“An associated “Dismantling Racism” workbook, linked within the toolkit, similarly identifies “objectivity” — described as “the belief that there is such a thing as being objective or ‘neutral'” — as a characteristic of White supremacy.
Instead of focusing on one right answer, the toolkit encourages teachers to “come up with at least two answers that might solve this problem.”
It adds: “Challenge standardized test questions by getting the ‘right’ answer, but justify other answers by unpacking the assumptions that are made in the problem.”
It also encourages teachers to “center ethnomathematics,” which includes a variety of guidelines. One of them instructs educators to “identify and challenge the ways that math is used to uphold capitalist, imperialist, and racist views.””
Comment: Does this mean that mathematics is something like quantum mechanics in which things may or may not be what they seem? My SWMBO was a math major as an undergraduate, that and physics as a minor. How she lives with a knuckle dragger but nevertheless a humanities person has always been a mystery. She expresses a bemused puzzlement over the concept of math as anything but rigorous.
I suppose that it is an open question as to whether someone imbued with Oregonian math philosophy could work for something like NASA, or in finance where simple arithmetic has long been the way the money was kept track of. pl
Business owner interviewing prospective accountants hire, “how much is 2 + 2?”
Not hired accountant,, “4”.
Hired accountant, “it’s whatever you want if to be, boss”.
Sorry, I know this is a serious discussion. I remember reading a letter to the editor when I was living in New Hampshire a decade ago. A teacher had written that she didn’t care if her students learned anything as long as they developed a sense of self-worth. I wondered where that self-worth was going to wind up when they got fired from their first job for being less than smart.
It’s an insult to bolshevism to compare it with this. Maybe closer to Pol Pot and the Khmer Rouge year zero innovation. Maybe worse though. Those geniuses at least could survive an overnight camping trip. During a damn pandemic, burning stores, looting and “educating” outdoor diners near and far.
An individual (no gender specified), goes into a store. Steals $100 cash from the cash register in the form of a hundred dollar bill. Chooses $70 of merchandise. Pays with stolen $100 bill. Receives $30 in change.
How much did the merchant lose?
Don’t pose this to question to too many American high school math teachers these days.
Spoiler – correct answer is $100.
An improved way to teach a lesson on that problem would be to give the answer ahead of time (egos are too fragile, people hate to feel stupid in public). Then distribute praise and encouragement to who finds the most convincing and easy to understand answer. And frankly, smart-ass wiseguy fast thinking nerds don’t get to do their thing – feel superior. Sorry chaps. Oops – folks. Guess that’s ok?
Not quite so simple, F&L. It could be argued that since the merchandise was “sold” at a profit, the merchant actually lost less than $100.
but the merchant also lost the profit from the sale of the merchandise – so still $100.
OK. Yes, the merchant at the end of the day may include his theoretical profit in his losses. Or he can console himself that in practical terms he is $30 dollars down in cash plus the wholesale price of his lost goods. Are not both viewpoints tenable? And, as a matter of interest, if he made an insurance claim would his insurers include or exclude the loss of his nominal profit?
I’ve read discussions of this puzzle before. It certainly can be confusing to all sorts of people. People who support the correct answer with ok arguments don’t always hold up to probing questions of their solutions because they have solved in their own way to their satisfaction and from what I can tell haven’t paused to consider the many possible objections. My own approach, after suffering my own confusion over these and other details such as profit margin was to find some way to demonstrate that they are red herrings, or beside the point irrelevancy though that they occur to us is a good, not a bad thing. Shows we are still thinking. To move people on I’d encourage seeing the big picture. To wit- how can the above problem possibly have a different outcome if instead of the original thief herself, directly after thievery, purchasing one $100 item with the one Hundred dollar bill, instead proceeds to leave the store. And then seek out 100 individual separate children and give them each a single One dollar bill on condition that they each proceed to the original store and each purchase 70 cents worth of say, candy, paying with the $1 bill provided, and graciously accepting and pocketing 30 cents change each? You can allow the kids a week, two days, however within reason. Well, that worked for me. How can the many other sundry possible variations matter? Nothing was lost except the one C note, value 100 dollars. The man was open for business for a day, week, month, whatever and by gosh someone snatched a hundred dollars out of the register. Where did it go? Right out the front door is a fine answer. All that candy could have been purchased by perfectly unconnected in any way perfect strangers and how could it be told or distinguished? For my money it can’t. But if you remain unconvinced or a bit perplexed, I don’t blame you. It’s confusing, with lots to think about. Obvious – maybe to you, and you and everyone over there. But not to everyone. That’s why the puzzle has lasted down through the ages. A worthy chestnut.
