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The Newest Math...

Graham2001

Graduate Poster
Graham2001
Joined
Aug 19, 2006
Messages
1,740
The 18th Century view on Africans and Maths...


"...in reason [blacks are] much inferior to [whites], as I think one could scarcely be found capable of tracing and comprehending the investigations of Euclid.”
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Thomas Jefferson



The 21st Century view on Africans and Maths...



"1. a focus on getting the “right” answer is “perfectionism” or “either/or thinking;”2. the idea that teachers are teachers and students are learners is wrong;
3. to think of it as a problem that the expectations you have of students are not met is racist;
4. to teach math in a linear fashion with skills taught in sequence is racist;
5. to value “procedural fluency” – i.e. knowing how to do the fractions, long division … -- over “conceptual knowledge” is racist. That is, black kids are brilliant to know what math is trying to do, to know “what it’s all about,” rather than to actually do the math, just as many of us read about what physics or astrophysics accomplishes without ever intending to master the math that led to the conclusions;
6. to require students to “show their work” is racist;
7. requiring students to raise their hand before speaking “can reinforce paternalism and powerhoarding, in addition to breaking the process of thinking, learning, and communicating.”
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(e.g. A much more elaborate way of saying the thing that Jefferson said in the 18th Century...)



From the 1st 'stride' of 'A Pathway to Equitable Math Instruction: Dismantling Racism in Mathematics Instruction."


A link to the document in question is here...


https://equitablemath.org/wp-content/uploads/sites/2/2020/11/1_STRIDE1.pdf


And critical commentary by an African-American writer is linked below...


https://johnmcwhorter.substack.com/p/is-it-racist-to-expect-black-kids
 
Graham2001 said:
The 18th Century view on Africans and Maths...





Thomas Jefferson



The 21st Century view on Africans and Maths...






(e.g. A much more elaborate way of saying the thing that Jefferson said in the 18th Century...)



From the 1st 'stride' of 'A Pathway to Equitable Math Instruction: Dismantling Racism in Mathematics Instruction."


A link to the document in question is here...


https://equitablemath.org/wp-content/uploads/sites/2/2020/11/1_STRIDE1.pdf


And critical commentary by an African-American writer is linked below...


https://johnmcwhorter.substack.com/p/is-it-racist-to-expect-black-kids
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Your quotation is from the critical commentary. Is this the 21st century view of maths as propounded by the equitable math organisation, or the commentator's own critical view of the gist of the pathway document?
 
Graham2001 said:
The 18th Century view on Africans and Maths...





Thomas Jefferson



The 21st Century view on Africans and Maths...






(e.g. A much more elaborate way of saying the thing that Jefferson said in the 18th Century...)



From the 1st 'stride' of 'A Pathway to Equitable Math Instruction: Dismantling Racism in Mathematics Instruction."


A link to the document in question is here...


https://equitablemath.org/wp-content/uploads/sites/2/2020/11/1_STRIDE1.pdf


And critical commentary by an African-American writer is linked below...


https://johnmcwhorter.substack.com/p/is-it-racist-to-expect-black-kids
Click to expand...

Yeah, so stupid, they designed the computer programmes for NASA.

Wielding little more than a pencil, a slide rule and one of the finest mathematical minds in the country, Mrs. Johnson, who died at 101 on Monday at a retirement home in Newport News, Va., calculated the precise trajectories that would let Apollo 11 land on the moon in 1969 and, after Neil Armstrong’s history-making moonwalk, let it return to Earth.

A single error, she well knew, could have dire consequences for craft and crew. Her impeccable calculations had already helped plot the successful flight of Alan B. Shepard Jr., who became the first American in space when his Mercury spacecraft went aloft in 1961.
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NY Times

Why even start on a false premise in the first place? It does not strengthen your claim.
 
What exactly does "7. requiring students to raise their hand before speaking" have to do with math skills?
 
Brainster said:
The latest fad in education is combating structural racism. If black kids are failing at math at higher rates than white kids (and they are), then it must be because math itself is a tool of white supremacy.
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...Or because they live in an unequal society called America.
 
