This article is about utilizing the process of building and exploiting models as a framework for inquiry in mathematics education research. We introduce and discuss a model of such a process and compare this model with key methodological features of design research in mathematics education. We argue that despite several communalities, educational…

Given the challenges of scaling up content-related professional development (PD), the PD facilitators have gained increasing attention in PD research. In this mainly programmatic and structural article, we try to systematize existing research strategies which take into account the multifaceted and multi-level structure of PD research. We discuss…

The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…

Areal data have been used to good effect in a wide range of sociological research. One of the most persistent problems associated with this type of data, however, is the need to combine data sets with incongruous boundaries. To help address this problem, we introduce a new method for identifying common geographies. We show that identifying common…

Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into "K" clusters. This "K"-balance partitioning problem also has more…

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for…

Radical behaviorism considers private events to be a part of ongoing observable behavior and to share the properties of public events. Although private events cannot be measured directly, their roles in overt action can be inferred from mathematical models that relate private responses to external stimuli and reinforcers according to the same…

Uses examples of hierarchical linear modeling (HLM) at local and national levels to illustrate proper applications of HLM and dummy variable regression. Raises cautions about the circumstances under which hierarchical data do not need HLM. (SLD)

This paper provides an introduction to basic issues concerning structural equation modeling (SEM), a research methodology increasingly being used in social science research. First, seven key issues that must be considered in any SEM analysis are explained. These include matrix of associations to analyze, model identification, parameter estimation…

The dangers of overlooking time-honored cautions in the making causal interpretations of data analyses from correlational studies when using highly sophisticated computer programs and their associated techniques are discussed. (JKS)

Illustrates the use of latent growth modeling (LGM) as an analytical tool in program evaluation using the hypothetical example of a high school drug prevention program. Demonstrates the use of LGM in assessing longitudinal impact and in incorporating predictors of status and growth into a model. Highlights advantages and limitations of LGM. (SLD)

Methodological implications of a person-oriented, holistic-interactionistic perspective in research on individual development are outlined, desirable properties of a mathematical model of a phenomenon are discussed, and selected methods for carrying out person-oriented research are briefly overviewed. These methods are: (1) the classificatory…

Ordinary least-squares regression treats the variables asymmetrically, designating a dependent variable and one or more independent variables. When it is not obvious how to make this distinction, a researcher may prefer to use orthogonal regression, which treats the variables symmetrically. However, the usual procedure for orthogonal regression is…

A longitudinal program evaluation approach used in the Vermont system of care for children and adolescents is described. The method focuses on movement between residential placements and compares system functioning to service system values using a person-level longitudinal database. This methodology can be useful in a number of fields. (SLD)

A modified version of the predominant economic impact model (Caffrey-Isaacs) is presented for use by higher education institutions in preparing and carrying out economic impact studies. Use of the modified version allows small institutional research offices to conduct studies in a timely manner with a methodology that remains within the boundaries…