We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of…

Theoretical and practical foundations of basic electrochemical concepts of heterogeneous charge transfer reactions that underline electrochemical processes are presented for their detailed study by undergraduate and postgraduate students. Several simple methods for calculating key variables, such as the half-wave potential, limiting current, and…

The purpose of this guide is to provide strategies and materials for developing and implementing lessons for students who need intensive instruction in the area of place value, numeracy, and counting. Resource room teachers, math interventionists, and others working with struggling students may find this guide helpful. Within college- and…

Place-value is an essential concept that is foundational for understanding our number system and for developing procedures for multidigit operations, but there has been limited research into the place-value understanding of students with learning disabilities. This research is a two-part mixed-methods study that links basic research to…

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

With COVID-19 continuing to make meeting face-to-face impossible, the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) executive decided that, for the first time, the CMESG/GCEDM meeting would be held virtually. By necessity, the program had to be much compressed with no topic…

In the middle years of school, it is important that mathematics is challenging, engaging and focuses on worthwhile mathematics. In this article, Anne Roche describes a lesson that seemed to have all three of these characteristics, as students grappled with issues of scale to create a fun run, given a range of challenging mathematical constraints.…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

This study explores the utility of a set of tablet-based personal computers in the K-12 science, technology, engineering, and mathematics classroom. Specifically, a lesson on food-chain dynamics and predator-prey population controls was designed on the Apple® iPad platform and delivered to three sophomore-level ecology classes (roughly 30 students…

Advances in technology have caused high schools to update their computer science curricula; however there has been little analogous attention to technology-related education in middle schools. With respect to computer-related knowledge and skills, middle school students are at a critical phase in life, exploring individualized education options…

Fluency with basic number facts is vital for students' progress in mathematics. Not only does it contribute to students' facility with mental computation and algorithms, but an understanding of numbers and their properties builds a foundation for future mathematical work including algebra. There are many activities that can help students…

Thinking strategies that are related to counting are discussed and activities that are necessary for the understanding of number and counting are suggested. (Author/MP)

This method of teaching the division of fractions emphasizes the use of concrete materials and helps students understand what division of fractions means. (MP)