Vixen said:
...Or because they live in an unequal society called America.
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Racism exists, certainly, and blacks are disproportionately impacted, and we should take steps to try to reduce real racism. But 2+2=4 is not racist and claims that it is are transparently ridiculous. Not teaching black kids to learn math is putting them at a huge disadvantage in life.

But perhaps you disagree and feel the hard math should be reserved for whites and Asians?
 
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Brainster said:
Racism exists, certainly, and blacks are disproportionately impacted, and we should take steps to try to reduce real racism. But 2+2=4 is not racist and claims that it is are transparently ridiculous. Not teaching black kids to learn math is putting them at a huge disadvantage in life.

But perhaps you disagree and feel the hard math should be reserved for whites and Asians?
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Don't be silly. Academia has always been a class/cultural thing, nothing at all to do with race.

The worst qualifications in the UK are working class boys.
 
Lplus said:
Is this the 21st century view of maths as propounded by the equitable math organisation, or the commentator's own critical view of the gist of the pathway document?
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Probably both. It is based on a brain child of William Spady called "Method Learning" which seems to be based on the concept that if you can get a student to think critically then they will automatically learn all of the necessary skills without being needed to be taught anything.

Although Method Learning proved to be a spectacular failure compared to other methods of teaching, politicians and bureaucrats became enamoured by the idea and forced schools to adopt it. It subsequently became to be called "Outcomes Based Education" and although public outrage forced many governments to scale back on this plan, I understand that it is still practised religiously in places like California.
 
This is a discussion video on the 'Anti-Racist Math' booklet, one of the speakers is John McWhorter and the other is Glen Loury. The first is the man who wrote the critique I linked to in the OP, they point out just how racist the proposals actually are. This quote from Erich Von Daniken's 'Signs of the Gods' is as good (and sadly ironic) a summary of what the 'Woke' believe 'Black Culture' to be:


“Nearly all negroes are musical: they have rhythm in their blood.”
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Erich Von Daniken (From Jason Colavito's blog.)
Link: http://www.jasoncolavito.com/blog/the-astonishing-racial-claims-of-erich-von-daniken


And here is the full 'In Defence of Knowledge."



https://www.youtube.com/watch?v=CbJWi6KkcHs
 
Graham2001 said:
This is a discussion video on the 'Anti-Racist Math' booklet, one of the speakers is John McWhorter and the other is Glen Loury. The first is the man who wrote the critique I linked to in the OP, they point out just how racist the proposals actually are. This quote from Erich Von Daniken's 'Signs of the Gods' is as good (and sadly ironic) a summary of what the 'Woke' believe 'Black Culture' to be:





Erich Von Daniken (From Jason Colavito's blog.)
Link: http://www.jasoncolavito.com/blog/the-astonishing-racial-claims-of-erich-von-daniken


And here is the full 'In Defence of Knowledge."



https://www.youtube.com/watch?v=CbJWi6KkcHs
Click to expand...

Here's the bind that math teachers are in. If they fail Black students at higher rates than white students, then they will be providing evidence of structural racism. This of course is not a desirable outcome, so they have two options--find a way to make Black students as good as white students at math or just declare that they are as good and don't need to actually prove it. It's not hard to see what the path of least resistance is going to be.
 
p0lka said:
Couldn't you just create a different course about black maths or something?

Black folks will ace it and the white folks will be left behind. Cos it's black maths.
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The Oregon curriculum includes a section on "Ethnomathematics."

Recognize the ways that communities of color engage in mathematics and problem solving in their everyday lives.
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I am struggling to think of a way that communities of color engage in mathematics that white people don't that doesn't involve explicitly racist assumptions about the former.
 
Brainster said:
The Oregon curriculum includes a section on "Ethnomathematics."



I am struggling to think of a way that communities of color engage in mathematics that white people don't that doesn't involve explicitly racist assumptions about the former.
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I don't get it.

Regardless of ancestry, if kids of whatever colour grow up in a culture learning maths from a young age then they are all equally ready for more maths.

To posit that there's a difference is back to the "lesser people" stuff.
 
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p0lka said:
I don't get it.

