This dissertation reports on three studies about students' conceptions and learning of the idea of instantaneous rate of change. The first study investigated 25 students' conceptions of the idea of instantaneous rate of change. The second study proposes a hypothetical learning trajectory, based on the literature and results from the first study,…

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead…

This paper presents the importance of the visual expression of factor decomposition in regression analysis, which is particularly worthwhile for undergraduate students whose majors are not mathematics but social science. The conventional purpose of regression analysis is to examine specific hypotheses empirically. In particular, the statistical…

Previous research has shown that students form fragmented understandings about variability even after instruction and that these primitive notions function as obstacles to a robust understanding of variability. To investigate the effect of disruptions to students' primitive notions of variability, we examined undergraduate students' reasoning…

Understanding rational numbers is critical for secondary mathematics achievement. However, students with mathematics difficulties (MD) struggle with rational number topics, including fractions, decimals, and percentages. The purpose of this systematic review was to describe the instructional foci of rational number interventions, determine the…

This study was aimed at exploring the key factors affecting postgraduate students-teachers' translation of a theoretical framework from English into their native language. The research was carried out with 21 Turkish postgraduate students who were also mathematics teachers, based on the theoretical framework of the documentational approach to…

In mathematics education, researchers often contrast conceptual and procedural teaching approaches, although labels and conceptualizations often vary across studies. Prior research has extensively examined empirical relationships between the two teaching approaches and mathematics achievement. In our study, we aimed to extend this research by…

New perspectives on executive functions propose a greater involvement of context. These perspectives have implications for research in mathematical cognition. We tackle the problem that although individuals clearly exercise inhibitory control in mathematical contexts, researchers find that the relations between inhibitory control and mathematics…

Virtual reality (VR) research in mathematics education has centred largely on geometry content. This paper contributes by describing VR modules developed for another area that heavily involves three-dimensional objects: multivariable calculus. This paper also contributes by describing an empirical study on students' experiences inside the VR…

Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…

This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; M[subscript age] = 79.5 months; 55% female; 88% White) and adults (N = 93; M[subscript age] = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged:…

The Dynamic and Interactive Mathematical Expressions (DIME) Map system automatically generates DIME maps, which are personalizable and manipulable concept maps that allow students to interact with the mathematical concepts contained in any portable document format (PDF) textbook or document. A teacher can automatically upload a PDF textbook…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

We investigate three 8th-grade students' mathematical meanings developed in the context of using linked representations to generate animations of figural models tuned in musical rhythm in "MaLT2," a programmable Turtle Geometry in 3D resource affording dynamic manipulation of variable values. We adopted a modified version of the UDGS…

In spring 2018, an inquiry-oriented differential equations course was offered at the Lebanese American University. This paper highlights students' comprehension of some qualitative aspects of differential equations, namely their understanding of the equations and their solutions. It also explores the students' success in moving between the…