Everyday encounters with graphical representations include a variety of graphs that superficially appear similar due to their use of bars. This article examines students' conceptions and misconceptions regarding the interpretation of variability in histograms, bar graphs, and value bar charts. A multiple choice assessment with brief written…

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…

Results from a study of 16 community college students are presented. The research question concerned how students reasoned about p-values. Students' approach to p-values in hypothesis testing was procedural. Students viewed p-values as something that one compares to alpha values in order to arrive at an answer and did not attach much meaning to…

The mathematical concept of function has been revisited and further developed with regularity since its introduction in ancient Babylonia (Kleiner, 1989). The difficulty of the concept of a function contributes to complications when students learn of functions and their graphs (Leinhardt, Zaslavsky, & Stein, 1990). To understand the concept of…

Histograms are adept at revealing the distribution of data values, especially the shape of the distribution and any outlier values. They are included in introductory statistics texts, research methods texts, and in the popular press, yet students often have difficulty interpreting the information conveyed by a histogram. This research identifies…

To understand the mathematical concept of function, students must understand certain subconcepts, such as domain and range. Many researchers have studied students' understanding of functions, but no study has focused on how students come to understand the domain and range for the graphs of functions. In this study, we identified four common…

This study explored how the challenges encountered during integral sign determination process change after various learning processes. In this comparative investigation which is based on qualitative data, the students in the CAS group were subjected to technology enhanced teaching whereas the students in the traditional group were subjected to the…

Proposes elements of a model of knowledge structures used in comprehending and generating graphs. Uses the competence model to attempt to organize and interpret findings on misconceptions in graphing. Discusses two types of common misconceptions; treating the graph as a picture and slope-height confusions. (YP)

This present study investigated engineering students' conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the…

Durer's method for drawing an ellipse is used to explain why some people think an ellipse is egg shaped and to show how this method can be used to derive the Cartesian form of the ellipse. Historical background and suggestions for further reading are included. (KR)