In this paper we analyze excerpts of "Paradoxes of the Infinite", the posthumous work of Bernard Bolzano (1781-1848), in order to show that Georg Cantor's (1845-1918) approach to the problem of defining actual mathematical infinity is not the most natural. In fact, Bolzano's approach to the paradoxes of infinity is more intuitive, while remaining…

This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range, while keeping other…

Students of General Physics often complain that the course is too abstract and remote from daily life. As teachers, we emphasize that the abstract concepts of physics are indispensable for understanding our daily experiences, and we try to give the impression that quantitative descriptions can be achieved by adopting concrete mathematical…

The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…

This study introduces three growth modeling techniques: latent growth modeling (LGM), hierarchical linear modeling (HLM), and longitudinal profile analysis via multidimensional scaling (LPAMS). It compares the multilevel growth parameter estimates and potential predictor effects obtained using LGM, HLM, and LPAMS. The purpose of this multilevel…

This paper presents a model for compensating school districts for implementing effective prereferral programs, in order to promote the most appropriate service delivery for all students. The model develops formulae based upon changes in regular and special education enrollment, and includes state monies allocated to special education. Variables in…

This handbook provides information and guidelines to assist college administrators and researchers in calculating the economic impact of their community college on its locality. First, background is presented on an economic impact project conducted in New Jersey to help support the case for increased state and county funding to community colleges.…

The accuracy and variability of 4 cross-validation procedures and 18 formulas were compared concerning their ability to estimate the population multiple correlation and the validity of the sample regression equation in the population. The investigation included two types of regression, multiple and stepwise; three sample sizes, N = 30, 60, 120;…

Direct and indirect effects in decomposed zero-order correlations among variables in causal models are considered. Under certain circumstances, the components of the decompositions could be interpreted as direct, indirect, and spurious causal effects, plus a component called joint associations. The sum of the direct and indirect effects is the…

The proper use of Pearson's chi-square for the analysis of contingency tables is reviewed. A 1949 article by Lewis and Burke, in which they cite nine primary sources of error in the use of chi-square, serves as the basis of the review. Those nine sources of error are re-examined in light of current research. In addition, techniques and research on…

The purpose of this study was to determine if a correlation existed between the classes of books checked out of the San Antonio College Library and the classes of books used in the Library. Data for out-of-library and in-library use were collected during February, 1978, and arranged by Dewey Decimal Classification (DDC) tens. By using the Pearson…

Arguments have recently been put forth that standard textbook procedures for determining the sample size necessary to achieve a certain level of power in a completely randomized design are incorrect when the dependent variable is fallible because they ignore measurement error. In fact, however, there are several correct procedures, one of which is…

When the school or district is the unit of analysis in school effects research, the outcome of interest is mean achievement, and the variance explained by school or district level predictors is between schools or between districts. When the individual is the unit of analysis, the outcome of interest is individual achievement and the variance…

Written for remedial/developmental students without algebraic skills, these three arithmetic modules for electronics cover measure, formulas, and pythagorean theorem. The self-paced modules incorporate use of calculators. With this aid the level of difficulty of comprehension is approximately seventh grade. Module 1, Measure, covers nine topics:…

An analysis is presented of the basic instructional productivity formula, PR = TL x CS, where PR is the index of productivity, TL is the index reflecting teaching load, and CS is the class-size index. Objectives of the analysis are to: extend the basic instructional productivity formula to include recognition of different types of instruction;…