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Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about the nature of knowledge and learning can hinder them…
In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…
The ability to categorize problems is a measure of expertise in a domain. In order to help students learn effectively, instructors and teaching assistants (TAs) should have pedagogical content knowledge. They must be aware of the prior…
Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving…
Scientists who study how the brain solves problems have recently verified that, because of stringent limitations in working memory, where the brain solves problems, students must apply facts and algorithms that have previously been well…
Developing expertise in physics requires appropriate integration and assimilation of physics and mathematics. Instructors and students often describe physics courses in terms of their emphasis on conceptual and quantitative problem-solving.…
Computational thinking in physics has many different forms, definitions, and implementations depending on the level of physics, or the institution it is presented in. In order to better integrate computational thinking in introductory…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
Teaching assistants (TAs) are often responsible for grading in introductory physics courses at large research universities. Their grading practices can shape students' approaches to problem solving and learning. Physics education research…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
Physics students can encounter difficulties in physics problem solving as a result of failing to use knowledge that they have but do not perceive as relevant or appropriate. In previous work the authors have demonstrated that some of these…
Developing and making sense of quantitative models is a core practice of physics. Covariational reasoning -- considering how the changes in one quantity affect changes in another, related quantity -- is an essential part of modeling…
The gap between theory and practice is well-documented in educational research. Physics teachers' willingness to apply research findings in practice may be influenced by a sceptical attitude towards science education research. This study…
Problem solving is central to physics instruction. Results from Physics Education Research (PER), however, demonstrate that traditional ways of teaching with problem solving are inefficient and ineffective for promoting true physics…
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…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
Neural networks are ubiquitous in applied machine learning for education. Their pervasive success in predictive performance comes alongside a severe weakness, the lack of explainability of their decisions, especially relevant in…
"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…
Expert problem solvers are characterized by continuous evaluation of their progress towards a solution. One characteristic of expertise is self-diagnosis directed towards elaboration of the solvers' conceptual understanding, knowledge…
In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometry and trig functions. The objective is to lead students to a…