Regardless of ancestry, if kids of whatever colour grow up in a culture learning maths from a young age then they are all equally ready for more maths.
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Sorry, that is white supremacist math:

White supremacy culture shows up in math classrooms when...Math is taught in a linear fashion and skills are taught sequentially without true understanding of prerequisite knowledge.
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The bit about prerequisite knowledge sounds a bit contradictory, but apparently the gripe is that some subjects shouldn't have as much prerequisite knowledge as they currently do:

While some mathematical skills and concepts build off each other, the forced construct of linear teaching reinforces objectivity. A prime example is how matrices is considered a precalculus standard, even though the only math skill needed as a prerequisite is arithmetic. This is highly detrimental to students because they are systematically deprived of knowledge they could access due to false constructs.
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I read through that guide and don't see what 'race' has to do with it. All of the examples point to culture, and some inherent differences in concept vs procedure- though exactly how that plays out, where certain non-white students understand a concept but somehow can't also follow a procedure is not explained. It's just assumed that this is some basic truth about students of color and that white supremacy is the reason. :confused:

As a parent who was taught the old "new math" before common core I can relate to this one part of it:
The point should be to have a dialogue about
their process and their learning, not require
every student to follow the exact same path to
the right answer.
The child of immigrants might have learned a
different way to solve a problem because that’s
how their parents were taught where they grew
up. If we just tell that student their way is the
wrong way, we risk turning them off to math for
life. If we take the opportunity to explore why
there are different ways to approach the same
problem, it can be a learning moment for the
entire class.
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In helping my kid with homework, I often say "Well, that's not the way I do it!". I have had to self-tutor just to help her- even with stuff back in first grade.

Last week she had an algebraic equation and I told her to get rid of the fractions on both sides first, then solve with whole numbers. She said that was "wrong" and the fractions are kept till the last step as the workbook showed.
Why make it more difficult? I told her it was a dumb way to do it and would likely lead to a higher rate of mistakes to carry all those extra numbers down. She gloated that "Mom got it wrong!".
This was empowering for her and hardly 'turned off'.
For the most part I usually just ask her to walk me through her process and most of the time she gets to a part where she says "Oh! Got it! ...never mind Mom".

I am not very useful with the new math. :p

If kids can get to the correct answer through a logical process and show their work, they should get full points.

To be more worldly as a STEM culture for all, maybe the US could fully adopt the metric system like they said we would 'very soon' when I was a kid in the 70's.
 
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Skeptic Ginger said:
:bigclap

That was an enjoyable 10 minutes. And who knew everyone around the world didn't get their number systems from their 10 fingers!
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Numberphile is a great channel. There are some other bases that actually turn out to be quite common. Apparently the Sumerians used base 60 which survives today in the form of minutes and seconds. This is extremely useful because it means hours can be broken down easily into halves, thirds, quarters, fifths and sixths without the need for fractions or decimal notation.

That said, I don't think many US kids are failing at math because they are accustomed to using a different base.
 
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Brainster said:
Numberphile is a great channel. There are some other bases that actually turn out to be quite useful. Apparently the Sumerians used base 60 which survives today in the form of minutes and seconds. This is extremely useful because it means hours can be broken down easily into halves, thirds, quarters, fifths and sixths without the need for fractions or decimal notation.....
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Thanks. That's another 'who knew' for my collection. :thumbsup:
 
I find that counting in base 2 with your fingers can make it really easy to show emotional content with just a number.
ie 4, or with both hands 132.
or the traditional british sign 6, or with both hands 390, can be helpful in text only environments.
1 or 513 is always nice.
 
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psionl0 said:
:confused: How could expecting students to show their work be classified as "white supremicist?
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It triggers racial memories of slave overseers demanding to see how much cotton each slave had picked that day or something I suppose. Again, you're looking at this the wrong way, expecting it to make actual sense. The real purpose is to give teachers a way to ensure that their grading results in similar %s of each race getting As, Bs, Cs, etc. If you don't have enough black kids getting As, you're going to be branded a racist. So you adjust for your racism by not demanding that students of color show their work. Magically, this results in higher grades for those students and you don't get branded a racist.
 
