Combinatorics is a field of mathematics that concerns enumeration and existence, and its most notable applications are in computer science and statistics. Most students are introduced to combinatorics through counting problems, where they are tasked with determining the cardinality of a set of outcomes. Such problems are well-known for being...
We now have broad consensus in the mathematics education research community that active, inquiry-based classrooms provide a wealth of learning benefits for students (Freeman et al., 2014; Laursen et al., 2014; Theobald et al., 2020). Classrooms that utilize inquiry throughout the entire structure of the course, as opposed to the...
Institutions of higher education have experienced a rapid increase in international student enrollment within a short period of time, especially in mathematics classrooms. It is therefore important for instructors to have the knowledge and skills to support international students in the learning of mathematics. There are few research studies of...
Mathematics Graduate Student Instructors (GSIs) have a significant impact on the teaching and learning of mathematics in post-secondary contexts through their work as instructors of record, tutors, graders, and recitation, laboratory, or discussion leaders for mathematics courses. Perhaps more importantly, GSIs are future teachers of mathematics: more than 60 percent...
There are many reasons toward why students withhold such negative mindsets toward the subject of mathematics. This thesis builds upon previously conducted research concerning affect and confidence in mathematical problem solving, confidence that students exhibit about themselves, and combinatorial thinking and activity.
The focus of this autoethnography was an in-depth analysis of the recorded experiences of a middle school math teacher's transitional development from classroom teacher, to teacher leader. The following research questions guided this study: (1) In what ways did the researcher’s view of self as a teacher leader change during...
The nonlinear Schrödinger equation is a well-known partial differential equation that provides a successful model in nonlinear optic theory, as well as other applications. In this dissertation, following a survey of mathematical literature, the geometric theory of differential equations is applied to the nonlinear Schrödinger equation. The main result of...
The study examined classroom instructional practices and teacher's
professed conceptions about teaching and learning college calculus in
relationship to the implementation of scientific-programmable-graphics (SPG)
calculators. The study occurred at a university not affiliated with any reform
project. The participants were not the catalysts seeking to implement calculus
reform, but expressed...
As a result of the calls for reform in mathematics education and the ever-changing nature of mathematics, today's teachers face the challenge of teaching unfamiliar content in ways that are equally unfamiliar. In view of this challenge, the purpose of this study was to investigate middle school teachers' subject matter...
This study described how and why a Korean elementary teacher taught mathematics as he did. Specifically, the study sought to describe his beliefs about the teaching and learning of mathematics and relate them to patterns of classroom interaction and norms.
An ethnographic inquiry guided the study of one third grade...