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Positive effects have been reported when graphic calculator (GC) is used in Mathematics classrooms as it influences the way Mathematics is taught and learned. This study aims to examine the effects of GC instructional approach on students' Probability performance, particularly for students with different levels of Mathematics performance. Two groups of students were involved in this study; Group A adopted the GC instructional approach while group B used the conventional teaching approach. Students from different Mathematics performance levels, particularly the low-performing students, gained benefits when the GC instructional approach was adopted in learning Probability.

AbstractThe purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a "mathematical mechanistic world picture" that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing (FTAP), the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument (DBA), the most popular justification for subjective probability. The paper's main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics ofphysicaandpractica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems.

Book reviewed in this article: De organisatie van de kwaliteitszorg, J. H. Enters, H. E. Stenfert Kroese N.V. Statistiek voor Medici. Korte inleiding, Chr. L. Rumke, C. van Eeden, uitgeverij L. Stafleu en ZoonDe bloemisterij in Nederland Characteristic Functions, E. Lukacs, Griffins Statistical Monographs and Courses no. 5 Charles Griffin and Cy. Ltd. Portfolio Selection, Efficient Diversification of Investments, H. M. Markowitz, Cowles Foundation Monograph 16 Finite Markov Chains, J. G. Kemeny en J. L. Snell, University Series in Undergraduate Mathematics, Van Nostrand, Princeton, New Jersey Operations Research and Systems Engineering, onder redactie van Charles D. Flagle, William H. Hugginsen Robert H. Roy Tables of the Hypergeometric Probability Distribution, G. L. Lieberman and D. B. Owen, Stanford Studies in Mathematics and Statistics III Probability with statistical applications, Frederick Mosteller, Robert E. K. Rourke, George B. Thomas, Jr. Probability: a First Course, F. Mosteller, R. E. K. Rourke, G. B. Thomas, Jr.

AbstractFor a young science and even for most old ones, the intensity and variety of activities involved in computer science are unsurpassed. In an effort to provide the extremely varied training needed in the field, curriculum planners have tended to slight probability and statistics. Rarely has it been a requisite and only occasionally a desired electiveHowever, not only is an adequate foundation in probability and statistics necessary for such external computer applications as tracking and other data reduction, Monte Carlo techniques, gaming, operations research, traffic analyses, etc., but it also plays an important role in internal applications to computer science and technologyThis effort in Rand's continuing study of computational mathematics and its applications offers a number of examples in various areas of computational mathematics and computing machine arithmetic‐to say nothing of computer design, time sharing, and the like‐to support the thesis that probability and statistics should be a requisite, not simply an elective or, even worse, ignored, at any institution offering a program in computer science. Further more, a potentially profitable source of research problems can be found in the interface between probability and statistics and computer science.

AbstractAyache presents a view of markets and mathematics that attempts to conform to the philosophies of Alain Badiou and Quentin Meillassoux. However, this attempt is unsuccessful because Ayache adopts a view of probability rooted in nineteenth-century conceptions that cannot accommodate the radical uncertainty of the markets. This is unfortunate as it is reasonable to believe that the ideas of Badiou and Meillassoux, when synthesised with contemporary ideas of probability, could offer interesting insights. Roffe presents a better argued synthesis of Deleuze and markets, however he makes similar assumptions about contemporary probability that undermine his conclusions.

Book reviewed in this article:Introduction to Probability and Mathematical Statistics, Z. W. BirnbaumThe Paper Industry and European Integration, R. BolaffiMethods of least squares and principles of the theory of observations, Yu. V. LinnikFundamentals of Scientific Mathematics, George E. OwenDecomposition of Superpositions of Distribution Functions, P. MedgyessyMathematical Methods and Theory in Games, Programming and Economics, S. K. arlinStatistical Analysis and Optimization of Systems, E. L. PetersonStudies in applied probability and management science, edited by Kenneth J. Arrow, Samuel Karlin and Herbert Scarf

Book reviewed in this article:Probabilities on Algebraic structures, U. GRENANDERErgodic Theory and Information, P. BILLINGSLEYLectures on Modern Mathematics, Volume I, edited by T. L. SAATYResearch Papers in Statistics, Festschrift for J. Neyman, F. N. DAVIDThe Theory of Road Traffic Flow, WINIFRED D. ASHTONAn Introduction to Probability Theory and its Applications, Volume II, W. FELLER

In this paper we study how the expectations of power means behave asymptotically as some relevant parameter approaches infinity and how to approximate them accurately for general nonnegative continuous probability distributions. We derive approximation formulae for such expectations as distribution mean increases, and apply them to some commonly used distributions in statistics and financial mathematics. By numerical computations we demonstrate the accuracy of the proposed formulae which behave well even for smaller sample sizes. Furthermore, analysis of behavior depending on sample size contributes to interesting connections with the power mean of probability distribution.

