A short history of mathematical Olympiads in the People's Republic of China is given. Sample problems are included. (MK)

The concept of infinite divisibility is shown by this research report to be intuitively contradictory. This intuition remains unaffected by age and the teaching process. (MP)

The intention of this investigation was to diagnose the retention of some basic skills in some topics in algebra and geometry and to reveal difficult steps in the learning processes in these topics. (MP)

The mathematical solution to a Piagetian experiment involving topological concepts reported in a recent book is labeled as a sham. The correct solution is given and discussed. (MP)

Several general aspects are discussed. These include the role of mathematics in scientific and technical progress, some deficiencies in training, the role of mathematics in engineering faculties, and methods of improving mathematical training. (MP)

Topics discussed include: reasons for strategies; the use of a hierarchy of spaces from topological to Euclidean in teaching; structural strategies; pedagogical strategies; and mathematical strategies. (MP)

An instructional program is described involving six booklets on descriptive statistics and four computer programs on statistical tests. (MP)

Problem solving is presented as a resource for creating curriculum through reflections on intuition such as: exploring available intuitions, making explicit the intuitions used, and using intuition to generalize. (MP)

The nature of insight is discussed as it relates to mathematical models. Intuition and the intuitively obvious are argued to have no necessary connection with models. (MP)

Discussed are difficulties which occur while the student is using mathematical induction as a tool to prove theorems. An appropriate approach is suggested. (MP)

The author explains what the IOWO is and the reason for the present conference and his part in it. He discusses the observation of learning processes and gives an example of an opportunity he had to observe a learning jump in a small boy. (MN)

The iconographic means of illustrating mathematical facts is discussed along with several examples of graphical solutions to descriptive mathematics problems proposed by pupils. (MN)

The author cites observations of his own children that reflect their concept of fractions and analyzes their conduct in each case. (MN)

The focus is upon the introduction of multiplication within the framework of an algorithm program. Analysis of some observations of student solutions to multiplication problems is included. (MN)

The students in a low-ability first-year classroom of a secondary school use a questionnaire and punched cards to collect and organize data about their classmates. The first five minutes and the first four minutes after the first quarter of an hour of the resulting class discussion are included. (MN)