This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

Numeration units (ones, tens, hundreds, etc.) are an epistemological foundation for place value. Here, we assume that they are a didactic support in countries where spoken numbers are incongruent with written numbers. In France, teaching practices neglect the relations between units, and numeration units are typically used only to designate the…

Wishing to explore the complexity of the conceptual, didactic and institutional aspects of learning a scientifically defined object of knowledge, we chose to study the link between the personal relation to numeration developed by six-year-old pupils in first grade ("cours preparatoire" the first level of primary school in France), and…

Describes a positive method of studying children which gives insight into the differences between "privileged" and "underprivileged", and makes possible analysis of the development of a logical concept (number). Preschool children were observed as they interacted in a controlled group situation. (ED)

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)

A fundamental question in developmental science is how brains with and without language compute numbers. Measuring young children's verbal reactions in Spain and Finland, we show that, although there is a general arithmetic ability for small numbers that is shared by monkeys and preverbal infants, the development of such initial knowledge in…

This study contributes to the debate about the Flynn effect by proposing a long-term comparison (1921-2001) of the numerical knowledge of two cohorts of three- to five-and-a-half year-old children. In 1921, Beckmann (1923) assessed the numerical development of children using four tasks (Production, Distinction, Recognition, and Naming). In 2001,…

An international numeracy scale compared how well adults in seven countries--the United Kingdom, France, Netherlands, Sweden, Japan, Australia, and Denmark--handled some basic tasks involving numbers. The questionnaire comprised a set of 12 numeracy tasks that respondents were asked to complete using pen and paper. Within each country, the…

Discusses how students at the end of the French primary school-cycle (10- to 11-year-old pupils) resolve multiplication and related division problems within an assessment perspective taking into account the 3 factors of the problem's representational structure, the numerical values used, and the context of the problem statement. (25 references)…

Examples are given of the variety of mathematical concepts and problems being studied by psychologically oriented researchers in France. Work on decimals, circles, natural numbers, decimal and real numbers, and didactic transposition are included. Comments on designing research on mathematics concept formation conclude the article. (MNS)

A class of 32 fourth graders, who studied inverse operations in grades 1-3, was given 3 written tests, each followed by an interview, to see how well they could simplify computations using inverse operations. Most could not evaluate 28 + 75 - 75, for example, without performing all operations. (GW)

Research on cognitive representation of numbers and understanding of place value of U.S. and Japanese first graders was extended to France, Sweden, and Korea (118 subjects; approximately 24 from each of the 5 countries). Basic differences in children's cognitive representations of number are influenced by characteristics of their languages. (SLD)