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…

Purpose: We developed the Goal Achievement Scale in Colleges of Education (GASCE) to address the lack of context-specific assessment tools for evaluating goal achievement in Nigerian colleges of education. Existing instruments fail to capture the unique challenges of these institutions, making a reliable and valid scale essential for assessing…

The rapid advancement of educational technologies worldwide and the ubiquitousness of technology-integrated teaching and learning have posed great challenges to teachers. Technology leadership is an emerging focus among educators, it involves using technologies to lead learners' knowledge, abilities, and values development. However, there are few…

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…

The author provides a checklist for educators who are selecting technically adequate tests for identifying and referring students for gifted education services and programs. The checklist includes questions related to how the test was normed, reliability and validity studies as well as questions related to types of scores, administration, and…

High-quality assessments are crucial to many aspects of the educational process. They can help policymakers monitor long-term educational trends, assist state educational agencies (SEAs) and local educational agencies (LEAs) in allocating resources and professional development opportunities, provide insights to teachers about how well students…

The Indiana Department of Education's (IDOE's) Accessibility and Accommodations Information for Statewide Assessments is a document intended for school-level personnel and decision-making teams as they prepare for and implement Indiana statewide assessments. Information is provided for school personnel as a reference to inform guidance on…

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…

LaPiere's pioneering study explored the tenuous connection between attitudes and behaviors in the context of racism. This activity provides a replication proposal framework that is useful for applying critical thinking skills, including new forms of measurement. Students read the study and provide written responses to several discussion prompts…

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…

Knowledge assessments in undergraduate mathematics education commonly evaluate response correctness to determine learner proficiency. However, simultaneous evaluation of learner metacognition more accurately assesses the multiple dimensions of knowledge and has been shown to increase assessment validity and reliability. Research into…

The RP Group's Multiple Measures Assessment Project (MMAP) produced this technical report as part of a series on how California's community colleges can ensure more English learners (ELs) successfully complete "gateway" English coursework -- courses that satisfy the English writing requirements for completion of an associate's degree as…

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…