Log-linear models for contingency tables are a key tool for the study of categorical inequalities in sociology. However, the conventional approach to model selection and specification suffers from at least two limitations: reliance on oftentimes equivocal diagnostics yielded by fit statistics, and the inability to identify patterns of association…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

"Who has been to Dairy Queen® and purchased a Blizzard?®" Ms. Bosetti asked her students. During the summer, Bosetti had seen many of her former and future students at the local Dairy Queen enjoying Blizzard desserts and wondered, "Which Blizzard size is the best value?" She used this context for a ratios and proportions task…

Amazon, Walmart, and other large-scale retailers owe their success partly to efficient inventory management. For such firms, holding too little inventory risks losing sales, whereas holding idle inventory wastes money. Therefore profits hinge on the inventory level chosen. In this activity, students investigate a simplified inventory-control…

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task…

This publication presents estimates of apprentice and trainee activity in Australia for the December quarter 2011. The figures in this publication are derived from the National Apprentice and Trainee Collection no.71 (March 2012 estimates). The most recent figures in this publication are estimated (those for training activity from the June quarter…

This publication presents estimates of apprentice and trainee activity in Australia for the September quarter 2010. The figures in this publication are derived from the National Apprentice and Trainee Collection no.66 (December 2010 estimates). The most recent figures in this publication are estimated (those for training activity from the March…

This publication presents estimates of apprentice and trainee activity in Australia for the June quarter 2012. The figures in this publication are derived from the National Apprentice and Trainee Collection no.73 (September 2012 estimates). The most recent figures in this publication are estimated (those for training activity from the December…

This publication presents estimates of apprentice and trainee activity in Australia for the September quarter 2012. The figures in this publication are derived from the National Apprentice and Trainee Collection no.74 (December 2012 estimates). The most recent figures in this publication are estimated (those for training activity from the March…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

As Duncomb and Yinger (2001) have stated, "School consolidation represents the most dramatic change in education governance and management in the United States in the twentieth century. Over 100,000 school districts have been eliminated through consolidation since 1938, a drop of almost 90 percent (NCES 1999, Table 90). This longstanding…

The interest in developmental sequences and learning hierarchies is growing. One approach to the study of such sequences is to gather data on several variables, each of which corresponds to a stage, step, or phase in the sequence and to examine the associations between the variables as displayed in a contingency table. If the variables are…

Sixteen tables are presented for critical values of the larger of two sample correlation coefficients from two independent samples, given the sample size and the value of the smaller correlation. These tables allow quick assessment of significance without requiring calculation of the test statistic. (SLD)

Manifest discrete time and latent Markov chain models are described, and the results given by each are compared for the re-analysis of a three-wave table of repeated behavior ratings of children. More recent developments in latent discrete time Markov chain modeling address the problems of the table more efficiently. (SLD)

An extended marginal homogeneity model is introduced for the analysis of square contingency tables with the same ordinal row and column classifications. The model hypothesizes that the ratio in each column of table delta will exhibit an exponential function of the column. (SLD)