This guide provides students with practice for all the major types of graphs they are likely to encounter. It includes information on graphs of various families of algebraic functions; bar, line, and circle graphs; the creation, reading, and interpretation of graphs; and the use of graphing calculators. (MVL)

Three examples of the use of intuitive geometrical ideas in clarifying analytical results. (MM)

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

Explores the effects of varying the coefficients in the general quadratic function using graphing calculators. (MKR)

Reports on how students managed some technical aspects of graphics calculators as they used them to study graphs of straight lines and parabolas. Identifies three common student difficulties: (1) tendency to be unduly influenced by the jagged appearance of graphs; (2) poor understanding of the zoom operation; and (3) limited grasp of the processes…

Explores an unexpected connection between a function, its inverse, and the arithmetic mean, algebraically and graphically. (MM)

Documents what high school students showed when asked to work on tasks that involved the use of various representations. Indicates that few students made proper connections between representations and the initial situation or problem on their own and exhibited competence in procedures such as expressing an area or solving quadratic equations, but…

Most people learn to drive without knowing how the engine works. In a similar vein, the author believes that students can learn economics without knowing the algebra and calculus underlying the results. If instructors follow the philosophy of other economics courses in using graphs to illustrate the results, and draw the graphs accurately, then…