This paper introduces two theoretical constructs, open-loop covariation and closed-loop covariation, that combine covariational reasoning and causality to characterize the way that three preservice mathematics teachers conceptualize a feedback loop relationship in a mathematical task related to climate change. The study's results suggest that the…

This commentary reviews each of the three content chapters in the integers section and offers questions to promote further discussion. In addition to the themes raised in the three chapters, I introduce the role of formal mathematical structure in generalizing systems of number, from natural numbers to integers, and analogously, from real numbers…

Literature suggests that "current characterizations of the terms procedural knowledge and conceptual knowledge are limiting and are, in fact, impediments to careful investigation of these constructs" (Star, 2005, p. 405). We examined secondary mathematics teachers' understanding of procedural and conceptual knowledge at superficial and…

This study investigated the computational thinking (CT) practices of eight pre-service teachers through their Scratch and Python programs. Conducted within an undergraduate-level computer science education course, students learned CT concepts via parallel instruction in block-based programming (Scratch) and text-based programming (Python). The…

Background: In scientific inquiry learning, students often have difficulties conducting hypothetical reasoning with multiple intertwined variables. Concept maps have a potential to facilitate complex thinking and reasoning. However, there is little investigation into the content of student-constructed concept maps and its association with inquiry…

Proofs are attempts to conclusively demonstrate the validity of the claim for all cases indicated within its domain, which implies that proving should involve thoughtful consideration of the domain. This study analyzed the enactment of three general claim tasks, or tasks where the domain of the claim referred to an infinite number of cases, that…

Experiential learning is a foundational element to agriscience education. The purpose of this study was to examine the effects of reflection type and abstraction order on students' scientific reasoning skills when teaching experientially. Three major conclusions can be drawn from this study: (1) reflection type and abstraction order are…

This paper argues that abductive reasoning has a central place in theorizing Health Professions Education. At the root of abduction lies a fundamental debate: How do we connect practice, which is always singular and unique, with theory, which describes the world in terms of rules, generalizations, and universals? While abduction was initially seen…

Dysexecutive syndrome has been consistently reported in children and adolescents with autism spectrum disorders (ASD). Particularly, impairments have been documented in working memory, inhibition, and mental flexibility. However, the relationship between executive impairments and intellectual functioning is far from clear in this population. This…

Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives -- base-ten blocks -- to support children's place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in…

In learning biologically inspired design (BID), the mapping process from problem to biological inspirations is crucial for generating novel ideas. This study determines the effects of knowledge representations related to design problems and inspirations on students' novelty of ideas generated in BID. Forty-four industrial design undergraduates…

This work is part of an investigation conducted in Italy, which aims to explore the effects of instruction on secondary school students' combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo's research to two groups of students with and without instruction on combinatorics in order to analyse the students' performances and…

Human thought can be characterised as being situated in the 'space of reasons'. That is to say that human thought is guided by the norms of theoretical and practical rationality which, in turn, enable autonomous thinking. But how do children learn to navigate the space of reasons? Building on the work of Tugendhat and Bakhurst, among others, we…

Understanding fraction magnitudes is especially important in daily life, but fraction reasoning is quite difficult. To accurately reason about fraction magnitudes, adults need to monitor what they know and what they do not know. However, little is known about which cues adults use to monitor fraction performance. Across two studies, we examined…

One-hundred-six 5-year-olds' (M[subscript age] = 5;6; SD = 0.40) were trained with second-order false belief tasks in one of the following conditions: (a) "feedback with explanation"; (b) "feedback without explanation"; (c) "no feedback"; (d) "active control." The results showed that there were significant…