This study analyzes the development of percentages knowledge by seventh graders given a sequence of activities starting with a realistic modeling task, in which students were expected to create a model that would facilitate the reinvention of percentages. In the first two activities, students constructed their own pricing model using fractions and…

The application of mathematics to real-world problems is moving more and more in the focus of attention of mathematics education; however, many learners experience huge difficulties in relating "pure" mathematics to everyday contents. In order to solve "modeling problems", it is first necessary to find a transition from a…

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

A two-step procedure is developed for the analysis of pretest-posttest data. Nonlinear canonical correlation analysis is followed by covariance analysis of optimally scaled pretest and posttest measures. The procedure is available in the computer program CANALS. Advantages of the two-step procedure are discussed. (SLD)

The reliability of residual scores created in the analysis of covariance in pretest-posttest designs, adjusted for a singe covariate, is compared with that of simple difference scores as relevant parameters vary. Little gain in reliability is created by analysis of covariance, which also suffers from reliability problems. (SLD)

Viewing the reliability for criterion-referenced tests as that of mastery classification decisions, three models for determining reliability were examined using two test administrations so that two estimates could be compared to a standard. A major purpose of the research was to determine how several reliability coefficients (coefficient kappa, an…

The accuracy with which regression models estimate treatment effects is dependent upon a number of conditions. The stability of the regression line (a function of sample size and correlation between pretest and posttest) is said to be the most important of these conditions. The utility of regression models is proportional to the size of the…

Two methods of reading instruction (homogeneous grouping and graded classes) are compared for 165 students in 8 rural North Dakota schools by raw gain scores, residual gain scores, and the analysis of covariance. (CK)