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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

> 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.

muricula 2y ago
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.
- zozbot234 2y ago
  > 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.
  - capitainenemo 2y ago
    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..)
SoftTalker 2y ago
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.
- liontwist 2y ago
  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.
  - SoftTalker 2y ago
    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.
- mistrial9 2y ago
  confirm that algebra was introduced wholly as an 8th grade math class, and only available to a tested subset to enroll in that.
- arjie 2y ago
  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 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.
mistrial9 2y ago
> 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..
seanmcdirmid 2y ago
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).
tauntz 2y ago
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).
- asielen 2y ago
  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.
bcrosby95 2y ago
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".

muricula 2y ago

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.

zozbot234 2y ago
> 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.
- capitainenemo 2y ago
  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..)

SoftTalker 2y ago

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.

liontwist 2y ago
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.
- SoftTalker 2y ago
  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.
mistrial9 2y ago
confirm that algebra was introduced wholly as an 8th grade math class, and only available to a tested subset to enroll in that.
arjie 2y ago
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 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.

mistrial9 2y ago

> 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..

seanmcdirmid 2y ago

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).

tauntz 2y ago

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).

asielen 2y ago
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.

bcrosby95 2y ago

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".