This paper focuses on the definitions and the mis-out and mis-in examples of rational numbers that four prospective elementary teachers presented while working on rational number assignments. The participants were first asked to respond, individually, to an Individual Rational Number Assignment, consisting of items aiming at detecting their…

Despite growing theoretical and empirical evidence that writing has the potential to be an effective tool for student learning in undergraduate mathematics, writing-to-learn integration in mathematics is rare. Major deterrents include perceived lack of alignment between writing and learning goals, deficit views of students' writing abilities, and…

In our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' ("Teaching Children Mathematics", 21(1), 18-25) "13 Rules That Expire" article has been a useful resource for us to…

This study looked at the effectiveness of differentiated learning in enhancing students' mathematical outcomes by incorporating varied content, processes, and products. Employing a mixed-methods experimental design, the research hypothesized that differentiated instruction significantly influences students' performance in mathematics exams. The…

The present bounded case study explored preservice teachers' experiences using a boundary object in the form of a mathematics course assignment during a pre-student teaching clinical experience. The study focused on preservice teachers' perceptions of how utilizing a boundary object influenced the dynamics of their hierarchical relationships with…

A variety of factors are associated with the learning difficulty in mathematics in the context of Pakistani schools. This study explored the different causes of learning difficulties in mathematics faced by primary school students in Karachi, Pakistan. Using a quantitative research design, the data was gathered from the parents and teachers of…

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

The practice assignments in a mathematics textbook or course can be arranged so that most of the problems relating to any particular concept are massed together in a single assignment, or these related problems can be distributed across many assignments--a format known as spaced practice. Here we report the results of two classroom experiments…

Many active learning practices highly depend on students' advance preparation for the class. However, reading Calculus can be a challenging task to students. We address this concern by assigning targeted pre-class readings in multiple Calculus courses. We report on our implementations, provide students' feedback, and discuss the lessons learned…

The practice assignments in a mathematics textbook or course can be arranged so that most of the problems relating to any particular concept are massed together in a single assignment, or these related problems can be distributed across many assignments -- a format known as spaced practice. Here we report the results of two classroom experiments…

Imbalances in problem distributions in math textbooks have been hypothesized to influence students' performance. This hypothesis, however, rests on the assumption that textbook problems are representative of the problems that students encounter in classroom assignments. This assumption might not be true, because teachers do not present all…

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…

This paper captures and reports on mathematics pre-service teacher (PST) voices. Mathematics PSTs, in a tertiary mathematics secondary curriculum teaching subject assessment, were asked to perform a small-scale literature review on an issue they identified as important in mathematics teaching. The assessment, written as an article, required…

The education of preservice teachers is a complicated process. Working toward a disposition that is inclusionary versus exclusionary is a logical and worthy goal, but that means teacher educators acknowledge the demographics and mindset of those involved in this process. The researchers believe culturally responsive teaching should be woven into…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…