The first step in documenting children's progress toward important goals, such as developing strong oral language and early literacy skills, requires measurable outcomes. Measurable outcomes contribute to teachers' understanding of whether the gains they observe in children are meaningful by adding quantitative evaluation of a child's progress…

The notions of "abstract" and "concrete" are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how…

A simple and readily understandable visual display of quantitative measures of academic efficiency and productivity is demonstrated in this article. This graphical construction facilitates annual comparisons of unit efficiency and productivity as well as an analysis of temporal changes in unit activity. By establishing a common framework upon…

The mathematics students are given a task to understand the fundamentals of liner functions by analyzing the height of the football stadium bleachers, as studying mathematical relationships in real-world contexts can enhance a student's knowledge of mathematics. The study of the stadium seating problem helps students to understand quadratic,…

This booklet contains a representative sample of the efforts of colleagues at 11 institutions to use graphing calculators to enhance the teaching of calculus and precalculus. The first section contains examples of graphs for teachers to choose from for presentations, including: simple examples to illustrate some standard ideas in precalculus,…

Expert/novice studies of conceptually rich problem solving have demonstrated a relationship between the correctness of a solution and the extent and organization of the solver's conceptual knowledge. This study examines meaningful problem solving and the relationship between the correctness of a solution and the extent of the solver's scientific…

Previous research has demonstrated particular inadequacies in conventional methods used to identify outlier cases in bivariate regression models. Only through a combination of methods can one detect all of the deviant points potentially overinfluencing a regression model's parameters. This paper investigates whether a range of data points might…

Two surveys were carried out to help increase knowledge of current graph usage in science. A detailed analysis of all graphs in one volume of the journal "Science" revealed that 30 percent had errors. Graphs are used more in some disciplines than in others; a survey of 57 journals revealed natural science journals use far more graphs…

This bilingual instructional text, one in a series of six texts covering various vocational and technical topics, provides secondary level English and Spanish instruction in drafting. Addressed in the individual units are the following topics: safety, drafting tools and techniques, sketching, geometric construction, working drawings, sectioning,…

Theorems about the hyperbola which are ordinarily introduced in calculus courses can be proved without using the calculus. (SD)

By converting functional equations to cylindrical coordinates, plotting points on cardboard, and connecting these points with thread, one can make three-dimensional string figures illustrating the behavior of functions for which the derivative is not always defined. (SD)

The author presents a method of producing a scatter diagram of data on two variables with Pearson product moment correlation of .50; he also provides a proof that the method will work for any number of data pairs. (SD)

A discussion of autosegmental phonology (AP), a theory of phonological representation that uses graphs rather than strings as the central data structure, considers its principal constraint, the "No Crossing Constraint" (NCC). The NCC is the statement that in a well-formed autosegmental diagram, lines of association may not cross. After…

The past decade has seen a substantial growth in methods and schemes for the display of multivariate data. This paper encompasses a sketch of the history of multivariate displays, from the pre-Columbian Quipu to Chernoff's Face; examines a number of techniques; describes their construction; illustrates their use; and comments on their efficacy.…

Although computer graphics professionals usually consider only technical graphic design issues, recent improvements may make the only limiting design factors the user's purpose, imagination, style, and taste rather than computer hardware or software technology. Computer graphics designers can be helped to avoid pitfalls by understanding the visual…