SE Anderson, 1990: “Worldmath Curriculum: Fighting Eurocentrism in Mathematics”. The 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 in the 1980s.
Section two: “The Eurocentric Basis of Mathematics”
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”. (See Joseph 1987 p 22-26).
- math is often specifically delinked from materialist concerns
- math is confined to an elite group with special gifts
- math discovery comes from “deductive axiomatic logic” not from “intuitive or empirical methods”
- math results needs to be presented in a particular style, so “new additions to mathematical knowledge” are from a small, special, Eurocentric group.
The narrative of mathematics is presented as going from the Greeks through “European men and their North American descendants”. “African, Indian, Chinese, or Mayan contributions” receive short mentions in textbooks.
In addition, an unappealing curriculum ends up reinforcing “racist assumptions about people of color”.
Section three: “Six Pedagogical Disasters in Mathematics Education”
- “separate arithmetic from algebra”
- “teach mathematics without any historical references”
- “use textbooks that are elitist and cryptic”
- “do work and be tested as an individual” (vs in study groups)
- “accept the myth that mathematics is pure abstraction”
1: the author asserts that arithmetic is taught first (for many years), followed by algebra: evidently these subjects are kept separate. I don’t have any thoughts on this.
2: teaching math as ahistorical: a bunch of European names are attached to math facts and abstractions, without the humans themselves being introduced.
3: cryptic texts: these make math appear unaccessible and not for most people.
4: the individual: math classes are often structured competitively / individually. this is not how people actually solve problems.
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.
6: memorization: math problem solving is often turned into the memorization of definitions, theorems, etc.
Section four: “An alternative curriculum and pedagogy”
See Bob Moses and his “algebra project” (learning algebra in elementary school via subway rides). See Arthur Powell and the “Writing in Math” project. See Marilyn Frankenstein and “radical math”. Look for alternatives “to the arithematic-algebra-precalculus-calculus `learning’ sequence that is so pervasive yet so devastating.” College-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”.
Section five: “How and what I teach”
- Via “psychological upliftment”, “emphasizing that ordinary people create mathematical ideas and ‘do’ mathematics”.
- By assuming “the role of a confidence builder”. Letting students know “they all have the intellectual capabilities to understand the material”
- Attributing not understanding to “my own or the textbook’s failure to communicate clearly”
- Choosing “the quality of mathematics knowledge” over the quantity. “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”
In a typical algebra class: first two classes focus on historical, cultural, sociopolitical. Relate math to “humanity’s ongoing struggle to understand Nature”. And to “capitalism’s attempts to control and dominate Nature”. Emphasize that “some of the very first mathematical/scientific thinkers were African women”. “Show how early mathematics and science led to the building of the pyramids, the Great Wall of China, and the road to Kathmandu”. Astronomy, astrology, iron-smelting, surgery, etc. Name 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”. Pythagoras also studied in Egypt (and perhaps India). The theorem attributed to him existed 1000 years before him in Babylonian documents.
The “intent… is to shatter the myth that mathematics was or is a `White man’s thing'”. “I show how certain aspects of European mathematics could not have developed had not the Europeans traded with more advanced societies”. Example: “The Vatican denounced Hindu-Arabic numerals”.
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”). “I also mention… the algebraist Omar Khayyam (c. 1050 – 1122 AD)”. See Nasir Eddin al-Tusi for non-Euclidean geometry, as well.
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”. “Developments in hydrodynamics (and its attendant mathematics) contributed … to the horror of .. the slave trade”.
“I further point that that calculus was created to facilitate the study of ballistics” in wars by England and Germany. Military needs “continue to inspire many mathematicians and scientists to purse the War Machine”.
Structuring class: (1) “About two weeks into a class, I facilitate the creation of study groups” (3-4 people whom students choose). These groups are used in and out of class. The groups complete progress reports (no tests). (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. (3) students are asked to make notecards of facts that they should bring to class. (4) computational tools are encouraged.
Section six: “Conclusion”
“a subtle but effective form of educational genocide is taking place”. “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”.