CA Dept. of Education opposes HS calculus?

Parents Forum
42

Depends on the student. Looks like the goal is to have a common +0.5 track starting in 8th grade, allowing for acceleration to +1 (and therefore calculus) by 12th grade for good students, versus the current system of early tracking (as early as elementary school) between +0, +1, +2, … that seems to have gotten out of hand (leading to the two year AB then rest of BC calculus sequence which dilutes the experience for true math talents, or the common trend of repeating calculus in college, because students are pushed too far ahead by parents in the “race to calculus so you can repeat it in college”).

But it really depends on whether the schools can allow the true math talents to accelerate or otherwise learn additional optional math as appropriate for them, while also saying “NO!” to parents who want to over-accelerate their good-but-not-great-in-math students.

1 Like
43

No curriculum will likely meet the needs of the true math talents.

44

No US curriculum perhaps. The UK curriculum, with almost all students taking GCSE and then a choice of maths and further maths A levels for the last two years of high school, accommodates true math talents (certainly up to the top 0.1% and perhaps slightly beyond that) pretty well, although not all schools are able to teach further maths competently.

1 Like
45

Please refrain in debating and from calling out individual users. State your point, defend once if needed, and move on.

2 Likes
46

This is also about money, isn’t it? Because deciding all 8th graders and all 9th graders must take the exact same class allows schools to lump all kids together rather than creating separate (possibly smaller) groups and having more math teachers to teach them all.

IMHO, reasonable pathways could look like this:
8th grade
Math Path A: Algebra1a+Geometry1a+Statistics 1a
or
Math Path B: Algebra1a+Statistics 1a

9th grade
Math Path 9A*: Algebra1B+2a+Geometry1b+Statistics1b
or
Math Path 9A: Algebra1b+ Geometry1b+Statistics 1b
or
Math Path 9B: Algebra1b+Statistics 1b
(After 9th grade, Path B students can take Geometry over the summer if they wish to join Math A)

10th grade
Math 10A*: Algebra2b+precalculus H (+AP stats optional)
or
Math 10A: Algebra2 (+AP stats optional)
or
Math 10B: Geometry
(Math 10A students who want to join Math 11A* must take Precalc over the summer, Math 10B who want to join Math 11A must take Algebra2 over the summer)

This system requires each school to offer sections of 3 different math classes for each grade in 9th&10th (6 different classes that aren’t interchangeable), since Math 10B is not the same as Math 9A. Unlike the current system, where all kids are put together, saving the district money, this would require extensive investments in recruiting (probably through college scholarships) math teachers and in funding math education. After 10th grade, the classes are easier to add, ie., Path B 12th graders and Path A 11th graders could be taking the same class, hence freeing teachers for math electives (or smaller, lower sections). Path A* and A get to calculus by 12th grade if they wish but other choices are offered.

11th grade
Path A*: Calculus (+ math electives: Discrete math, ?)
Path A: Precalculus&applied math
Path B: Algebra 2

12th grade
Variety of choices: AP Stats, Discrete Math, Applied Math, Data Science, Calculus, Math for personal finance…

2 Likes
47

For Eastern European Jews, they had the tests translated to Yiddish.

48

And I’m sure that there were a wide range of results on the test that was translated – assuming that the translations were accurate – because, you know, people are different. And there are many explanations other than “systemic racism” for poor results.

49

The translations were as good as any. However, the tests, just like today’s tests, were deeply embedded in the USA culture of the period, a culture which was entirely foreign to Jews from the Shtetls or the Jewish regions of East Europe.

Furthermore, the Jews were entirely unfamiliar with that particular format of a test. Even today, among kids who grow up surrounded by tests, there is, on average, a 60 point increase in the SAT score of kids who have already taken the test.

Again, because teaching and testing are cultural.

After all, a person who has never learned how to present a proof will never be able to answer any problem in geometry correctly, no matter how talented they are in geometry. Are you going to argue that the way that mathematical proofs are presented in geometry is NOT cultural?

I mean - the notations are in Greek and Latin. What does Q.E.D. stand for? Something in an Asian language?

Why is it “Euclidian” geometry?

2 Likes
50

I have to take issue with the assertion that geometry, or mathematics in general, is somehow cultural. Geometry proofs, or any mathematical proofs, are in the language of mathematics, which is universal. A proof written in German can be read by a Chinese, and vice versa.

Euclidean geometry? It’s just a name that mathematicians used to distinguish it from other forms of geometries that are based on different sets of axioms. It may be called something else in another culture as long as it’s defined in the same way.