I believe common core and earlier things like CPM were quite innovative but very demanding on teachers who were taught earlier methods. The result was often pretty bad. But I think connecting math with things more tangible results in better understanding and longer retention.

Math is best learned and retained when students can see what power it provides to solve problems.

My personal experience started off pretty bad. I was the slowest kid in the class learning arithmetic and math. And I hated school. Then, on the side, I got interested in what it actually meant. Logarithms became a shortcut to multiply and divide. How cool. Then I learned how it worked. Even more cool. Chemistry was interesting and used the math in clear ways. Same with Physics. It was all very interrelated and, because of that, suddenly became quite easy and natural. And it seemed memorizing was no longer needed which was good because I was particularly bad at that. It just all made sense. OTOH, most of what I learned was from library books as I'd peruse topics of interest. These interests migrated to different areas over time. By 9/10th grade calculus became intuitive making various physics and chemistry problems easily solved.

However, my formal study habits were non-existent and I hit a wall with quantum mechanics which were not intuitive. I flunked out, and had to retake the classes. Oddly, I did OK on the second pass as the math and physics started to make more sense.

In my career, I made heavy use of math much of which I learned after college.

It's clear to me that people learn in different ways but connecting what is learned in math to chemistry and physics helps overall and makes the knowledge stick. Also makes it fun and easy.
 
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marting said:
I believe common core and earlier things like CPM were quite innovative but very demanding on teachers who were taught earlier methods. The result was often pretty bad. But I think connecting math with things more tangible results in better understanding and longer retention.

Math is best learned and retained when students can see what power it provides to solve problems.

My personal experience started off pretty bad. I was the slowest kid in the class learning arithmetic and math. And I hated school. Then, on the side, I got interested in what it actually meant. Logarithms became a shortcut to multiply and divide. How cool. Then I learned how it worked. Even more cool. Chemistry was interesting and used the math in clear ways. Same with Physics. It was all very interrelated and, because of that, suddenly became quite easy and natural. And it seemed memorizing was no longer needed which was good because I was particularly bad at that. It just all made sense. OTOH, most of what I learned was from library books as I'd peruse topics of interest. These interests migrated to different areas over time. By 9/10th grade calculus became intuitive making various physics and chemistry problems easily solved.

However, my formal study habits were non-existent and I hit a wall with quantum mechanics which were not intuitive. I flunked out, and had to retake the classes. Oddly, I did OK on the second pass as the math and physics started to make more sense.

In my career, I made heavy use of math much of which I learned after college.

It's clear to me that people learn in different ways but connecting what is learned in math to chemistry and physics helps overall and makes the knowledge stick. Also makes it fun and easy.
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QM as in a primary grade class?

Or was that a college course?
 
Classroom teaching is hard, for not much financial reward. Many people who become teachers think life must be easier in administration, so they all get master's degrees or doctorates (usually in "education," not a primary subject area). Then, to justify their existence they have to constantly make up new crap for classroom teachers to do. So someone comes along with a bright idea that hey, instruction shouldn't be racist. That sounds good so it all comes down to better training for teachers. Which means people have to come up with structures for workshops or seminars to offer special training in how not to be racist. Training materials are needed, so someone puts together a document that then, IMO, takes on an inflated degree of importance because it get shared around the Internet to demonstrate that political correctness is out of control.

Teachers meanwhile are trying to be good sports, and they roll their eyes but follow the path of least resistance, which means acting like they're taking antiracism training seriously. But once they've received the training (often as part of required "continuing ed" time), quite possibly not much will come of it, since they're the same people using the same texts to teach the same mix of students to the same state standards. They might customize some problems, like changing names in word problems to "Josue, Jamal and Yuki" instead of "Joey, Bobby and Sue," or whatever.

Then, no matter what else happens, the same ideas will circulate for a brief time, be forgotten, then be resurrected the next time an administrator needs to justify their existence by making up new things for teachers to do.
 
Skeptic Ginger said:
QM as in a primary grade class?

