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The Newest Math...

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.
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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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