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The irony is that this is probably going to exacerbate social injustice. Cupertino kids are going to be taking extracurricular math through RSM or Kumon in ele

The irony is that this is probably going to exacerbate social injustice. Cupertino kids are going to be taking extracurricular math through RSM or Kumon in elementary school, and then the Cupertino school district (in the article) says that they have no intention to comply with the recommendations. SF kids aren't going to be exposed to algebra until 9th grade and then get a rude awakening in college when they realize all the cool courses have pre-reqs. I've heard a good argument that algebra specifically should be moved the other way: teach it in elementary school, when kids are first exposed to arithmetic. There's a really natural progression from addition/subtraction/zero and multiplication/division/one to inverses and identities, and from addition/multiplication to distribution and associativity. My 3-year-old understands that if he has 5 raspberries on his fingers and he takes away one, he has 4, and then if he grabs another one and puts it on his finger, he has 5 again. Not a huge leap from there to the concept of equations, inverse operations, and solving for unknowns.

csa 5y ago
> Not a huge leap from there to the concept of equations, inverse operations, and solving for unknowns. Unfortunately, for a child it typically is a huge leap. There are certain abstractions that young children simply cannot do. The ability to do certain abstractions is distributed along a bell curve (edit: of age), and maybe your child is on the very far left of that curve, but most kids won’t be able to handle the abstractions you speak of until at least a little later. To be fair, that “later” is definitely not 8th or 9th grade (much earlier), but it’s also not immediately after learning basic arithmetic.
- dkhenry 5y ago
  The only thing distributed along the bell curve is adults who are willing to help the kids. Yes for some kids it will come pretty easy, even at very young ages, but even very young children can learn these concepts if you would just spend some time teaching it to them. When you have a system set up to force one adult to teach 30+ children you will never be able to spend the time required to ensure everyone gets the concept, but that neglect comes at the cost of compressing the learning in later years which still only benefits those who have high aptitude. Which is exactly why they are pushing it back further, not because it will help kids learn more, but because more children will have the ability to learn it without much interaction from an instructor.
  - ryan93 5y ago
    Incredibly uncommon for 30 kids a class in elementary school. Also many students can barely handle arithmetic without massive handholding. Algebra in elementary school is out of the question
    - dkhenry 5y ago
      You are correct that 30 is on the high side, but I have seen classrooms in Philadelphia with 30 students to a single teacher ( 3rd grade, during the 2005 school year so it may have changed since then). However even at lower ratio's the point remains, you need to hand hold the kids, and we don't give our teachers the time or flexibility to do that.
  - csa 5y ago
    > but even very young children can learn these concepts if you would just spend some time teaching it to them. Many decades of cognitive science disagree with you. See Piaget for one of the earlier researchers on this topic. Even though his original ideas have been refuted or refined, the basic premises of his ideas are still prominent among the large group of modern researchers that some people dub neo-Piagetians.
    - dkhenry 5y ago
      Many decades of the lived experiences of children in other countries disagrees with that research. Children in eastern European countries learn advanced concepts from as early as second grade. In asian countries they are introducing Algebra in 6th grade or earlier. This is the problem California finds its self in. They have wonderful "research" showing that kids pick up the concepts better if you wait till they are older, but they ignore the lived reality of the rest of the world, that with the correct teaching you could actually have them doing this work at a much younger age. Even here in America, tutoring schools such as Russian Math or Kumon are successfully teaching advanced topics to children at much younger ages than the public schools. I know the temptation is to just say its its high aptitude kids that are being sent to these after school programs, but it's not. It is just rich kids whose parents want to give their children a leg up. Almost all children could learn the topics, but we won't put in the effort
- nostrademons 5y ago
  Counting and arithmetic are themselves abstractions. The concrete reality is "this is a raspberry. this is another raspberry" etc, and that's about where my kid was at 2 (his loveys are named "Owl" and "Another owl"). Then we learn that there can be 5 raspberries just like there might be 5 ducks or 5 bricks, and that taking away 1 raspberry is like taking away 1 duck or 1 brick. I could believe that the ability to abstract develops at different times in different kids. But I'd caution about taking Western research and generalizing it across all cultures, or generally assuming that kids are less adaptable than they are. There are existence proofs for kids learning algebra at much younger ages than most American schools do (3rd and 4th graders do in eastern Europe, as do Americans who participate in RSM).
threatofrain 5y ago
It's notable that Cupertino has some remarkable public schools, with high schools that have about half of their math faculty as Calculus teachers, and half of the students incoming from junior high are on track to finish Calculus by their junior year. Some students continue their math education at local colleges. Part of the success is most certainly the student culture, which pushes far harder than the faculty. It's one thing for a school to offer opportunity for advanced math (and in that sense Khan Academy already offers this); it's quite another for peer pressure to demand it.
- chrisseaton 5y ago
  > with high schools that have about half of their math faculty as Calculus teachers What does this mean? Is there some special qualification or licence to be allowed to teach calculus?
  - anonAndOn 5y ago
    Most of the student body is taking/has taken some level of Calculus.
  - sokoloff 5y ago
    Both my parents were public school math teachers. There are gradations of teaching qualifications* in some districts and, even where there aren’t, the math department head usually knows which teachers are incapable of teaching beyond Algebra II or incapable of teaching specifically Calculus. Presumably, if a teacher has ever been assigned to teach a Calculus class, they are a Calculus teacher. * Concrete example: our district had a shortage of high school qualified teachers. Middle school teachers were invited to apply with the understanding that they’d teach only general math, pre-Algebra, Algebra I, and Geometry.
    - chrisseaton 5y ago
      I don't really get how you can be a mathematics teacher and not know enough to be able to teach calculus? Like surely you've done calculus yourself?
unanswered 5y ago
I hate to be that guy, but... it's not irony. In this case, it's design. Increasing social injustice is the whole point, because that ensures increased political power for those who campaign on social justice.
lacker 5y ago
I've heard a good argument that algebra specifically should be moved the other way: teach it in elementary school, when kids are first exposed to arithmetic. I think the core problem here is trying to teach all kids math in the same way. Not all kids are equally capable of learning math. Some smart kids can learn algebra in elementary school. There are plenty of students capable of going through the standard curriculum and finishing calculus by the time they are 13 or 14. For these students, the faster the better. Go into even a "good" second-grade math class and you will find some of these students, acing tests and completely bored with everything taught in class. On the other hand, some students will never be able to have a good understanding of pre-calculus. It doesn't matter if they take it when they are 17 or in college, they will never really get it. Or at least, there is no known teaching method capable of doing it. How can you possibly design an education program that takes this into account? You just can't teach all 15-year-olds the same math curriculum without wasting the time of many of the students, either it's too hard or too easy.
- mixmastamyk 5y ago
  It's not really a problem that not everyone will get it the first time. There's always the second, or third attempt. The latter handled by differing levels thru high-school math.
bcrosby95 5y ago
Seems like it's already part of the California standard for 1st grade: https://www.ixl.com/standards/california/math/grade-1 https://www.ixl.com/standards/california/math/grade-1 E.g. "Find the missing number: _ + 1 = 5". Same thing with subtraction. Based upon my experience with my 6 year old (in a public California elementary school), they actually seem to teach math in a huge variety of ways in 1st grade. Word problems, number problems, relationships between plus and minus, and boatloads of ways to solve any given problem. I think they introduced it in Kindergarten too. But it was way beyond her at the time.
deleted 5y ago
[deleted]

