Triangular numbers are used to unravel a new sequence of natural numbers here-to-fore not appearing on the Encyclopedia of Integer Sequences website. Insight is provided on the construction of the sequence using "buildings" as a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating…

We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

Included herein is the conference proceedings of the 27th Annual Conference on the Teaching of Psychology: Ideas and Innovations, sponsored by the Psychology Department of the State University of New York at Farmingdale. The conference theme for 2013 was: The Science of Learning. The Conference featured a keynote address by Victor Benassi, Ph.D.…

Dartmouth College mathematicians have developed a free online calculus course called "Open Calculus." Open Calculus is an exportable distance-learning/self-study environment for learning calculus including written text, nearly 4000 online homework problems and instructional videos. The paper recounts the evaluation of course elements since 2000 in…

This book presents a numerical problem-solving environment for middle grade students using the computerized spreadsheet. It offers a package of spreadsheet models and suggested activities that promote student thinking with numbers. (ASK)

While functions and relations are important concepts in the teaching of mathematics, research suggests that many students lack an understanding and appreciation of these concepts. The present paper discusses an approach for teaching functions and relations that draws on the use of illustrations from database management. This approach has the…

A WICAT Computer Assisted Instructional (CAI) System began operation at St. Anne Consensus School (Tennessee) in August, 1986. Iowa Test of Basic Skills (ITBS) scores for the years 1984 through 1988 for ten students in each of the grades 4th through 8th (as of May 1988) were analyzed. The average gain for all subjects during the two years before…

The article describes the three-year Education Development Center/Technical Education Research Center Middle School Technology Integration Project which is investigating how technology is integrated into language arts and mathematics curricula, and its impact on mainstreamed mildly handicapped students. The evolution of computer use at four…

We report research on meanings of scale generated by pairs of 14 year-old students engaged in joint map-construction. Characteristics of the learning environment, such as the communicational orchestration, the use of experientially familiar objects in space as starting points for creating figural representations and the interrelated…

Can textbook exercises be transformed into problem solving activities that encourage students to develop mathematical thinking? This study documents what high school students showed when they were explicitly asked to use technological tools to examine and solve a routine problem from different angles or perspectives. In this process, students…

The concept of function is the single most important mathematical concept studied from kindergarten to graduate school and is critical throughout the full range of education. Thus, the goals of this book are to contribute to research in learning the concept of function and to provide a resource for mathematics teachers that could help them in…

Computer algebra systems (CAS) have now become much more readily accessible for use in secondary school mathematics on both hand-held and computer platforms. While the initial focus of work with CAS from the early 1980's has generally been with respect to pedagogical and curriculum issues, as familiarity with CAS in senior secondary mathematics…

Presents an activity that establishes a graphical foundation for parametric equations by using a graphing output form called tubeplots from the computer program Maple. Provides a comprehensive review and exploration of many previously learned topics. (ASK)

Presents an activity on the sum of the measures of the interior angles of a five-pointed star by using The Geometer's Sketchpad. (ASK)

Describes a series of activities in which students collect data on personal information and interests and use them to create a database file. Constructing a database gives students the opportunity to satisfy their natural curiosity and use numbers as they make predictions, develop number and operation sense, and explore data, fractions, and…