Outils pour utilisateurs

Outils du site


mathematiques:start

Différences

Ci-dessous, les différences entre deux révisions de la page.

Lien vers cette vue comparative

Les deux révisions précédentesRévision précédente
Prochaine révision
Révision précédente
mathematiques:start [2021/01/12 11:23] villersdmathematiques:start [2023/07/30 19:01] (Version actuelle) – [Références diverses] villersd
Ligne 12: Ligne 12:
     * Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C.-N. (in press). A randomized controlled trial of interleaved practice. Journal of Educational Psychology, 107, 900-908. DOI: /10.1037/edu0000367 [[http://uweb.cas.usf.edu/%7Edrohrer/pdfs/Rohrer_et_al_InPressJEdPsych.pdf|PDF]] + [[http://uweb.cas.usf.edu/%7Edrohrer/pdfs/Interleaved_Mathematics_Practice_Guide.pdf|Interleaved Mathematics Practice Guide]]     * Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C.-N. (in press). A randomized controlled trial of interleaved practice. Journal of Educational Psychology, 107, 900-908. DOI: /10.1037/edu0000367 [[http://uweb.cas.usf.edu/%7Edrohrer/pdfs/Rohrer_et_al_InPressJEdPsych.pdf|PDF]] + [[http://uweb.cas.usf.edu/%7Edrohrer/pdfs/Interleaved_Mathematics_Practice_Guide.pdf|Interleaved Mathematics Practice Guide]]
   * [[https://www.understood.org/en/school-learning/for-educators/teaching-strategies/evidence-based-math-instruction-for-struggling-students|Evidence-Based Math Instruction for Struggling Students]], Kim Greene, Reviewed by Daniel Ansari, september 2019 → Best Practices for Math Teaching   * [[https://www.understood.org/en/school-learning/for-educators/teaching-strategies/evidence-based-math-instruction-for-struggling-students|Evidence-Based Math Instruction for Struggling Students]], Kim Greene, Reviewed by Daniel Ansari, september 2019 → Best Practices for Math Teaching
 +  * [[https://www.thescienceofmath.com/|Science of Math]], a movement focused on using objective evidence about how students learn math in order to make educational decisions and to inform policy and practice. 
  
 ===== Enseignement primaire ===== ===== Enseignement primaire =====
 +  * [[https://irem.univ-grenoble-alpes.fr/revues/grand-n/|Grand N]], la revue de mathématiques, sciences et technologie pour les maîtres de l’enseignement primaire
  
 ==== Nombres et dénombrement ==== ==== Nombres et dénombrement ====
Ligne 25: Ligne 27:
 ==== Motivation ==== ==== Motivation ====
   * [[https://onlinelibrary.wiley.com/doi/abs/10.1111/cdev.12458|Intrinsic Motivation and Achievement in Mathematics in Elementary School: A Longitudinal Investigation of Their Association]] Gabrielle Garon‐Carrier, Michel Boivin, Frédéric Guay, Yulia Kovas, Ginette Dionne, Jean‐Pascal Lemelin, Jean R. Séguin, Frank Vitaro, Richard E. Tremblay Child Development Volume87, Issue1 January/February 2016 Pages 165-175 DOI: 10.1111/cdev.12458 [[https://www.researchgate.net/publication/282135309_Intrinsic_Motivation_and_Achievement_in_Mathematics_in_Elementary_School_A_Longitudinal_Investigation_of_their_Association|lien RG]] → "Contrary to the hypothesis that motivation and achievement are reciprocally associated over time, our results point to a directional association from prior achievement to subsequent intrinsic motivation"   * [[https://onlinelibrary.wiley.com/doi/abs/10.1111/cdev.12458|Intrinsic Motivation and Achievement in Mathematics in Elementary School: A Longitudinal Investigation of Their Association]] Gabrielle Garon‐Carrier, Michel Boivin, Frédéric Guay, Yulia Kovas, Ginette Dionne, Jean‐Pascal Lemelin, Jean R. Séguin, Frank Vitaro, Richard E. Tremblay Child Development Volume87, Issue1 January/February 2016 Pages 165-175 DOI: 10.1111/cdev.12458 [[https://www.researchgate.net/publication/282135309_Intrinsic_Motivation_and_Achievement_in_Mathematics_in_Elementary_School_A_Longitudinal_Investigation_of_their_Association|lien RG]] → "Contrary to the hypothesis that motivation and achievement are reciprocally associated over time, our results point to a directional association from prior achievement to subsequent intrinsic motivation"
 +  * [[https://par-temps-clair.blogspot.com/2019/12/attributions-movitation-et-reussite-en.html|Attributions, motivation et réussite en mathématiques]] décembre 29, 2019, Didier Goudeseune
  
