Retrieval-induced forgetting (RIF) is a widely studied phenomenon of human memory, but RIF of arithmetic facts remains relatively unexplored. In 2 experiments, we investigated RIF of simple addition facts (2 + 3 = 5) from practice of their multiplication counterparts (2 x 3 = 6). In both experiments, robust RIF expressed in response times occurred…

In many theories, forgetting is closely linked to the passage of time. In the present experiments, recall in a short-term memory task was less accurate when the retention interval included a difficult arithmetic addition task, compared with an easy task. In a novel condition, the interfering task was switched from hard to easy partway through the…

Textbooks, like many other resources teachers have at hand, are meant to be an aid for instruction; however there is little research with textbooks or on their potential to develop metacognitive knowledge. Metacognitive knowledge has received substantial attention in the literature, in particular for its relationship with problem-solving in…

Investigates the commonly suggested rounding rule for addition and subtraction including its derivation from a basic assumption. Uses Monte-Carlo simulations to show that this rule predicts the minimum number of significant digits needed to preserve precision 100% of the time. (Author/KHR)

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…

Simple and complex addition problems were presented for true/false verification to 30 undergraduate students to test a general model for cognitive addition. Problems were presented on a microcomputer, with reaction time (RT) and response accuracy recorded. Models for addition were fit to average RT data using multiple regression techniques. These…

A sample of 24 subjects was presented with 800 addition problems to test a general model of simple and complex addition. According to this model, an addition problem is encoded and verified by column, with specific addition strategies determined by the size of the problem. Two hundred problems each of the following four types were presented: (1)…

Investigates children's knowledge of concrete versions of additive composition, commutativity, and associativity. Reports that in study one, four-to five-year-olds (n=24) and five- to six-year-olds (n=25) judged the equivalence of conceptually related addition problems using groups of objects. States that in study two, five- to six-year-olds…

Presents a method using weighted averages to approximate partial sums of alternating series. Examples are included. (PK)

Analyzes a teaching experiment conducted within the context of teacher education designed to support preservice teachers' understandings of place value and multidigit addition and subtraction. Analyses of the teaching ex-periments document the learning of the preservice teachers and how that learning was supported by initial conjectures grounded…

Research on the structures and processes involved in simple mental arithmetic is reviewed. Results suggest that mental arithmetic is a memory retrieval phenomenon, which develops with the experiences of elementary school and can be understood in general as retrieval from organized network representations. Simple mental addition with basic facts…

Investigated the effects of individual difference variables of field dependence/independence and spatial visualization ability on the performance of college students in three modes. The extent to which four variables account for variability in retention test performance on certain tasks was also viewed. (MP)

Investigates the effects of children solving addition and subtraction problems collaboratively in contrast to solving problems on their own. Explores the effects of ability and gender on the outcomes of group collaboration. Presents and discusses the results. Includes references and an appendix. (CMK)

Students in grades 1, 3, 4, 5, 6, and college were timed as they produced the answers to simple addition problems or verified a given problem as true or false. First graders clearly relied on a counting process for their performance, as advanced by the Groen and Parkman "min" (for minimum addend) model. Third grade appears to be a…

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)