Eighteen college students solved addition problems using the Hutchings Low Fatigue Addition Algorithm, which requires a written record of running sums, and the standard algorithm, which does not. Students using the Hutchings algorithm had significantly higher reaction times to a tone, indicating that the Hutchings method requires less cognitive…

Twenty preschool children with specific language impairment (SLI) were compared to matched peers on counting abilities. SLI children demonstrated knowledge of rules associated with counting but exhibited marked difficulty in counting objects. They showed difficulty with rote counting, displayed a limited repertoire of number terms, miscounted…

Presents examples taken from an existing K-9 program to show how children of various ages can be engaged in intellectual experiences, some of which might not seem to be mathematical by traditional standards. (ASK)

In Experiment 1, adults (n = 48) performed simple addition, multiplication, and parity (i.e., odd-even) comparisons on pairs of Arabic digits or English number words. For addition and comparison, but not multiplication, response time increased with the number of odd operands. For addition, but not comparison, this parity effect was greater for…

Patients with category-specific deficits have motivated a range of hypotheses about the structure of the conceptual system. One class of models claims that apparent category dissociations emerge from the internal structure of concepts rather than fractionation of the system into separate substores. This account claims that distinctive properties…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

Because of the educational importance of mathematics and science, IEA's (International Association for the Evaluation of Educational Achievement) Trends in International Mathematics and Science Study, widely known as TIMSS, is dedicated to providing countries with information to improve teaching and learning in these curriculum areas. Conducted…

This article describes how the concept of "key idea" can be used in high school geometry to connect students' informal explorations with rigorous mathematical proof. (Contains 6 figures.)

Three models have been proposed to account for the relationship between the principle of commutativity and the development of more economical addition strategies, which disregard addend order. In the first and second models, it has been proposed that either discovery or assumption of commutativity is a necessary condition for the invention of…

Three experiments evaluated performance on a mental multiplication task and the adequacy of several different models of mental addition as extended to multiplication. Results are discussed in terms of a network-retrieval approach to mental arithmetic, the commonalities between addition and multiplication, and rule- versus retrieval-based…

We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic…

Though cognitive science has given psychology a new, more detailed and specific way of expressing models of cognition, correspondingly detailed and precise arguments analyzing and supporting those models have not been forthcoming. Consequently, the new models often fail to meet the traditional criteria of scientific theories. Tools are available…

Three preliminary studies and one exploratory main study investigated the effect of calculator use on elementary, middle, and secondary school students' solution methods on routine mathematical problems. Items were identified for which a longer and a shorter solution method existed. Half of the sample worked these using a calculator and half used…

Experiments dealing with quantification processes in adults were run as part of an attempt to formulate an information processing model of cognitive development. The existence of three quantification operators--subitizing, counting and estimation--was first postulated. Experiments were then designed to refine the parameters which define the…

Basic skills are defined as the method of inquiry or the process of mathematics. The calculator is discussed as being potentially useful in extending process skills. (MP)