How and why did White British Colonists ‘Stuff Up’ the Better Ideas of Brown, Black & Yellow Mathematics Teachers so Badly?
Hint: History is written by the oppressors not the oppressed!
“Children do 5 – 2 in grade 1. They do 2 – 5 six years later? Is this like not one of most insidious mistakes in our curriculum?”
The above quote appeared in an article titled Racism and a Global Pandemic Has Given Math Education a New Telescope. Where is the Microscope?
Before we answer the question of when and how to teach 2 – 5, ask this. In 50 years will primary level math education be much different? Will math teachers as transmitters of knowledge be online digital avatars powered by interactive one-on-one AI programs or classroom robots assisted by human aids? Will computers finally teach us the truth about mathematics?
Before I address the black and white history of mathematics education, I suggest you add the following YouTube video to your ‘watch list’ as it provides the necessary evidence to support much of what follows.
In case you’re not interest in academic lectures, let it be known I use plenty of cartoons to make my points in the video, like the following.
Later on in this article you will come to know that in mathematics, 2 – 5 and its negative answer are really simple to understand. So, if your reaction is “Negative numbers are really confusing”, can we look to the Collins dictionary for the meaning of ‘negative’ in both general and mathematical usage?
Let’s try…
DICTIONARY & ‘NEGATIVE’
1. ADJECTIVE
A fact, situation, or experience that is negative is unpleasant, depressing, or harmful.
The news from overseas is overwhelmingly negative. All this had an extremely negative effect on the criminal justice system.
…
10. ADJECTIVE [usually ADJECTIVE noun]
A negative number, quantity, or measurement is LESS THAN ZERO. (My bold caps.)
The weakest students can end up with a negative score.
Not only do negatives sound depressing, they also seem confusing!
Numbers simply count or measure quantities (nouns) and actions (verbs) and it is impossible (in our universe) to have any quantity of matter or energy (the stuff our universe is made of) that is less than zero. Similarly, it’s impossible to have a number of actions that is ‘less than zero’. As we will discover, Bharatiya (Ancient Indian) Maths is consistent with modern laws of physics, yet the western math ideas taught in classes 1 to 8 are not. Crazy!
For centuries, the West has been defining negative numbers as those numbers that are less than zero, which is why so many understand maths about as much as they understand ancient Greek! Ask the next person you meet what the answer is to negative seven minus negative four and you’ll see why!
To put you out of any negative math misery, imagine you’re in Grade/Class 1 and it’s time to play the Happy Harappan Brick & Hole Game!
In this story you have a square-sided bucket and spade along with 2 cube-shaped bricks you made the day before. Yet, today’s challenge is to sell 5 bricks! Starting with two bricks, five bricks need to be taken away! (This is a real-world story for 2 – 5.)
2 – 5? NO PROBLEM SAY THE HAPPY HARAPPAN KIDS!
You don’t have enough bricks, so you dig 3 holes and make 3 more bricks. Now there are 5 bricks and 3 holes. 5 bricks get taken away and 3 holes remain!
Pretty soon, perhaps by Grade 2, some children will be extend their imagination from pictures to words and then symbols like 2B – 5B = 3H before they arrive at ⁺2 – ⁺5 = ⁻3.
NOTE: The Harappan or Indus Civilisation flourished around 5000 years ago. It was famous for its precise math-based brickmaking. In 1947 it became part of Pakistan with the exit of the colonial British Raj rulers and the formation of modern India.
RESEARCH
In What Teens Want from Their Schools: A National Survey of High School Student Engagement, among students considering dropping out, half cite lack of engagement with the school as a main reason.
Of the 2000 year 10 to 12 American students in this survey, mathematics is liked the least by a huge margin.
In the surveys I’ve seen, science is rarely the least liked subject at school, while mathematics nearly always is. So, could it be that math pedagogies have failed to evolve according to the scientific method or simply, to reflect reality? If failure is feedback then why hasn’t mathematics education ever been fixed? Kids failing to learn maths is the same thing as adults failing to teach maths.