1 Like
51

Math PhD programs do tend to require a reading knowledge of French, German, and/or Russian due to the necessity of reading math papers in those languages. Since they actually test for such reading knowledge, it does not look like they assume that everyone can automatically read a math paper in a language that they do not otherwise know, even though the reading knowledge for math purposes is only a subset of the knowledge that one would use for general purposes (and some colleges have courses specifically to teach and emphasize reading knowledge of some languages for these purposes).

2 Likes
52

There may be explanations in writer’s own language if it’s a very complicated proof published in a research journal. Even in those circumstances, the expressions and vocabularies used tend to be highly standardized in any language that readers can easily follow.

The proofs and such that we’re discussing here are much simpler. They can almost always be presented with very few simple words (or even none) in one’s own language.

1 Like
53

The notations are different.
When you multiply or divide, where do you put a line? Vertical or horizontal? How can you imagine their vertical line is your horizontal one (or the opposite)?
What about an angle and a number in it, is it geometry or arithmetic?
When you read 1 1/2 do you read “one half” (Europe) or “one and a half” (US)?
Do you know that a 1 with a little line under it and a 2 below are linked by the little line and are the same thing as 1/2?
Do you count in base 10… or in base 60?
What if you’re never seen a watch and dont know time in terms of hour, minute, second but rather sun up noon sun down and are asked a question involving hours and minutes?

There were also puzzles for illiterate adults (many immigrants were illiterate) - if you’ve never seen a puzzle before, how do you understand that you’re supposed to assemble it and that how quickly you put it together is going to indicate how smart you are? What if you try to put the same colors together rather than assemble the shapes?

Imagine yourself having to do Roman math (with Roman numbers and their notation), or Egyptian math… and having just 2mn to figure out what they’re asking.

2 Likes
54

I don’t think the mathematical/arithmetic notations are that different in different cultures/languages that someone who study math can’t figure out such minor differences (if they even exist). If s/he is illiterate, that’s an entirely different situation. Presumably, we dont’ put her/him in a regular English class either.

1 Like
55

Q.E.D. stands for “quod erat demonstrandum” (thus it is demonstrated); and I didn’t have to google it to find that out. It’s Latin.

It’s called Euclidian geometry after the Greek mathematician Euclid, who developed the basic underlying theories.

And, so? I’m sure that once they learned the language of their new country, they were able to do just fine; and that they showed variation in results just as any human population would, because, you know, people are different and have different abilities that produce different outcomes.

By and large, the standards that are being complained of are not being taught to children in a foreign language. And having to deal with an abbrevation such as “Q.E.D.” (a small part of the theorem at any rate) is not an excuse for not doing well; after all, the English language uses abbreviations such as “i.e.” and “e.g.”; nobody can credibly claim that children or others are impeded in learning how to speak and write English because of a couple of abbreviations of Latin words. Likewise, encountering “Q.E.D.” in a proof is not credibly an impediment to learning or understanding the mathematical concepts involved.

56

The examples used came from the test given to immigrants arriving from (mostly) Europe&Russia until the 40s I think, which concluded that Eastern European Jews were “inferior”. Some Southern Europeans (Italians) were also seen as “inferior” BTW. All these groups, in aggregate, did terribly on all those tests.

The immigrants tested thus were not mathematicians or future engineers, as they wouldn’t be given the test in the first place - first and second class immigrant passengers weren’t “processed” in the same way as steerage immigrants. Being of means was assumed to be sufficient “pre-vetting”. Basically, if you were middle class or had attended school long enough in your country of origin, you were presumed “smart enough” to be accepted into the US without any further ado.

Math was used because it wasn’t considered “cultural” and the small problems were even translated, including into Yiddish. The puzzles were for the non literate. So the system was considered very “fair”, especially for the times.
And yet it managed to classify Eastern European Jews as of “inferior” intelligence.
(The same belief that math was “a-cultural” and thus inherently more “fair” was used when switching “elite” curricula in France, when they switched from Latin/Ancient Greek as the subjects determining elite status and access to the most powerful programs/colleges, to Math. Turns out that mastering and manipulating abstract math concepts with ease didn’t end up being “fair” to middle class kids without parents who attended the special classes where such math is taught.)

However, the “fair” test shows that math is, to a certain extent, cultural since some groups did much better than others - unless you subscribe to the idea that being Jewish and/or of Eastern European and/or of Italian descent makes one inherently inferior.
Obviously once you get to more advanced math, the content rests on previous learning, which is why math is sequential and can be “accelerated” and/or “deepened”. But those tests were very simple – the immigrants simply didn’t recognize what was being asked or misunderstood the instructions or notations.

