Related papers: Just Math: A new epistemic frame
Students in inquiry science classrooms face an essential tension between sharing new ideas and critically evaluating those ideas. Both sides of this tension pose affective risks that can discourage further discussion, such as the…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
I believe that most teachers develop a belief in a set of pedagogical practices. As we teach, we try different ways to teach topics and then judge how successful the methods were. After several years, we have a compilation of techniques in…
Current investigations into pedagogical goals of introductory algebra-based physics students at the University of Central Arkansas, by learning orientation towards an in-class metacognitive group problem solving task, seek to determine…
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence…
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
In collaborative small-group work, physics students need to both manage social conflict and grapple with conceptual and epistemological differences. In this paper, we document several outlets that students use as tools for managing social…
During the past several years the authors have developed a new approach to the teaching of Physical Science, a general education course typically found in the curricula of nearly every college and university. This approach, called `Physics…
Acquiring the mathematical, conceptual, and problem-solving skills required in university-level physics courses is hard work, and the average student often lacks the knowledge and study skills they need to succeed in the introductory…
$E$-frames are a new generalization for the concept of frames for $\mathcal{H}$, where $E$ is an infinite invertible complex matrix mapping on $\bigoplus_{n=1}^{\infty}\mathcal{H}$. This article is dedicated to investigating some notions…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
Student learning in undergraduate physics laboratory courses has garnered increased attention within the PER community. Considerable work has been done to develop curricular materials and pedagogical techniques designed to enhance student…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…
The amount of published research in Physics Education Research (PER) shows, on one hand, an increasing interest in the design and development of high performance physics teaching strategies, and, on the other hand, it tries to understand…
Most educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
The purpose of this paper (which, in many passages, I take the liberty of writing in the first person singular for bringing a personal experience) is to show how teachers of Physics and Mathematics in Basic Education can teach, through a…
Quantum mechanics is difficult to learn because it is counterintuitive, hard to visualize, mathematically challenging, and abstract. The Physics Education Technology (PhET) Project, known for its interactive computer simulations for…