Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

The aim of this study is to investigate the trends in research related to problem posing in mathematics education. The study focuses on the articles on problem posing in the Web of Science database between 1990 and 2021. The term co-occurrence map, which was created depending on the data in the text with the bibliometric analysis of the articles…

Logical reasoning as part of critical thinking is becoming more and more important to prepare students for their future life in society, work, and study. This article presents the results of a quasi-experimental study with a pre-test-post-test control group design focusing on the effective use of formalisations to support logical reasoning. The…

We report on a study in which we observed 73 mathematics majors completing 7 proof construction tasks in calculus. We use these data to explore the frequency and effectiveness with which mathematics majors use diagrams when constructing proofs. The key findings from this study are (a) nearly all participants introduced diagrams on multiple tasks,…

Graphical representations are an important tool used to model abstract processes in fields such as chemistry. Successful interpretation of a graph involves a combination of mathematical expertise and discipline-specific content to reason about the relationship between the variables and to describe the phenomena represented. In this work, we…

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded pre-algebraic reasoning instruction, improves word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or one of two variants of word-problem intervention.…

This study contributes to the literature by examining in more detail the correlations among contextual factors defined by the teachers' technical confidence, lesson planning skills, and the extent of IWB usage in mathematics classroom discourse. The sample for the current study consisted of 134 elementary school teachers in grades K-5 using…

This study investigated the effect of systematic early numeracy skill instruction on grade-aligned 4th and 5th grade Common Core math skill acquisition for three 4th and 5th grade students with a significant intellectual disability. Students were taught early numeracy skills (e.g., number identification, making sets to five items, simple addition)…

The purpose of this study was to determine if a typical third-grade boy and fifth-grade girl and a boy with learning disabilities could benefit from the combined use of Direct Instruction (DI) flashcard and math racetrack procedures in an after-school program. The dependent variable was accuracy and fluency of saying basic multiplication facts. A…

We describe the development of measures of teachers' recognition of an instructional norm--that proof problems in high school geometry are presented in a diagrammatic register. A first instrument required participants to openly respond to depictions of classroom scenarios in which the norm was breached. A second instrument was a survey that…

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers' content knowledge for teaching. However, there is no course…

A treatment/control study (N = 773) was conducted to determine the extent to which use of interactive whiteboard technology (IWB) was associated with upper elementary students' self-reported level of motivation in mathematics. Students in the treatment group reported higher levels of motivation relative to control students, but the effect was…

K-12 teachers lack training in best practices of interactive lesson development. It is essential that teachers utilize interactive whiteboards effectively. Using a collaborative mentor training, this factorial between-within groups study investigated how student achievement was impacted when teachers applied a set of effective interactive…