This article describes an alternate way to utilize a circular model to represent thirds by incorporating areas of circular segments, trigonometric functions, and geometric transformations. This method is appropriate for students studying geometry and trigonometry at the high shool level. This task provides valuable learning experiences that…

This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…

Grading on the curve is a common practice in higher education. While there are many critics of the practice it still finds wide spread acceptance particularly in science classes. Advocates believe that in large classes student ability is likely to be normally distributed. If test scores are also normally distributed instructors and students tend…

This article examines how conversations during design reviews in which 8th-grade mathematics students shared population models with visiting specialists expanded the disciplinary expertise of the classroom. "Re-contextualizing" is a conversational exchange that visiting specialists initiated to invite groups to consider their models in novel…

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

AN INQUIRY INTO RECRUITMENT OF APPRENTICES TO SKILLED TRADES IN WESTERN AUSTRALIA INDICATED LITTLE CORRELATION BETWEEN THE NUMBER OF NEW APPRENTICES AND THE LEVEL OF INDUSTRIAL EMPLOYMENT OR THE TOTAL NUMBER OF APPRENTICES. THIS ARTICLE ATTEMPTS TO OUTLINE A MATHEMATICAL MODEL OF AN APPRENTICESHIP SYSTEM AND DISCUSS ITS IMPLICATIONS. THE MODEL, A…

Equations are derived for product correlation between variables derived from two or fewer original variables. Index correlation and spurious index correlation are briefly discussed. Exact equations for product correlation are derived, and spurious product correlation is demonstrated under various conditions. (RC)

This paper is written with the underlying philosophy that any theory aimed at understanding the functional organization of the brain must begin with an analysis of perception and must also be firmly based on experimental evidence. (Author)

The possibility of using component analysis for nominal data is discussed. Two nominal scale correlation coefficients are applicable. Tschuprow's coefficient and the J index. The reason is that they satisfy the requirements of a scalar product between normalized vectors in a Euclidean space. Some characteristics of these coefficients are…

Estimates of the mean and standard deviation of the tetrachoric correlation are compared with their expected values in several two by two tables. Significant bias in the mean is found when the minimum cell frequency is less than five. Three formulas for the standard deviation are discussed. (Author/JKS)

Coefficient Alpha can be used to estimate the reliability of a test when the test is split into several parts. It is known that alpha can severly underestimate test reliability when the parts have an unequal number of items. A generalization of alpha is proposed to correct this defect. (Author/JKS)

Two models for scaling of paired comparison data are compared to the Thurstone case III model. Two goodness of fit indices are presented for each model for five data sets. The results illustrate the inability of the Thurstone model to adequately account for data when the scale includes extreme stimuli. (Author)

Two forms of stationarity prior to criterion in absorbing Markov chains are examined. Both forms require that the probability of a particular response on a particular trial before absorption be independent of trial number. Simple, necessary and sufficient conditions for both forms are developed and applied to several examples. (Author)

One of the innovative approaches in the use of hierarchical linear models (HLM) is to use HLM for Slopes as Outcomes models. This implies that the researcher considers that the regression slopes vary from cluster to cluster randomly as well as systematically with certain covariates at the cluster level. Among the covariates, group indicator…

Item response theory (IRT) is a useful and effective tool for item response measurement if used in the proper context. This paper discusses the sets of assumptions under which responses can be modeled while exploring the framework of the IRT models relative to response testing. The one parameter model, or one parameter logistic model, is perhaps…