The least squares method of fitting a line is not one that naturally occurs to students. We present three tasks to understand student views on how lines may be fit.

In mathematics, as in baseball, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, avoiding errors is not always a good idea. Sometimes an analysis of errors provides much deeper insights into mathematical ideas. Certain types of errors, rather than something to be eschewed, can…

We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion…

The purpose of this study was to determine the extent to which performance on the TOEFL iBT speaking section is associated with other indicators of Japanese university students' abilities to communicate orally in an academic English environment and to determine which components of oral ability for these tasks are best assessed by TOEFL iBT. To…

When conducting item reviews, analysts evaluate an array of statistical and graphical information to assess the fit of a field test (FT) item to an item response theory model. The process can be tedious, particularly when the number of human reviews (HR) to be completed is large. Furthermore, such a process leads to decisions that are susceptible…

This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The…

The topic of waves is one that many high school physics students find difficult to understand. This is especially true when using some A-level textbooks used in the U.K., where the concept of waves is introduced prior to the concept of simple harmonic oscillations. One of the challenges my students encounter is understanding the difference between…

A partially unusual behaviour was found among 14 sophomore students of civil engineering who took a pre test for a free fall laboratory session, in the context of a general mechanics course. An analysis contemplating mathematics models and physics models consistency was made. In all cases, the students presented evidence favoring a correct free…

Chat conversations and other types of online communication environments are widely used within CSCL educational scenarios. However, there is a lack of theoretical and methodological background for the analysis of collaboration. Manual assessing of non-moderated chat discussions is difficult and time-consuming, having as a consequence that learning…

The 2017 Graduate Study in Psychology Summary Report reflects data collected from more than 500 departments and programs offering master's and doctoral degrees in psychology and related training. This report represents data from the 2014-2015 academic year and aggregates these data in the following areas: survey participation; admissions review,…

The South was the central focus of the "Brown v. Board of Education" decision from the U.S. Supreme Court in 1954. The landmark ruling held that laws mandating segregation in the school systems of the eleven states of the Old Confederacy, along with D.C. and six other states, violated the U.S. Constitution. Intense opposition met the…

Network forensic analysis is a process that analyzes intrusion evidence captured from networked environment to identify suspicious entities and stepwise actions in an attack scenario. Unfortunately, the overwhelming amount and low quality of output from security sensors make it difficult for analysts to obtain a succinct high-level view of complex…

The learning sequence described in this article was developed to provide students with a demonstration of the development of box plots from authentic data as an illustration of the advantages gained from using multiple forms of data representation. The sequence follows an authentic process that starts with a problem to which data representations…

If a teacher asked their students what thinking looks like, what would they say? Would they just look at the teacher quizzically? The question is challenging because thinking is largely an invisible endeavor, and developing thoughtful students can be a daunting task. However, the job of mathematics teachers is to develop students who think about…

This study investigates university students' understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was…