One expected outcome of physics instruction is for students to be capable of relating physical concepts to multiple mathematical representations. In quantum mechanics (QM), students are asked to work across multiple symbolic notations, including some they have not previously encountered. To investigate student understanding of the relationships…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

In this literature review, we survey student naïve ideas (frequently referred to as 'misconceptions') that plausibly relate, at least in part, to difficulty in understanding probability. We collected diverse naïve ideas from a range of topics in physics: Non-linear Dynamics; Cosmology; Thermal Physics; Atomic, Nuclear, and Particle Physics;…

This dissertation presents results from research and curriculum development related to student understanding of the principle of superposition in introductory optics and upper-division quantum mechanics courses. The focus is on the extent to which students are able to relate the mathematical formalism used in physics to real-world phenomena. In…

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data…

This article is devoted to practical aspects of teaching and learning of probability at university. It presents the difficulties and attitudes of first-year university science and engineering students towards using paradoxes and counterexamples as a pedagogical strategy in teaching and learning of probability. It also presents a student's point of…

We study different ways of determining the mean distance (r[subscript n]) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating…

Discusses the probability of seeing a tire explode or disintegrate while traveling down the highway. Suggests that a person observing 10 hours a day would see a failure on the average of once every 300 years. (MVL)

We report on the development of students' ideas of probability and probability density in a University of Maine laboratory-based general education physics course called "Intuitive Quantum Physics". Students in the course are generally math phobic with unfavorable expectations about the nature of physics and their ability to do it. We…

Twelve resource units are presented for the teaching of science and mathematics to gifted students in secondary school. The units present an introduction, tips for teachers, objectives, activities, and materials lists. The units include: "Functions, Relations, and Graphs" (Priscilla Watts); "More Wham to the Gram (A Study of the…

This publication contains Arizona public schools' academic standards for Grade 1. The contents of this document include the following: (1) The Arts Standard 2006--Grade 1; (2) Comprehensive Health Education/Physical Activity Standards 1997--Foundations (Grades 1-3); (3) Foreign and Native Language Standards 1997--Foundations (Grades 1-3); (4)…

This publication contains Arizona public schools' academic standards for grade 2. The contents of this document include the following: (1) The Arts Standard 2006--Grade 2; (2) Comprehensive Health Education/Physical Activity Standards 1997--Foundations (Grades 1-3); (3) Foreign and Native Language Standards 1997--Foundations (Grades 1-3); (4)…

This publication contains Arizona public schools' academic standards for grade 3. The contents of this document include the following: (1) The Arts Standard 2006--Grade 3; (2) Comprehensive Health Education/Physical Activity Standards 1997--Foundations (Grades 1-3); (3) Foreign and Native Language Standards 1997--Foundations (Grades 1-3); (4)…

This publication contains an updated academic standards of Arizona public schools for grade 5. The contents of this document include the following: (1) The Arts Standard 2006--Grade 5; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Foundations (Grades…

This publication contains an updated academic standards of Arizona public schools for grade 6. The contents of this document include the following: (1) The Arts Standard 2006--Grade 6; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades…