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  1. added 2020-04-20
    Essay on Machines in General (1786) Text, Translations and Commentaries. Lazare Carnot's Mechanics - Volume 1.Raffaele Pisano, Jennifer Coopersmith & Murray Peake - forthcoming - Springer.
    This book offers insights relevant to modern history and epistemology of physics, mathematics and, indeed, to all the sciences and engineering disciplines emerging of 19th century. This research volume is the first of a set of three Springer books on Lazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines in General (Essai sur les machines en général [1783] 1786). The other two forthcoming volumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) and Géométrie de position (1803). Lazare Carnot (...)
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  2. added 2020-03-31
    Berkeley: El origen de la crítica a los infinitesimales / Berkeley: The Origin of his Critics to Infinitesimals.Alberto Luis López - 2014 - Cuadernos Salmantinos de Filosofía 41 (1):195-217.
    BERKELEY: THE ORIGIN OF CRITICISM OF THE INFINITESIMALS Abstract: In this paper I propose a new reading of a little known George Berkeley´s work Of Infinites. Hitherto, the work has been studied partially, or emphasizing only the mathematical contributions, downplaying the philosophical aspects, or minimizing mathematical issues taking into account only the incipient immaterialism. Both readings have been pernicious for the correct comprehension of the work and that has brought as a result that will follow underestimated its importance, and therefore (...)
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  3. added 2020-03-20
    Ancient Greek Geometry of Motion and its Further Development by Galileo and Newton.Mario Bacelar Valente - manuscript
    in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...)
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  4. added 2020-03-20
    On the Correctness of Ancient Mathematical Procedure Texts.Mario Bacelar Valente - manuscript
    It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts. We (...)
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  5. added 2020-03-20
    From Practical to Pure Geometry and Back.Mario Bacelar Valente - manuscript
    The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...)
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  6. added 2020-02-14
    Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D'Alessandro - 2020 - Synthese:1-44.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
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  7. added 2020-01-04
    Deleuze on Leibniz : Difference, Continuity, and the Calculus.Daniel W. Smith - 2005 - In Current Continental Theory and Modern Philosophy. Northwestern University Press.
  8. added 2019-12-11
    Non-Euclidean Geometry and Weierstrassian Mathematics.Thomas Hawkins - 1983 - In Joseph Warren Dauben & Virginia Staudt Sexton (eds.), History and Philosophy of Science: Selected Papers. New York Academy of Sciences.
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  9. added 2019-11-21
    Cultivating the Herb Garden of Scandinavian Mathematics: The Congresses of Scandinavian Mathematicians, 1909-1925.Laura E. Turner & Henrik Kragh Sørensen - 2013 - Centaurus 55 (4):385-411.
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  10. added 2019-11-21
    Abel and His Mathematics in Contexts.Henrik Kragh Sørensen - 2002 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 10 (1-3):137-155.
    200 years ago, on August 5, 1802, Niels Henrik Abel was born on Finnøy near Stavanger on the Norwegian west coast. During a short life span, Abel contributed to a deep transition in mathematics in which concepts replaced formulae as the basic objects of mathematics. The transformation of mathematics in the 1820s and its manifestation in Abel’s works are the themes of the author’s PhD thesis. After sketching the formative instances in Abel’s well-known biography, this article illustrates two aspects of (...)
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  11. added 2019-10-03
    On Archimedes’ Statics.Mario Bacelar Valente - forthcoming - Theoria. An International Journal for Theory, History and Foundations of Science.
    Archimedes’ statics is considered as an example of ancient Greek applied mathematics; it is even seen as the beginning of mechanics. Wilbur Knorr made the case regarding this work, as other works by him or other mathematicians from ancient Greece, that it lacks references to the physical phenomena it is supposed to address. According to Knorr, this is understandable if we consider the propositions of the treatise in terms of purely mathematical elaborations suggested by quantitative aspects of the phenomena. In (...)
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  12. added 2019-07-15
    The Concept of “Character” in Dirichlet’s Theorem on Primes in an Arithmetic Progression.Jeremy Avigad & Rebecca Morris - 2014 - Archive for History of Exact Sciences 68 (3):265-326.
    In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.
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  13. added 2019-06-06
    Forms of Mathematization.Sophie Roux - 2010 - Early Science and Medicine 15 (4-5):319-337.
    According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. When this grand narrative was brought into question, our perspectives on the question of mathematization should have changed. It seems, however, that they were instead set aside, both because of a general distrust towards sweeping narratives that are always subject to the suspicion that they overlook the unyielding complexity of real history, (...)
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  14. added 2019-06-06
    Joan Weiner. Frege Explained: From Arithmetic to Analytic Philosophy. Chicago: Open Court, 2004. Pp. Xvi + 179. ISBN 0-8126-9460-0. [REVIEW]Michael Beaney - 2007 - Philosophia Mathematica 15 (1):126-128.