“For historical reasons, we often discuss contributions to the field of mathematics from the Egyptians, Babylonians, Greeks, Chinese, Indians and Arabs and refer to them as distinct entities. They have all contributed through a unique cultural dialogue to the creation of a truly magnificent edifice accessible today to every man and woman on the planet. Though we pay tribute to great historical figures who inform the practice of mathematics, the subject can be taught — and often is — with no reference to the individuals who have contributed to it. In that sense it is uniquely universal…”
i am convinced that the people advocating for this & similar nonsense (critical race theory, intersectionality) don’t themselves believe a word of it. they are simply predators attempting to insert themselves into the fabric of our culture, & enrich themselves in the process. they are proselytizers of belief systems that they themselves have invented out of whole cloth…
they are white-collar, college-educated grifters. & intimidation somehow seems to have become their primary weapon…
Was in conversation with a friend who is a Certified Public Accountant and he mentioned the term “voodoo economics.” I laughed. “Voodoo economics?” I said. “That’s the only kind of economics there is.”
A better model for teaching mathematics is the story behind the movie “Stand and Deliver” where inner city Latino high school students were successfully taught AP calculus. The real program took years of preparation to work up to AP calculus along with dedicated teachers who believed in themselves and their students.
The Oregon program content seems to be more in line with that concept. The anti-racist idea is more of a latching on to the latest gimmick or fad. That “Dismantling Racism” workbook has absolutely nothing to do with mathematics. It’s a marketing scheme. I don’t see how that approach will produce better students of mathematics.
The idea of teaching how to work on problems as a team rather than individually also has nothing to do with racism. That’s the way most programming works in the real world and that the way colleges are moving their methods of instruction. It might be capitalist, but it’s not imperialist or racist.
“It’s a marketing scheme. ”
It’s a racist polemic meant to divide along ethnic lines. It’s right out the ’60s leftist agenda.
It’s not a fad either. I first heard woke-speak when I went to grad school. That was 25 years ago. The minorities and women were quite outspoken about it. It was all new to me and I thought it was nuts. These were people that one encountered in the business school building because they were in the public administration program, which was in the same building, or they were in the public health program at the medical college and had to come into my world for some basic statistics courses (with which they struggled horribly). Real mediocre IQs that had obviously got ahead on playing the social justice/oppressed special class card.
It was the same crap as today. Systemic racism, overt racism, oppression by white imperialism, the US destroyed Latin America (all of it) and has kept the Latinos down, open the borders, The South West should be returned to Mexico, imperialism destroyed Africa, Africa used to be the high point of human civilization, capitalism is evil, maleness is evil, Ebonics is just as good as the king’s English, standardized curriculum and tests are unfair to minorities and racist.
Wokeness has only grown more widespread and gained greater social acceptance as reality since then. 25 years and growing stronger is hardly a fad. It’s what is taught to children in public schools and colleges these days. That’s the real world programming.
They were in the liberal arts school when I was an undergrad. There weren’t too many then, even though I minored in anthropology. I remember one prof who was passionate about Bolivia, except for the part about living there. That part hasn’t changed much.
