementations of CT concepts (decomposition, abstraction, pattern recognition, and…

Systems and system models are recognized as a crosscutting concept in the newly released framework for K-12 science education (NRC [National Research Council], 2012). In previous work, I developed a learning progression for systemic reasoning in ecology at the elementary level. The learning progression captured five levels of students' reasoning…

With the increasing attention and surge of empirical research in providing academic instruction for students with autism spectrum disorder (ASD) comes the need to provide teachers with research-supported strategies. Using one evidence-based strategy for teaching mathematics to students with high incidence disabilities, and another for teaching…

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

The present study addressed the effectiveness of an educational math game for improving proportional reasoning in prevocational education, and examined the added value of support in the form of reflection. The study compared four conditions: the game with reflection prompts, the game with reflection prompts plus procedural information, the game…