I hated math at school yet loved building things with electronics kits and writing computer programs. I also loved art and music even if I wasn’t very good. Kids love solving puzzles and are natural problem-solvers so math should reflect the way the world actually works.
WHY MATH IS ALL GREEK TO ME!
Western elementary math education has been built upon arithmoi or Ancient Greek pure number theory when it should have been built on the arithmos or applied applications of Ancient India. Ancient Greek arithmetic was based on theoretical logic where geometry was not allowed to have numbers by people like Aristotle and numbers were not allowed to have units by people like Nicomachus!
Thus, today we are told negative four is greater than negative seven, which is and has always been absolute nonsense! Teachers often say negatives are like debts, yet a debt of $7 is GREATER THAN a debt of $4.
Why is ⁻7 > ⁻4?
ARGUMENT 1 Larger numbers squared exceed smaller numbers squared.
⁺7 × ⁺7 = ⁺49 and ⁺4 × ⁺4 = ⁺16. As 49 > 16 we MUST accept ⁺7 > ⁺4.
⁻7 × ⁻7 = ⁺49 and ⁻4 × ⁻4 = ⁺16. As 49 > 16 we MUST accept ⁻7 > ⁻4.
ARGUMENT 2 Equality is preserved across sign.
⁻4/⁻7 = ⁺4/⁺7 as both ratios of top/bottom are the same. 4 negatives are less than 7 negatives just as 4 positives are less than 7 positives.
ARGUMENT 3 The East got it correct!
In both ancient Chinese and Indian maths, a larger number subtracted from a smaller number of the same sign changes the sign of the answer.
⁺4 – ⁺7 = ⁻3 therefore, ⁺7 > ⁺4
⁻4 – ⁻7 = ⁺3 therefore, ⁻7 > ⁻4
ARGUMENT 4 It’s how physics works!
7 positrons are greater than 4 positrons.
7 electrons are greater than 4 electrons.
7 (negative) electrons are greater than 4 (positive) positrons because after they meet 3 (negative) electrons remain, so ⁻7 > ⁺4.
“LESS THAN ZERO” IS NONSENSE!
Numbers simply count or measure quantities (nouns) and actions (verbs) and it is impossible (in our universe) to have any quantity of matter or energy (the stuff our universe is made of) that is less than zero. Similarly, it’s impossible to have a number of actions that is ‘less than zero’. As you will discover at my new podometic maths website Ancient Indian Maths foundations are consistent with modern laws of physics from Class 1. Dishonest complexity is out and true simplexity is in!
Kids not liking maths or dropping mathematics at the first opportunity at school have reduced career choices because math is an important foundation for further study at university, especially for Science, Technology, Engineering and Medicine.
OK, many fear school mathematics, but WHY?
- British Maths was built for 1, 2, 3… based on Ancient Greek philosophy and looking to the ground 300 BCE.
- India’s simpler Maths was built for …⁻3 ⁻2 ⁻1 0 +1 +2 +3… based on science and looking to the stars 628 CE.
So, the maths education ideas the British Empire spread throughout its settlements and colonies were based on ideas that were almost 1000 years out-of-date! You update your computer’s operating system every few years. You might also update your phone every few years. What about your maths?
As a historian with decades of learning and research, it’s OBVIOUS to me why the world dislikes British primary level maths education. MANY TEACHING IDEAS ARE WRONG!!! My research (download PDF here) reveals the West NEVER updated its thinking from the 7th Century about the true meaning of India’s zero and negative numbers! That’s truly bizarre!
Importantly, so bridges didn’t fall down, many laws and rules were invented to FORCE answers to have the correct answer. Let that sink in a moment. Many laws and rules of maths we were told to commit to memory at school were actually workarounds and bug fixes needed to fix broken western maths foundations!