    This book is an expanded version of Joan Weiner's introduction to Frege's work in the Oxford University Press ‘Past Masters’ series published in 1999. The earlier book had chapters on Frege's life and character, his basic project, his new logic, his definitions of the numbers, his 1891 essay ‘Function and concept’, his 1892 essays ‘On Sinn and Bedeutung’ and ‘On concept and object’, the Grundgesetze der Arithmetik and the havoc wreaked by Russell's paradox, and a final brief chapter on Frege's (...)
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  15. added 2019-06-06
    Reinhard Siegmund-Schultze, Rockefeller and the Internationalization of Mathematics Between the Two World Wars: Documents and Studies for the Social History of Mathematics in the 20th Century. Science Networks – Historical Studies, 25. Basel, Boston and Berlin: Birkhäuser Verlag, 2001. Pp. XIII+341. Isbn 3-7643-6468-8. $94.95. [REVIEW]Jon Agar - 2003 - British Journal for the History of Science 36 (1):87-127.
  16. added 2019-06-06
    The Way of Logic Into Mathematics.Volker Peckhaus - 1997 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 12 (1):39-64.
    Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical omnibus discipline logic into new philosophical subdisciplines and separate disciplines such as psychology, epistemology, philosophy of science, and formal logic. In the 19th century a growing foundational need in mathematics provoked the emergence of a structural view on mathematics and the reformulation of logic for mathematical means. As a result formallogic (...)
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  17. added 2019-06-06
    The Imperialist Space of Elizabethan Mathematics.Amir Alexander - 1995 - Studies in History and Philosophy of Science Part A 26 (4):559-591.
    The structural and magnetic properties of Y(Fe1-xMnx)12 compounds and their nitrides (x = 0.2 and 0.4) have been studied by using X-ray diffraction and magnetic measurements. It is found that the lattice parameters increase, while the saturation magnetization and Curie temperature decrease with Mn content increment in Y(Fe1-xMnx12 compounds. Y(Fe0.8Mn0.2)12 compound shows a weak easy-c axis magnetization direction, but Y(Fe0.6Mn0.4)12 compound is in a paramagnetic state at room temperature. Upon nitrogenation, the lattice parameters, Curie temperature are notably increased and the (...)
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  18. added 2019-06-06
    Strategies for Conceptual Change: Ratio and Proportion in Classical Greek Mathematics.Paul Rusnock & Paul Thagard - 1995 - Studies in History and Philosophy of Science Part A 26 (1):107-131.
    …all men begin… by wondering that things are as they are…as they do about…the incommensurability of the diagonal of the square with the side; for it seems wonderful to all who have not yet seen the reason, that there is a thing which cannot be measured even by the smallest unit. But we must end in the contrary and, according to the proverb, the better state, as is the case in these instances too when men learn the cause; for there (...)
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  19. added 2019-06-06
    P. M. Harman . Wranglers and Physicists. Studies on Cambridge [Mathematical] Physics in the Nineteenth Century. Manchester: Manchester University Press, 1985. Pp. Viii + 261. ISBN 0-7190-1756-4. £27.50. [REVIEW]Frank James - 1987 - British Journal for the History of Science 20 (2):233-234.
  20. added 2019-06-05
    Exploring Predicativity.Laura Crosilla - 2018 - In Klaus Mainzer, Peter Schuster & Helmut Schwichtenberg (eds.), Proof and Computation. World Scientific. pp. 83-108.
    Prominent constructive theories of sets as Martin-Löf type theory and Aczel and Myhill constructive set theory, feature a distinctive form of constructivity: predicativity. This may be phrased as a constructibility requirement for sets, which ought to be finitely specifiable in terms of some uncontroversial initial “objects” and simple operations over them. Predicativity emerged at the beginning of the 20th century as a fundamental component of an influential analysis of the paradoxes by Poincaré and Russell. According to this analysis the paradoxes (...)
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  21. added 2019-06-05
    Paul Erickson. The World the Game Theorists Made. Chicago: University of Chicago Press, 2015. Pp. 384. $35.00.Philip Mirowski - 2017 - Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (1):160-163.
  22. added 2019-06-05
    Snezana Lawrence and Mark McCartney, Eds. Mathematicians and Their Gods: Interactions Between Mathematics and Religious Beliefs. Oxford: Oxford University Press, 2015. Pp. Vi+298, Index. $44.95. [REVIEW]Madeline Muntersbjorn - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):333-336.
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  23. added 2019-06-05
    The History of Mathematics. Joseph E. Hofmann, Frank Gaynor, Henrietta P. Midonick.Edward A. Maziarz - 1959 - Philosophy of Science 26 (4):378-379.
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  24. added 2019-04-26
    Abstraction and Intuition in Peano's Axiomatizations of Geometry.Davide Rizza - 2009 - History and Philosophy of Logic 30 (4):349-368.
