In this study, we applied multilevel piecewise linear regression with a random-effects model under a Bayesian estimation framework to a total of 5,072 7th grade students in 35 schools to search for an optimum time in terms of the effect of homework time on student academic achievement. First, we found a nonlinear relationship between time spent on…

This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video…

In recent years, mathematical models of decision making, such as the diffusion model, have been endorsed in individual differences research. These models can disentangle different components of the decision process, like processing speed, speed-accuracy trade-offs, and duration of non-decisional processes. The diffusion model estimates individual…

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author's observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was…

This paper aims to investigate how stability varies with the approach used in estimating school performance in a large sample of English primary schools. The results show that (a) raw performance is considerably more stable than adjusted performance, which in turn is slightly more stable than growth model estimates; (b) schools' performance…

Over the past several years, we have been exploring and researching a phenomenon that occurs among undergraduate students that we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase,…

In longitudinal studies data is collected in a series of waves. Each wave after the first suffers from attrition. Therefore it can be difficult to discriminate between changes in sample parameters due to a longitudinal process (e.g. ageing) and changes due to attrition. The problem is particularly vexing if one of the purposes is to compare…

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves…

Studied the teaching and learning of fractions in two matched groups of 10 9-10-year-olds in the Netherlands. In the experimental group, fractions were introduced using the bar and number line as mental models, while the control group used fair sharing and the circle model. The experimental group showed more proficiency in fractions after 1 year.…

A crossed random effects model is presented that applies to data with a nested structure to provide maximum likelihood estimates through the EM algorithm. The procedure is illustrated in studies of neighborhood and school effects on educational attainment in Scotland and classroom effects on mathematics learning in the United States. (SLD)

Summarizes results of a longitudinal study fitting multilevel models to three waves of data on literacy progress for three cohorts of Australian elementary students. Provides estimates of prior achievement and social background influences on student progress and examines effects of grouping practices and other classroom variables. Attentiveness…

The Lisrel-model with structured means was used to study similarities and differences in the development of mathematical ability between two student groups as measured by two tests on three successive occasions. Procedures for testing models to assess the contribution on an individual parameter to the goodness of fit are described. (Author/BS)

This paper evaluates empirically the impact of elementary school related factors on the academic achievement of Montreal francophone children. A three-equation model explains simultaneously the level of achievement in mathematics and French and the self-concept of the students in the sample. (Author/LMO)

The causal relationship between metaphonological skills (sound blending and segmentation) and reading/spelling was investigated in two studies of first graders. One tested causal models using data from a longitudinal study of 46 dyslexics and 44 control children. The other studied the effects of metaphonological training versus general language…

This report is the Proceedings of the third conference of its type. Included are 23 of the 25 papers presented at the conference, discussion of these papers by invited discussants, and symposium papers by a group of leaders in adaptive testing and latent trait test theory research and applications. The papers are organized into the following…