The paper presents analyses of multivariable calculus learning-teaching phenomena through the lenses of DNR-based instruction, focusing on several foundational calculus concepts, including "cross product," "linearization," "total derivative," "Chain Rule," and "implicit differentiation." The…

Frozen peas and carrots are commonly available in grocery stores in the United States. The carrots are cut into cubes roughly 8 mm on a side, while the peas are roughly spherical with a diameter of about 6 mm. They are prepared together in water that is brought to a boil. The peas and carrots, which are initially mixed together, separate as the…

White light refracted by a glass edge or a prism might be split into the colors of the rainbow but, when restricted by a suitable arrangement of edges, might also yield a sequence of colors complementary to the rainbow. We studied the creation of these color fields experimentally with a setup consisting of RGB light-emitting diodes that cover all…

This paper conceptualizes children's mathematical thinking from a materialist perspective on language and mathematics. This perspective considers human and non-human bodies as ontologically equivalent; that is, as both being agentive, vibrant, and animated, thus resisting static representations. This conceptualization is an alternative to the…

Natural language helps express mathematical thinking and contexts. Conventional mathematical notation (CMN) best suits expressions and equations. Each is essential; each also has limitations, especially for learners. Our research studies how programming can be a advantageous third language that can also help restore mathematical connections that…

This paper reports the first empirical investigation of the hypothesis that epistemic appraisals form part of the structure of concepts. To date, studies of concepts have focused on the way concepts encode properties of objects and the way those features are used in categorization and in other cognitive tasks. Philosophical considerations show the…

Introduction: Subitizing, a quick apprehension of the numerosity of a small set of items, is consistently utilized to support early number understanding. Perceptual subitizing is the innate ability to recognize less than five items without consciously using other mental or mathematical processes. Conceptual subitizing, which requires higher-level…

The history of particle physics can be considered nothing less than a huge triumph for science. Over the course of a little more than a century of effort, our understanding of the world of atomic and subatomic physics went from a vague understanding of atoms, to one that is much more detailed. Early in this hundred-year-long period, we learned…

The fundamental mechanism of biochemistry lies on the reaction kinetics, which is determined by the reaction pathways. Interestingly, the reaction pathway is a challenging concept for undergraduate students. Experimentally, it is difficult to observe, and theoretically, it requires some degree of physics knowledge, namely statistical and quantum…

In a dynamic labor market, it is important to help people combine information and generate creative solutions to cope with complex career challenges. In the present research, we apply the theory of information structure to creative career idea generation and hypothesize that flat information structures--that is, structures in which the information…

Obtaining adequate understanding of scientific concepts is considered challenging due to learners' misconceptions about natural phenomena. Misconceptions may coexist with scientific knowledge in the brain. Therefore, misconceptions must be cognitively inhibited in order to select the scientific knowledge. There is, however, lack of substantial…

Undergraduate engineering students usually face difficulties understanding electric circuit concepts. Some of those difficulties regard with misconceptions students bring into the classroom and develop during the learning process. Additionally, the increasing complexity of the topics along the fundamental electric circuit course constitutes…

In recent years, chemistry educators are increasingly adopting immersive virtual reality (IVR) technology to help learners visualise molecular interactions. However, educational studies on IVR mostly investigated its usability and user perceptions leaving out its impact on improving conceptual understanding. If they evaluated students' knowledge…

Knowing the temporal direction of causal relations is critical for producing desired outcomes and explaining events. Existing evidence suggests that children start to grasp that causes must precede their effects (the temporal priority principle) by age 3; however, whether younger children also understand this has, to our knowledge, not previously…

Concepts relating to enzymes and energy are central to understanding chemical and biological processes at the molecular level. Student learning of these crosscutting concepts can be challenging, so it is important to identify misconceptions and remediate them early, especially in introductory classes. Here we describe an activity in which…