As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

Bell's theorem is a topic of perennial fascination. Publishers and the general public have a steady appetite for approachable books about its implications. The scholarly literature includes many analogies to Bell's theorem and simple derivations of Bell inequalities, and some of these simplified discussions are the basis of interactive web pages.…

The mathematical egg hunt is a hands-on activity designed to help students understand mathematical relations in an Introduction to Proofs course. This activity gives students the opportunity to practice selecting which ordered pairs do and do not belong to a given relation in a moderately competitive egg hunt. It is designed to be low-stakes, yet…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

While noncompliance is a concerning challenging behavior and commonly reported by educators, its measurement is likely to be invalid and inaccurate given the subjectivity of the operational definition. Engagement is offered as a more valid, accurate measurement that may provide data regarding the amount of instruction accessed by the student. In…

This paper presents a novel figure for teaching multiple geometric proofs of the Pythagorean theorem. Because it consists only of congruent given right triangles, the figure can be constructed using a template of the given right triangle or, if available, a computer program. Within the figure, called a Pythagorean multi-proof square, there are…

This article aims to share five practical approaches for how teachers can identify, adapt, and create their own writing prompts they assign to students: (1) Promote Students' Solution Paths; (2) Go beyond Asking Students to Simply "Explain"; (3) Prompt Students to Share Their Reasoning; (4) Have Students Consider the Validity of a Given…

A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

Test writing is a fundamental component of teaching. With increasing pressure to teach larger groups of students, conduct formal assessment of learning outcomes, and offer online and hybrid classes, there is a need for alternatives to constructed response problem-solving test questions. We believe that appropriate use of multiple-choice (MC)…

The author discusses valid and reliable ways to assign grades in an academic course in any discipline. "Validity" means the accuracy of a grade's reflection of student learning and achievement. "Reliability" concerns the degree of random error that might be present and affect validity. First the author defines a grade as a…

We have revamped a classic analytical chemistry laboratory experiment, "Determination of an Unknown Acid", to provide students an opportunity to learn about new advances in the material sciences and their applications in analytical chemistry in an effort to reinforce the key concepts of chemical analysis. Specifically, students were…

Valid proofs need not be in the traditional two-column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

Courses: Interpersonal Communication, Relational Communication Objective: This article teaches students to explain and evaluate Knapp's Relational Staircase Model through the creation of personalized greeting cards for each relational stage. The in-class activity encourages students to be creative and succinct in capturing the essence of an…

Vocabulary learning is an incremental process. Vocabulary knowledge, especially for second-language learners, may develop across a lifetime. Teachers with experience in providing feedback on their students' vocabulary use in writing or speech might have noticed that it is sometimes difficult to pinpoint one aspect of word knowledge. The reason is…

The debate on the validity of teaching students how to identify their own preferred learning style is not going to go away anytime soon as evidenced by the number of articles still being written about the topic. One can find numerous research studies that say students have different strengths and weaknesses when it comes to learning and retaining…