Generalization is a critical aspect of doing mathematics, with policy makers recommending that it be a central component of mathematics instruction at all levels. This recommendation poses serious challenges, however, given researchers consistently identifying students' difficulties in creating and expressing normative mathematical…

Carbon cycle pool-and-flux reasoning is a critical facet of climate literacy. This article begins with discussion of why this type of reasoning is both challenging and important. Results from two studies are reported. The first describes students' approaches to carbon cycle pool-and-flux reasoning. The second describes and reports results from an…

Researchers studying parent-child reminiscing in the preschool years have often focused on parents' and children's elaborative talk (i.e., provision of unique details). The current study proposes a novel conceptualization of parent-child reminiscing narratives by examining 4 levels of abstraction (i.e., a continuum of literal to inferential…

The social studies curriculum travels through time and space and is bigger on the inside than it is on the outside. To an outsider, the social studies curriculum is a single line on a program of studies, 45 minutes of a student's school day. Those on the inside, however, know that the field covers history, geography, civics, economics, and much…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

The purpose of this study is to describe, critically analyse and discuss the Swedish system of assessing ethics education in compulsory school through national tests. The publicly available tests from 2013 for grades six and nine have been studied as have the assessment instructions for teachers. Staff responsible for the test construction have…

Even though a school in Southern Virginia had been utilizing a variety of manipulatives, calculators, and computers to transition students through the concrete-representational-abstract (CRA) sequence; students did not meet the state proficiency requirement on the standardized math assessment. A qualitative descriptive case study design, grounded…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

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…

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…

We examined subjects' ability to judge the soundness of informal arguments. The argument claims matched or did not match subject beliefs. In all experiments subjects indicated beliefs about spanking and television violence in a prescreening. Subjects read one-sentence arguments consisting of a claim followed by a reason and then judged the…

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 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…

Understanding how students learn is crucial for helping them succeed. We examined brain function in 107 undergraduate students during a task known to be challenging for many students--physics problem solving--to characterize the underlying neural mechanisms and determine how these support comprehension and proficiency. Further, we applied module…