That’s kind of the point: that people deemed “inferior” based on those supposedly “fair” tests of their intelligence did just fine and so did their kids.
The tests were abandonned in part because their results didn’t correlate with innate intelligence, but (surprise!) mostly with previous access to a school and length of schooling back in the home country. Even if they were literate, some of the notations were just impossible to decipher for people who had, for the most part, only attended some primary school. In regions where schooling depended on family wealth (do you need 6 and 8 year olds’ work to get by) or religion (religious discrimination) or just on luck (having a local school v. not having one), schooling and those tests meant nothing about the people’s ability to succeed in their new country.
Many would never become fluent in their new language, but they weren’t dumb – the appetite for learning led to the US having a uniquely developed network of public libraries and night classes for adults. The role of schooling wrt economic prosperity also led the US to being the first country pushing for universal post-grade school attainment and with a comprehensive public high school system for all “white” and “immigrant” kids – the 1906 reform aimed explicitly at “assimilating” immigrant kids and keeping all kids through 8th grade rather than till the end of grade school, a goal achieved by 1910 or so (Western states developed K-8 schools to emphasize that understanding).
This circles back to something that’s often presented on this forum wrt college success in the US: your success depends on your motivation, work ethics, curiosity, willingness to try and challenge yourself, etc.

2 Likes
57

This is correct. And, conversely, those who aren’t motivated (by themselves or their parents or their community), or who have a poor work ethic, or who are not intellectually curious, or who don’t try to challenge themselves, are mostly not going to succeed. It isn’t a question of cultural oppression or “structural racism” (which appears to be the underlying rationale in the California program); it is, at its most fundamental level, based on each individual and their unique set of attributes. Suggesting that an inability to learn math is, for example, caused by seeing “Q.E.D.” in a theorem, or being confronted with a foreign name as the author of a concept, is a way of improperly shifting the blame for lack of academic success away from the individual, which is where it needs to be.

I am not familiar, by the way, with the abbreviation “wrt”.

1 Like
58

I am privileged to be married to a person who has a PhD in theoretical CS, and undergrad in mathematics, and even has a pretty low Erdős number. This is based on what I have learned from her.

Mathematics is a language.

Unless somebody learns that language, they cannot perform mathematics.

It doesn’t matter how smart a person is, they cannot understand a language that they have not learned.

It is no difference than claiming that an immigrant is stupid because their English is not as a good as that of a native speaker of English.

But it’s worse than that.

The reason that most kids in the USA are bad at math is because they are not taught to understand that language, but to parrot sections of it, and plug in numbers to it. Most math tests in the USA test how well kids have memorized the formulas and templates, not how well they understand the math.

Kids who are not trained in a culture of memorization of formulas and templates will not do well on math tests, even if these kids have mad talents in math.

Again, regarding culture:

1 + 1 = 2

The use of 1 and 2 are cultural - they were adopted from Arabic, and did not exist in any European language before the 10th century CE.

The use of “+” started in Europe in the 14th century, and “=” in the 16th century.

Had you asked anybody in the Roman Empire to solve “1 + 1 = ?” they would have no idea what you wanted.

Again, “1 + 1 = 2” is not “universal”.

Even within our cultural contest 1 + 1 = 2 is only true for specific case.

If we multiply each by 359, we get:

359 + 359 = 718.

Except, if we are looking at angular measurements in a circle:

359 + 359 = 358.

So, again, 1 + 1 = 2 isn’t even universal in mathematics.

Also, as long as we are talking about angular measurements, the division of a circle into 360 degrees (as opposed to 100, 160, or any other number) is about as cultural as you can get.

Mathematics is also a logical framework, and it is based on a particular cultural background. If we look at calculus, everything from its axioms to to calculating the area under a curve by the use of infinitesimals is based on a logical framework which is culturally based. The notations used in calculus are culturally based. The way that proofs are set up are culturally based.

Overall, mathematics works in modeling real life. However, there very well may be a different framework which does just as good a job in describing the patterns and processes of everyday life. One that would not require the use of imaginary numbers to describe subatomic behavior.

As I wrote, math is a language. As we know, there are many different languages, and their structures and frameworks differ. Yet all can be used the effectively convey information. Perhaps the same can be said for mathematics.

It would be almost impossible to develop one from scratch, since we are so embedded in this one. It would be very difficult for a person from a literate culture to look at vocal communication as anything but a series of discrete words, divided into discrete sentences. There is no evidence that this is the only way to convey information through vocal means, but it would be very difficult for anybody in a literate culture to conceive of one, much less to develop one from scratch.

“wrt” - What Is 'WRT'? - Meaning of WRT