{"id":226,"date":"2020-06-05T13:47:55","date_gmt":"2020-06-05T17:47:55","guid":{"rendered":"https:\/\/blogs.harvard.edu\/siams\/?p=226"},"modified":"2020-06-05T13:48:10","modified_gmt":"2020-06-05T17:48:10","slug":"notes-on-worldmath-curriculum-fighting-eurocentrism-in-mathematics","status":"publish","type":"post","link":"https:\/\/archive.blogs.harvard.edu\/siams\/2020\/06\/05\/notes-on-worldmath-curriculum-fighting-eurocentrism-in-mathematics\/","title":{"rendered":"Notes on: “Worldmath Curriculum: Fighting Eurocentrism in Mathematics”"},"content":{"rendered":"

SE Anderson, 1990: “Worldmath Curriculum: Fighting Eurocentrism in Mathematics”. \u00a0The Journal of Negro Education<\/span><\/p>\n

Section one: “A few grim statistics”<\/p>\n

The manuscript starts with “A few grim statistics”, looking forward to 2000 and to 2010 and providing numbers about low numbers of Black, Latino, and Native American scholars receiving PhDs in mathematics, physics, and astronomy in the 1980s.<\/p>\n

Section two:\u00a0“The Eurocentric Basis of Mathematics”<\/p>\n

The author writes that educators have a duty to build a system “based on the assumption that any person can learn anything”, with the “true beauty of mathematics” coming from the creation of “logical systems that help explain the complexities of Nature”. \u00a0(See Joseph 1987 p 22-26).<\/p>\n

Eurocentrism:<\/p>\n

    \n
  1. math is often specifically delinked from materialist concerns<\/li>\n
  2. math is confined to an elite group with special gifts<\/li>\n
  3. math discovery comes from “deductive axiomatic logic” not from “intuitive or empirical methods”<\/li>\n
  4. math results needs to be presented in a particular style, so “new additions to mathematical knowledge” are from a small, special, Eurocentric group.<\/li>\n<\/ol>\n

    The narrative of mathematics is presented as going from the Greeks through “European men and their North American descendants”. \u00a0“African, Indian, Chinese, or Mayan contributions” receive short mentions in textbooks.<\/p>\n

    In addition, an unappealing curriculum ends up reinforcing “racist assumptions about people of color”.<\/p>\n

    Section three: “Six Pedagogical Disasters in Mathematics Education”<\/p>\n

      \n
    1. “separate arithmetic from algebra”<\/li>\n
    2. “teach mathematics without any historical references”<\/li>\n
    3. “use textbooks that are elitist and cryptic”<\/li>\n
    4. “do work and be tested as an individual” (vs in study groups)<\/li>\n
    5. “accept the myth that mathematics is pure abstraction”<\/li>\n
    6. “memorize”<\/li>\n<\/ol>\n

      1: the author asserts that arithmetic is taught first (for many years), followed by algebra: evidently these subjects are kept separate. \u00a0I don’t have any thoughts on this.<\/p>\n

      2: teaching math as ahistorical: a bunch of European names are attached to math facts and abstractions, without the humans themselves being introduced.<\/p>\n

      3: cryptic texts: these make math appear unaccessible and not for most people.<\/p>\n

      4: the individual: math classes are often structured competitively \/ individually. \u00a0this is not how people actually solve problems.<\/p>\n

      5: real math is abstract: “erudition, abstraction, and compartmentalization”, distance people from creative sources and make math seem unnatural, rather than a natural human act.<\/p>\n

      6: memorization: math problem solving is often turned into the memorization of definitions, theorems, etc.<\/p>\n

      Section four: “An alternative curriculum and pedagogy”<\/p>\n

      See Bob Moses and his “algebra project” (learning algebra in elementary school via subway rides). \u00a0See Arthur Powell and the “Writing in Math” project. \u00a0See Marilyn Frankenstein and “radical math”. \u00a0Look for alternatives “to the arithematic-algebra-precalculus-calculus `learning’ sequence that is so pervasive yet so devastating.” \u00a0College-level courses should (1) “show the interconnectedness of mathematics and real-world problems” and (2) should “show how people throughout history have created mathematical techniques to solve problems”.<\/p>\n

      Section five: “How and what I teach”<\/p>\n

        \n
      1. Via “psychological upliftment”, “emphasizing that ordinary people create mathematical ideas and ‘do’ mathematics”.<\/li>\n
      2. By assuming “the role of a confidence builder”. \u00a0Letting students know “they all have the intellectual capabilities to understand the material”<\/li>\n
      3. Attributing not understanding to “my own or the textbook’s failure to communicate clearly”<\/li>\n
      4. Choosing “the quality of mathematics knowledge” over the quantity. \u00a0“I may set out to cover six chapters… if they complete only three or four chapters and learn those well, then I am confident they can pick up the rest”<\/li>\n<\/ol>\n

