This article describes the Lissajous generalized figure and the original instrument for its investigation. Two specially prepared electrodynamic loudspeakers--a horizontal and a vertical--cause oscillations in two mirrors. It is possible to precisely control the motion of the mirrors, achieve a high frequency of oscillation and investigate…

Twenty-nine peer-reviewed journal articles that analyzed intervention implementation in schools using single-case experimental designs were meta-analyzed. These studies reported 171 separate data paths and provided 3,991 data points. The meta-analysis was accomplished by fitting data extracted from graphs in mixed linear growth models. This…

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 research compared undergraduate Novices and PhD Experts in psychology and business in their exploration of psychology and business domain graphs. An overall expertise effect in graph explanation was found. Results indicated that Novices paused longer than Experts before beginning their explanations. Qualitative analyses showed that Experts…

The nation continues to recover from one of the worst recessions since the Great Depression. States were hit hard, incurred significant losses, and many are only just now showing signs of meaningful recovery. Whether it is efforts to bring investments in pre-K back to pre-recession levels or creating new investments, states have indicated, for the…

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…

In third grade the focus on math word problems becomes prominent. In the limited third grade research, teacher-mediated explicit instruction with multiple exemplars, teaching students to use visual representations, and the incorporation of self-strategies, have proven effective. For these practices to reach their full potential though, their…

With the advances in mobile network technology, the use of portable devices and mobile networks for learning is not limited by time and space. Such use, in combination with appropriate learning strategies, can achieve a better effect. Despite the effectiveness of mobile learning, students' learning direction, progress, and achievement may differ.…

What do you do when you want to get your Stage 3 students authentically and enthusiastically engaged in the active construction of their understanding and fluency with measurement, data collection, representation and interpretation? How do you enable them to make choices about their learning, to measure with purpose, to record and organise the…

Structural behavioral assessment (SBA) involves a series of heuristic approaches similar to those used with functional behavioral assessment (FBA). It involves assessing contextual variables that precede the occurrence of a behavior. These variables have also been termed antecedents, setting events, or establishing operations. Once these variables…

The "syntactic bootstrapping" hypothesis proposes that syntactic structure provides children with cues for learning the meaning of novel words. In this article, we address the question of how children might start acquiring some aspects of syntax before they possess a sizeable lexicon. The study presents two models of early syntax…

Detailed logs of students' computer use, during independent study sessions, were captured in an open-access computer laboratory. Each log consisted of a chronological sequence of tasks representing either the application or the Internet domain displayed in the workstation's active window. Each task was classified using a three-tier schema…

We introduce a set of biologically and computationally motivated design choices for modeling the learning of language, or of other types of sequential, hierarchically structured experience and behavior, and describe an implemented system that conforms to these choices and is capable of unsupervised learning from raw natural-language corpora. Given…

We have recently developed a Graphs and Tracks model based on an earlier program by David Trowbridge, as shown in Fig. 1. Our model can show position, velocity, acceleration, and energy graphs and can be used for motion-to-graphs exercises. Users set the heights of the track segments, and the model displays the motion of the ball on the track…

The equilibrium between phases is a key concept from the introductory physical chemistry curriculum. Phase diagrams display which phase is the most stable at a given temperature and pressure. If more than one phase has the lowest Gibbs energy, then those phases are in equilibrium under those conditions. An activity designed to demonstrate the…