This paper presents a novel method for introductory teaching of the sample linear correlation coefficient from a bivariate dataset. Linear correlation is typically included in curriculums at the secondary and introductory tertiary levels of education. The method discussed herein can be used by educators in elementary courses at either of these…

Sound educational policy recommendations require valid estimates of causal effects, but observational studies in physics education research sometimes have loosely specified causal hypotheses. The connections between the observational data and the explicit or implicit causal conclusions are sometimes misstated. The link between the causal…

This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

We describe a meta-analytic scatterplot that indicates precision of points for two variables paired within studies; this is equivalent in form to a 'cross-hairs' plot used to portray specificity and sensitivity in diagnostic testing. At the user's discretion, the plot also displays boxplots for each of the X and Y variable distributions, means for…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

This article revisits how the end points of plotted line segments should be selected when graphing interactions involving a continuous target predictor variable. Under the standard approach, end points are chosen at ±1 or 2 standard deviations from the target predictor mean. However, when the target predictor and moderator are correlated or the…

At first glance it seems easy to attribute cause and effect when it's not applicable, either through mistakenly taking every correlation as a cause and effect relationship, misinterpreting the meaning of independent and dependent variables, or not focusing on direct causes. Sometimes it's easy to help students understand where…

The need for statistical analysis in single-subject designs presents a challenge, as analytical methods that are applied to group comparison studies are often not appropriate in single-subject research. "SSD for R" is a robust set of statistical functions with wide applicability to single-subject research. It is a comprehensive package…

Every day, students collect, organize, and analyze data to make decisions. In this data-driven world, people need to assess how much trust they can place in summary statistics. The results of every survey and the safety of every drug that undergoes a clinical trial depend on the correct application of appropriate statistics. Recognizing the…

Data literacy is complex. When students investigate the natural world, they must be able to gather data, organize it in tables and spreadsheets, analyze it in context, and describe and interpret it--usually as evidence to support a scientific argument. These skills are echoed in the science and engineering practices of the "Next Generation…

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…

Functions are one of the most important and powerful tools in mathematics because they allow the symbolic, visual, and verbal representation of relationships between variables. The power of functions, as well as the numerous real-world uses of functions, make them an important part of the development of algebraic reasoning in the middle grades.…

The "Almanac of American Education" helps users understand and compare the quality of education at the national, state, and county levels. Compiled from official U.S. government and reliable private sources, the book contains historical and current data, insightful analysis, and useful graphs that provide compelling insights into the…

A common activity--having students collect data to measure the radius and circumference of circular objects--can be given a new twist. These data can be viewed virtually using technology. A dynamic geometry environment coupled with the powerful capabilities of a spreadsheet can greatly enhance student learning. The activity in this article…