The Bill & Melinda Gates Foundation has funded a radical-left fringe group that believes mathematics, as it is presently taught, is racist. This is a preposterously anti-intellectual notion.
The foundation has pumped $1 million into an organisation that promotes A Pathway to Equitable Math Instruction, a resource kit that claims to ‘support Black, LatinX and Multilingual students to thrive in grades 6-8’.
The organisation ‘offers guidance and resources for educators to use now as they plan their curriculum, while also offering opportunities for ongoing self-reflection as they seek to develop an anti-racist math practice’.
One may wonder why one might need anti-racist math practice, and what kind of math practice is indeed racist. The resource kit answers that question by, and I quote, ‘visibilizing [sic] the toxic characteristics of white supremacy culture with respect to math’.
Again, one might wonder how white supremacy rears its ugly head in the mathematics classroom. It turns out it has nothing to do with racist teachers using racial epithets, or refusing to teach children who are not white.
‘White supremacy culture’
According to the Pathway, ‘White supremacy culture’ (with a capital ‘W’, like the Apartheid schools taught us) shows up in the maths classroom when the focus is on getting the ‘right’ answer, and mistakes are characterised as ‘wrong’.
‘The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so,’ says the guide. ‘Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict.’ (Their italics, used to indicate undesirable concepts.)
So the pursuit of objectivity is, ipso facto, undesirable, and the pursuit of open conflict is noble, according to these pedagogues. In their view, it’s okay to have different, inconsistent answers, and wishing to resolve them into right and wrong is racist.
In reality, mathematics is about as objective a study as one could possibly find. At school level, there are indeed always right and wrong answers. In higher level mathematics, it would be more accurate to distinguish between ‘valid’ and ‘invalid’, or even ‘useful’ and ‘useless’, but the principle is the same. The entire notion of a proof presupposes that mathematical statements can be shown, incontrovertibly, to be either correct or incorrect.
The Pathway authors, however, seem to think that the sum of two and two depends on what you look like, or how you feel.
Litany of oppression
As a solution to the conundrum that correct answers are racist, teachers are encouraged to ‘choose problems that have complex, competing or multiple answers’, and to ‘engage with true problem solving’. As a classroom activity, they recommend: ‘Using a set of data, analyze it in multiple ways to draw different conclusions.’
This sounds a lot like letting children come up with whatever answers they choose, and interpreting data to fit their preconceived ideas. The first is confusing, and the second is only useful in politics.
White supremacy, the Equitable Math Pathway insists, turns up when ‘teachers are teachers and learners are learners’, because ‘this reinforces the ideas of paternalism and powerhoarding’. The same is true for requiring students to raise their hands before asking a question. Presumably, one ought to permit chaotic indiscipline, lest one promote white supremacy.
We learn that perfectionism is a symptom of white supremacy. So is meritocracy. Teaching so-called ‘real-world mathematics’ is problematic because ‘this can result in using mathematics to uphold capitalist and imperialist ways of being and understandings of the world’.
And so we discern their political objective: tearing down capitalism.
‘Math teachers ask students to show work so that teachers know what students are thinking, but that’ – our woke maths pedagogues aver – ‘centers the teacher’s need to understand rather than student learning. It becomes a crutch for teachers seeking to understand what students are thinking and less of a tool for students in learning how to process. Thus, requiring students to show their work reinforces worship of the written word as well as paternalism.’
So when a student concludes that two plus two is five, you cannot call it wrong. And you cannot ask the student to show how they reached this conclusion either, in the hope of being able to help them correct their mistakes, because both calling it wrong and asking for an explanation is racist.
One solution to this problem, they claim, is to avoid answering mathematical problems with words or numbers, but to let students create TikTok videos instead. Seriously.
Dumbing down mathematics
They argue that grades are ‘traditionally indicative of what students can’t do rather than what they can do, reinforcing perfectionism’, and that is a bad thing.
It is better to focus on what students do know, than on what they don’t know. How they are to learn what they don’t know by being praised for what they do know, the Pathway leaves as an exercise for the reader.
And so the absurdity continues. In essence, the call is to dumb down mathematics so even the worst performers can earn a pass, because that will resolve the perceived problem that minorities struggle with mathematics. (Being blindly US-centric, the Equitable Math Pathway authors appear oblivious to the fact that white people are not everywhere in the majority.)
