Conditional independence (CI) between response time and response accuracy is a fundamental assumption of many joint models for time and accuracy used in educational measurement. In this study, posterior predictive checks (PPCs) are proposed for testing this assumption. These PPCs are based on three discrepancy measures reflecting different…

Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; "Good practice in primary mathematics: evidence from 20 successful schools," was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a "high…

This paper addresses the reform of mathematics education in the Netherlands and the attacks that presently take place against this reform. The attacks concentrate on primary education and criticize in particular the program for teaching calculation skills with long division as a case in point. The paper gives an overview of what Realistic…

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…

Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)

Efforts to develop a mathematics curriculum that meets the needs of a modern society are reflected in reform recommendations across the developed world. A common requirement is for students to understand the calculation procedures they are taught and to develop "number sense". This paper will analyse students' strategies for calculating…

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…

Hypothesized that arithmetic calculating procedures and types of problems that necessitate more subproblems will lead to longer solution times. Data from 36 third grade students who mentally computed problems with sums greater than 20 and less than 100, confirmed both hypotheses. (RH)