    Peano's axiomatizations of geometry are abstract and non-intuitive in character, whereas Peano stresses his appeal to concrete spatial intuition in the choice of the axioms. This poses the problem of understanding the interrelationship between abstraction and intuition in his geometrical works. In this article I argue that axiomatization is, for Peano, a methodology to restructure geometry and isolate its organizing principles. The restructuring produces a more abstract presentation of geometry, which does not contradict its intuitive content but only puts it (...)
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  25. added 2019-02-27
    Religion and Ideological Confrontations in Early Soviet Mathematics: The Case of P.A. Nekrasov.Dimitris Kilakos - 2018 - Almagest 9 (2):13-38.
    The influence of religious beliefs to several leading mathematicians in early Soviet years, especially among members of the Moscow Mathematical Society, had drawn the attention of militant Soviet marxists, as well as Soviet authorities. The issue has also drawn significant attention from scholars in the post-Soviet period. According to the currently prevailing interpretation, reported purges against Moscow mathematicians due to their religious inclination are the focal point of the relevant history. However, I maintain that historical data arguably offer reasons to (...)
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  26. added 2019-02-24
    Mathematics, Core of the Past and Hope of the Future.James Franklin - 2018 - In Catherine A. Runcie & David Brooks (eds.), Reclaiming Education: Renewing Schools and Universities in Contemporary Western Society. Sydney, Australia: Edwin H. Lowe Publishing. pp. 149-162.
    Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it has become (...)
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  27. added 2018-11-26
    The Invariant Twins.Michael Meo - 2008 - Metascience 17 (1):27-32.
    Two recently published scholarly biographies of leading nineteenth-century British mathematicians, pioneers in abstract algebra and personal friends, provide an informed comparison of their lives and work.
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  28. added 2018-09-28
    A Life in Science, Philosophy, and the Public Domain: Three Biographies of PoincaréJeremy J. Gray. Henri Poincaré: A Scientific Biography. Princeton, NJ: Princeton University Press, 2013. Pp. Xii+592. $35.00/£24.95 .Ferdinand Verhulst. Henri Poincaré: Impatient Genius. New York: Springer, 2012. Pp. Xi+260. $49.95 ; $39.95 .Jean-Marc Ginoux and Christian Gerini. 2012. Henri Poincaré: Une Biographie au Quotidien. Paris: Ellipses, 2012. Pp. Iv+298. €24.00 . [Henri Poincaré: A Biography Through the Daily Papers. Singapore: World Scientific, 2013. Pp. 260. $29.00 ; $22.00 .]. [REVIEW]David J. Stump - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):309-318.
  29. added 2018-06-07
    Lautman on Problems as the Conditions of Existence of Solutions.Simon B. Duffy - 2018 - Angelaki 23 (2):79-93.
    Albert Lautman (b. 1908–1944) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that: ‘in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe’ (Lautman 2011, 87). He goes on to characterize this (...)
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  30. added 2018-03-19
    On A.A. Markov’s Attitude Towards Brouwer’s Intuitionism.Ioannis M. Vandoulakis - 2015 - Philosophia Scientae 19:143-158.
    The paper examines Andrei A. Markov’s critical attitude towards L.E.J. Brouwer’s intuitionism, as is expressed in his endnotes to the Russian translation of Heyting’s Intuitionism, published in Moscow in 1965. It is argued that Markov’s algorithmic approach was shaped under the impact of the mathematical style and values prevailing in the Petersburg mathematical school, which is characterized by the proclaimed primacy of applications and the search for rigor and effective solutions.
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  31. added 2018-02-17
    Interpreting Gödel: Critical Essays.Juliette Kennedy (ed.) - 2014 - Cambridge: Cambridge University Press.
    The logician Kurt Gödel published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and (...)
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  32. added 2018-02-17
    "Mathesis of the Mind": A Study of Fichte’s Wissenschaftslehre and Geometry.David W. Wood - 2012 - New York/Amsterdam: Editions Rodopi (Brill Publishers). Fichte-Studien-Supplementa Vol. 29.
    This is an in-depth study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that (...)
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  33. added 2018-01-08
    Discours de la methode pour bien conduire sa raison & chercher la verité dans les sciences. Plus La dioptrique. Les meteores. Et La geometrie. Qui sont des essais de cete methode.René Descartes - 1637 - Leiden: Jan Maire.
  34. added 2017-07-07
    Whitehead and Pythagoras.Arran Gare - 2006 - Concrescence 7:3 - 19.
    While the appeal of scientific materialism has been weakened by developments in theoretical physics, chemistry and biology, Pythagoreanism still attracts the allegiance of leading scientists and mathematicians. It is this doctrine that process philosophers must confront if they are to successfully defend their metaphysics. Peirce, Bergson and Whitehead were acutely aware of the challenge of Pythagoreanism, and attempted to circumvent it. The problem addressed by each of these thinkers was how to account for the success of mathematical physics if the (...)