Or was that a college course?
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Last semester sophomore in college. I was used to partying, skating, and not going to class, but just taking midterms and finals. Got by on what I'd already learned. Worked great up until QM then had a rude awakening.

Wound up going to many, but not most, of my classes after that. Got C- in the ones I didn't like and A+ in the ones I did. Used math extensively working. Especially linear analysis, statistics, and Galois math. Probably spent $10k/y on texts after college.
 
I can't speak for all teachers but in my experience students are so individually different from each other that I never get around to sorting them by race.

Also, as a group they are so different from me that I might as well be a cultural anthropologist studying some remote tribe. That they come in different colors is a detail.

I watched a vid recently about working an abacus. It would be fun to have a lesson around it because a) no one's going to be very good at it and b) conceptually it might be a game-changer for some kids. But I would never have that lesson IRL because it does not address any state standards regarding what students should be able to do at the end of a course of study. It's too bad in a way that so much of math must be learned sequentially. But that's how math itself developed to some extent. That does make it less "democratic" in a sense.
 
Minoosh said:
I watched a vid recently about working an abacus. It would be fun to have a lesson around it because a) no one's going to be very good at it and b) conceptually it might be a game-changer for some kids
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Funny you mention that. In the summer between 6th and 7th grade, I ran across an abacus at the Boston Museum of Science's library. Checked it out and got quite good at it. I hated doing arithmetic and an abacus became my scratch pad. Slide rule and abacus together can't be beat.

So yeah, it might well be a useful teaching tool though what attracted me was removing most of the drudgery of adding/subtracting when I was playing with ideas. Had I been born 15 years later, it would not have interested me. I valued it as a tool.

Of course the HP35 came out a year after I graduated college and the abacus/slide rule was retired. Still have them and the abacus is on the coffee table.
 
marting said:
Funny you mention that. In the summer between 6th and 7th grade, I ran across an abacus at the Boston Museum of Science's library. Checked it out and got quite good at it. I hated doing arithmetic and an abacus became my scratch pad. Slide rule and abacus together can't be beat.

So yeah, it might well be a useful teaching tool though what attracted me was removing most of the drudgery of adding/subtracting when I was playing with ideas. Had I been born 15 years later, it would not have interested me. I valued it as a tool.

Of course the HP35 came out a year after I graduated college and the abacus/slide rule was retired. Still have them and the abacus is on the coffee table.
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When I retired last year after 46 years in mechanical engineering I walked out of the office with a few personal items and left all of my accumulated "technical" stuff in my desk drawers for young engineers to find and puzzle over. Among the things I left was my slide rule. I sometimes think I should have kept it.

I would like to have been there to see some EIT discover things like eraser shields, lettering guides, and railway curves.
 
marting said:
Funny you mention that. In the summer between 6th and 7th grade, I ran across an abacus at the Boston Museum of Science's library. Checked it out and got quite good at it. I hated doing arithmetic and an abacus became my scratch pad. Slide rule and abacus together can't be beat.

So yeah, it might well be a useful teaching tool though what attracted me was removing most of the drudgery of adding/subtracting when I was playing with ideas. Had I been born 15 years later, it would not have interested me. I valued it as a tool.

Of course the HP35 came out a year after I graduated college and the abacus/slide rule was retired. Still have them and the abacus is on the coffee table.
Click to expand...

I tell the kids I tutor that when I started out, spreadsheets were quite literally lined sheets of paper that we filled in with pencils. Changing a single assumption (let's say the inflation rate) was a whole afternoon's work. However, we did at least have calculators.
 
psionl0 said:
:confused: How could expecting students to show their work be classified as "white supremicist?
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It goes something like this


1) do you agree different cultures around the world teach and learn math using different methods?

2) do you agree they grade differently?

3) do you agree different cultures in the same country teach and learn math differently?

4) do you agree white culture dominates in the US?

5) do you agree the methods of teaching and learning of the white culture are imposed on other cultures in the US?


Now, one can reject those premises, but that appears to be the gist of it. The implication is that in China the system is han supremacist, and in South America it would have its own supremacy, etc.
 