One might counter that any inequality in mathematics education outcomes could be addressed by improving the quality of mathematics education for non-white students, but that, too, won’t do: ‘This reinforces either/or thinking by reinforcing stereotypes about the type of mathematical education that certain groups of students receive. It allows the defensiveness of Western mathematics to prevail, without addressing underlying causes of why certain groups of students are “underperforming”, a characterization that should also be interrogated. It also presupposes that “good” math teaching is about a Eurocentric type of mathematics, devoid of cultural ways of being.’
Non-European roots
The first time I came across the notion that mathematics is racist was in 2017, when a professor at the Illinois College of Education, Rochelle Gutierrez, made the claim that mathematics subjects such as algebra and geometry perpetuate ‘unearned privilege’ among white people.
Her ‘scholarship’, if one can call it that, ‘focuses on issues of identity and power in mathematics education’.
Gutierrez frets that mathematicians have a disproportionately high status compared to social studies and English professors, which constitutes ‘unearned privilege’, and is therefore racist. Her position seems born of insecurity, not academic rigour.
She worries that ‘curricula emphasizing terms like Pythagorean theorem and pi perpetuate a perception that mathematics was largely developed by Greeks and other Europeans’.
‘On many levels, mathematics itself operates as Whiteness,’ she argues. ‘Who gets credit for doing and developing mathematics, who is capable in mathematics, and who is seen as part of the mathematical community is generally viewed as White.’
There we have the racialist’s capital ‘W’ again.
Of course, these claims are quite baseless. Mathematics has its roots outside Europe. The very first notched tally bones, dating back 37 000 years, were found in Africa. Mathematics is first and foremost a human discipline. It doesn’t belong to any particular race, and is entirely agnostic to the identity of its students.
The very term ‘algebra’ comes from a 9th century treatise entitled al-mukhtasar fi hisab al-jabr wa al-muqabala (‘the compendium on calculation by restoring and balancing’) by the Baghdadi mathematician Abu Ja’far Muhammad ibn Musa al-Khwarizmi. This is the mathematician to whose name we owe the term ‘algorithm’.
The Arabic numerals we use today originated with Indian mathematicians in about 500CE, and were later modified in North Africa into the forms that the Italian mathematician Fibonacci would eventually encounter and popularise in Europe.
The foundational developments in mathematics were Egyptian, Sumerian, Babylonian, Chinese and Indian, and happened long before the Greeks entered the picture in about 600BCE.
Pre-Greek mathematics included arithmetic, geometry, fractions, equations, and algebra. The ancients knew Pythagorian triples and had good approximations for numbers such as √2 and what we today know as π, a symbol that was only introduced in 1706 by Welsh mathematician William Jones.
Microaggressions
Gutierrez argues that not doing well in mathematics is a racial phenomenon, and non-white students ‘have experienced microaggressions from participating in math classrooms… [where people are] judged by whether they can reason abstractly’.
You should have seen the microaggressions directed at white students who were incapable of abstract reasoning in my mathematics classes at school and university! Many of them were unceremoniously booted out of the discipline, and told to take up social studies, commerce, farming or trades.
The Greeks did build a solid foundation in mathematics, at the height of their culture. Between the decline of the Greeks and Romans in the 4th century and the rise of European mathematics in the 15th and 16th centuries, mathematics was not dead, however. It was preserved and advanced by Persian, Arabic, Indian and Chinese mathematicians.
