Describes a method for teaching multiplication of fractions based on Piaget's constructivism. Instead of teaching the algorithm of multiplying the numerators and denominators, students are presented with many problems and ask to invent their own ways of solving them. (DDR)

Mental arithmetic strategies were studied with 91 Dutch third graders who computed by splitting off 10s and units in both numbers or counting by 10s up or down from the first unsplit number. Results reveal flexibility in changing between and within strategy use. Implications for instruction are discussed. (SLD)

The purpose of this paper is to provide researchers with a shared framework, terminology and tool to improve the coherence of research into learning mathematics with CAS and to assist its findings to accumulate into a significant body of knowledge. Experience with calculators in arithmetic led to a framework for number sense. There is an obvious…

This study investigated the effects of second language (L2) proficiency and task-induced cognitive workload on participants' speech production and retention of information in an environment designed to simulate the demands faced by pilots receiving instructions from air-traffic controllers. Three groups of 20 participants (one…

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…

Accurate and automatic production of the basic number combinations is a major objective of elementary mathematics education. Typically, it is not an objective that is easily and quickly attained. Indeed, teachers regularly lament about how difficult it is to get their students to master the basic "number facts." This problem may be due,…

In order to describe developments in children's conceptions of numbers and numerical relations, judgments of similarities between numbers were solicited from adults and from children in kindergarten and grades 3 and 6. A nonmetric multidimensional scaling analysis suggested that children gradually become sensitive to an expanding set of numerical…

Compares performance of 172 children aged 7 to 13 years on tasks involving visual or auditory presentation of rhyming and nonrhyming letters and an oral or written response. Results indicate insensitivity to phonological similarity for young children with disabilities; sensitivity improves with age, but deficits in short-term memory remain at…

The paper is focused on recent researches in neuroscience and developmental psychology regarding mathematical abilities of infants. A model that tries to explain these findings is developed. The model underlies the mental operations that could be systematically trained to generate efficient school learning. The model is built from a cognitive…

Prekindergarten children were given a perceptual discrimination task using letterlike forms and their transformations. The magnitude of the relation to subsequent achievement in reading varied according to the difficulty of a transformation. More easily discriminated transformations were associated with higher correlations. Patterns were similar…

This special section on cognition and mathematics contains an introduction and 13 articles on advances in the psychology of mathematics learning. The articles focus on how students learn to solve mathematics problems, including arithmetic computation problems, arithmetic word problems, and computer programing problems. (SLD)

Illustrates the multiple strategies used by second graders to solve a problem with three addends and how their teacher tries to map their thinking into the system of mathematical notation. Describes the American Federation of Teachers' Thinking Mathematics program that the teacher uses. (MKR)

This is the second of two papers that propose an expanded and enriched view of arithmetic problem solving by stressing the need to provide learning activities that include problems of varying structures. The first paper included a framework for the enhancement of text-based problems. This second paper proposes a scheme for the development of…

Three factors associated with arithmetical processes (sequence skills, arithmetical strategies, and information processing capacity) were measured in individual interviews with 35 first-grade pupils, aged 7.6 to 8.6, in one Finnish school. Mathematics achievement was determined from information supplied by teachers. Attitudes were assessed twice,…