Discusses the notion that knowledge grows exponentially and describes its growth mathematically by an exponential function. Growth patterns in subfields of knowledge or research areas are described citing related research. Interpretation of growth rate statistics and forecasts are included. Thirty-three references and statistics used for graphs…

Graphs are used to help students keep records of their scores as they learn the basic facts. (MNS)

A method for finding the complex roots of a graph is detailed. A conjecture is made regarding the nature of zero points of fourth-degree polynomial functions, but it is not proven in general. Mathematical induction is viewed as a promising tool to prove the conjecture that turned out unproductive. (MP)

This investigation concerns student understanding of the concept of gradient. Six items are discussed from a series of tests constructed for Technical Education Council (TEC) qualification. It is concluded that confusion exists, and a summary of apparent student difficulties is presented. (MP)

Topics covered are: a game to provide drill with linear equations; the relationship between area and perimeter in a triangle; a new form for factoring polynomials; and a technique for graphing inverse functions. (MP)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

Describes a graphical method for representing image formation in lenses and mirrors. (MLH)

Examines graphical presentations of quantitative data within corporate annual reports in Hong Kong. Finds that approximately 35% of companies included graphics in their annual report. Notes that half of all graphs violated sound principles of chart graphics and were therefore misleading; and misleading graphs occurred across all industrial…

Discussion of the nature of the algebraic and graphical representations of functions focuses on a study integrating cognitive research and the development of an intelligent tutoring system (ITS), the Function Characteristics Tutor, to evaluate the effects of pairing representations of mathematical functions on high school students. (Author/LRW)

Presents an alternative perspective that conceives of graphing as observable practices employed to achieve specific goals rather than as knowledge represented in students' minds. Highlights the nature of graphs as semiotic objects, rhetorical devices, and conscription devices. Illustrates the plausibility and fruitfulness of the new perspective in…

Two intact chemistry classes participated in a study and the same teacher taught both a line graphing unit with computer-supported activities and one without. Results indicate that there were no statistically significant interaction effects among treatments and scientific reasoning levels. (Contains 40 references.) (Author/NB)

Investigated effects of sparse versus real contexts on understanding abstract mathematical concepts regarding the interpretation of linear graphs. Results of four experiments showed that a sparse context facilitated understanding of abstract concepts more than real contexts. Activation of abstract logic-mathematical knowledge structures was…

Introduces a problem that can be used to help children develop graph sense. Involves two graphs of which students must determine which one applies to which situation. (KHR)

Introduces the concept of function using graphs or pictorial representations of functions. Presents four activities for grade levels 8-14 that use the natural progression from qualitative graphs to quantitative graphs to tables to equations for introducing the theme of distance from an object as a function of time. (Author/NB)