Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

There is growing interest in implementing reform-based lab courses in undergraduate physics that are student driven rather than instructor driven. In these courses, students develop and carry out experiments while simultaneously reasoning about their hypotheses, data collection procedures, collected evidence, and the relevant physics content.…

Educational systems worldwide underscore the importance of developing higher-order thinking skills (HOTS) to prepare students for the new challenges of the XXI century. Some pressing issues faced by educators include the ambiguity of the construct; the implementation of HOTS in classroom practices; and the implications for teaching students from…

The use of scientific modeling has been shown to be highly effective in the learning of science content in multiple disciplines for non-English Learners (EL). However, the benefits of using this pedagogy with ELs have not been heavily explored. This article discusses the use of modeling-based evolution and population ecology pedagogical units in a…

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…

Successful analogical reasoning requires an analogue in a source domain to have high degrees of structural and surface similarity with a learning task in a target domain. It also requires learners to have sufficient source- and target-domain knowledge. We review the literature and speculate that "less" might create "more"; in…

Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b)…

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we…

Teaching and learning is a growing field of research and practice globally, and increasing investments are being made in developing academics as teachers. An inability to adequately account for disciplinary knowledge can lead to academic development inputs that are unable to fully address the needs of students, educators, or disciplines…

This paper uses a comparative methodology to examine the teaching of abstraction in two mathematics lessons, in Denmark and England. In doing so it aims to extend previous work by the authors, examining the effect of local, cultural issues on the form of teaching in order to understand how these also affect the subject content too. The analysis…

Analogical reasoning is an important mechanism for social cognition in typically developing children, and recent evidence suggests that some forms of analogical reasoning may be preserved in autism spectrum disorder. An unanswered question is whether children with autism spectrum disorder can apply analogical reasoning to social information. In…

This article explains four kinds of inquiry exercises, different in purpose, for teaching advanced-level high school and college students the hypothetico-deductive (H-D) method. The first uses a picture of a river system to convey the H-D method's logic. The second has teams of students use the H-D method: their teacher poses a hypothesis…

Background: The use of visual representations (i.e., photographs, diagrams, models) has been part of science, and their use makes it possible for scientists to interact with and represent complex phenomena, not observable in other ways. Despite a wealth of research in science education on visual representations, the emphasis of such research has…

Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…

This case study deals with a solitary learner's process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we…