The 60′ leftist agenda was nothing like what goes on today in Wokeland, it dissipated, and made a lot of its’ adherents into corporate, elitist scum. This lot of snowflakes can only be reformed by a cap busting. Else this country, besides not continuing as a republic, its’ cities and countrysides will have the appearance of a 12th century land of peasants.
And now for the good news (depending on how you look at it) Other western countries are much more Woke than ourselves. We can then watch on the Tube as their Titanics sink beneath the waves. I would add “hopefully playing their national anthems,” but I think their original tunes would no longer be in use, replaced by the Woke anthem of the Schwabian Reset Song.
The same ‘racism is the cause’ is still informing public policy, just like in the “Great Society” programs that destroyed the black family in America. That, Keynesian economists – where debt isn’t even a consideration – and other government driven programs are all alive and well in this administration, just like before. “Woke” is just marx applied to culture.
I used to detest the word “Woke” when it first came into use in England. It was American idiom that resonated in an American context but used over here in a knowing “I’m really up to date” way that said more about the speaker than what he was saying.
So it was uncomfortable. Rather like hearing a German swearing in English. It’s a subtle idiom, competent swearing in a foreign language, and they never quite get it right. It’s why I never swear in German. All too conscious that one’s going to look a fool the other way. So too with the inexpert use of “Woke” in England. It set one’s teeth on edge.
But like all loanwords it’s become naturalised and is now used indiscriminately by many for “Prog”. Which itself is replacing the old “PC”. “Leftist” would do as well, except that that word here summons up associations with the old UK Labour Left.
Loopy, that old UK Labour Left, in that they were wedded to command economy thinking and that draws a whole mix of horrors in its train, but underneath it all the best of them stoutly patriotic and genuinely on the side of those who’d drawn the short straw in the battle of the cronies against the plebs.
Gone, those types, replaced by Blairite monstrosities who, Conservative or Labour, now represent or accede to the strange alliance we see both in the States and here. The strange alliance of the cronies and the neocons and the progs that bids fair to sink more countries than America.
Who is to oppose that strange alliance? Trump? Some successor in his mould?
The acid dissection of Trump’s personality I disregard. I saw a kindly man beneath the bluster truly wishing to serve his country. I think TTG delivered a similar charitable verdict here not long back. In Biden, though I wish him well personally as he seeks to shoulder the huge burden of living up to the Presidency, I don’t think I’m that far out in seeing an essentially vicious man given to venality.
But these personality traits that all have so minutely dissected in the case of Trump and that will be in Biden’s case, are for me beside the point. In essence Trump was never about personality, nor yet about partisan politics. He was the cry of a people for renewal, a cry heard here in Europe also and as frantically suppressed as in the States.
The suppression’s in full flood now. Those tall fences round the Capitol have little practical purpose but a symbolic significance that says more than a thousand speeches. Woke Fortress, if one may venture the use of that word oneself, defending the strange alliance in the only way it can be defended; by the power of force since it lacks now any power of conviction.
“The acid dissection of Trump’s personality I disregard. I saw a kindly man beneath the bluster truly wishing to serve his country. I think TTG delivered a similar charitable verdict here not long back. In Biden, though I wish him well personally as he seeks to shoulder the huge burden of living up to the Presidency, I don’t think I’m that far out in seeing an essentially vicious man given to venality.” Memorable.
Not really. The AP test that the Stand and Deliver students were prepping for doesn’t accept more than one answer as correct, and is always taken (and scored) individually. It is not a team effort. Please don’t defame Jaime Escalante like that.
We have to make excuses for the fact that children of color do so bad in STEM.
The Progressives can not admit that good teachers (Democratic Operatives) are racist and refuse to go into schools that have children of color.
The Progressive can not admit that they are the racist, so they have to create systematic racisms to hide their racism.
Mathematics is discovered, not invented. Thus for math to be “racist” must imply that reality is racist as well, along with the known universe. The contributions of humans of any stripe to mathematics (beyond the past and present discoveries) are generally those of the symbols that make manipulations simpler and less error-prone, e.g., Arabic instead of Roman numerals in arithmetic, or the integral symbol from Leibniz in the calculus.
