The purpose of this study was to investigate how a set of physical and digital instructional activities can serve as an example space to help further develop a concept image that is aligned with the formal concept definition for the limit of a sequence. In addition, the unique affordances and constraints allowed by using either a physical or…

The educational laws establish an organization and a grouping of the contents of the educational system they rule. As far as we know, the set of experts who design it neither follow precise objective criteria nor use computer tools. That is why they are not usually rotund. We consider that defining precise objective criteria is the key to develop…

The objective of this piece of research is to interpret and investigate systematically an observed brain functional phenomenon which is associated with proceeding of e-learning processes. More specifically, this work addresses an interesting and challenging educational issue concerned with dynamical evaluation of elearning performance considering…

The concept of variability is central to statistics. In this research report, we review mathematics education research on variability and, based on that review and on feedback from an expert panel, propose a learning progression (LP) for variability. The structure of the proposed LP consists of 5 levels of sophistication in understanding…

The method of least squares (LS) yields exact solutions for the adjustable parameters when the number of data values n equals the number of parameters "p". This holds also when the fit model consists of "m" different equations and "m = p", which means that LS algorithms can be used to obtain solutions to systems of…

We present a case study of how five instructors used gesture when introducing the second derivative test in a first semester calculus class. The second derivative test and optimization naturally evoke hand motions while teaching, making this a fertile ground for studying gesture use in the classroom. Each of the five instructors used a classic…

Recent studies of the transition from school to university mathematics have identified a number of epistemological gaps, including the need to change from an emphasis on equality to that of inequality. Another crucial epistemological change during this transition involves the movement from the pointwise and global perspectives of functions usually…

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of…

This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

Not only will young adults bear the brunt of the effects of climate change, but they are also the ones who will be required to take action-to mitigate and to adapt. Framing, as both a theory and an analytic method, has been used to understand how language in the media can affect the audience's concern and intention to act. The theory and the…

Summary writing is an important skill that students use throughout their academic careers, writing supports reading and vocabulary skills as well as the acquisition of content knowledge. This exploratory and development-oriented investigation appraises the recently released online writing system, "Graphical Interface of Knowledge…

The research literature on L2 writing processes contains a multitude of insights that could inform writing instruction, but writing teachers are constrained in their capacity to make use of these insights insofar as they lack detailed information about how their students actually engage in the processes of writing. At the same time,…

During the first years of teaching, new special education teachers (SETs) face many unique challenges as they work to establish themselves as professionals. Upon entering the classroom on the first day of instruction, SETs are expected to be prepared, and they are presented with a daunting list of responsibilities and expectations, including the…

We designed and implemented a modified eight-week Direct Instruction (DI) program intended to teach a third grade student with learning disabilities to tell time. The first objective was to determine whether or not the appearance (interesting or boring) of the worksheet affected performance. These data suggested the use of large-scale clocks and…

This meta-analysis synthesizes research findings on the effects of computer-supported collaborative learning (CSCL) based on its three main elements: (1) the collaboration per se, (2) the use of computers, and (3) the use of extra learning environments or tools, or supporting strategies in CSCL. In this analysis, 425 empirical studies published…