An investigation of pedagogical techniques in Descartes' La géométrie

Bibliography

• Aspinwall , L , Haciomeroglu , E S and Presmeg , N C . ‘Students’ verbal descriptions that support visual and analytic thinking in calculus’, in O Figueras, J Cortina, S Alatorre, T Rojano, and A Sepulveda (eds), Proceedings of the joint meeting of the 32nd conference of the International Group for the Psychology of Mathematics Education. Morelia, Michoacán, Mexico: PME, 2008
   Google Scholar
• Bashmakova , I G , Smirnova , G S and Shenitzer , A . 1999 . The literal calculus of Viète and Descartes . The American Mathematical Monthly , 106 : 260 – 263 .
   Google Scholar
• Beck , L J . 1952 . The method of Descartes: a study of the regulae , Clarendon Press .
   Google Scholar
• Boyer , C B . 1959 . Descartes and the geometrization of algebra . The American Mathematical Monthly , 66 : 390 – 393 .
   Google Scholar
• Brown , T M . ‘Descartes, René du Perron’, in Dictionary of scientific biography, C C Gillispie (ed), vol IV, Charles Scribner's Sons, 1971, 51–65
   Google Scholar
• Common Core State Standards Initiative, Common core state standards for mathematics, http://corestandards.org/assets/CCSSI_Math%20Standards.pdf. Accessed on 1 May 2011
   Google Scholar
• Cooney , T J . 1985 . A beginning teacher's view of problem solving . Journal for Research in Mathematics Education , 16 : 324 – 336 .
   Google Scholar
• Cubberley , E P . 1920 . Readings in the history of education: a collection of sources and readings to illustrate the development of educational practice, theory, and organization , Cambridge, MA : Riverside Press .
   Google Scholar
• Dennis , D . 1997 . Rene Descartes curve-drawing devices: experiments in the relations between mechanical motion and symbolic language . Mathematics Magazine , 70 : 163 – 174 .
   Google Scholar
• Descartes, R, ‘Rules for the direction of the mind’, (trans E Anscombe and P T Geach, 1954a), Wikisource, http://en.wikisource.org/wiki/Rules_for_the_Direction_of_the_Mind. Accessed on 6 April 2010
   Google Scholar
• Descartes , R . The geometry of René Descartes with a facsimile of the first edition, (trans D E Smith and M L Latham), Dover Publications, 1954b (original work published 1637)
   Google Scholar
• Descartes , R . Discours de la méthode/Discourse on the method: a bilingual edition with an interpretive essay. (G Heffernan, ed and trans), Notre Dame, Indiana: University of Notre Dame Press, 1994 (original work published 1637)
   Google Scholar
• Devlin , K . 1996 . Good-bye Descartes? . Mathematics Magazine , 69 : 344 – 349 .
   Google Scholar
• Drake , F D and Brown , S D . 2003 . A systematic approach to improve students' historical thinking . The History Teacher , 36 : 465 – 489 .
   Google Scholar
• Farmer , J D . 2000 . Geometric series Descartes, and the fundamental theorem of calculus . The Mathematical Gazette , 84 : 227 – 231 .
   Google Scholar
• Florida Department of Education, Next generation sunshine state standards, http://www.floridastandards.org. Accessed on 1 May 2011
   Google Scholar
• Go , J . 2000 . “ Response to John W Padberg ” . In The Jesuit ratio studiorum: 400th anniversary perspectives , Edited by: Duminuco , V J . 101 – 106 . Fordham University Press .
   Google Scholar
• Gordon , B W , Yunker , L E , Crosswhite , F J and Vannatta , G D . 1997 . Advanced mathematical concepts: precalculus with applications Glencoe
   Google Scholar
• Grabiner , J V . 1988 . The centrality of mathematics in the history of western thought . Mathematics Magazine , 61 : 220 – 230 .
   Google Scholar
• Grabiner , J . 1995 . Descartes and problem-solving . Mathematics Magazine , 68 : 83 – 97 .
   Google Scholar
• Grosholz , E R . 1980 . “ Descartes' unification of algebra and geometry ” . In Descartes: philosophy, mathematics and physics , Edited by: Gaukroger , S . 156 – 168 . Harvester Press .
   Google Scholar
• Krüger , J . 2010 . Lessons from the early seventeenth century for mathematics curriculum design . BSHM Bulletin , 25 : 144 – 161 .
   Google Scholar
• Larson , R , Boswell , L , Kanold , T D and Stiff , L . 2007 . Algebra 2 , Evanston : McDougal Littell .
   Google Scholar
• Lenoir , T . 1979 . Descartes and the geometrization of thought: the methodological background of Descartes' Géométrie . Historia Mathematica , 6 : 355 – 379 .
   Google Scholar
• Mahoney , M S . ‘The beginnings of algebraic thought in the seventeenth century’, in Descartes: philosophy, mathematics and physics, S Gaukroger (ed), Harvester Press, 1980, 141–155
   Google Scholar
• Meo , S L . 2000 . In their own eyes: using journals with primary sources with college students . The History Teacher , 33 : 335 – 341 .
   Google Scholar
• Moorman , R H . 1943 . The influence of mathematics on the philosophy of Descartes . National Mathematics Magazine , 17 : 296 – 307 .
   Google Scholar
• Serra , M . 2008 . Discovering geometry: an investigative approach , 4 , Key Curriculum Press .
   Google Scholar
• Shulman , L S . 1986 . Those who understand: knowledge growth in teaching . Educational Researcher , 15 : 4 – 14 .
   Google Scholar
• Smolarski , D C . 2002 . Teaching mathematics in the seventeenth and twenty-first centuries . Mathematics Magazine , 75 : 256 – 262 .
   Google Scholar
• Society of Jesus . 1970 . The Jesuit ratio studiorum of 1599, trans A P Farrell, S J , Conference of Major Superiors of Jesuits, http://bc.edu/sites/libraries/ratio/ratio1599.pdf. Accessed on 1 May 2011
   Google Scholar
• Tall , D . 2003 . “ Using technology to support an embodied approach to learning concepts in mathematics ” . In Historia e tecnologia no ensino de matemática , Edited by: Carvalho , L M and Guimaraes , L C . 1 – 28 . Rio de Janiero : Brazil .
   Google Scholar
• Zodik , I and Zaslavsky , O . 2008 . Characteristics of teachers choice of examples in and for the mathematics classroom . Educational Studies in Mathematics , 69 : 165 – 182 .
   Google Scholar