Let’s list a few:
- Sun Tzu, of The Art of War fame, who gave us the first definitive statement of the Chinese Remainder Theorem;
- Liu Hui, who calculated π to five decimal places, solved linear equations using matrices, and introduced early forms of differential and integral calculus;
- Aryabhata, who defined trigonometric functions, solved simultaneous quadratic equations, and recognised that π is an irrational number;
- Brahmagupta, who established basic rules for dealing with zero and negative numbers, including negative roots of quadratic equations and solutions of quadratic equations in two unknowns;
- Bhaskara I, who was the first to write numbers in the Hindu-Arabic decimal system with a circle representing zero, and made a remarkably accurate approximation of the sine function;
- The aforementioned Muhammad Al-Khwarizmi, who popularised Arabic numerals in the Islamic world, and created the foundations of modern algebra;
- Ibrahim ibn Sinan, who advanced Archimedes’ understanding of geometric concepts such as areas, volumes, and tangents to a circle;
- Muhammad Al-Karaji, who was the first to use the principle of mathematical induction, including to prove the Binomial Theorem;
- Ibn al-Haytham, also known as Alhazen, who derived a formula for the sum of fourth powers (Alhazen’s Problem), and established the beginnings of a link between algebra and geometry;
- Omar Khayyam, the astronomer-poet of Persia of Rubáiyát fame, who generalized Indian methods for extracting square and cube roots to include fourth, fifth and higher roots;
- Bhaskara II, who established that dividing by zero yields infinity, found solutions to quadratic, cubic and quartic equations including negative and irrational solutions as well as to second order Diophantine equations, and introduced some preliminary concepts of calculus;
- Nasir al-Din al-Tusi, who developed the field of spherical trigonometry and formulated law of sines for plane triangles;
- Qin Jiushao, who found solutions to quadratic, cubic and higher power equations using a method of repeated approximations;
- Yang Hui, who invented Chinese ‘magic’ squares, circles and triangles and developed Yang Hui’s Triangle, which was an early version of Pascal’s Triangle of binomial coefficients;
- Kamal al-Din al-Farisi, who applied the theory of conic sections to solve optical problems, explored amicable numbers, and investigated factorisation and combinatorial methods; and
- Madhava, who used infinite series of fractions to give an exact formula for π, worked on the sine formula and other trigonometric functions, and contributed to the development of calculus.
None of their work was met with ‘microaggressions’, because it was sound work. The European mathematicians who followed them more often than not stood on their shoulders, not the shoulders of Ancient Greeks.
Although the rapid development of mathematics of the last few centuries happened to a large degree throughout Europe, that continent’s wide language and cultural differences, with treatises and papers being written in Latin, English, French, German and Russian, also demonstrates that mathematics is entirely independent of cultural differences.
Critical theory
Gutierrez says: ‘Things cannot be known objectively; they must be known subjectively,’ thereby neatly tying her views to the core principle and primary defect of critical race theory, namely that there is no such thing as objective knowledge, and everyone’s subjective experience is equally valid as an epistemological basis.
If this were true, the countries in which mathematics and science developed would not have outperformed the countries in which it did not. ‘Other ways of knowing’ would have had equally good outcomes for the development of engineering, manufacturing and finance in countries that rejected supposedly ‘Western’ science and mathematics.
Sadly, the Equitable Math Pathway has influence. According to Newsweek, the group names as partners the Association of California School Administrators, Monterey County Office of Education, the Sacramento County Office of Education, and the Lawrence Hall of Science at UC Berkeley. The Oregon Department of Education has reportedly encouraged its teachers to register for the Equitable Math training, and a version of it is already functioning at schools in Seattle.
The overt support of the Bill & Melinda Gates Foundation gives the cancer of critical race theory even more room to metastasise into every nook and cranny of academia, corrupting the edifice of human knowledge and progress from within.
The beauty of mathematics
The teaching of mathematics can undoubtedly be improved. At school level, maths teaching too often prioritises rote learning and recipe-following over inculcating a deep understanding of mathematical concepts and methods. Too many students hate this, and drop the subject before they get a chance to encounter the true beauty and power of mathematics at university.
Changing this requires many things, but it certainly does not require nonsensical ‘anti-racist math practice’.
The beauty of mathematics is that it transcends petty human differences and follies. It cares not who we are, what we look like, or to which tribes we belong. It stands on its own. Its truths are universal.
It is characteristic of anti-intellectuals – who distrust and despise science, philosophy, art, literature and education – to view intellectual pursuits such as mathematics as elitist and exclusionary, and to portray themselves as noble champions of ordinary people.
The efforts of critical race theorists, who espy ‘white supremacist culture’ everywhere they look, are intended to drag mathematics and the other sciences down into a morass of subjective ignorance. They are not progressive. They are profoundly regressive.
Their purpose is not to ‘support Black, Latinx and multi-lingual students to thrive’. Their purpose is to drag everyone down in order to achieve equality of outcomes in a world where excellence is racist, right is wrong, war is peace, freedom is slavery and ignorance is strength.
Gates should fight this, not fund it.
[Image: Gerd Altmann from Pixabay]
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