        In a typical algebra class: first two classes focus on historical, cultural, sociopolitical. \u00a0Relate math to “humanity’s ongoing struggle to understand Nature”. \u00a0And to “capitalism’s attempts to control and dominate Nature”. \u00a0Emphasize that “some of the very first mathematical\/scientific thinkers were African women”. \u00a0“Show how early mathematics and science led to the building of the pyramids, the Great Wall of China, and the road to Kathmandu”. \u00a0Astronomy, astrology, iron-smelting, surgery, etc. \u00a0Name that Euclid “spent 21 years studying and translating mathematical tracts in Egypt” and “Egypt is in Africa and that the people who inhabit the land were and are Africans”. \u00a0Pythagoras also studied in Egypt (and perhaps India). \u00a0The theorem attributed to him existed 1000 years before him in Babylonian documents.<\/p>\n

        The “intent… is to shatter the myth that mathematics was or is a `White man’s thing'”. \u00a0“I show how certain aspects of European mathematics could not have developed had not the Europeans traded with more advanced societies”. \u00a0Example: “The Vatican denounced Hindu-Arabic numerals”.<\/p>\n

        The research university of Bait al-Hikma is important because of Mohammed ibn-Musa al-Khwarizmi (the name “al-djabr or `algebra’ comes from a text he wrote) and the term “algorithms” is a corruption of his name (dating to his second book, “Algorithmi de Numero Indorum”). \u00a0“I also mention… the algebraist Omar Khayyam (c. 1050 – 1122 AD)”. \u00a0See Nasir Eddin al-Tusi for non-Euclidean geometry, as well.<\/p>\n

        In the 1600s, when Europeans were trying to build very large ships to carry African slaves, they used the knowledge of “Gambian, Chinese, and Indian mariners”. \u00a0“Developments in hydrodynamics (and its attendant mathematics) contributed … to the horror of .. the slave trade”.<\/p>\n

        “I further point that that calculus was created to facilitate the study of ballistics” in wars by England and Germany. \u00a0Military needs “continue to inspire many mathematicians and scientists to purse the War Machine”.<\/p>\n

        Structuring class: (1) “About two weeks into a class, I facilitate the creation of study groups” (3-4 people whom students choose). \u00a0These groups are used in and out of class. \u00a0The groups complete progress reports (no tests). \u00a0(2) “I also incorporate a weekly 15- to 20-minute class discussion” of a news article from the Science Times, to emphasize the relationships between math and the social \/ natural sciences. \u00a0(3) students are asked to make notecards of facts that they should bring to class. \u00a0(4) computational tools are encouraged.<\/p>\n

        Section six: “Conclusion”<\/p>\n

        “a subtle but effective form of educational genocide is taking place”. \u00a0“To offer an alternative that is genuinely egalitarian and truthful we must open our eyes to the centrality of the contributions made by the vast majority of the world’s people”.<\/p>\n","protected":false},"excerpt":{"rendered":"

        SE Anderson, 1990: “Worldmath Curriculum: Fighting Eurocentrism in Mathematics”. \u00a0The Journal of Negro Education Section one: “A few grim statistics” The manuscript starts with “A few grim statistics”, looking forward to 2000 and to 2010 and providing numbers about low numbers of Black, Latino, and Native American scholars receiving PhDs in mathematics, physics, and astronomy […]<\/p>\n","protected":false},"author":8032,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[157887,1010],"tags":[],"class_list":["post-226","post","type-post","status-publish","format-standard","hentry","category-learning-and-teaching","category-math"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7E5LF-3E","jetpack-related-posts":[{"id":32,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2017\/08\/25\/reading-student-learning-objectives-and-mathematics-teaching\/","url_meta":{"origin":226,"position":0},"title":"Reading “Student learning objectives and mathematics teaching”","author":"siams","date":"25 August 2017","format":false,"excerpt":"I am working to write learning objectives for multivariable calculus this Fall. This article helped distinguish between overarching goals (that students are able to fit the math in the course into a greater understanding of math and of the world) and the learning objectives, of what I hope students will\u2026","rel":"","context":"In "Learning and teaching"","block_context":{"text":"Learning and teaching","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/learning-and-teaching\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":173,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/07\/18\/reading-high-school-algebra-students-busting-the-myth-about-mathematical-smartness-counterstories-to-the-dominant-narrative-get-it-quick-and-get-it-right\/","url_meta":{"origin":226,"position":1},"title":"Reading “High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative \u201cGet It Quick and Get It Right\u201d”","author":"siams","date":"18 July 2019","format":false,"excerpt":"Dunleavy 2018, \"High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative \u201cGet It Quick and Get It Right\u201d\". \u00a0Education Sciences. 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I don't have a systematic curriculum related to it, though, and need to develop clearer computational learning goals, as well as a pathway for students to develop computational skills. 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