Peer assessment has great potential to improve student learning. However, assessment is not an everyday activity for students, and thus providing appropriate guidance to students is a key component of creating a successful peer assessment experience. This paper explores how to structure peer feedback in the guided process Peer-Assisted Reflection…

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

This article describes some reflections from the first Calculus I undergraduate teaching assistant in our department as she explored the various ways in which she was able to support both novice and experienced Calculus teachers and the effect of her experience on her academic and career plans.

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

It is no easy feat to engage young people with abstract material as well as push them to greater depths of understanding. Add in the extra pressures of curriculum expectations and standards and the problem is exacerbated. Projects designed around standards and having multiple entry points clearly offer students the best opportunity to engage with…

In this paper, we present a set of activities for an introduction to solving counting problems. These activities emerged from a teaching experiment with two university students, during which they reinvented four basic counting formulas. Here we present a three-phase set of activities: orienting counting activities; reinvention counting activities;…

This article argues for a shift in how researchers discuss and examine students' uses and understandings of multiple representations within a calculus context. An extension of Zazkis, Dubinsky, and Dautermann's (1996) visualization/analysis framework to include contextual reasoning is proposed. Several examples that detail transitions between…

There is a low enrollment of African American high school students in advanced mathematics. High school advanced mathematics are prerequisites to college calculus, one of the basic courses in science, technology, engineering, and mathematics disciplines. African Americans earned only 7.6% of all bachelor's degrees in science, technology,…

As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

Prior research suggests that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students'…

Widening participation initiatives in higher education have grown overall student numbers while also increasing the diversity of student cohorts. Consequently, enhancing student experiences and outcomes has become increasingly challenging. This study implemented personalised emails in two first-year mathematics courses as a scalable strategy for…

This article identifies a self-sustaining system of deficit narratives about students of color as an entry point for studies of cognition to engage with the sociopolitical context of mathematical learning. Principles from sociopolitical perspectives and Critical Race Theory, and historical analyses of deficit thinking in education research,…

Scaffolding is defined as help that can assist students to solve problems or understand concepts that were not able to complete independently. In modern times, the concept of technology-based Scaffolding in learning has developed. In this study an educational game called "Telolet" was designed with the aim of providing Scaffolding to…

This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore,…

At the University of Hartford we transformed our approach to Calculus I--moving it away from a lecture-dominant format to one that focuses squarely on students solving problems and discussing and presenting their mathematical ideas for the majority of class time. In this article, we discuss our Flipping Calculus project and how a departmental…