We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

This article compares marriage patterns by race, education and religion in the United States during the 20th century, using a variety of data sources. The comparative approach allows several general conclusions. First, racial endogamy has declined sharply over the 20th century, but race is still the most powerful division in the marriage market.…

Over the last decade or so, faculty in a wide range of disciplines have become more interested in and open to the scholarship of teaching and learning. That scholarship has taken many forms, including personal accounts of experimentation and change, descriptions of recommended practices, and quantitative research on students' gains. In this…

Developing good record-keeping habits is essential for organizing, processing, and communicating experimental results objectively. Therefore, the authors designed an interactive method of teaching first graders to record, organize, and interpret data as they studied the life cycle of the spotted salamander ("Ambystoma maculatum"). In their…

The critical role of accountability on schools has intensified the need to understand the impact of intervention strategies and best practices on literacy. Of particular concern is the underachievement of boys and identifying the learning differences between boys and girls. Examined in this quantitative study were the strategies and practices…

The purpose of this paper is to present evidence supporting the conjecture that graphs and gestures may function in different capacities depending on whether they are used to develop an algorithm or whether they extend or apply a previously developed algorithm in a new context. I illustrate these ideas using an example from undergraduate…

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…

The present study investigated the extent to which providing students with individualized performance feedback informed and directed their learning behavior. Individualized performance feedback was delivered to students using curriculum-based measurement progress indicators, either as a visual representation of ongoing performance in the form of a…

Curriculum materials designed to provide students with practice interpreting plotted evidence of global climate change were developed using graphs from the scientific literature and tested with one hundred urban high school students from a high-poverty school in a major northern city in the US. The graph interpretation lessons followed a…

With the development of e-learning technology, many specifications of instructional design have been proposed to make learning activity sharable and reusable. With the specifications and sufficient learning resources, the researches further focus on how to provide learners more appropriate learning activities to improve their learning performance.…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

Teaching students to collect data to answer questions is an important life skill that will serve them well throughout their adult lives. The purpose of this manuscript is to describe the implementation of an action research project in a fifth grade resource classroom. Students with mild disabilities were taught how to conduct surveys using three…

Although behavior analysis relies primarily on visual inspection for interpreting data, previous research shows that the method of display can influence the judgments. In the current study, 26 Board-Certified Behavior Analysts reviewed two data sets displayed on each of three methods--equal-interval graphs, tables, and Standard Celeration…

This study examined the fractional graph area (FGA), the proportion of page space used to display statistical graphics, in 11 behavioral journals and places behavior analysis on a continuum with other natural, mathematical, and social science disciplines. The composite FGA of all 11 journals puts behavior analysis within the range of the social…