Comment by zozbot234 | Hacker News Reader

Comment by zozbot234 | Hacker News Reader

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> My oldest is in 4th grade now, and the most relevant maths are from 2nd and 3rd grade. Basic division, multiplication, and fractions matters (3rd grade) - but so does adding and subtracting multi-digit numbers (2nd grade) because multiplication/division is now multiple digit (which is the actual, new, 4th grade material)

Are the standards really that low? AIUI in most developed countries w/ the significant exception of the U.S. (and to a lesser extent, other English speaking countries), 4th and 5th grade math are for teaching the earliest elements of pre-algebra. (Meaning that algebraic expressions are very much not used, but the style of reasoning is clearly intended as preparation for that). They may get a lot of practice with fractions or multiple-digit arithmetic, but the basic procedures are not new to them in 4th grade. It seems to me that the U.S. educational system is underserving these kids quite significantly by not catering to their potential and actual skills for mathematical reasoning, which while not fully developed (and very much tied to "concrete" skillsets, as opposed to a real capacity for abstraction) are still quite substantial.

You might double check that the way you number the grades is the same as the way the parent comment numbers them. For example, as I understand it, in the US most kindergarteners are 5 years old and most first graders are 6, while in NZ most first graders are 5 years old and most second graders are six. So to convert from US grades to NZ you add one because in the US kindergarten isn't given a number.

The US has a highly regional system, but as I understand it pre-algebra is taught starting around sixth grade (~11 year olds), which may line up a little closer to your expectations.

> The US has a highly regional system, but as I understand it pre-algebra is taught starting around sixth grade

In most advanced countries this would be the beginning of Junior High a.k.a. Middle School. By that time the students have been thoroughly introduced to pre-algebraic reasoning already, and are broadly getting practice in it (and being taught some more advanced notions around, e.g. exponents and powers, which are of course foundational for later teaching) as preparation for actual algebraic expressions to be introduced.

I can attest that in this US state, 6th graders are being taught those same concepts, at least at the local middle school. (systems of equations with single unknown, introducing multiple unknowns, powers, roots, types of numbers, irrationals, simple geometric problems using multiple shapes, pythagorean triples..)

Anecdotal data from Estonia: I just checked what's the level of maths we have for the 3rd grade (which here corresponds to 9-10 year olds): (Google Translate):

* reads, writes, sorts and compares natural numbers 0–10,000;

* presents a number as the sum of units, tens, hundreds and thousands;

* reads and writes ordinal numbers;

* adds and subtracts numbers mentally within 100, and in writing within 10,000;

* knows the multiplication table (multiplies and divides by single-digit numbers mentally within 100);

* knows the names of the members and results of four arithmetic operations;

* finds the numerical value of a letter in equations by trial and error or by analogy;

* determines the correct order of operations in an expression (parentheses, multiplication/division, addition/subtraction).

So you have elements of pre-algebra but actual algebra will be covered only in the 4th/5th grade (10-12 yo).

Interesting that is 3rd grade at 9-10. 10 year olds in the US are typically in 5th grade. What ages do earlier grades align to?

Generally in the US it is:

* K ~5 yo

* 1st ~6 yo

* 2nd ~7 yo

* 3rd ~8 yo

* 4th ~9 yo

* 5th ~10 yos

Give or take of course since birthdays don't align perfectly.

That seems to roughly align to US standards for the same age but not the same grade.

There is a strong push in many districts to delay algebra until high school, since many students are ready for it much earlier but would get an advantage over students who aren’t ready for it. But ya, we are short changing our students while China mostly isn’t (at least in urban schools).

> 4th and 5th grade math are for teaching the earliest elements of pre-algebra

at one large public school district -- 80 elementary schools, middle schools and high schools -- almost half of 8th graders cannot do basic elementary school math problems.. (edit) official estimates are that about 13% of the students do not finish high school at all.. that is the local school district here in a crowded port city in California near San Francisco. also note that more than forty unique non-English languages are spoken at homes existing in this school district.. also a non-zero number of homes where serious drug abuse occurs.. things like that..

Even 40+ years ago algebra was not introduced until 8th grade (13-14 years old), and only the kids who passed a qualifying exam got that option—the rest took it in 9th grade.

My experience in India is that simultaneous linear equations were taught in the 7th standard (12 years of age). I looked it up and it is common https://www.youtube.com/watch?v=beMAypc7ju4

I do not recall it being particularly difficult and most students were able to do this stuff. I'd say that by the end we had 100% success at this out of the 50 students or so in my class. Is this algebra in the US or is it the group theory stuff we studied later on. The group theory stuff was _much_ later (12th standard - 17+ years) and we didn't go too advanced. Mostly simple stuff like proving something is a group or Abelian, etc.

The syllabus I studied was the Tamil Nadu State Board, which is considered less rigorous than the Central Board, so I can only assume the kids elsewhere were studying more advanced stuff. But overall, that sort of timing hasn't hampered me or most of my classmates from then, so one must assume it's not too bad to study group theory that late.

> I do not recall it being particularly difficult and most students were able to do this stuff. I'd say that by the end we had 100% success at this out of the 50 students or so in my class. Is this algebra in the US or is it the group theory stuff we studied later on.

Your parent comment is talking about solving a single linear equation such as "5x + 2 = 1". That's where "algebra" begins in a US pre-university context.

In a university context, "algebra" does indeed refer to group theory, and the basic concept of manipulating a numeric variable goes by the more elevated name "college algebra".

Thank you for explaining. Hard to believe that 13 year olds could fail to do this, or at least formally manipulate the equation till they have a satisfactory answer. Something is wrong with pedagogy or the process of practice.

What's wrong with the pedagogy is the idea that no one should be taught any material until everybody is capable of learning that material. Variable manipulation can be easily learned by 4th graders. But it can't be learned by all 4th graders, so everyone has to wait.

Just in case you think I might be misleading you somehow, here's a cheat sheet product for a "college algebra" course; again, "college algebra" refers to the material that would normally be covered in or before high school, except that it's being covered in college. So the idea of this product is that current college students will buy it to help them understand what's going on in class, or to review for a test.

https://www.amazon.com/College-Algebra-Quick-Study-Academic/...

> RULE: if a, b, and c are any real numbers and a = b, then a + c = b + c.

[later]

> Some equations require more than one inverse operation to solve.

> EX[AMPLE]: Solve the equation 5x + 3x - 1 = 15

Many 4th graders would have genuine trouble grokking the notion that a variable (a "letter") may be used in an expression to stand for some arbitrary number. This is why it may be more sensible to reinforce quasi-algebraic reasoning at that age by indirect means, such as practice with non-trivial word problems and with e.g. computing expressions that involve a variety of operations w/ rules of precedence, parentheses etc.

40 years ago was 1984. They certainly did algebra.

In the really old days algebra was A LOT harder too. Look up an old book like Chrystal.

Yeah I'm just saying that even at that time, algebra as a subject was high school or for the "advanced" 8th graders. Calling 4th/5th grade math topics "pre-algebra" would be a real stretch IMO.

confirm that algebra was introduced wholly as an 8th grade math class, and only available to a tested subset to enroll in that.

Don't take my post to be exhaustive of what they learn in those grades. I'm only focusing on the major elements required to succeed in 4th grade math.

While not a focus, very basic forms of algebra is introduced as early as 1st grade through problems such as "4 + _ = 9".

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