This qualitative case study analyzed how first year university mathematics students used words, images, and symbols to convey the same mathematical ideas. The study was located within the interpretivist paradigm and took naturalistic methodology. Twenty-six first year students were purposefully selected to participate in the study. Data was…

Achieving meaningful educational outcomes requires scalable strategies for mastering mathematical concepts and skills, with student engagement at the core. This paper examines the use of comprehensive, technology-enhanced activities designed to promote active learning and deeper conceptual understanding. Specifically, it focuses on the integration…

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…

This is an exploratory study considering instructional methods in mathematics education. The study examined misconceptions arising from selected assignments undertaken by sixty-five students. The students were attending a calculus mathematical course unit on limits of functions, in different academic areas offered at selected tertiary institutions…

The aim of this research was to study and investigate first year university calculus students' misconceptions about how to use the definition of limit to find the first derivative of functions and then remediate these misconceptions by using APOS theory (Action, Process, Object, and Schema). Students (n = 82 female and male) were selected based on…

The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of…

Roots is one of these mathematical topics that students encounter multiple times in their studies of mathematics. Growing from the commognitive framework, this study is concerned with intra-commognitive conflicts where the same discursant develops incommensurable discourses on 'the same' mathematical object (square roots, in this case) and…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The…

Two studies (Trautwein 2007 and Dettmers et al. 2010) show a positive correlation between high-quality homework and mathematics achievement. Students who completed their homework assignments scored better on assessments. However, these studies also showed no relationship between time spent on homework and resulting student achievement. This helped…

Enhancing students' conceptual understanding and increasing student motivation to effectively participate in classroom discussions are important for instructors of mathematics. Web-based homework management systems provide alternatives to the traditional pen-and-paper based approaches. In addition, these tools facilitate the creation of a…

Growing from the commognitive framework, this study is concerned with objectification -- a special way of talking about mathematical objects, which is key to one's concept formation. The study explores how objectification can be manifested in the discourse on square roots that unfolds in writing. The data comes from a class in a foundation…

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

Elementary pre-service teachers in an upper-division algebra mathematics content course explored graphing through the use of Calculator-Based Rangers™ (CBRs). This study explores how they used the "Distance Match" feature of the technology to engage in algebraic thinking. Operating CBR technology, pre-service teachers' perceptions…

Nationally, student performance in math has been flat, and achievement gaps persist. And with a growing economy driven by industries in the science, technology, engineering, and math (STEM) fields, educators are tasked with instilling interest in and preparing students for college studies and careers that will supply these in-demand jobs. Now,…