The caterwauling about racism in mathematics is all-too-often about fear (innumeracy) and envy (STEM jealousy in those who cannot “do the math” and who resent those who can). Thus an appropriate response to those peddling this claptrap is simple pity for their inability to grasp the beauty of this essential body of knowledge.
Cieran and Walrus, I don’t see any of those articles arguing that mathematics is racist. They’re arguing that the teaching of mathematics is racist. I think that’s bullshit. It’s incompetence, not racism. Incompetence on the part of the teachers and administrators and on the part of the parents of those kids. If the parents or guardians don’t impress the importance of an education on the kids, they’re definitely part of the problem.
Mathematics is discovered, not invented.
Thank you for succinctly writing what I would have written less gracefully.
From the article:
The program argues that “white supremacy culture shows up in the classroom when the focus is on getting the ‘right’ answer” or when students are required to show their work, while stipulating that the very “concept of mathematics being purely objective is unequivocally false”.
This is wrong, but dangerously close to something right. Bright students have an easy time getting the ‘right’ answer but often burn out young because getting the ‘right’ answer is the only focus of their lives. For bright and advanced students, getting the “right” answer should be secondary to putting forth the best effort — which may mean creative problem solving or some other heroic effort. For dull students, they must focus on the getting the ‘right’ answer because it is not easy for them.
students are required to show their work,
Being required to show one’s work is very valuable for some students who are almost idiot savants. As a child, I had a gift for voicing correct math answers without consciously understanding the problem. That gift would have hindered me if I had been allowed to always use it. My teachers wisely taught me to show calculations, and that taught me to be rational — to give REASONS for my claims. I revere those teachers more than I revere saints.
the very “concept of mathematics being purely objective is unequivocally false”.
I think I see this. The lecturer is a postmodernist, and therefore the lecturer can say ANYTHING, without ever being criticized. If the lecturer says it is false, we must believe him.
Now, if the lecturer had to give reasons or show his work, his claim would be hard to defend. What is “objectively false”? I think we can’t define that without using mathematical logic.
If I had a very patient audience and access to my favorite textbooks, I might put on a mathematical song-and-dance number to show that all math is a logical construction, dependent on arbitrary definitions, axiom sets, and rules of inference. From there we might agree that any meaning for any mathematical calculation is “subjective” because it is a human experience — but we come back to the Platonistic discovery that while our experiences of math are imperfect perceptions, colored by our cultures — the realities that we see through calculation are eternal Forms. Or, more succinctly:
Mathematical truth is discovered, not invented.
Maybe you’re another Fisher. He could see solutions so fast that he was rejected early on in his career. The gaps in the steps of his reasoning were so great that other mathematicians might have to spend an afternoon puzzling out from one line of a proof to another. And Gauss was beaten as a schoolboy for summing the numbers one to a hundred by other means than plodding addition.
But your teachers must have been right. Some children, lucky devils, find school maths so easy that they get top marks without ever needing to break sweat. I’m told that sometimes, when they get to university and really do need to put the hard work in, they’ve never acquired the habit so they drop out.
I gather that some English maths departments are holding conferences on just the subject under discussion, critical race theory in its application to mathematics. Weird to think of mathematicians fooling around like that but I like the idea. It would give the critical race merchants a clean sweep – they’ve got at just about every other subject – and would put them to the trouble of discovering an alternative reality. Then they could go away and live in it. That’d get them out of our hair.
If math is raycis, then by definition, the products of that math – technology products – are also racist, yet the “victims” still want these poisoned products? How does that work?
It’s great to get into theoretical math, things like number theory and modal logic, but for the target audience it doesn’t seem to have much if any practical utility. Likewise it might be great to have different tools in your toolkit, but at least have one tool that you know and can trust.
