This quasi-treatment study, using a non-equivalent group design, explored how a set of animations related to various concepts in algebra impacted students' ability to learn as measured by changes in quiz and test scores. The concepts that were investigated were addition and subtraction of rational expressions, solving equations involving rational…

Sample size determination is an important issue in planning research. In the context of one-way fixed-effect analysis of variance, the conventional sample size formula cannot be applied for the heterogeneous variance cases. This study discusses the sample size requirement for the Welch test in the one-way fixed-effect analysis of variance with…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

In this study, differential item functioning (DIF) methods utilizing 14 different matching variables were applied to assess DIF in the constructed-response (CR) items from 6 forms of 3 mixed-format tests. Results suggested that the methods might produce distinct patterns of DIF results for different tests and testing programs, in that the DIF…

The main purpose of this study is to evaluate eleventh grade Turkish pupils' comprehension of various general chemistry concepts which in turn enables to investigate chemistry concepts which are easier and harder for students to comprehend. Examining the effect of gender and last semester chemistry course grades on pupils' comprehension of general…

Problem statement: Although there is agreement on the potential of project based learning (PBL) and virtual manipulatives (VMs), their positive impact depends on how they are used. This study was based on supporting the use of online PBL environments and improving the efficacy of the instructional practices in PBL by combining the potentials of…

The sample size determination is an important issue for planning research. However, limitations in size have seldom been discussed in the literature. Thus, how to allocate participants into different treatment groups to achieve the desired power is a practical issue that still needs to be addressed when one group size is fixed. The authors focused…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…