Equivalence is mostly associated with the strand of Number and Algebra and is fundamental in both of the substrands. Equivalence is considered a key and foundational concept of algebra, and whereas an assumption might be made that equivalence is a relatively "easy" concept; studies have shown that when asked to balance an equation such…

The derivative of a composite function, taken with the chain rule is one of the important notions in calculus. This paper describes a study conducted in Turkey that shows that the chain rule was given with the formula in function notation and/or the Leibniz notation without relating these formulas to life-related problem situations in the…

This article reports on the collaborative initiative of two primary school teachers who created and implemented innovative pedagogy in order to foster a culture of thinking in their classrooms. The paper outlines teaching strategies that were used with the intent of making students mindful of themselves as learners and thinkers. A…

The plethora of data that confronts teachers on a daily basis requires that they know more than simply being able to calculate. It demands that they understand the context in which the mathematical ideas are embedded and what those ideas are telling them in relation to that context. Also, it necessitates that they are prepared to question how…

Mathematics games are often used in the classroom as a reward or warm-up activity before the "real" learning takes place. Many teachers have witnessed how useful games are for tuning-in students to the impending mathematics lesson. However, have teachers considered playing games as the central part of the lesson? This article explores…

Twenty-nine students in grades four, six, and eight were asked to find solutions to fraction equivalence problems and to verify their solutions using discrete material. Discontinuities were observed between strategies students used for producing solutions and supporting knowledge grounded in physical reality. (Author/MNS)

This book details the findings from a research team that used cognitive principles and a large range of experiments to devise a variety of instructional designs. Their recommendations are based on 20 years of objective, published research. Although the program focused on technical subjects, the findings can easily be applied to a range of…

Presents results from an Australian study examining whether children who use cognitive strategies in solving simple addition questions develop greater proficiency in addition than children who do not use such strategies. Describes the subjects, instruments, procedure, and instructional treatment. Concludes that the development of cognitive…

Argues that contemporary society requires new and more sophisticated ways of thinking. Reviews several approaches to teaching new cognitive processes in schools. Includes lists of characteristics that inhibit and promote higher order thinking skills. (CFR)

Summarized are the findings from five studies carried out in Australia in 1979-80. First was a cross-sectional survey designed to determine the memory capacity of a population of children in grades 1-3. The second study investigated performance differences on a variety of mathematically related developmental tasks for the same group. Data from…

Discusses how students construct mental images that aid estimation skills in the measurement of angles. Reports research identifying four strategies that students use to estimate sizes of angles. Strategies include utilization of the mental images of (1) a protractor; (2) a right angle; (3) a half-turn; and (4) angles of a polygon. (MDH)

Reports on a study of four Australian 11th-grade biology students that used stimulated recall to evaluate student thinking processes.The study confirmed the complexity of the teaching-learning process. (MD)

This study investigated problem solving skills in mechanics problems that required the use of diagrams. These skills were examined in two ways. First, the study examined student problem solving skills using solution scripts from the Western Australian Tertiary Admission Examination in physics. Solution attempts by students in the 1978 and 1979…

Studies the development of moral autonomy in 720 Australian secondary school and university students between the ages of 12 and 21. Examines autonomy development in the context of moral judgments. Finds the need to add a dimension of individual differences to the single dimension used to describe developmental changes. (Author/NL)

A common thread in contemporary research in student learning refers to the ways in which students go about learning. A theory of learning is presented that accentuates the interaction between the person and the situation. Research evidence implies a form of meta-cognition called meta-learning, the awareness of students of their own learning…