Perhaps they never heard of Chicana Erica Camacho from East LA, who went to her East LA high school with holes in her shoes to study advanced calculus? And who later graduated, cum laude, from Wellesly and went on to get her PhD in applied mathematics at Cornell University.
I read a little about ethnomathematics because I was intrigued that an RPI graduate was involved. It’s about studying and understanding the mathematics of non-western cultures. It’s cultural anthropology. It’s understanding the use of such things as base 8 and base 20 systems. It’s understanding how counting is done in other languages. I can see how a math teacher can use the teaching of how mathematics is done in other cultures to spark an interest in students. This wasn’t clear, or wasn’t present, in a rapid reading of the articles referred to in the Colonel’s post. It’s certainly not saying mathematics is racist.
For example, Steven Willett is a gifted translator and interpreter of classical poetry. Certainly no one here would call him racist for his interests in languages and ideas outside the dominant western culture. We hold him in high esteem for his interest and skill with these classical languages. Just as with classical languages and foreign languages, we should encourage an interest in the mathematics of other cultures. The same goes for non-western sciences and technology. Just don’t do it to the exclusion of culturally dominant STEM concepts. That would be just as detrimental as teaching only classical Latin or Greek at the exclusion of modern English in the US school system.
I dont think its mathematics which is racist. I think its the idea of objectivity or neutrality in economics, politics, tax policy government. That the kind of thing which discredits the very notion of “objectivity” and “neutrality”.
Euclid was always objective although not realistic or “neutral”. The world is non-Euclidean as any airline pilot will tell you. And yet there was quite a hue and cry when non-euclidean geometry was first developed. Same as the complaints from the establishment about Mr. Galileo’s observations. I suppose its easy to misunderstand or misconstrue mathematical or scientific results. And its similarly easy to think the status quo is always an objectively beneficial outcome or a natural state.
Sometimes it isnt either.
In elementary school (forget which grade) we were taught to use an abacus. It must have been racist because the problems we solved with it had only one right answer. The truth is the woke ones are the racists for believing minorities incapable of understanding math.
2+2=4, but 2+2=10 in a quaternary number system. Such a system was used by several coastal California tribes and certain ancient Indian and Central Asian peoples. It was also used in some computers in the early 60s. So to say that there is always one right answer is wrong.
We spent at least a week playing with different number systems in 7th or 8th grade. Although we didn’t go into cultural or historical backgrounds of these systems, it was interesting and spurred many of our imaginations and helped develop critical thinking skills.
So our K-12 system shouldn’t teach base 10 math but include all the other varieties of advanced mathmatical theory, which they never did before, because……
“we should encourage an interest in the mathematics of other cultures”
we should and must teach American culture first, and leave the rest for extra-curricular activities.
adding two of any object to two more of the same object will always give you four of that object. 2+2 = 4 or 2 + 2 = 10 is a mere matter of notation. And just because certain cultures used other systems of notation does not make those systems their exclusive property. The use of bases other than ten is a concept that belongs to all of mathematics and hence to all.
‘Repeat after me, Winston: two plus two equals five.’ – O’Brien
Wrong answer, 2+2=22……..there’s a video on woke math (youtube somewhere), where a teacher is ‘released’ for not teaching wokism. Great twist at the end……where 2+2 really is 22.
When counting physical objects, such as abacus beads, 2+2 can only equal 4. I don’t know how many times I’ve been given too much change by a young person behind the counter of market. I always return the excess. Higher math depends on first learning addition and subtraction.
It’s almost funny were it not evidence of lazy thinking and premature surrender. Saying base 10 number representation is “cultural” is a quintissential example.
