This paper aims to reveal the potential of inferentialism, an emerging philosophy in mathematics education, to extend contemporary constructivist research regarding conceptual development. Going against the traditional view of a notion as the name of a corresponding concept and a constructivist way of naming second-order models, we provide a new…

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.…

The focus of this article is on the development of expertise in interpreting literature within English Language Arts (ELA). Experts and novices differ significantly in how they approach problems and acquire information, with experts demonstrating more sophisticated pattern recognition, nuances, and conceptual understandings and approaches than…

Students often fail to utilize what they know about one topic (e.g., hemodynamics) when attempting to master another topic involving a similar phenomenon (e.g., airflow in airways). What accounts for this difficulty that students have? And how can students be assisted in doing a better job of applying what they already know to new topics? The…

Learning progressions have become increasingly prevalent in mathematics education as they offer a fine-grain map of possible learning pathways a child may take within a particular domain. However, there is an opportunity to build upon this research in ways that consider learning from multiple perspectives. Many current forms of learning…

This article describes students learning to build their own numbering system by recognizing and identifying patterns with interlocking cubes in different place values. The students used the Egyptian hieroglyphic numeral system in conjunction with this activity to connect learning in other subjects. Students used prior knowledge of place value to…

Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Professor Gordon argues for a significant reorientation in the focus and impact of assessment in education. For the types of assessment activities that he advocates to prosper and positively impact education, serious attention must be paid to two important topics: (1) the conceptual underpinnings of the assessment practices we develop and use to…

Metacognition refers to a set of processes an individual uses in monitoring ongoing cognition so as to effectively control his or her own behavior. In this article, I discuss key frameworks for characterizing metacognition and describe approaches to measuring metacognition. Modern research in metacognition assumes that monitoring of cognition…

Cognitive conflict arises when students' expectation about a physical situation, such as the relative temperatures of metal and cloth, are not experimentally verified. The paper reviews this approach as a tool for promoting conceptual learning in undergraduate engineering courses, through three case studies. These cases demonstrate that cognitive…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

The author relates their involvement in the process of testing a picture storybook to teach science concepts. The project asked: If children were learning through a story where the science content was explicit, would children be able to explain the science in the context of the story and then in real-world contexts? Would the learning become…

Although teachers are eager to facilitate community of inquiry (CoI) in their classrooms, they also fear being unable to convey the necessary knowledge to their students in an inquiry due to the inherent involvement of conflicting views, confusion, and a lack of strict definitions about the concepts. The author argues that the banking model of…

Representation in science is anything that stands for something else--drawings, pictures, graphs, or other representational forms (Danish et al. 2020). Representations serve as public displays of phenomena that make aspects of those phenomena explicit (Gilbert 2008). They can serve to make the invisible visible, communicate ideas, display…

Learning progressions (LPs) are descriptions of students' growing sophistication in the understanding of a particular construct through a curricular sequence. They are particularly useful for organizing complex constructs for which students do not necessarily connect concepts as taught in different courses. However, they are challenging to…