The derivative framework described by Zandieh (2000) has been an important tool in calculus education research, and many researchers have revisited the framework to elaborate on it, extend it, or refine certain aspects of it. We continue this process by using the framework to put forward a suggestion on what might constitute a "target…

This concluding commentary takes the perspective of research on practicing scientists and engineers to consider what open areas and future directions on relational thinking and learning should be considered beyond the impressive research presented in the special issue. Areas for more work include (a) a need to examine educational applications of…

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we…

Many qualitative and quantitative studies performed on peer instruction based on interactive engagement method used in many different disciplines and courses were reviewed in the present study. The researchers examined the effects of peer instruction on students' cognitive skills (conceptual learning, problem solving, reasoning ability, etc.) and…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

This research study shows that it is possible to advance the use of proportional reasoning of many secondary school students by means of a well-designed teaching program. (MP)

The article describes a study to determine how instruction on the distinction between two theoretical ideas will affect the intake, interpretation, and recall of new information related to but different from the first. (Author/SB)

Discusses issues stimulated by Elizabeth Hatton's examination of teachers' work as "bricolage" in a prior article. Explores the connection between creative potential and pedagogic knowledge and the science of the abstract and the concrete. Presents potential reforms that could enhance teachers' capacity to gain pedagogic knowledge. (JS)

Reports that complex abstractions may be easily acquired by persons of less than 75 IQ if the method of presentation of the abstractions ensures maximum visibility of relevant details. (FL)

Observation of practices in V. V. Davydov's laboratory school suggests that students proceed from concrete example to abstract generalization--rather than from abstract to concrete, as Davydov has claimed. (GDC)

The focus of this paper is on some of the difficulties students experience in learning from texts and in solving other types of academic problems, because of their failure to distinguish between skills needed for everyday thinking and those needed for academic thinking. The paper discusses the types of processing problems children experience when…

Seventh-grade students enrolled in two average classes were pretested, randomly assigned to two training groups--an active group in which physical materials were employed and a verbal group in which standard textbook procedures were employed--immediately posttested and posttested one month later. The active group showed greater achievement and…

Report of a study, using 7 13 year-old boys and girls, which sought to determine if the growth of underlying spatial abilities are enhanced more if technical drawing activities requiring multiview spatial ability are presented before surface development activities, or vice versa. Includes implications for teaching technical drawing. (TA)

The purpose of this study was threefold: to determine whether adding a mnemonic to systematically designed instruction would improve verbal retention, to establish whether retention is better for concrete or abstract information, and to determine whether mental imagery or verbal elaboration is more effective for learning concrete or abstract…

Investigates spontaneous reasoning of 709 French, Belgian, and British students in elementary dynamics using the relations between force, energy and motion as the study topic. Students were selected from the last year at secondary school to the third year at university. (HM)