> 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..)

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.

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.

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.

> 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..

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).

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.

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".

I have a preschooler, it's been observed by the local preschools that kids need OT and other interventions at substantially higher rates in the covid cohort than in the non-covid cohort. We are likely to see an ongoing wave of kids experiencing some disruption due to the covid period.

For much of my child's formative infant year, people were screaming bloody murder if we wanted our infant to develop a sense of facial expression in strangers and in public. They were also hell bent on banning much of the social events that people might bring infants to that may help develop early socialization. You do not get a more neuroplastic year than the first one.

There was a lot of stuff going on where one has to wonder how much we disproportionately sacrificed the children for disproportionately the elderly. It still deeply bothers me what effect this could have had on my child.

Only time will vindicate this belief. If you said the same thing two years ago you would have been shouted down and labeled as a “bad person”.

It now is getting to the point where this topic can be discussed without it immediately devolving to attacks.

I agree with your take, humans are also very poor at making long term tradeoffs. Just look at the environment and global warming and what we are doing as a species to stop that. You also have to consider how covid lockdowns further split class divides. Since we didn’t produce as many things for 3 years there are less things to go around which causes the price of things to go up, hence inflation. Those who belong to unions and have higher leverage (tech workers, MBAs, etc) can push for higher wages to keep up for inflation but those who do not have that leverage are left behind and become poorer.

Im a little bit worried about the reverberations of covid which are causing global instability, and possibly war. A second order effect of lockdowns and inflation is that it makes any government which was in power during lockdowns very unpopular, this has and will continue to lead to more dramatic leadership changes across the board which further reduces stability.

It caused a shitstorm for our family. The prices of houses went 3x in our area due to covid era ~0% interest rate policies, leading me to work so hard to try and keep up I had health issues and was working ~80 hours a week just to be able to buy 1/2 the house I could have before the great leaders printed their way through their policies. I finally managed to secure housing but only after working twice as hard and physically building the house myself one block at a time with completely undeveloped land (this was the only real estate not exploded into oblivion by mortgage bidders), something last done by common people circa the great depression.

The cure may have been worse than the disease. They basically carpet bombed anyone who started a family right at the time the pandemic broke out.

And you are not alone either.

There is general discontent in the population, who would have expected that a CEO being assassinated would be the strongest point of unity for the American people maybe since 9-11.

As more average people get pushed to the margins it will accelerate change. People will realize that it isn’t about left vs right, or race, or creed. It is about class, and those in the higher class echelons don’t want you to know that.

Absolutely agree, except that class awareness is what the left is all about.

IMO the real culprit there isn't "people screaming bloody murder," it's that because we have no social insurance for pandemic type events, lots of single parent working households, lots of two income working households, lots of one child households, etc., so kids could not get sufficient socialization at or near home despite getting lots of socialization at or near home being totally possible, especially if parents were able to organize a bubble pairing to another household with kids. Instead, kids screwed around on mobile devices at home by themselves while parents worked rather than engage with them.

Many societies covered their faces when outdoors all the time for practical reasons - to protect against the cold, the sun, dust, etc. Some for cultural or religious reasons.

Babies in as diverse of backgrounds as Alaskans to Arabians were raised for thousands of years with significant face-coverings donned before going outside as the norm.

Being worried about "facial expression in strangers in public" because people covered their mouths as a harm to your baby's development is... about 10 steps past absurd. This isn't even making mountain out of a mole hill, this is making a mountain out of a grain of sand.

And of course, compared to the risks of permanently-lowered IQ due to covid brain damage, or permanent lung damage or the various fatigue and other issues millions of people suffered from covid, the risk from the infection to a baby is literally millions of times worse.

This is an interesting strategy you've taken. You're basically setting a trap where you want me to specifically go after Alaskans or Arabians to prove my point.

I'm not taking the racist bait.

I have no reason to think it causes any more or less issues in Alaskans/Arabians a anyone else. The fact that Arabians or Alaskans did or didn't cover in public doesn't sway the outcome one way or another. There are all sorts of cultural factors that compound outcomes, and both mainstream America and Arabs have some that succeed with in spite of, others they succeed because of.