Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

Part I reviews the mathematical definition of function, and then presents some practical uses of functions in such areas as substitution in a formula, equation solving, and curve fitting. Part II gives examples of functions that can be used to describe some real life situations. (RP)

A discussion of the relation between traffic density, speed and flow, used as an illustration of the ideas of functions and mathematical models. (MM)

This five-lesson unit is designed to give students a flavor of what the study of economics is about, to strengthen mathematical concepts the students already know, to allow them to experience the interrelationship between the two fields of mathematics and economics and to experience success and enjoyment. Topics of instruction include: (1) types…

A collection of brief articles on mathematics and teaching mathematics. (FL)

Argues that children need to be given regular opportunities to gather, organize, display, and interpret their own data. They should have regular opportunities to pose their own questions and represent the results in their own way. Offers five sample survey questions children can pose to each other and examples of data representation by children.…

Describes four laboratory activities in algebra and precalculus classes that provide hands-on experiences related to functions: slowing down the acceleration of gravity; calculating the acceleration of gravity; generating a parabola using a steel ball and a tilted board; and photographing projectile motion. (YP)

Differing treatments of graphs in mathematics and science are discussed. A teaching sequence to develop contrasts between real and ideal data is suggested. (MP)

Describes a graphing activity that promotes mathematical connections with social studies lessons. Students should be familiar with graphing on the Cartesian coordinate system to play this variation of the game Battleship on maps of various regions of the world. (AIM)

Uses the process of normalization in the Cartesian coordinate system which entails radial projection onto a transect to compare different compositions of minerals. Warns that the ternary diagram should not be used as a framework for calculations. (MVL)

This study was designed to extend the schema-theoretic perspective of understanding general discourse to include graph comprehension. The sample included 204 fourth-grade and 185 seventh-grade pupils. Data were collected on achievement in reading and mathematics, sex, prior knowledge of topic, mathematical content, graphical form, and graph…

Investigates students' conceptions and misconceptions relating to the construction of graphs. Qualitative analysis of students' responses identified three main alternative conceptions. Quantitative analyses of the data indicated that overall students did not enter the learning situation as a tabula rasa. Discusses the theoretical and practical…

Shows that graphs can reveal much about feedback systems that formula conceal, especially as microcomputers can provide complex graphs presented as animations and allow students to interact easily with them. Describes feedback systems, evolution of the system, and phase diagram. (YP)

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…