 ==== Thèses ==== ==== Thèses ====
Ligne 36: Ligne 39:
   * [[https://www.reseau-canope.fr/notice/mathematiques-les-points-forts-de-lapproche-de-singapour-dans-lenseignement-des-mathematiques-comment-sen-inspirer.html|Mathématiques - Les points forts de l'approche de Singapour dans l'enseignement des mathématiques. Comment s'en inspirer ?]] Monica Neagoy, GMF, Ministère de l'Education nationale et de la Jeunesse, Réseau Canopé, AFINEF- 2019   * [[https://www.reseau-canope.fr/notice/mathematiques-les-points-forts-de-lapproche-de-singapour-dans-lenseignement-des-mathematiques-comment-sen-inspirer.html|Mathématiques - Les points forts de l'approche de Singapour dans l'enseignement des mathématiques. Comment s'en inspirer ?]] Monica Neagoy, GMF, Ministère de l'Education nationale et de la Jeunesse, Réseau Canopé, AFINEF- 2019
   * [[https://onlinelibrary.wiley.com/doi/abs/10.1111/cdev.12458|Intrinsic Motivation and Achievement in Mathematics in Elementary School: A Longitudinal Investigation of Their Association]] Gabrielle Garon‐Carrier, Michel Boivin, Frédéric Guay, Yulia Kovas, Ginette Dionne, Jean‐Pascal Lemelin, Jean R. Séguin, Frank Vitaro, Richard E. Tremblay, Child Development Volume87, Issue1 January/February 2016, Pages 165-175  DOI: 10.1111/cdev.12458 → "Contrary to the hypothesis that motivation and achievement are reciprocally associated over time, our results point to a directional association from prior achievement to subsequent intrinsic motivation. "   * [[https://onlinelibrary.wiley.com/doi/abs/10.1111/cdev.12458|Intrinsic Motivation and Achievement in Mathematics in Elementary School: A Longitudinal Investigation of Their Association]] Gabrielle Garon‐Carrier, Michel Boivin, Frédéric Guay, Yulia Kovas, Ginette Dionne, Jean‐Pascal Lemelin, Jean R. Séguin, Frank Vitaro, Richard E. Tremblay, Child Development Volume87, Issue1 January/February 2016, Pages 165-175  DOI: 10.1111/cdev.12458 → "Contrary to the hypothesis that motivation and achievement are reciprocally associated over time, our results point to a directional association from prior achievement to subsequent intrinsic motivation. "
 +  * [[https://mathies.ca/learningTools.php#Nn1&gsc.tab=0]]
 +  * [[https://fillingthepail.substack.com/p/tessellated-with-good-intentions|Tessellated with good intentions - Jo Boaler and the Data Science takeover]] Greg Ashman, 07/12/2021
  
 ===== Enseignement secondaire ===== ===== Enseignement secondaire =====
 +  * [[https://irem.univ-grenoble-alpes.fr/revues/petit-x/petit-x-365064.kjsp|Petit x]], revue de didactique des mathématiques et d’analyses de pratiques pour l’enseignement secondaire
 +
  
 ==== Divers ==== ==== Divers ====
Ligne 44: Ligne 51:
   * Outils pour la remédiation, la remise à niveau, ...   * Outils pour la remédiation, la remise à niveau, ...
     * [[https://exomath.info.ucl.ac.be/syllabus/functions-series/index.html|Exomath, syllabus,...]], en cours de développement (exos à venir : [[https://uclouvain.be/fr/instituts-recherche/icteam/ingi/exomath.html]])     * [[https://exomath.info.ucl.ac.be/syllabus/functions-series/index.html|Exomath, syllabus,...]], en cours de développement (exos à venir : [[https://uclouvain.be/fr/instituts-recherche/icteam/ingi/exomath.html]])
 +  * [[https://eduscol.education.fr/2485/les-reseaux-academiques-en-mathematiques|Les réseaux académiques en mathématiques]] (France)
 +  * [[https://eduscol.education.fr/251/mathematiques-cycle-3|Ressources d'accompagnement du programme de mathématiques (cycle 3)]] (eduscol, France)
 +    * [[https://eduscol.education.fr/document/32206/download|Les guides fondamentaux pour enseigner - La résolution de problèmes mathématiques au cours moyen]] (janvier 2022)
 +  * [[https://eduscol.education.fr/280/mathematiques-cycle-4|Ressources d'accompagnement du programme de mathématiques (cycle 4)]] (eduscol, France)
 +    * [[https://eduscol.education.fr/document/13132/download|Les guides fondamentaux pour enseigner - La résolution de problèmes mathématiques au collège]] (décembre 2021)
  