Base 10, (more properly base ten) is as utilitarian and brilliant a construct for human beings of the past and future as are base 2 and base 8 (and base 16) in the context of electronic computers with their binary (on or off) switching-circuit states. The zero – may it be praised! Notice all the base representations make use of it. Want to use base three, or seven? Go for it. Write out their respective positive powers 1,3,9,27,81,243 … or 1, 7, 49, 343, 2401 … . Compare with 1, 10, 100, 1000, … . Now an honest person would pause and concede that in a base three or seven culture’s number representational system the users would invent another set of symbols standing in for 012, and 0123456 respectively. Maybe I could use a smiley emoji for one in base three and a heart emoji for one in base 7 (but I don’t know if emojis print here). In which case the respective powers would be rendered: smiley, smiley 0, smiley 00 .. and heart, heart 0, heart 00 .. etc. Notice those folks, creatures, supremo-wokificents, howsomever, would have needed the idea of zero, and a symbol for zero – who knows what it might look like? An emoji of a gay, elderly, disabled, transgender mulatto albino (with purple hair, of course). Oh, let us not oveook tattooed and at least several tongue piercings, let us not, please never condescend to exclusion and patent bigotry, no. Well let’s say then that that emoji has been designed, crafted, voted on by all sentient internet connected beings, and cast into acceptable form within a drop-down menu in six different hues, or hopefully twelve, allowing for handedness, yes that’s better. Then simply letting one of those culturally diversified zeros be denoted by X, we can redo the base three and base seven integer exponent series of powers as respectively: smiley, smiley X, smiley XX .. and heart, heart X, heart XX .. etc. So how inferior therefore to 1, 10, 100, etc ? Not inferior at all, as X, smiley and heart would be learned and memorized in childhood.
But that’s not the point. We as a species have ten fingers if you count thumbs, two fists, two open hands and can elect to display various combinations. Base ten makes great sense for people who resorted to such sign language for generations. Just as base two did and does for digital computers as well as base eight and sixteen for shortening the length of the very long string of zeros and ones in pure binary displays of large numbers.
The wokester program is not in the bloody crying-out-loud least miniscule tiny sub-microscopic bit about “inclusion.” It is perfectly and diametrically the cruel and pitiless opposite. It is an operation Chaos directed at our society’s and individual’s sense of subjectivity and/or ownership thereof and therefore a death blow to cohesiveness and potential forcinterpersonal affections and bonding. It’s a part of a networked color revolution directed and human hearts and minds. It exposes, unclothes, makes public the domains which for ages were kept private for generations. It actually advertises, trains surgeons and endocrinologists for and promotes as path-breaking and virtuous the practice of widespread genital, metabolic and hormonal self-mutilation. For people barely out of childhood. It didn’t have to get so absurd as to be a parody of itself. But it has. From Brokeback Mountain to our current 1970s Cambodia-style forced march to the jungles in how many years? This time led by college professors and prestigious newspapers. Confusing? Not for an Operation Chaos.
Using the 10 as the base standard in math allows society to function smoothly. Throwing away standards in math and time would create a chaotic society, an Anarchist Free Based Dreamland.
I am afraid, I can not measure up to the quality of commenters such as Cieran, Walrus, English Outsider, Forth and Long (and several others whose names escape me this moment) – and I just want to “throw in” the importance of the use of symbols in mathematics and STEM. In this context I would not underrate the achievement of inventing symbols – such the arabic numerals or integral sign (mentioned by Cieran above) and others symbols. This is seemingly close to the science of semiotics.
The ability to abstract from the “real thing” to give a name for it is one step, and writing it down is yet another step. I wanted to study physics when I was in high school, but was afraid of higher mathematics and chose medicine instead. My older brother who had the talent for mathematics tried to tell me that “the university math is totally different from your school algebra, don´t be afraid…” I did not believe him and I am jealous of people who have that talent.
This article with comments is really enjoyable.
Metric is logically easier than the King’s foot. We’re just use to it.
If you want to know about various number systems, from the counting numbers on up (including, of course, the different bases for integers), this is a serious reference:
Numbers by Ebbinhaus et al
Oh, and let me add a really beautiful four minute video on Geometry:
the trailer for “Dimensions”
Here is the full playlist from which that is an excerpt: