The importance of algebra instruction has increased in the United States in the past few years. Thus, in most states, middle school students are required to take Algebra 1. Middle school students with math difficulties in inclusion algebra settings may require a different instructional approach. The purpose of this research was to compare student…

An individualized project is introduced to accompany a differential equations course with different modules ranging from standard to advanced levels with "Matlab" scripts. (Contains 1 figure.)

Cabri3D is a potentially very useful software for learning and teaching 3D geometry. The dynamic nature of the digital diagrams produced with it provides a useful aid for helping students to better develop concept images of geometric concepts. However, since any Cabri3D diagram represents three-dimensional objects on the two dimensional screen of…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

This paper examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The children and their teachers were participating in a 3-year longitudinal teaching experiment in…

This report presents a model and an approach that institutions of higher education can use to analyze and project the impact of endogenous and exogenous factors on both net and gross tuition in the context of the increasing practice of tuition discounting. It is noted that two key questions drive this effort: (1) what influence does gross tuition…

Five issues relative to the use of different Ordinary Least Squares (OLS) and Hierarchical Linear Modeling (HLM) models to identify effective schools and teachers were examined using data from all students in the Dallas (Texas) public schools in grade 3 in 1994 and grade 4 in 1995. OLS models using first- and second-order interactions produced…

Classical test theory, item response theory, and generalizability theory all treat the abilities to be measured as continuous variables, and the items of a test as independent probes of underlying continua. These models are well-suited to measuring the broad, diffuse traits of traditional differential psychology, but not for measuring the outcomes…

The role of prior knowledge in skill acquisition is to enable the learner to detect and to correct errors. Computational mechanisms that carry out these two functions are implemented in a simulation model which represents prior knowledge in "constraints". The model learns symbolic skills in mathematics and science by noticing and…

This paper discusses the requirements of Interactive Geometry Systems (IGSs) and how they can be fulfilled, explains how a geometry tool can benefit from the Internet, and presents Cinderella's Cafe. Cinderella's Cafe is a new IGS with a high mathematical background that uses the most general mathematical models whenever possible, is highly…

A study was conducted to determine if the centralization of braille operations for the national free library program would be feasible, economical, and desirable. This report presents the findings of the study in three sections. Section 1 provides background information, a summary of the first phase of operations, and the study objective for phase…

An important topic presented in introductory statistics courses is the estimation of population parameters using samples. Students learn that when estimating population variances using sample data, we always get an underestimate of the population variance if we divide by n rather than n-1. One implication of this correction is that the degree of…

This first-year report of the National Effective Transfer Consortium (NETC) summarizes the progress made by the member colleges in creating standardized measures of actual and expected transfer rates and of transfer effectiveness, and establishing a database that would enable valid comparisons among NETC colleges. Following background information…

Regression-based adjustment of student outcomes for the assessment of the merit of schools is considered. First, the basics of causal modeling and multiple regression are briefly reviewed. Then, two common regression-based adjustment procedures are described, pointing out that the validity of the final assessments depends on: (1) the degree to…

In multiple-choice items the response probability on an item may be viewed as the result of two distinct latent processes--a cognitive process to solve the problem, and another random process that leads to the choice of a certain alternative (the process of giving the actual response). An incomplete latent class model is formulated that describes…