As Europe reverted to ancient Greek mathematics during the Renaissance, it failed to realise that the 300 BCE ‘Euclidean’ foundations that underpinned its definition of ‘number’ and ‘multiplication’ for example, should have been updated (as per the scientific method) around 700 CE after the writings of Brahmagupta, who gave mathematical rules of zero, negative and positive.
Around 300 BCE, Euclid (whom Raju argues may have been a black woman) had defined number as a multitude of units. That meant 1 was not considered a number because 1 was not a multitude. The Medieval Arabic world, as evident in the influential writings of al-Khwārizmī, al-Uqlīdisī and others, had also been led to believe that 1 was not a number.
Brahmagupta’s definition of zero as the number that is the sum of equal and opposite quantities, (consistent with modern laws of physics), sadly amounted to nothing.
Three quick points…
- Brahmagupta defined zero as a number and wrote the original simple laws of mathematics in the 7th century.
- Yet his definition of zero and laws of (+ – × ÷) on positive and negative numbers were not understood in the Arabic world!
- Maths is confusing today because the West got its knowledge of India’s maths via the Arabic world!
So, the white British Raj in India was unaware it was forcing a corrupted system of mathematics onto those very people whose original black maths teachers like Āryabhaṭa, Bhāskara and Brahmagupta originally crafted it to perfection!
WHY?
Actually, even if the British did know, it didn’t care. You oppress people most effectively by denying them their own culture.
Indian Professor Dr. C. K. Raju has undertaken considerable (confronting) research into the history of mathematics his book ‘The Cultural Foundations of Mathematics’.
=== [The APA Citation for educators follows]
Raju, C. K., & Project of history of Indian science, philosophy, and culture. (2007). Cultural foundations of mathematics: The nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE. (Towards independence.) Delhi: Pearson Longman, Project of history of Indian Science, philosophy and culture.
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My guess is you were once taught the 600 BCE Ancient Greek Pythagoras’ Theorem at school.
The area of the square on the longest side (hypotenuse) of a right-angled triangle is equal to the sum of the squares on the other two sides.
My guess is you were not told the first known country to state the theorem was India, around 200 years before the Greeks. It should be called the Baudhayana Theorem. Is it just a coincidence that as the British Empire extracted wealth from India it argued for the supremacy of Western Greek knowledge via Pythagoras and Euclid?
“Decolonization requires contesting the false history of science used to set up colonial education essential to colonization — the same false history that was used to morally justify racism, by asserting the noncreativity of Blacks.” (Raju, C. K. (2017). Black Thoughts Matter.)
More thoughts from C. K. Raju include:
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… for the colonized, “expertise” and the validity of all knowledge must be decided by reference to “reputed” Western (or Western-approved) experts. This epistemic dependence has political value, but for the master not the slave.
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Macaulay used a false history that science was a Western creation to justify imposing colonial education needed to win the consent of the ruled.
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This was the classic colonial line, to use colonial education to produce White minds in Black or Brown skins, enslaved minds who would hence help run colonial empires.
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To send a spacecraft to Mars, NASA still uses (a minor refinement of) much the same numerical method developed by Aryabhata, and today wrongly named as “Euler’s” method of numerically solving ordinary differential equations.
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Hence the conclusion to undo both colonialism and racism one must start by teaching a more honest history of science.
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Thus, the British Empire displaced indigenous knowledge bases and the world remains infected with mathematical nonsense today that without its bug fixes and workarounds (known as laws) has no connection with physical reality!
If you’d like to learn more about the superiority of India’s ancient original zero-based mathematics, head over to www.podometic.in or follow me on Twitter at www.twitter.com/jcrabtree
Thanks for reading and make your life count! Maths sense is Black over White!
Best wishes
Jonathan J. Crabtree
Education Researcher + Historian
Founder of www.Podometic.in (Bharatiya) Maths
P.S. The story of how zero and the great ideas of maths teachers like Brahmagupta went astray are noted in the 36 minute slideshow below (followed by a Q&A).
P.P.S. Show some support! Sign the petition @ www.change.org/Brahmagupta
