The role of imagery in mathematical thinking and learning is discussed. The use of diagrams and charts is suggested as promoting imagery. (MP)

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…

Presents evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale, and angle. Participants responded to a simple but non-standard task concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches termed…

Investigates students' abilities to draw inferences. Introduces cognitive conflict in the form of video clips of reasoning expressed by students. Documents change with regard to the levels of observed response for the protocol and the use of displayed variation in the graphs. Analyzes change associated with the presentation of cognitive conflict.…

This study reports the cognitive processing of a Year 8 female student (Kerri) during a test, and during her subsequent homework as she consolidated as part of abstracting; a topic of recent research interest. This case adds to the body of knowledge about how constructing and consolidating can occur simultaneously. The analysis captured the…

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)

A study determined the abilities of students to interpret and represent graphs by asking 15-year-old female students (n=10) to write stories to accompany any 3 of 12 graphs presented. Results indicated that the students were not able to accurately relate real life situations to graphical forms. (MDH)

Research in this project studied cognitive processes involved in understanding and solving problems used in instruction in the domain of mathematics, and explored implications of these cognitive analyses for the design of instruction. Three general issues were addressed: knowledge required for understanding problems, knowledge of the conditions…

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)

These proceedings contain the papers of the 11th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2014), October 25-27, 2014, which has been organized by the International Association for Development of the Information Society (IADIS) and endorsed by the Japanese Society for Information and Systems in…

This paper discussed the use of structured observations as a research strategy in two recently completed studies that investigated students thought processes and behaviors in a microcomputer-based laboratory (MBL) environment and in other instrument-based laboratory environments. In the first study, students' behaviors and thought processes were…