As part of a larger research study, this paper describes calculus students' reasoning about the Intermediate Value Theorem (IVT) in verbal, written, and graphical form. During interviews, students were asked to verbally describe the IVT in their own words. They then provided written descriptions, watched video of their verbal descriptions,…

This paper focuses on the professional and academic development of mid-career teacher educators from two universities in England. The objectives of the study were to analyse and compare the career experiences of teacher educators; in particular, to identify stages of development, landmark events and contextual factors affecting professional…

Students often are confused about the differences between bar graphs and histograms. The authors discuss some reasons behind this confusion and offer suggestions that help clarify thinking.

The Tukey mean-difference plot, also called the Bland-Altman plot, is a recognized graphical tool in the exploration of biometrical data. We show that this technique deserves a place on an introductory statistics course by encouraging students to think about the kind of graph they wish to create, rather than just creating the default graph for the…

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of…

Newer statistical procedures are typically introduced to help address the limitations of those already in practice or to deal with emerging research needs. Quantile regression (QR) is introduced in this paper as a relatively new methodology, which is intended to overcome some of the limitations of least squares mean regression (LMR). QR is more…

Chocolate chip cookies are used to illustrate the importance and effectiveness of control charts in Statistical Process Control. By counting the number of chocolate chips, creating the spreadsheet, calculating the control limits and graphing the control charts, the student becomes actively engaged in the learning process. In addition, examining…

Graphical model validation techniques for linear normal models are often used to check the assumptions underlying a statistical model. We describe an approach to provide "instant experience" in looking at a graphical model validation plot, so it becomes easier to validate if any of the underlying assumptions are violated.

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

A growing body of literature has identified quantitative and covariational reasoning as critical for secondary and undergraduate student learning, particularly for topics that require students to make sense of relationships between quantities. The present study extends this body of literature by characterizing an undergraduate precalculus…

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

In this paper, the use of guided hyperlearning, unguided hyperlearning, and conventional learning methods in mathematics are compared. The design of the research involved a quasi-experiment with a modified single-factor multiple treatment design comparing the three learning methods, guided hyperlearning, unguided hyperlearning, and conventional…

The purpose of this study was to determine effectiveness of a modified version of Azrin and Foxx's (1971) intensive toilet training method on teaching of toilet skills to children with autism. This method consists of administering extra fluids and a time schedule, but does not use overcorrection procedures. Implementation requires a study of…

Nonoverlap is widely used as a statistical summary of data; however, these analyses rarely correct unwanted positive baseline trend. This article presents and validates the graph rotation for overlap and trend (GROT) technique, a hand calculation method for controlling positive baseline trend within an analysis of data nonoverlap. GROT is…

This paper draws on social capital theory to discuss the way social class plays out in the friendships of teenage students. Based on data from individual interviews and focus groups with 75 students in four London secondary schools, it is suggested that students tend to form friendships with people who belong to the same social-class background as…