A common homework problem in many introductory physics courses is similar to the following. "A car drives at constant speed over a hill on a road in the shape of a vertical circular arc. What is the maximum speed the car can have and not lose contact with the road at the crest of the hill?" Unfortunately this problem is flawed, because…

The negative effects of bullying in school are substantial, yet educators trying to intervene face significant barriers. Such obstacles include ineffective intervention techniques and perceptual bias that gets in the way of recognizing bullying. Promising ways to overcome these barriers include the following strategies: using intervention methods…

Ultraviolet (UV)-visible (Vis) spectroscopy is widely used in all modern laboratories as a routine method of analysis. The monitoring of chemical reactions in an aqueous solution involving a gas product is a demanding task but particularly for oscillatory reactions which are obtainable in a narrow concentration range. In this work, the…

Friedel-Crafts alkylation reactions using a curated set of alcohols provide students with the opportunity to combine the study of electrophilic aromatic substitution with carbocation rearrangements. In this experiment students may be presented with up to nine alcohols that yield six products, all synthesized under identical reaction conditions.…

As a follow-up to their article, "Emojis and Their Place in the Mathematics Classroom" (EJ1358586), the authors examine how emojis can be used as bridging representations to support student understanding of proof and algebra in upper primary school. They take a problem from reSolve, Level 3, (AAMT, 2020), look at it from the perspective…

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…

The OECD's Programme for the International Assessment of Adult Competencies (PIAAC) represents a comprehensive international comparative assessment of the information processing skills of adults vital for the full participation in social and economic life in the 21st century. PIAAC is now in its second cycle and continues a series of international…

ePUZSOLVED is designed to help students understand the general communication models and experience the advantages and disadvantages of each. It will highlight how various modes of communication, when used appropriately, may lead people to solve problems, as exemplified by the online puzzle. Courses: Introduction of Communication Models, Review of…

Providing students with opportunities to build, and test and revise ideas, can help them develop critical thinking and problem-solving skills. In this article, the authors describe how core measurement and geometry concepts were embedded within a "Model It!" task. They replicate an industry-based, interdisciplinary problem, but only…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…

This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students' horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the…

The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

For 15 years, Complete College America (CCA) has been building movements for scaled systemic change and transforming institutions. While CCA has expanded their efforts over the past 15 years, they have studied the best ideas and co-designed the most promising practices to move the needle on college completion. They have learned a lot about how to…

Students with disabilities often face significant challenges in developing mathematical problem-solving skills, which are critical for academic success. Traditional problem-solving interventions have primarily focused on skill acquisition, leading to issues with knowledge application in real-world contexts. Enhanced Anchored Instruction (EAI)…

In this abstract, I share a field report. It is an administration manager's experience of how solutions to wicked problems can be developed by approaching the task with an action-learning attitude and using democratic methods in a Catholic parish association. In detail, it had to be worked out, how pastoral work can be shaped under the…