One of the most important applications of the definite integral in a modern calculus course is the mean value of a function. Thus, if a function "f" is defined on an interval ["a", "b"], then the mean, or average value, of "f" is given by [image omitted]. In this note, we will investigate the meaning of other statistics associated with a function…

The Landau-Zener formula provides the probability of non-adiabatic transitions occurring when two energy levels are swept through an avoided crossing. The formula is derived here in a simple calculation that emphasizes the physics responsible for non-adiabatic population transfer. (Contains 2 figures.)

The fun thing about teaching measurement topics is allowing students to create three-dimensional objects from cardboard or paper and then to use them to calculate volume and surface area. The project described in this article is one that author Shafer has used for many years at the high school and college levels to reinforce the concepts of volume…

Today's students demand that their lessons be real, interesting, relevant, and manageable. Mathematics is one subject that eludes many students partly because its traditional presentation lacks those elements that encourage students to learn. Easy accessibility through electronic media has exposed people all over the world to a variety of sports…

In this paper, we accurately estimate the ground-state energy and the atomic radius of the helium atom and a helium-like Hookean atom by employing the uncertainty principle in conjunction with the variational approach. We show that with the use of the uncertainty principle, electrons are found to be spread over a radial region, giving an electron…

In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the…

This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Due to budgetary concerns, the FDOE restructured the Writing portion of the FCAT assessment program for 2010. Among the changes was a difference in how the writing essays were scored. In the past, two people independently judged each essay and each assigned a score from 1 to 6. In the event of a disagreement between judges, the average of the…

Early algebraic thinking in a primary context is not about introducing formal algebraic concepts into the classroom but involves reconsidering how one thinks about arithmetic. Early algebraic thinking assists young students to engage effectively with arithmetic in ways that support engagement with arithmetic structure rather than arithmetic as a…

Subtraction has two meanings and each meaning leads to the different strategies. The meaning of "taking away something" suggests a direct subtraction, while the meaning of "determining the difference between two numbers" is more likely to be modeled as indirect addition. Many prior researches found that the second meaning and…

Failure rates in first year calculus courses are high in most post-secondary institutions across North America and other parts of the world. This Inukshuk-funded open education project involved the development of five stand-alone pre-calculus learning modules. The design and revision phases of this project occurred between the fall of 2007 and…

Over the past 60 years the internal rate of return (IRR) has become a major tool in investment evaluation. Many executives prefer it to net present value (NPV), presumably because they can more easily comprehend a percentage measure. This article demonstrates that, except in the rare case of an investment that is followed by a single cash return,…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

The purpose of this study was to investigate the nature of preservice mathematics teachers' understanding of inequalities. The design of the study was a multi-case study of secondary mathematics education preservice teachers with a focus on their understanding and the lessons that they plan and implement. Data from individual interviews,…