The purpose of this study was to analyze the activities in the Problem-Based Learning (PBL) methodology among high school students when solving problems related to the field of plane figures, both in extra-mathematical and intra-mathematical environments. The research was qualitative and constituted a case study. The technique used to select the…

Visual imagery has been an effective tool to communicate ideas connected with basic mathematics concepts since the dawn of mankind. The development of educational visualisation technology allows these ideas to be demonstrated with the help of some educational software. In this paper, we specifically consider the use of GeoGebra, a free,…

This qualitative case study investigated teachers' Technological Pedagogical Content Knowledge (TPACK) for teaching high school geometry in Turkey. Four TPACK components and their corresponding five TPACK level descriptions were used for examining three geometry teachers' TPACK through their technological instructional plans, microteaching…

While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the…

Elementary students' difficulties with angles in geometry are well documented, but we know little about how they conceptualize angles while solving problems and how their thinking changes over time. In this study, we examined 26 third and fourth grade students completing a body-based angle task supported by the Kinect for Windows. We used…

Every day, people use data to make decisions that affect their personal and professional lives, trusting that the data are correct. Many times, however, the data are inaccurate, as a result of a flaw in the design or methodology of the survey used to collect the data. Researchers agree that only questions that are clearly worded, unambiguous, free…

Latent variable models, such as the popular Knowledge Tracing method, are often used to enable adaptive tutoring systems to personalize education. However, finding optimal model parameters is usually a difficult non-convex optimization problem when considering latent variable models. Prior work has reported that latent variable models obtained…

As the use of educational technology becomes more ubiquitous, an enormous amount of learning process data is being produced. Educational data mining seeks to analyze and model these data, with the ultimate goal of improving learning outcomes. The most firmly grounded and rigorous evaluation of an educational data mining discovery is whether it…

The National Assessment of Educational Progress (NAEP) is the only continuing and nationally representative measure of trends in academic achievement of U.S. elementary and secondary school students in various subjects. For more than four decades, NAEP assessments have been conducted periodically in reading, mathematics, science, writing, U.S.…

Research in Educational Data Mining could benefit from greater efforts to ensure that models yield reliable, valid, and interpretable parameter estimates. These efforts have especially been lacking for individualized student-parameter models. We collected two datasets from a sizable student population with excellent "depth" -- that is,…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

Lim and Leek (2012) presented a formalization of information along object contours, which they argued was an alternative to the approach taken in our article (Feldman & Singh, 2005). Here, we summarize the 2 approaches, showing that--notwithstanding Lim and Leek's (2012) critical rhetoric--their approach is substantially identical to ours,…

This study examined the impact of computer-assisted instruction on the mathematics performance of underachieving fifth-grade students in a rural school district in South Carolina. The instructional technology program ([IF) is South Carolina's response to addressing the needs of its young, struggling math students. The 449 fifth-grade students in…

Although research on the effectiveness of differentiated and enriched instruction in improving the achievement of diverse students is still emerging, some studies suggest that students in academically diverse classrooms benefited academically from differentiated learning experiences. The primary research question explored in this study was…

The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…