This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

Middle-school students are expected to understand key components of graphs, such as slope and y-intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and…

Examines the line graphing ability of middle/high school students (N=625) to provide baseline data on the mastery of line graphing subskills. Results show that seventh- and eighth-grade students were less successful in graphing than high school students, suggesting that graphing skills should be introduced and emphasized in earlier grades. (JN)

Examines pencil-and-paper graphs produced by students at the beginning of a 1-week summer teacher/student institute as well as computer-based graphs produced by those same students at the end of the institute. Initial problems with managing data sets and producing meaningful graphs disappeared quickly as students used the process of "building…

In a classroom environment in which continual access to graphing calculators is assumed, items that have been used to assess students' understanding of functions often are no longer appropriate. Describes strategies for modifying such items including requiring students to explain their reasoning, using calculator-active items, analyzing graphs and…

Addresses three issues of Calculator-based Ranger (CBR) activities on graphing abilities: (a) the effect of CBR activities on graphing abilities; (b) the extent to which prior knowledge about graphing skills affects graphing ability; and (c) the influence of instructional styles on students' graphing abilities. Indicates that CBR activities are…

Examines the difficulties 19 preservice elementary and middle school teachers experienced when creating and interpreting graphs in which speed is one of the variables. Identifies four cognitive obstacles held by the preservice teachers and provides excerpts of their graphical constructions and verbal interpretations. Discusses potential causes for…

Explores whether the differences in use of terminology were related to respective fields or to idiosyncratic characteristics of experience and education. Reports differences among college teachers, high school teachers, and college students from a 16-item survey on algebraic and graphing terminology used in mathematics and science. (YP)

Describes how prospective elementary teachers examined, analyzed, and evaluated four students' written responses on a graphing task for an end-of-course performance assessment in a mathematics methods course. Provides evidence of the prospective teachers' pedagogical content knowledge. Indicates the importance of process and correct answers and…

Reports a study to examine the role of context on the ability to interpret graphs. Graph tests involving 2 ecological contexts were presented to 14- and 15-year-old students (n=23) in the form of an interview. Results indicated how students used their contextual knowledge in interpreting the graphs. (MDH)

Investigated the effects of studying an ecological system via computer simulation on 14- and 15-year-old students' (n=9) abilities to pose hypotheses; control and manipulate variables; and learn via icon, graph, and table display formats. Working with a simulation encouraged students to think hypothetically and test their hypotheses by controlling…

Examines the influence of two factors of the process of graphing on rural students' (n=93) ability to comprehend kinematics graphs on constant velocity events. Students exhibited difficulty in constructing and comprehending graphs of derived variables and were unaware of their own graphing skills deficiencies. (34 references) (MDH)

Provides an example of the integration of science and mathematics learning of one high school physics student in a constructivist classroom. Discusses the student's integration of mathematical and nonmathematical representations and of different mathematical representations in a nonuniform acceleration experiment. Describes a model for integrating…