The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…

A study of 104 Japanese-speaking 2- to 5-year-olds tested the relation between numeral and quantifier acquisition. A first study assessed Japanese children's comprehension of quantifiers, numerals, and classifiers. Relative to English-speaking counterparts, Japanese children were delayed in numeral comprehension at 2 years of age but showed no…

The main purpose of this study is to determine the strategies of using the generalizing patterns of the primary fifth grade students. The practice of this research is conducted on twelve students, which have high, middle and low success levels. Task-based interviews and students journals are used as the tools for data collection. For the analysis…

We explored children's early interpretation of numerals and linguistic number marking, in order to test the hypothesis (e.g., Carey (2004). Bootstrapping and the origin of concepts. "Daedalus", 59-68) that children's initial distinction between "one" and other numerals (i.e., "two," "three," etc.) is bootstrapped from a prior distinction between…

According to one theory about how children learn the concept of natural numbers, they first determine that "one", "two", and "three" denote the size of sets containing the relevant number of items. They then make the following inductive inference (the Bootstrap): The next number word in the counting series denotes the size of the sets you get by…

In this article, the author presents his tales of very large numbers. He discusses the concept of infinity and extremely large numbers such as "googol" and "googolplex". "Googol" which could be written as 1, followed by one hundred zeros, was popularized by Edward Kasner and James Newman. Moreover, "googol"…

This article describes Realistic Mathematics Education (RME), a design theory for mathematics education proposed by Hans Freudenthal and developed over 40 years of developmental research at the Freudenthal Institute for Science and Mathematics Education in the Netherlands. Activities from a unit to develop student understanding of logarithms are…

This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

An activity providing practice with whole number addition and subtraction, as well as enlarging on the idea of numeration systems, is described. (DT)