BobTheCoward said:
It goes something like this


1) do you agree different cultures around the world teach and learn math using different methods?

2) do you agree they grade differently?

3) do you agree different cultures in the same country teach and learn math differently?

4) do you agree white culture dominates in the US?

5) do you agree the methods of teaching and learning of the white culture are imposed on other cultures in the US?


Now, one can reject those premises, but that appears to be the gist of it. The implication is that in China the system is han supremacist, and in South America it would have its own supremacy, etc.
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Except that there is an exception in the US called: The Asians (not mentioned in that anti-racist math guide)

I'm sure there could be reasons given for selective immigration for Chinese, Korean and even Filipino students here in California (which is the state the guide is meant for)
But what of the Vietnamese? the Cambodians?

These were refugees that came in the 70's and 80's with very little in terms of education, English skills, and nearly all were in the poverty bracket.
So I looked at the main public high school in Little Saigon here in Westminster. 80% Asian (nearly all are Vietnamese), 3% white. 62% of students considered low income. 17% are learning English.

In every metric, they still do better than every other ethnicity. Better than the nearby majority white school in the affluent beach community of Corona del Mar where low income students are just 9%. (it was actually difficult to find a public school around here with majority white students that was near enough to compare).
This result is repeated again and again and again in schools across the state.

Recommendations on race inequalities in Math that focus on "white supremacy" when the top scores are by far the Asian students- no matter their income or culture or English skills when they get here is quite a big omission. At the very least they should give some theory on why they excel.

Asian students are more than double the population of black students in the state and second in immigration only to hispanics.
 
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Sherkeu said:
Except that there is an exception in the US called: The Asians (not mentioned in that anti-racist math guide)

I'm sure there could be reasons given for selective immigration for Chinese, Korean and even Filipino students here in California (which is the state the guide is meant for)
But what of the Vietnamese? the Cambodians?

These were refugees that came in the 70's and 80's with very little in terms of education, English skills, and nearly all were in the poverty bracket.
So I looked at the main public high school in Little Saigon here in Westminster. 80% Asian (nearly all are Vietnamese), 3% white. 62% of students considered low income. 17% are learning English.

In every metric, they still do better than every other ethnicity. Better than the nearby majority white school in the affluent beach community of Corona del Mar where low income students are just 9%. (it was actually difficult to find a public school around here with majority white students that was near enough to compare).
This result is repeated again and again and again in schools across the state.

Recommendations on race inequalities in Math that focus on "white supremacy" when the top scores are by far the Asian students- no matter their income or culture or English skills when they get here is quite a big omission. At the very least they should give some theory on why they excel.

Asian students are more than double the population of black students in the state and second in immigration only to hispanics.
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Why does that change anything? If a dominant culture is forcing their cultural standards on others, whether a group succeeds or fails wouldn't change that.
 
There was some theory that Chinese math ability was to some extent linked to the Chinese language. I'm alluding to Malcom Gladwell from memory so I'll be vague: If the word for "thirty-two" is "3 tens 2" and you add it to "5 tens 7," you will be linguistically primed to turn this into "8 tens 9," or to add the 10s then adjust if something has to be carried.

Gladwell must have at least implied that this is a trait of the Mandarin language.

"Mental math" capacity was linked to the number of syllables that could be retained. If numbers were represented by single syllables people could (apparently, allegedly) retain info a little better as they went along.

He also proposed that the culture was more predisposed to counting due to the nature of its feudal system - overperforming farmers paid fixed taxes and got to keep more grain in "profit" as opposed to the Russian system, where authorities kept a percentage or just took almost everything.

Culturally and historically, memorization skills offered a path of upward mobility for people gifted with such talents. To be literate required a great deal of memorization as there are so many words that are characters and characters that require a lot of brush strokes. To become a clerk or an accountant was a foot in the door with the ruling class.

Now, this all could be horse****, Gladwell can pull everything together pretty convincingly as you're reading him, but he's kind of glib, and not necessarily super rigorous from a research standpoint.
 
He's obviously a member of the notorious terrorist organisation Al-Gebra. Haul him in and charge him with possession of weapons of maths instruction.
 
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