A context-based approach to education aims to improve students' meaningful learning and uses authentic situations in which scientific concepts are applied. The use of contexts may contribute to the learning of abstract concepts such as algorithms. The selection of appropriate contexts, however, is challenging for teachers. It is therefore…

Offers a simple classification of problems and seeks to explore the many factors that may be important in the successful solving of problems. Considers the place of procedures and algorithms. Solving open-ended problems is extremely important in education and offering learners experience with this in a group work context is a helpful way forward.…

Describes a study with the main objective of constructing models based on strategies students use to solve chemistry problems and to show that these models form sequences of progressive transitions termed "problemshifts" that increase the explanatory/heuristic power of the model. Results implies that the relationship between algorithmic…

Common mistakes pupils make when adding fractions are categorized and analyzed. (MP)

The calculator is used to explore the distributive property of a unary operator over a binary operator. This is an extension of an earlier paper. The emphasis is on student discovery of the property for various combinations of the operators. Instructional material contained in the report include a reference sheet of questions for potential…

Investigating properties and characteristics of unary operations is shown to be facilitated by using calculators. Several avenues for instructional exploration are suggested and examples given. These include questions relating to relations, inverses, commutativity, distributivity, and iterations. A discussion of the calculator algorithm for…

Results of this study, done with underachieving ninth graders, indicate that flow charting as a structure for basic skills instruction can be considered as effective as the traditional approach. (MK)

Examines solutions presented by preservice teachers for solving graphical and numerical problems involving the arithmetic mean. Participants presented two methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing…

A study to investigate one of the mechanisms teachers may use to convince themselves incorrectly that students have learned science concepts requiring formal operational ability is presented. The investigation indicates instructors may actually teach and test for memorization of algorithms rather than understanding. (MP)

Describes a prototype package that uses algorithms created within the symbolic algebra system Axiom, numerical routines from the NAG Libraries together with the easy-to-use facilities of modern graphical interfaces. Considers the implementation of different techniques, both symbolic and numeric, for the analysis and calculation of interpolating…

The calculator is used to investigate properties and characteristics of certain unary operations. These include how a number is related to the number resulting from a unary operation and the result of two unary operations. A discussion of the calculator algorithm to accomplish a series of unary operations is given. Record sheets to summarize…

Students recognized as less successful individuals in mathematics are tested for their understanding of fractions. The data reveals that most were only able to apply remembered rules to problems without actually knowing if the rule worked for the given situation. (MP)

Attempted to establish the incidence of using taught algorithms versus invented methods of subtraction in (n=1,370) male secondary school students and to relate the use of invented methods to age, mathematical achievement, and lateral thinking ability. Use of invented algorithms increased with age. (23 references) (MKR)

To assess whether movement artifacts reported in visual inspection time (IT) tasks were under metacognitive control, 29 young adults in Edinburgh (Scotland) were tested on a dual-task paradigm in which IT was conducted along with a concurrent task. Reports of movement artifacts are not usually examples of metacognitive processing. (SLD)

A theoretical framework for incorporating item response theory into the measurement of attitude and other personality processes is presented. The person by item model is introduced by considering the conceptual usefulness of such a model in understanding item responding, outlining the form of the model, briefly discussing methods for examining the…