Thirty-eight sixth graders were trained in fraction calculation through progressive transformation dialectics (PT) whereas a control group of 38 was taught through a traditional mathematics education framework. The PT group, encouraged to form network-type knowledge representations, performed better on problems that required more than mere…

A study with 29 preschoolers showed that a statistically significant number of them successfully reassigned tags in counting (ordinality) but failed to predict that differently ordered counts would produce the same outcome (cardinality). Results indicated that children may not entirely understand implications of their counting actions. (Contains…

The relationship between elementary operations underlying processing of numerical information and performance on psychometrically derived ability measures requiring processing of numbers but defining separate ability factors was studied for 102 Air Force recruits (54 males and 48 females). Patterns of convergent and discriminate relationships for…

Describes two main categories of mental activity used by students in mathematics classes: mental mathematics and mathematical thought. Calls for the continuation of teaching mental mathematics and asks for the inclusion of mathematical thought in the national curricula. (MKR)

Twenty-seven children (ages 7-10) with learning disabilities and 42 controls were tested on three different mathematics tasks. Significantly more controls abstracted composite unit structures suggestive of operational logic on modified nonverbal and associativity of length tasks. On a flash card task, children with learning disabilities achieved…

From Aesop to Sun Tzu, the importance of working together has long been acknowledged. Yet as long as cooperation has existed, so have the difficulties associated with it. Pooling two fields might mean twice the power, but this union also brings twice the jargon, twice the competing theories, and twice the head butting. Nonetheless, in this…

Object perception requires interpolation processes that connect visible regions despite spatial gaps. Some research has suggested that interpolation may be a 3-D process, but objective performance data and evidence about the conditions leading to interpolation are needed. The authors developed an objective performance paradigm for testing 3-D…

This study investigates children's ability to use language to guide their choice of individuation criterion in the domains of objects and events. Previous work (Shipley, E. F., & Shepperson, B. (1990). Countable entities: developmental changes. "Cognition," 34, 109-136.) has shown that children have a strong bias to use a spatio-temporal…

The aim of the 2018 International Association for Development of the Information Society (IADIS) Cognition and Exploratory Learning in the Digital Age (CELDA) conference was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There have been advances in both cognitive…

Preschoolers 4 and 5 years of age were found to use four strategies differing in temporal characteristics as they solved simple addition problems with sums of 10 or less. Three strategies had visible and/or audible aspects, and one was covert, involving retrieval from memory. The harder the problem, the more often the children used an overt…

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

Two simple quantitative models were derived from a series of experiments which explored the role of information storage in working memory when performing mental arithmetic. The decay model is a tractable analysis of a complex task which assumes a decay process in working storage. Similar analyses are recommended for problem solving activities…

Kindergartners appeared to differ in their readiness to use a concrete counting strategy for addition. Many persisted in counting with objects. Mental counting strategies were sequenced. (MNS)

Establishing and maintaining the desirable kind of balance between meaning and computational competence is the subject of this reprint from a 1956 issue of the journal. Sources of the dilemma and suggestions for solution are discussed. (MNS)

The history of mental computation in the elementary school curriculum is briefly described, followed by discussion of the benefits of mental computation. How thinking skills are enhanced is then illustrated. (MNS)