Teaching math as strictly a set of algorithms and processes isn’t the best solution. Just because a kid can do something doesn’t mean he understands what he’s done. Let’s teach both – including lots of practice on the ‘doing’ math.

That certainly didn’t prove to be the case with Spanish-speaking immigrant children here in California. The so-called “bilingual” education they received, until the practice was ended by voter initiative a few years ago, was, in practice, Spanish-only or Spanish-mostly instruction and high school graduation rates were abysmal.

More broadly, if it is the intention of a foreign-born resident to live and work, long-term, in the United States, lack of facility with English is pretty much a guarantee of a marginal, ghettoized economic and social existence. Not only can such a person not interact easily with “regular Americans,” he or she is also handicapped to the same degree in most interactions with other foreign-born residents of America who just happen to be from countries where neither English nor the first party’s native language is spoken. This is an especially significant barrier in places like Los Angeles which are linguistically and ethnically so diverse as to render any approach other than the use of English as “lingua franca” totally absurd. I live in a suburb of Los Angeles. If I had to know how to speak “natively” to anyone from any ethnic group whose members operate businesses here in town of which I have been a customer in, say, the past year, I’d have to speak at least eight languages (Japanese, Cantonese, Mandarin, Korean, Vietnamese, Khmer, Tagalog & Spanish) in addition to English. As it happens, I speak none of these, and yet I can buy what I want from people who do speak them because each of them also speak English.

Note also that Asian languages, because so many are represented among immigrant populations in Los Angeles and most are completely mutually incomprehensible, were almost never part of the “bilingual instruction” edifice even when it existed here. Only Spanish was the language of enough immigrant speakers to make it an even marginally practical second language of instruction. Leaving aside the racism implicit in a program predicated on the idea that only native Spanish speakers were at an otherwise insuperable linguistic disadvantage in English-based American classrooms, the objectively wretched results of this ill-considered exercise in cultural condescension were more than sufficient to warrant its termination with extreme prejudice. In the event – a powerful and self-interested bilingual education lobby having grown up around the program and rendered it the usual corrupt cash cow that most government programs seem to eventually become for their staffers – it required the force majeure of a public plebiscite to finally send the thing to its just reward.

In a recent college class (4-year liberal arts college), I did not have one student who could tell me the answer to 10% of 200 or could add and subtract proper fractions without common denominators. Most could not do long division without a calculator.

Allen is exactly right–we are so screwed! Wait a minute–I’m not screwed–I can do basic math. My kids aren’t screwed–they can do basic math. They did writing in subjects where writing was appropriate. Of course, they attended a school where math was done in math class. Silly me.

Such nonsense.

High school graduation is MORE likely if (as with those German language public schools in the US prior to WW I), the language of instruction is the student’s first language.

“If you can’t explain it then you don’t really know it.”

Verbalization of mathematics is valid because math is more than symbols and operations. Even in the most abstract situation those symbols and operations are being used to complete a task. What’s the task? Why are you doing this step as opposed to another? Does this symbol mean what you intend it to mean?

With that said, executing mathematical processes is important in its own right. A quote from sports that I like is: “tactical knowledge is useless without technical knowledge” which basically translates as “knowing what to do but not how to do it is pointless”. At some point you do have to go back to the symbols and operations and show how you can manipulate them so that when its time to apply them you have the necessary tools.

Assignments like those given in Connected Math are garbage because they ignore how you acquire information. I like to spend money but if I don’t know how to acquire money (legally) then my opinions on spending it are irrelevant.

On a separate note, one of the ultimate goals of education should always be communications and integration of culture. Speaking a common langugage and having a common identity should be the goal of any nation. Diversity is only possible when there is sufficient attributes in common to bind individuals together. Switzerland is the exception that proves the rule: historically nations that have multiple first langugages and identities struggle because ultimately communications break down (see Belgium, Canada, Czechoslovakia, East and West Pakistan, Spain, et.al.)

You have evidence for that claim? No, I didn’t think so.
Kids who get all their instruction in their native language work out fine if as adults they live in a country where their native language is dominant. If they’re going to live in a different country, for instance this one, they are at a lifelong disadvantage (as was your Korean student with limited English). High school graduation is unlikely, college graduation essentially impossible.

The success of foreign graduate students in certain fields demonstrates only that the very smartest students, who are the only ones who qualify for study abroad, can overcome this disadvantage in fields where native-language fluency is moderately less crucial. At the time I taught in China, about 20 years ago, only about 2 percent of high school graduates went to university, and only a tiny fraction of those were approved for foreign study. They do well? Sure, but so does the comparable segment of American students.

A. The way to teach tolerance of diversity is to tolerate diversity, seems to me. The multiple language culture works fine for Switzerland. According to Thomas Sowell, there were public schools in the US where the language of instruction was German up to WW I.

Kids also work out fine (better, probably) if they get all their instruction in their native language. Consider people who attend an undergraduate institution in China or India and transfer to US grad schools. They dominate Math, Physics, and Engineering programs.

B. I recently had the great privelege of tutoring a Korean 5th grader who was in the US for a year for English immersion. She returned to Korea last June. In Korea she attended a program for GT students which operated out of some university (she was not in school with age-mates). Her parents hired me to supplement the wretched Math instruction she received at a rather exclusive independent school. I introduce the notation of set theory and logic as early as possib;e, and then spend as much time as it takes to develop facility with the notation of lines in 2-space. This we could do, and I could use some notation which involved definition by recursion and proof by induction, but I could not explain these ideas to her. I found this very frustrating. She deserved a teacher fluent in Korean.

I tutored her second cousin from 3rd through 6th grade, and we continued to discuss his coursework after I turned him over to the University Math faculty. One day he asked me if a limit had to be a number, and I explained that the line tangent to a curve is the limit of a sequence of secant lines, that the plane tangent to a surface is the limit of a sequence of secant planes. This question could occur in any language, and it can be answered in any language. It cannot be expresed in an unfamiliar language, and it cannot be answered in English if the recipient doesn’t understand English.

He just got his MS (Math). He’ll be 20 next January. Homeschooled after 7th grade. He came to the US at age 3 and read English fluently before we met. The language barrier which limited my ability to help his cousin did not exist for us.

C. “(I)f they’re recent arrivals, they should be focusing on English first.” Dunno what you mean by “should”.

My first experience with math and writing was being tortured by my geometry teacher’s “always, sometimes, never” questions. While taking Calculus, I would do a sample problem but also write out in step by step format how to do it in my notes. When I was substituting in high school math classes, I used my double technique and was amazed when a couple of kids thanked me for it.

My kids’ fifth grade math teacher makes her students keep a math journal. It was very interesting. I loved that she would sometimes make the students write out how to solve a problem rather than just solve it.

Joanne’s example of a sixth grade math journal is pretty disgusting. Don’t throw the baby out with the bathwater though.

So let’s Balkanize America. Because it’s worked so well for Canada. Though they’ll have to work harder, I bet those Koreans will end up just fine.

Though, unless they’re recent arrivals, I’m a bit mystified as to why they’re still not literate in English if they’re studying recursion and proof by induction. And if they’re recent arrivals, they should be focusing on English first.

Unless they want to live like Hutterites.