In 2008, Browder and colleagues published a meta-analysis on mathematics instruction for learners with significant cognitive disabilities and found that most skills taught to these students were only from two of the five strands recommended by the National Council for Teachers of Mathematics (i.e., Number and Operations, and Measurement). A review of the literature since Browder et al. yielded an additional 29 studies. When results from both reviews were compared, a greater percentage of studies taught skills from three strands (i.e., Number and Operations, Geometry, and Algebra), whereas the percentage teaching skills from the Measurement strand decreased and the percentage teaching skills from the Data Analysis and Probability strand was unchanged. In addition, a systematic evaluation of the studies' instructional components found evidence to support the use of systematic instruction, in vivo instruction, system of least prompts strategy, constant time delay strategy, and task-analytic instruction as evidence-based practices for teaching mathematics to learners with significant cognitive disabilities. Implications for practice include the use of systematic instruction and in vivo procedures, the need for practitioners to have a deep understanding of mathematics, and the importance of relevancy when teaching a variety of mathematics skills.

Abstract

Background and purpose: The purpose of the article is to analyse results of entrance exams and of regularly exams for foreign students in the Czech language undergraduate study programs at four faculties of University of Economics, Prague (UEP) with the intention to investigate the dependency between the results of Entrance exams from English and mathematics and (1) results of regularly exams during the study and between (2) completion rate of the study.

Design/Methodology/Approach: We have analysed 4.381 records for applicants from foreign countries who applied for studies between years 2009 and 2015. We used standard statistics methods and the method of logistic regression in the form of logit model.

Results: We identified weak statistical correlation between entrance exam results from mathematics and results of regular exams. The correlation coefficient varies between 0.078 – 0.283 for investigated faculties of UEP. The same indicator for English language exams presents better values and it varies between 0.218 – 0.312. If an entrance exam result is higher by one point, the probability of successful completion of studies is multiplied by values between 1.017 - 1.042 for individual faculty per one additional point.

Conclusion: The results of the research in mathematics and English language show that excellent results in entrance exam cannot not guarantee successful regularly exams. Conclusion for the probability of completing studies is that the acceptable level of points for admission foreign students is between 150 and 170 points, depending on the faculty.

AbstractWe determined the relative importance of the so‐called approximate number system (ANS), symbolic number comparison (SNC) and verbal and spatial short‐term and working memory (WM) capacity for mathematics achievement in 1,254 Grade 2, 4 and 6 children. The large sample size assured high power and low false report probability and allowed us to determine effect sizes precisely. We used reading decoding as a control outcome measure to test whether findings were specific to mathematics. Bayesian analysis allowed us to provide support for both null and alternative hypotheses. We found very weak zero‐order correlations between ANS measures and math achievement. These correlations were not specific to mathematics, became non‐significant once intelligence was considered and ANS measures were not selected as predictors of math by regression models. In contrast, overall SNC accuracy and spatial WM measures were reliable and mostly specific predictors of math achievement. Verbal short‐term and WM and SNC reaction time were predictors of both reading and math achievement. We conclude that ANS tasks are not suitable as measures of math development in school‐age populations. In contrast, all other cognitive functions we studied are promising markers of mathematics development.

Book reviewed in this article:An introduction to mathematics for students of economics, J. Parry LewisIntroduction to Probability and Statistics, B. W. Lindgren and G. W. McElrathStatistical Theory and Methodology in Science and Engineering, K. A. BrownleeInformation and Decision Processes, edited by R. E. MacholDynamic Programming and Markov Processes, Ronald A. HowardDe bedrijfsleiders in de Belgische economie, door P. Mandy, G. de Ghellinck, P. Duvie usart o.l.v. Michel WoitrinInleiding tot de Sociale Statirtiek I, H. Rijkenvan Olst