Examples of topics and problems which demand Piaget's formal operational thought at an early stage in the secondary school are provided. (DT)

An example is used to illustrate the four levels: rote, observational, insightful, and formal. (MP)

An algebra test was constructed within a Piagetian framework. Results of a selection of the test items are given and discussed. (MP)

Mathematical concepts and experiences are recalled and organized in a flow chart format. The power of unifying ideas in mathematics often causes this sequence to be forgotten or assigned less importance than it should be. (SD)

Analyzed was the mental activity required to answer Profile Test questions. This was then related to the results of pupils with differing profiles. Most of the mental activity could be reduced to three categories of knowledge: data, short operations, and paths. These categories are then discussed and applied. (MNS)

Ways in which parents, the media and commercial educational materials contribute to the development of erroneous number concepts in pre-school children are identified. Cautions against these practices are suggested which include the use of more than one set of numerals for representing numbers. (JP)

Problems of teaching low achievers are discussed, based on the author's own experiences. A knowledge of each individual child is deemed essential and questions to ask when considering a topic for inclusion in the curriculum are suggested. Motivation, discussion, repetition, and the teaching of concepts are discussed. (LS)

Five steps described by Dienes by which mathematics is learned are illustrated through the use of the topic of direct proportion. (MP)

Thirty-five students from all ability levels in the first and second year of secondary school were interviewed to determine their understanding of appropriate application of number operations. Results of the interviews are classified into five different levels of understanding. (DT)

Preservice teachers observed the performance of primary children (age 8) doing a variety of concrete mathematical tasks. (SD)

Children between the ages of 10 and 13 were asked to write stories to accompany five computational problems. Stories were scored for suitability and it was found that students were most successful on subtraction and least successful on multiplication stories. Scores on this test correlated with mathematics achievement scores. (SD)

A view is presented that there are people with inborn mathematical talent, and that people with such talent need to receive the best instruction possible. (MP)

The author argues on theoretical grounds that not all "logical" pre-number activities are equally relevant for numeracy, and concludes with a practical suggestion for the kind of activity which does have particular relevance. (MN)

This discussion centers around the dangers in making too precise a particular concept in educational psychology that distinguishes between two types of understanding, instrumental and relational. (MP)