This study applies the Mathematics Acquisition Framework (MAF) (Bossé, Ringler, Bayaga, Fountain, & Young, 2018) to investigate fifth- through seventh-grade students' comprehension of fractions and decimals and examines how students build understanding of mathematical principles and concepts regarding fractions and decimals. Based on case…

Technology is now being utilized in schools in an effort to address the lack of engagement most students have experienced in mathematics when learning foundational skills at the elementary school level. While there are a number of studies that have described teacher perceptions of engagement through the use of technology during the school day,…

Mathematical problem solving typically involves manipulating visual symbols (e.g., equations), and prior research suggests that those symbols serve as diagrammatic representations (e.g., Landy & Goldstone, 2010). The present work examines the ways that instructional design of student engagement with these diagrammatic representations may…

The importance of mathematical concept development and language is recognized early in children's schooling as they mature through shape and counting experiences. The reader may recall instances of a youngster referring to a "corner" of a shape before the reader has the language of vertex. This language precision needs to continue to…

Dynamic Geometry Software (DGS) is a powerful tool which enables students to move geometric objects interactively. Through experimental simulations with DGS, mathematical facts and background mechanisms are accessible to students. However, especially when those facts and mechanisms are complicated, it is not so easy for some students to record and…

According to a 2012 study from the Program for International Student Assessment, twenty-nine out of sixty-five participating nations and other jurisdictions outperformed the United States in mathematics by a statistically significant margin (up from twenty-three in 2009) (Heitin 2013). To improve students' mathematical understanding, the authors…

We introduce "virtual duoethnography" as a novel research approach in mathematics education, in which researchers produce a text of a dialogic format in the voices of fictional characters, who present and contrast different perspectives on the nature of a particular mathematical phenomenon. We use fiction as a form of research linked to…

Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan. This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme…

Several factors have motivated the use of CAS or DGS in the teaching-learning process, such as: the development of new technologies, the availability of computers, and the widespread use of the Internet, among others. Even more, the trend to include CAS and DGS in the curricula of some undergraduate studies has resulted in the instruction of the…

Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…

Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional…

To prepare students for participation in our society, where interpreting, representing, and manipulating of dynamic phenomena are becoming key activities, we believe that one should start developing a mathematical understanding of change at an early age. We therefore started a design research project to teach the concept of instantaneous speed in…

The recent review of Australian Curriculum represents an opportunity to significantly change the teaching of primary mathematics in Australia and perhaps elsewhere. The current curriculum document presents content in a linear and compartmentalized manner that dominates its structure and doesn't explicitly accentuate the links and connections found…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This tenth installment of "Explorations in Statistics" explores the analysis of a potential change in some physiological response. As researchers, we often express absolute change as percent change so we can…

Previous mathematics and science education research indicates that knowledge and beliefs, including teaching efficacy, affect teachers' actions and effectiveness in a classroom. Our middle grades and high school Self-Efficacy to Teach Statistics (SETS) instruments, aligned with the statistical concepts in national and state guidelines such as the…