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  35. added 2017-03-16
    Die Entstehung des Tensorkalkuls: Von den Anfangen in der Elastizitatstheorie Bis Zur Verwendung in der BaustatikDieter Herbert. [REVIEW]Renatus Ziegler - 1994 - Isis 85 (1):178-179.
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  36. added 2017-02-17
    La Logique Symbolique En Débat À Oxford À la Fin du XIXe Siècle : Les Disputes Logiques de Lewis Carroll Et John Cook Wilson.Mathieu Marion & Amirouche Moktefi - 2014 - Revue D’Histoire des Sciences 67 (2):185-205.
    The development of symbolic logic is often presented in terms of a cumulative story of consecutive innovations that led to what is known as modern logic. This narrative hides the difficulties that this new logic faced at first, which shaped its history. Indeed, negative reactions to the emergence of the new logic in the second half of the nineteenth century were numerous and we study here one case, namely logic at Oxford, where one finds Lewis Carroll, a mathematical teacher who (...)
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  37. added 2017-02-17
    The Interplay Between Mathematical Practices and Results.Mélissa Arneton, Amirouche Moktefi & Catherine Allamel-Raffin - 2014 - In Léna Soler, Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost (eds.), Science After the Practice Turn in the Philosophy, History, and Social Studies of Science. New York - London: Routledge. pp. 269-276.
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  38. added 2017-02-15
    Review of Gabriele Lolli, Numeri. La creazione continua della matematica. [REVIEW]Longa Gianluca - 2016 - Lo Sguardo. Rivista di Filosofia 21 (II):377-380.
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  39. added 2017-02-15
    Second-Order Models of Students' Mathematics: Delving Into Possibilities.T. Dooley - 2014 - Constructivist Foundations 9 (3):346-348.
    Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I look at the different possibilities offered by the trajectory of second-order models in mathematics education. It seems to me that although possibilities are extended as models become more elaborate, this is only the case if teacher/researchers remain cognisant of a radical constructivist perspective. I also suggest that broad-ranging research on the models affords (...)
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  40. added 2017-02-15
    The Teacher as Mathematician: Problem Solving for Today's Social Context.Holly Brewster - unknown
    A current trend in social justice oriented education research is the promotion of certain intellectual virtues that support epistemic responsibility, or differently put, the dispositions necessary to be a good knower. On the surface, the proposition of epistemically responsible teaching, or teaching students to be responsible knowers is innocuous, even banal. In the mathematics classroom, however, it is patently at odds with current practice and with the stated goals of mathematics education. This dissertation begins by detailing the extant paradigm in (...)
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  41. added 2017-02-15
    Postmodern Mathematics Education: Script For Animated Movie Discussion.Paul Ernest & Allan Tarp - 2013 - Philosophy of Mathematics Education Journal 27.
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  42. added 2017-02-15
    The Scope and Limits of Critical Mathematics Education.Paul Ernest - 2010 - Philosophy of Mathematics Education Journal 25.
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  43. added 2017-02-15
    A Well-Grounded Education: The Role of Perception in Science and Mathematics.Robert Goldstone, David Landy & Son & Y. Ji - 2008 - In Manuel de Vega, Arthur Glenberg & Arthur Graesser (eds.), Symbols and Embodiment: Debates on Meaning and Cognition. Oxford University Press.
  44. added 2017-02-15
    Deconstructing the Scholarly Literature on Gender Differentials in Mathematics Education: Implications for Research on Girls Learning Mathematics in Botswana.Alakanani Nkhwalume - 2007 - Philosophy of Mathematics Education Journal 20.
  45. added 2017-02-15
    What has Power Got to Do with Mathematics Education?Paola Valero - 2007 - Philosophy of Mathematics Education Journal 21.
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  46. added 2017-02-15
    Supporting a Discourse About Incommensurable Theoretical Perspectives in Mathematics Education.Paul Cobb - 2006 - Philosophy of Mathematics Education Journal 19.
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  47. added 2017-02-15
    Early Mathematics Education.Stephen Campbell - 2002 - Philosophy of Mathematics Education Journal 15.
  48. added 2017-02-15
    The Question of Knowing Others: Doing Research in Mathematics Education.Margaret Walshaw - 2001 - Philosophy of Mathematics Education Journal 14.
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  49. added 2017-02-15
    Towards a Philosophy of Critical Mathematics Education. [REVIEW]Paul Ernest - 1996 - Philosophy of Mathematics Education Journal 9.
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  50. added 2017-02-15
    Is 'the Discipline Of Noticing' A New Paradigm For Research In Mathematics Education?Paul Ernest - 1995 - Philosophy of Mathematics Education Journal 8.
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