AN INVESTIGATION INTO CHILDREN'S UNDERSTANDING OF THE ORDER OF OPERATIONS

An investigation into children’s understanding of the order of operations This thesis reports on the findings of an international study into the way in which children approach calculations which involve the order of operations. The study involved 203 pupils aged between 12 to 14 years from four different countries: England, The USA (New York State), Japan and The Netherlands. Many pupils in England are taught to use mnemonics such as BODMAS or BIDMAS to remember the correct order of operations, and in the USA pupils are often taught to use PEMDAS. However in Japan and The Netherlands these methods are not used, and the approach to teaching mathematics differs considerably across the countries. In this study pupils from classes in these four countries have been given calculations to perform and their work has been analysed for misconceptions. The analysis of their work has involved use of the Key Recorder software as a data collection tool, in which the pupils’ calculator keystrokes have been recorded and played back to give a unique insight into their thinking. Analysis of the children’s work has resulted in the categorisation of the misconceptions that were observed, and suggests that the nature of the mathematics curriculum and the teaching methods employed may have a significant effect on the way in which children approach calculations of this sort

Upon Aeschylus—I

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The Procedure of the Gortynian Inscription

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Methods of Early Church History

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Wright on the Date of Cylon The Date of Cylon, by John Henry Wright. Reprinted from the 'Harvard Studies in Classical Philology.' Boston : U.S.A. Ginn and Co. 1892. (80 pp.)

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Disseminated bacillus Calmette-Guérin (BCG): a cause of delirium in an older adult

Intra-vesical Bacillus Calmette-Guérin (BCG) immunotherapy is an effective treatment for high-risk bladder cancer. Less well known is that fewer than 1% of patients receiving BCG treatment can develop disseminated BCG. The reaction can range from a mild flu-like illness to a systemic disorder with a fulminant course which in the most severe cases can lead to death. The diagnostic yield is low and diagnosis is often made after a comprehensive exclusion of more common causes of pyrexia of unknown origin. A high level of suspicion is therefore required in those who may be at risk. We report a case of disseminated BCG in an older patient for whom early involvement of his family was pertinent to determining the precipitant for delirium

Accidental Politicians: How Randomly Selected Legislators Can Improve Parliament Efficiency

We study a prototypical model of a Parliament with two Parties or two Political Coalitions and we show how the introduction of a variable percentage of randomly selected independent legislators can increase the global efficiency of a Legislature, in terms of both the number of laws passed and the average social welfare obtained. We also analytically find an "efficiency golden rule" which allows to fix the optimal number of legislators to be selected at random after that regular elections have established the relative proportion of the two Parties or Coalitions. These results are in line with both the ancient Greek democratic system and the recent discovery that the adoption of random strategies can improve the efficiency of hierarchical organizations.Comment: 19 pages, 7 figures, new improved and longer versio