 ===== Interdisciplinarité ===== ===== Interdisciplinarité =====
   * avec les enseignants de latin sur les fractions, et les appellations numérateur et dénominateur : "Dans une fraction, le mot numérateur vient du latin "numerator" ("celui qui compte") et le mot dénominateur vient de "denominator" ("celui qui désigne"). Le dénominateur indique donc par combien on partage et le numérateur indique combien de morceaux de ce partage on prend." source : [[https://twitter.com/AnecdotesMaths/status/1291751641583095809]]   * avec les enseignants de latin sur les fractions, et les appellations numérateur et dénominateur : "Dans une fraction, le mot numérateur vient du latin "numerator" ("celui qui compte") et le mot dénominateur vient de "denominator" ("celui qui désigne"). Le dénominateur indique donc par combien on partage et le numérateur indique combien de morceaux de ce partage on prend." source : [[https://twitter.com/AnecdotesMaths/status/1291751641583095809]]
  
 +
 +===== Géométrie dynamique =====
 +  * [[http://www.cnesco.fr/wp-content/uploads/2021/02/210218_Cnesco_Soury-Lavergne_Numerique_Geometrie_dynamique.pdf|La géométrie dynamique pour l’apprentissage et l’enseignement des mathématiques]] Sophie SOURY-LAVERGNE, Institut français de l’éducation ENS Lyon, Université Grenoble Alpes, octobre 2020
  
 ===== Vulgarisation ===== ===== Vulgarisation =====
Ligne 58: Ligne 73:
   * [[https://www.arte.tv/fr/videos/082190-000-A/cedric-villani/|Mathématique de la chauve-souris]], par Cédric Villani (Arte)   * [[https://www.arte.tv/fr/videos/082190-000-A/cedric-villani/|Mathématique de la chauve-souris]], par Cédric Villani (Arte)
   * [[https://www.youtube.com/watch?v=cTYvCpLRwao|The Mathematics of Music (with Vled Tapas) — Science étonnante #41]]   * [[https://www.youtube.com/watch?v=cTYvCpLRwao|The Mathematics of Music (with Vled Tapas) — Science étonnante #41]]
 +  * [[https://www.youtube.com/watch?v=CwqoAVMzgp4|Comment écrire les nombres ayant une infinité de décimales ? - Science Etonnante, 27/08/2021]]
 +
  
 Animations : Animations :
   * [[http://matrixmultiplication.xyz/]] : multiplication matricielle   * [[http://matrixmultiplication.xyz/]] : multiplication matricielle
   * [[https://www.reddit.com/r/educationalgifs/comments/6zxt3q/here_is_why_spacecraft_orbits_almost_look_like/|Here is why spacecraft orbits almost look like sine waves on maps]] + [[https://twitter.com/amazingmap/status/1283432726281019392]]   * [[https://www.reddit.com/r/educationalgifs/comments/6zxt3q/here_is_why_spacecraft_orbits_almost_look_like/|Here is why spacecraft orbits almost look like sine waves on maps]] + [[https://twitter.com/amazingmap/status/1283432726281019392]]
 +  * La trajectoire la plus courte n'est pas nécessairement la plus rapide (rampe, brachistochrone, calcul variuationnel, Johann Bernouilli 1696)) : [[https://curiosamathematica.tumblr.com/post/92414882714/the-brachistochrone-this-animation-is-about-one?utm_content=buffer9b8f4&utm_medium=social&utm_source=twitter.com&utm_campaign=buffer]] + [[https://twitter.com/Rainmaker1973/status/1444340958674423810]]
 +
 +Sur les réseaux sociaux
 +  * Chaînes Youtube :
 +    * [[https://www.youtube.com/c/ElJj42/videos]] → El Jj
 +    * ...
 +  * [[https://mobile.twitter.com/sc_cath/status/1409381185495748608]] (probabilités appliquées)
 +  * [[https://mobile.twitter.com/pickover/status/1404584903283548164]] (sommes binômes, nombres)
 +    * [[https://mobile.twitter.com/linusable/status/1404987710142652416]] → 
 +
 +<blockquote><code>21²+22²+23²+24² = 25²+26²+27²
 +isolating the median term, this is equivalent to :
 +(27²-21²)+(26²-22²)+(25²-23²) = 24²
 +As a²-b² = (a+b)(a-b), we have for LHS :
 +(27+21)(27-21)+(26+22)(26-22)+(25+23)(25-23)
 += 48*6 + 48*4 + 48*2 = 48*(6+4+2) = 48*12
 += (24*2)*12 = 24*(2*12) = 24²
 +</code></blockquote>
 +
 +Livres :
 +  * [[https://www.stevenstrogatz.com/books/infinite-powers|Infinite Powers — Steven Strogatz]]
 +
 +===== Articles généraux =====
 +  * [[https://www.scientificamerican.com/article/a-deep-math-dive-into-why-some-infinities-are-bigger-than-others/|A Deep Math Dive into Why Some Infinities Are Bigger Than Others]] : The size of certain infinite sets has been a mystery. Now, it turns out, each one is different than the next, and they can all be ordered by size - By Martin Goldstern, Jakob Kellner on August 16, 2021, Scientific American
 +
 +
 +===== Curriculum et réformes =====
 +  * international
 +    * [[https://fillingthepail.substack.com/p/a-revolution-in-teaching-methods|A revolution in teaching methods - by Greg Ashman]]
 +    * [[https://fillingthepail.substack.com/p/back-to-the-future-with-discovery|Back to the future with discovery learning - by Greg Ashman]]
 +    * [[https://www.cde.ca.gov/ci/ma/cf/index.asp|Mathematics Framework - Mathematics (CA Dept of Education)]]
 +    * [[https://www.independent.org/news/article.asp?id=13604|Replace the Proposed New California Math Curriculum Framework: News: The Independent Institute]]
 +    * [[https://fillingthepail.substack.com/p/tessellated-with-good-intentions|Tessellated with good intentions - by Greg Ashman]]
 +    * [[https://www.iejme.com/download/designing-mathematics-standards-in-agreement-with-science-13179.pdf|Designing mathematics standards in agreement with science]] Hartman, J. R., Hart, S., Nelson, E. A., & Kirschner, P. A. (2023). International Electronic Journal of Mathematics Education, 18(3), em0739. DOI: 10.29333/iejme/13179 → conclusion : **“Science has discovered that when the brain tries to reason with not-well-memorized information, stringent limits apply. In publications for educators, the importance of automaticity to work around WM limits has been noted since 1996 (Hirsch, 1996). Yet since that time in most states, key K-12 standards have continued to require young students to solve math problems by reasoning in ways science says their brains simply cannot manage.”**
 +
  
