Analogy has played an important role in developing modern mathematics. However, it is unclear to what extent students are granted opportunities to productively reason by analogy. This article proposes a set of lessons for introducing topics in ring theory that allow students to engage with the process of reasoning by analogy while exploring new…

The purpose of this paper is to propose a new ontology of reasons for inferentialism. The existing inferentialist approach to mathematics education has a methodological challenge in retrospective analysis and a noncollaborative issue stems from a narrow view of learning. The proposed ontology, built on a radical interpretation of the…

In the context of a rapid digital transformation, digital competence is now regarded as a fourth cultural skill complementing reading, writing, and arithmetic. We argue that a well-structured and sound competence model is needed as a shared foundation for learning, teaching, pedagogical diagnostics and evaluative schemes in the school system.…

Mark Creager noticed that how we teach students to reason mathematically may be counter-productive to our teaching goals. Sometimes a linear approach, focusing on sub-processes leading to a proof works well. But not always. Students should be made aware that reasoning is not always a straight forward process, but one filled with false starts and…

The third edition of the ASE's "Teaching Secondary Biology" sets out a vision for teaching and learning biology. Learning biology is not about learning the contents of a textbook. It is about conceptual learning, learning what it means to do biology and learning what it means to be a biologist. Our hope is that "Teaching Secondary…

Learning with activities is a method of learning where learning process is much easier with practical applications rather than theoretical structure of information given to learn a subject. As learning with activities contain practical applications, it is of great importance in teaching a learning outcome of any teaching program. For that reason,…

The hammer-and-nail phenomenon highlights human tendency to approach a problem using a tool with which one is familiar instead of analyzing the problem. Pedagogical suggestions are offered to help students minimize their mathematical impulsivity, cultivate an analytic disposition, and develop conceptual understanding.

Research on teaching and learning quantum physics (QP) frequently explores students' conceptual difficulties to identify common patterns in their reasoning. The abstractness of QP is often found to be at the origin of students' conceptual difficulties. Due to this abstract nature students resort to common sense reasoning or classical thinking when…

Analogy is a powerful tool for fostering conceptual understanding and transfer in STEM and other fields. Well-constructed analogical comparisons focus attention on the causal-relational structure of STEM concepts, and provide a powerful capability to draw inferences based on a well-understood source domain that can be applied to a novel target…

This article examines a common proportional reasoning problem used in schools, often referred to as the Orange Juice task. The authors show how these six strategies described by Nikula (e.g., Unitizing, Norming, etc.) and one additional strategy can be used to either solve or make progress in the Orange Juice task. The article presents work from…

Herein we present an engaging description of the existent analogy between social distancing during the COVID-19 pandemic and the collision cross-section of particles as defined in the collisional model for a chemical reaction. In addition, the link between collision cross-sections and kinetic rate constants is thoroughly established, bridging…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form--where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach…

To span the great distance from the solar system to the farthest clusters of galaxies in the universe, astronomers break down the distance indicators into steps. The nearest ones are measured geometrically, with what is known as parallax. Among the objects whose distances are thus directly measured are a rare type of star known as a Cepheid…

By bringing everyday phenomena into the classroom, teachers can more readily engage students in authentic scientific inquiry. When working with young children, the best phenomena are those that students can directly experience and investigate. Meaningful phenomena can be identified by watching children at play, listening to the conversations they…

Some of the subjects have complex concepts, which are currently taught using deductive methods in the first years of University Degree. However, the experience shows the results obtained from students' learning goals were quite low. Therefore, the use of inductive method is a crucial factor to improve students' learning results and re-thinking the…