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de Freitas, Elizabeth; Sinclair, Nathalie – Canadian Journal of Science, Mathematics and Technology Education, 2018
Human reasoning about and with uncertainty is often at odds with the principles of classical probability. Order effects, conjunction biases, and sure-thing inclinations suggest that an entirely different set of probability axioms could be developed and indeed may be needed to describe such habits. Recent work in diverse fields, including cognitive…
Descriptors: Mathematical Models, Mathematical Concepts, Probability, Thinking Skills
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Kazak, Sibel; Pratt, Dave – Research in Mathematics Education, 2021
We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…
Descriptors: Teaching Methods, Mathematics Instruction, Faculty Development, Probability
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Pearl, Judea – Sociological Methods & Research, 2015
This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain circumstances, meet legal criteria of causation.…
Descriptors: Mathematical Models, Probability, Computation, Cognitive Mapping
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Auer, Richard E.; Knapp, Michael P. – Mathematics Teacher, 2013
The modern era of professional baseball playoffs began in 1903, when the champions of the American League and the National League played the first World Series. Except for one year, 1904, this playoff system was maintained until 1969. Beginning in 1969, each of the two leagues in Major League Baseball (MLB) was divided into two divisions to…
Descriptors: Probability, Team Sports, Mathematical Models, Game Theory
Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu – International Association for Development of the Information Society, 2012
There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…
Descriptors: Cooperative Learning, Mathematical Models, Probability, Calculus
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Sawtelle, Vashti; Brewe, Eric; Kramer, Laird H. – Journal of Research in Science Teaching, 2012
The quantitative results of Sources of Self-Efficacy in Science Courses-Physics (SOSESC-P) are presented as a logistic regression predicting the passing of students in introductory Physics with Calculus I, overall as well as disaggregated by gender. Self-efficacy as a theory to explain human behavior change [Bandura [1977] "Psychological…
Descriptors: Higher Education, Introductory Courses, Physics, Calculus
Thorne, David R. – Journal of the Experimental Analysis of Behavior, 2010
Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…
Descriptors: Behavioral Science Research, Economics, Responses, Reinforcement
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Rozeboom, William W. – Multivariate Behavioral Research, 2009
The topic of this article is the interpretation of structural equation modeling (SEM) solutions. Its purpose is to augment structural modeling's metatheoretic resources while enhancing awareness of how problematic is the causal significance of SEM-parameter solutions. Part I focuses on the nonuniqueness and consequent dubious interpretability of…
Descriptors: Structural Equation Models, Equations (Mathematics), Matrices, Probability
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Bonacich, Phillip; Bienenstock, Elisa Jayne – Social Psychology Quarterly, 2009
This paper presents and tests a general model to predict emergent exchange patterns and power differences in reciprocal exchange networks when individual actors follow the norm of reciprocity. With an interesting qualification, the experimental results reported here support the power-dependence approach (Emerson 1972a, b): those who acquire the…
Descriptors: Interpersonal Communication, Power Structure, Prediction, Interpersonal Relationship
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Ramon Barrada, Juan; Veldkamp, Bernard P.; Olea, Julio – Applied Psychological Measurement, 2009
Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…
Descriptors: Item Banks, Adaptive Testing, Item Analysis, Psychometrics
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Kroll, Neal E. A. – Journal of Educational Statistics, 1989
Three potential models for the 2 X 2 contingency table are discussed: (1) the hypergeometric Independence Trial; (2) the double-binomial Comparative Trial; and (3) the multinomial Double Dichotomy Trial. Subsequently, the critical regions of seven statistical tests are evaluated within each of these models. (TJH)
Descriptors: Chi Square, Mathematical Models, Probability
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Wilcox, Rand R. – Educational and Psychological Measurement, 2006
Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…
Descriptors: Nonparametric Statistics, Mathematical Models, Regression (Statistics), Probability
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Levine, Douglas W.; Rockhill, Beverly – Teaching Statistics: An International Journal for Teachers, 2006
We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how…
Descriptors: Probability, Statistical Analysis, Hypothesis Testing, Mathematical Models
Lad, F. R.; And Others – 1987
B. De Finetti's "Fundamental Theorem of Probability" is reformulated as a computable linear programming problem. The theorem is substantially extended, and shown to have fundamental implications for the theory and practice of statistics. It supports an operational meaning for the partial assertion of prevision via asserted bounds. The…
Descriptors: Linear Programing, Mathematical Models, Probability, Statistical Analysis
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ten Berge, Jos M. F. – Psychometrika, 1991
The phenomenon of 2 x 2 x 2 arrays having nonmaximal rank with positive probability, pointed out by J. Kruskal (1989), is generalized to 2 x "n" x "n" arrays. It is concluded that a pair of asymmetric square matrices can be diagonalized simultaneously with positive probability. (SLD)
Descriptors: Equations (Mathematics), Generalization, Mathematical Models, Matrices
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