Out-of-school learning opportunities can improve student academic achievement and support social-emotional learning. Such programming is valued by the public and in high demand. Teachers can also benefit from seeing students engage in learning in contexts that promote creativity, safe risk-taking, and a tolerance for ambiguity and failure. This…

In summer 2013, Manhattan College introduced an online summer "bridge to calculus" course for incoming first-year students in science, engineering, and mathematics education who marginally did not receive a calculus recommendation based on a mathematics placement test. In this paper, we describe the development of the bridge course and…

Equivalence is a concept that comes up across the entire K-12 grade span and in many different areas of mathematics. Students who are bureaucratically designated as "English Learners" can explore equivalence across their K-12 academic careers while developing language to connect ideas. Drawing on what is known generally from theory and…

In a classroom environment where students are encouraged to talk and share their thinking about mathematics, it comes as no surprise to find an abundance of ideas flooding the room. Yet, what does one do with all these ideas? How do teachers and students use these ideas as they learn in the classroom? Moreover, how do teachers and students manage…

Most children, when presented with the option between two drink items, will choose the one with "more." But what exactly do children consider when they recognize one object as having more than another? Is it the perceived surface area or volume of an object? Depending on children's cognitive development, the aspect of measurement on…

Data reasoning and digital literacy skills, especially the ability to find, represent, and accurately interpret the relevant data, are critical in workplaces and lifetime experiences. Given the importance of developing data reasoning skills from learners' experiences, this article aims to describe teacher and student actions that contributed to…

Teacher professional learning occurs across various contexts. Previous studies on teacher learning and changes in practice have focused on either classroom contexts or learning communities outside of school, but have rarely investigated teacher learning across multiple contexts. Investigating teacher learning across the double contexts of…

Reasoning and problem solving are both critical acts in mathematics learning. The author has met many teachers who tell her they would love to highlight them more but feel they cannot because of the pressures of content coverage, pacing guides, and district tests. In this article, she describes a teaching intervention that highlighted problem…

This paper offers a strategic initiative designed to boost the level of collaborative mathematical research involving undergraduate mathematics students at Butler University. It describes goals, program design, logistics, and outcomes for an 8-day intensive summer experience in which undergraduate mathematics majors engaged in original…

A summary of an experimental course on algebraic curves is given that was held for young learners at age 11. The course was a part of Epsilon camp. a program designed for very gifted students who have already demonstrated high interest in studying mathematics. Prerequisites for the course were mastery of Algebra I and at least one preliminary year…

Community colleges have long provided students a gateway to greater economic opportunities, primarily through two pathways: completing two years of college courses while preparing to transfer to earn a four-year degree or career training that can lead to stable, well-paying positions. Eva L. Rivera Lebrón, a professor of mathematics at…

This paper provides mentor teacher experiences involved with the planning, preparation, implementation, and reflection of a virtual mathematics and science summer camp in the summer of 2020. In the wake of the COVID-19 pandemic, the annual the summer camp was forced to pivot to a completely online format. Primary concerns discussed by mentor…

It is difficult but important for mathematics teachers to help students see themselves as capable mathematics learners, that is, to help each student develop a positive mathematics identity. A student's mathematics identity is a powerful influence on his or her engagement and participation in mathematics. Students act in ways that are consistent…

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…

An understanding of unit fractions, and especially of one-half, one-third, and one-fourth, is crucially important for elementary school children's development of number sense (CCSSI 2010). We describe multimodal activities designed to assist elementary school students in gaining a rich understanding of unit fractions. Research has shown (Zhang,…