Notes for a history of the teaching of algebra

Abundant literature is available on the history of algebra. However, the history of the teaching of algebra is largely unwritten, and as such, this chapter essentially constitutes some notes that are intended to be useful for future research on this subject. As well as the scarcity of the works published on the topic, there is the added difficulty of drawing the line between the teaching of algebra and the teaching of arithmetic—two branches of knowledge whose borders have varied over time (today one can consider the arithmetic with the four operations and their algorithms and properties taught in schools as nothing more than a small chapter of algebra). As such, we will be very brief in talking about the more distant epochs, from which we have some mathematics documents but little information on how they were used in teaching. We aim to be more explicit as we travel forwards into the different epochs until modern times. We finish, naturally, with some reflections on the present-day and future situation regarding the teaching of algebra.info:eu-repo/semantics/publishedVersio

The Texas Mathematics Teachers' Bulletin, Volume XI, No. 1, edited by C.D. Rice

CONTENTS: Foreword by Editor (p.5) -- Algebra by T. U. Taylor (p.7) -- The Transition from High School to College by C. D. Rice (p.9) -- Learning to Talk by J. W. Calhoun (p.12) -- To Prospective Secondary School Teachers From Brown University (p.14) -- The German Gymnasium by C.D. Rice (p.16

Training in the technique of study

Bibliography: p. 57-66

Galois Got his Gun

This paper appeals to the figure of \'Evariste Galois for investigating the gates between mathematics and their "publics." The figure of Galois draws some lines of/within mathematics for/from the outside of mathematics and these lines in turn sketch the silhouette of Galois as a historical figure. The present paper especially investigates the collective categories that have been used in various types of public discourses on Galois's work (e.g. equations, groups, algebra, analysis, France, Germany etc.). In a way, this paper aims at shedding light on the boundaries some individuals drew by getting Galois his gun. It is our aim to highlight the roles of authority some individuals (such as as Picard) took on in regard with the public figure of Galois as well as the roles such authorities assigned to other individuals (such as the mediating role assigned to Jordan as a mediator between Galois's "ideas" and the public). The boundary-works involved by most public references to Galois have underlying them a long-term tension between academic and public legitimacies in the definition of some models for mathematical lives (or mathematics personae

Task-Specific Experience and Task-Specific Talent: Decomposing the Productivity of High School Teachers

We use administrative panel data to decompose worker performance into components relating to general talent, task-specific talent, general experience, and task-specific experience. We consider the context of high school teachers, in which tasks consist of teaching particular subjects in particular tracks. Using the timing of changes in the subjects and levels to which teachers are assigned to provide identifying variation, we show that much of the productivity gains to teacher experience estimated in the literature are actually subject-specific. By contrast, very little of the variation in the permanent component of productivity among teachers is subject-specific or level-specific. Counterfactual simulations suggest that maximizing the value of task-specific experience could produce nearly costless efficiency gains on the order of .02 test score standard deviations

‘Walking in a Foreign and Unknown Landscape’ : studying the history of mathematics in initial teacher education

This article develops the argument that students in initial teacher education benefit in terms of who they are becoming from developing awareness of and engagement in the history of mathematics. Initially, current school mathematics practices in the UK are considered and challenged. Then the role of teachers’ relationship to mathematical subject knowledge and of teachers’ engagement in critical thinking are considered. Connections are made between these concerns and studying the history of mathematics in initial teacher education classrooms. I then draw on the perspectives and practices of the mathematics teacher educators at one institution to understand these connections better and to exemplify them. Issues of equity are threaded throughout

Augustus De Morgan and the development of university mathematics in London in the nineteenth century.

This thesis investigates the teaching of mathematics at university level in London, and in particular by Augustus De Morgan (1806-1871) during his period as founder professor of mathematics at London University (later University College London) from 1828 to 1867. An examination of De Morgan's life and professorial career is followed by a review of changes in instruction at the college under his successors, together with a survey of higher mathematical tuition at other university-level institutions in the capital up to the turn of the twentieth century. Particular attention is paid to original teaching material and the set of students who later achieved distinction in mathematics and other disciplines. A key feature of the research undertaken for this project has been its intensive use of previously unpublished archival documents, hitherto mostly unstudied. Consequently, much of the information which has been gleaned from these sources (such as De Morgan's lecture material, student notes and contemporary correspondence) has never appeared in print before. The data thus derived has been used in conjunction with publications from the period, as well as more recent works, to produce a contribution to the history of mathematical education which gives a more complete picture of how well nineteenth-century London was served for mathematical instruction than was previously available. Previous studies of De Morgan have mainly concentrated on his work in algebra and logic, with little or no reference to his mathematical teaching, while published histories of relevant institutions (e. g. University College, University of London) are similarly localised, with few comparisons being drawn with other bodies, and almost no reference to mathematical tuition. By concentrating on the work of De Morgan as a teacher in the context of London mathematics, this thesis will attempt to fill these two important gaps in the literature