The treatment of kurtosis in textbooks is both sparse and contradictory with applications rarely discussed. To address this, an easily understood definition of kurtosis is introduced and important applications are demonstrated. Two different approaches to teaching kurtosis are presented based on a financial application.

The quantal hypothesis is central to the modern understanding of how a neurotransmitter is released from synapses. This hypothesis expresses that a neurotransmitter is packaged together in quanta that are released probabilistically. The experiments that led to the quantal hypothesis are often related in introductory neuroscience textbooks, but…

The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…

"WeBWorK," an online homework system, can be be used to deliver daily reading questions to students. The author studied its use for this purpose with a lower division Introduction to Programming course and an upper division Probability and Statistics course. In the lower division course, "WeBWorK" significantly improved peer…

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play…

Introductory statistics textbooks rarely discuss the concept of variability for a categorical variable and thus, in this case, do not provide a measure of variability. The impression is thus given that there is no measurement of variability for a categorical variable. A measure of variability depends on the concept of variability. Research has…

Often the differences students see in science and mathematics classrooms are in perspective, approach, or application. Understanding those differences can help teachers to present a unified picture of mathematics and science to their students. In this article, the science teacher is given a glimpse of the treatment of topics shared by both…

Everyone knows that teachers do not have unlimited time, a log of experience, or a deep understanding of all the mathematics they teach. To solve this problem, teachers often use textbooks, and the accompanying teacher's resource books, as sources of activities and advice about how to help students learn mathematics. The activity that prompted…

Discusses need for introducing material to educate students about the relationship of philosophy to physics and science in general, particularly in light of quantum mechanics. Suggesting the dual nature of electrons as a starting point and citing several supplemental texts, a demonstration is described to be used to introduce the topic. (JM)

Three basic theorems concerning expected values and variances of sums and products of random variables play an important role in mathematical statistics and its applications in education, business, the social sciences, and the natural sciences. A solid understanding of these theorems requires that students be familiar with the proofs of these…