  
 ===== Histoire des mathématiques ===== ===== Histoire des mathématiques =====
   * [[https://hist-math.fr/]]   * [[https://hist-math.fr/]]
 +  * Les éléments d'Euclide : 
 +    * [[https://www.c82.net/euclid/]]
 +    * [[https://www.kroneckerwallis.com/product/euclids-elements-completing-oliver-byrnes-work/]], cf [[https://twitter.com/marcmonticelli/status/1171748182243663872?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1171748182243663872%7Ctwgr%5E%7Ctwcon%5Es1_&ref_url=https%3A%2F%2Fwww.kroneckerwallis.com%2Fproduct%2Feuclids-elements-completing-oliver-byrnes-work%2F|Tweet]]
  
  
Ligne 83: Ligne 138:
   * [[https://www.nap.edu/catalog/15269/the-mathematical-sciences-in-2025|The Mathematical Sciences in 2025]] National Research Council. 2013. Washington, DC: The National Academies Press. DOI: 10.17226/15269   * [[https://www.nap.edu/catalog/15269/the-mathematical-sciences-in-2025|The Mathematical Sciences in 2025]] National Research Council. 2013. Washington, DC: The National Academies Press. DOI: 10.17226/15269
   * [[http://capes-math.org/index.php?id=archives|CAPES de Mathématiques - Site du jury du CAPES externe et du CAFEP]]   * [[http://capes-math.org/index.php?id=archives|CAPES de Mathématiques - Site du jury du CAPES externe et du CAFEP]]
 +  * Théorème de Pick et calculs de surfaces ([[https://fr.wikipedia.org/wiki/Théorème_de_Pick]])
 +  * [[https://amiealbrecht.com/2023/07/21/the-shape-of-our-mathematical-beliefs/|The shape of our mathematical beliefs – Wonder in Mathematics]]
 +  * Mathias Sablé-Meyer. Human cognition of geometric shapes, a window into the mental representation of abstract concepts. PhD thesis, PSL, 2022.
 +    * [[https://www.unicog.org/biblio/Author/SABLE-MEYER-M.html]]
 +    * [[https://s-m.ac/]] (liens directs)
 +
 +
 ==== Textes plus généraux ==== ==== Textes plus généraux ====
   * [[http://act-r.psy.cmu.edu/papers/misapplied.html|Applications and Misapplications of Cognitive Psychology to Mathematics Education]] Anderson, John R.; Reder, Lynne M.; Simon, Herbert A. (1999).   * [[http://act-r.psy.cmu.edu/papers/misapplied.html|Applications and Misapplications of Cognitive Psychology to Mathematics Education]] Anderson, John R.; Reder, Lynne M.; Simon, Herbert A. (1999).
  
mathematiques/start.1610446994.txt.gz · Dernière modification : 2021/01/12 11:23 de villersd