Young Children's Symbol‐Making Tools and Factors Influencing Their Availability,Selection and Use: An International Survey

Families and schools play essential roles introducing children to the tools of their culture, including pencils and other symbol‐making instruments. Child development and education specialists from Africa, Asia, Europe, and North and South America confirm these roles and reveal that symbol‐making tools, as cultural artifacts, reflect countries’ levels of human development, including life expectancy, literacy, and purchasing power.

In countries of low and moderate levels of human development children are more likely to use commercial symbol‐making tools first in schools, not homes. The symbol‐making tools most widely available to young children are pencils and crayons. Yet, when commercial tools are unavailable, children create their own, using objects from the natural environment.

The pencils used by most young children are standard adult‐sized while crayons, brushes, and markers are more varied in size. In most countries children use symbol‐making tools freely and with adult direction. Nonetheless, adult‐directed tool use decreases and free use increases as human development levels rise.

Place of residence, socio‐economic status, teacher and parent educational levels, and commercial availability account for often wide within‐country variations in child access to and use of symbol‐making tools. Finally, symbol‐making tool design and use appear to be based on tradition rather than research.

     

Curriculum variables,theory and goals: A comment on Begle's Critical Variables in Mathematics Education

The following text was prepared for the Begle Memorial Series on Research in Mathematics Education of the IV ICME Congress at Berkeley in August 1980. Several sessions of this series were devoted to Begle's¹ last book Critical Variables in Mathematics Education, and I was asked to discuss one of its chapters. However, in my view, the more interesting questions Begle's survey raises concern basic problems related to the study as a whole, though these may be identified in each of its parts. Therefore, I have divided my text into two parts: the first sticks more closely to the chapter on curriculum variables which I was to review, and the second is devoted to a more general view on the problems. This procedure may be justified beyond the original purpose: reconstructing one single part of the book may supply a concrete basis for the reflections subsequently explicated and may help in visualizing them.     

An Application of Item Response Time: The Effort-Moderated IRT Model

The validity of inferences based on achievement test scores is dependent on the amount of effort that examinees put forth while taking the test. With low-stakes tests, for which this problem is particularly prevalent, there is a consequent need for psychometric models that can take into account differing levels of examinee effort. This article introduces the effort-moderated IRT model, which incorporates item response time into proficiency estimation and item parameter estimation. In two studies of the effort-moderated model when rapid guessing (i.e., reflecting low examinee effort) was present, one based on real data and the other on simulated data, the effort-moderated model performed better than the standard 3PL model. Specifically, it was found that the effort-moderated model (a) showed better model fit, (b) yielded more accurate item parameter estimates, (c) more accurately estimated test information, and (d) yielded proficiency estimates with higher convergent validity.