Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

Barlow et al. (2018) discussed three types of mistakes worthy of inspection: procedural errors, inappropriate solution processes, and misconceptions. Here, the authors focus on procedural errors, as these often led the teachers in their professional development project to limit their inspection of mistakes to correcting. Despite this narrow focus,…

COVID-19 pandemic policies requiring disease testing provide a rich context to build insights on true positives versus false positives. Our main contribution to the pedagogy of data analytics and statistics is to propose a method for teaching updating of probabilities using Bayes' rule reasoning to build understanding that true positives and false…

This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…

Undergraduate biochemistry students frequently find the quantitative treatment of weak acids and bases troublesome. Given the p"K"[subscript a] of a weak acid "HA," for instance, many students struggle to calculate the pH of a solution of the conjugate base A[superscript -] at concentration "C," pH(A[superscript -],…

We discuss the limits of the equation of the period of a simple pendulum, T[subscript s] = 2[pi][square root]l/g, frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one,…

The goal of parkour is to cross various obstacles in an efficient and creative way by jumping, swinging, climbing, and running. Parkour aligns with the SHAPE America national standards for K-12 physical education and has demonstrated its potential to highly engage both boys and girls in moderate-to-vigorous physical activity (MVPA). In this…

Although our students correctly define the terms p-value, Type I and Type II errors, they sometimes misinterpret results from real data. In this work we present an assignment intended to clear up these misconceptions.

Video analysis helps students to connect physical, mathematical, and graphical models with the phenomena that the models represent and improves student kinematic graph interpretation skills. The wide-spread availability of easy to use software packages like Logger Pro (Vernier), Capstone (PASCO), and Tracker have led to many introductory physics…

Error analysis consumes much of the focus in introductory physics labs. Catastrophic cancellation is a spike in error that occurs when subtracting two measurements of roughly equal magnitude. Often termed "loss of significance" or "subtractive cancellation," this effect can easily relegate experimental results to utter…

Running records can be the assessments that teachers are looking for when searching for an efficient way to plan meaningful literacy instruction. Running records can give teachers immediate insights to guide on-the-fly prompting and teaching decisions to build reader independence. The authors use classroom examples to illustrate how taking and…

Using a behavioral ethics framework and YouTube video clips, this exercise engages students in a demonstration of how people employ cognitive errors and self-deception to protect their interests when making ethical decisions. This approach helps instructors supplement lessons using normative theories to teach business ethics. Normative theories…

R and Python are commonly used software languages for data analytics. Using these languages as the course software for the introductory course gives students practical skills for applying statistical concepts to data analysis. However, the reliance upon the command line is perceived by the typical nontechnical introductory student as sufficiently…

The role of gesture in second language acquisition (SLA) has recently become a promising area of research, characterized by the growing number of empirical research studies that examine the potential of incorporating gestures in such areas as the teaching of grammar, vocabulary, and pronunciation. This paper focuses on how gesture can be…

The logos of many atomic energy regulatory bodies present a paradox in that the depictions of atomic structure that they portray tend to be 'wrong' in relation to the rules that govern pictorial representations of atomic structure that we teach. These logos present chemistry educators with excellent classroom resources to enhance critical thinking…