IQ and general intelligence are often measured by the ability to understand and apply abstract concepts. You can’t teach math to your dog, for example. Very simple addition (food items, only, nothing abstract) is the absolute maximum for a dog.
Do you think, USA may need some differentiated education tracks? For kids who do understand abstract concept and kids that have issues with abstract concepts but may work with direct examples? Like, “you had 3 apples and gave away one apple”, instead of 3-1=? There are 300 million Americans, many kids are able to understand abstract concepts.
Unless you have (at least some kids) in an advanced math track, unless you teach some K-12 students abstract concepts, ALL R&D would move abroad. If a 12-year old is not able to understand x-3=5, despite all efforts to teach him/her, … you really can’t train him/her to become an engineer or STEM scientist. Ever.
Manufacturing had moved to China. Computer programming is increasingly outsourced to India. Most STEM graduate students and scientists at the top universities are foreign-born. I mean … what kind of jobs will our kids have without advanced math? Service providers? Sales and marketing?
quote Stats is a separate department in a lot of universities. The attempt to integrate probability theory (where one has to use a number to measure probability) with mathematics, as you know, ran into the measurability problem, a fundamental issue with real numbers, hence the awful Kolmogorov stuff. (There’s a cute alternative by John Nelson that would probably be better than real numbers and it avoids all those problems. Did it bother you that all thru calculus you were told to use Real Numbers and they never told you what they are?) This is not a probability specific problem. You can’t really apply calculus to physical problems either, or anything else with real numbers.
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These days, a lot of the probability research is a subset of measure theory, which is what you allude to. There are statistics departments of course, and they are the ones that cover statistics and probability on the more applied level, but this still doesn’t get at the real problem. It ties better into the later part of your post so I’ll cover it below.
Maybe I didn’t really express this as well as I should have.
I’m well aware of the importance of analysis, algebra, and the like. I know about their theoretical importance and their relevance to other fields. I don’t think that we should abandon or scale down research in these fields at all. The problem is, math departments self-select against the most applied aspects of their fields and “push it over the hill” into other fields that use mathematical results, such as the engineering, science, and business departments. So “math” turns into “abstract theoretical math” in the sphere of academia.
Problem is, “math” is very important in the applied sense, and who will have the most influence on math pedagogy? Mathematicians, obviously. You don’t ask a business or engineering professor their thoughts on math nearly as often as you would ask a math professor. And since math academia has generally distanced itself from the practical and applied aspects of its curriculum, guess what that means for the math professor influenced curriculum that students learn?
I see complains about European/Asian teaching methods.
I believe in evolution. If something works, it means that it is successful, even if it looks like unfair to us. Asian students are great in math. They outperform Americans, big time. Maybe they are doing something … right? Even if it looks creepy / unfair / non-exclusive. In the end: students, know math, economy is growing, American companies transfer manufacturing (and recently, R&D) to Asia.
To get American passport, that opens all borders and provides significant benefits? It enables travel, doing business around the world, opens bank accounts. It shields you from political persecution (just in case). It instantly raises your salary, if you are working for an international company. It gives all kinds of social benefits for you, and your family.
European and Asian international students are NOT coming to USA to learn math. Math is great in a number of a select USA colleges, but most faculty/students at these colleges are foreign born.
Well, this is a much bigger topic than this thread, but I’d be very, very cautious about reading the results of international tests like the PISA exam, no matter what educational reformers in this country like to do with them. While such exams do test for ability, they (like pretty much any standardized exam) disproportionately reward those systems that “teach to the test”. There are a number of countries’ educational systems that are quite open about teaching specifically those things that are dealt with on the PISA instrument and the like, but not branching out beyond that except for select students.
I would suggest that such a country’s students doing well on the math portion of the PISA exam relative to US students does not mean that there is higher math ability among that nation’s students. In actual fact, it means effectively nothing either way.
Getting an American passport wasn’t their intention and most went back to their home countries when they completed undergrad in the US.
They came to the US because if they stayed in their home countries, they’d be confined to the lower vocational tracks or be content with working the rest of their lives in the unskilled farming/labor force as the routes to academic track and college education was closed to them because of how they were assessed by educators/exam by the end of middle school.
Back in their home countries, such students weren’t considered “college material” and as such, no viable route for them to get on the path to college if they had wanted/later changed their mind.
According to Hacker, math is the subject requirement that most often results in failure to graduate. Since failure to graduate it is not evenly distributed across subjects, it think that it is fair to scrutinize how math is taught & required, which is what his book does.
Most American public schools are “teaching-to-test” nowadays. I don’t know about Asia, but European schools are less “teaching-to-test” than American schools. PISA is not on the radar screen of most European public schools (I was told by European colleagues).
My personal experience tells me that many Chinese students go back to China after getting green card. However, I have to say that these4 students are very bright. I don’t think that they very ever considered “non-college” material. Maybe we met different subpopulations of Asian students.
OK, maybe not every student in k-12 is able to graduate in non-sheltered track. Do we have to through Algebra 1 from school curriculums, because some kids need sheltered math?
^^^ If students were most often not earning their HS diploma because of History, we would be right to ask:
-How is it being taught?
-Precisely why are we requiring it?
-How useful it is to learn, with real-world examples
-Why are so many students failing it?
This is what Hacker is asking about Math.
-Precisely why are we requiring it? we don’t require it, life does. For the last 3,000 years people are using math for everything.
-How useful it is to learn, with real-world examples Math doesn’t care if you learn it or not. If you want money, you better know how to count money.
-Why are so many students failing it? There are 300 million people in America. Not everyone is capable of learning math. The reason, why people, who know math earn lots of money is because not every person is capable of learning math.
Students can get HS diploma with sheltered math. At least in our school district. My friend’s son is autistic, he can’t learn math, he is taking sheltered classes and getting his HS diploma.
I have 4 daughters. I am used to answer questions “why do I need to learn math”. You don’t have to. If you don’t want to learn math - somebody else would. Somebody else would get a nice car, nice jacket, nice toys. Math=money. Toys=money. Math=toys.
If 19% of high school graduates can’t read (15 seconds on google, someone please tell me it’s overstated), should they have graduated? Why criticize math for its rigor instead of singling out the humanities and social sciences for their appalling lack of standards?
Because everyone has to graduate from HS and everyone has to go to college. Once we will achieve it, wars, crime, famine, and diseases would disappear and we will all live in paradise. Happily Ever After. Don’t you want to live in paradise?