csa 5y ago

> Not a huge leap from there to the concept of equations, inverse operations, and solving for unknowns. Unfortunately, for a child it typically is a huge leap. There are certain abstractions that young children simply cannot do. The ability to do certain abstractions is distributed along a bell curve (edit: of age), and maybe your child is on the very far left of that curve, but most kids won’t be able to handle the abstractions you speak of until at least a little later. To be fair, that “later” is definitely not 8th or 9th grade (much earlier), but it’s also not immediately after learning basic arithmetic.

dkhenry 5y ago
The only thing distributed along the bell curve is adults who are willing to help the kids. Yes for some kids it will come pretty easy, even at very young ages, but even very young children can learn these concepts if you would just spend some time teaching it to them. When you have a system set up to force one adult to teach 30+ children you will never be able to spend the time required to ensure everyone gets the concept, but that neglect comes at the cost of compressing the learning in later years which still only benefits those who have high aptitude. Which is exactly why they are pushing it back further, not because it will help kids learn more, but because more children will have the ability to learn it without much interaction from an instructor.
- ryan93 5y ago
  Incredibly uncommon for 30 kids a class in elementary school. Also many students can barely handle arithmetic without massive handholding. Algebra in elementary school is out of the question
  - dkhenry 5y ago
    You are correct that 30 is on the high side, but I have seen classrooms in Philadelphia with 30 students to a single teacher ( 3rd grade, during the 2005 school year so it may have changed since then). However even at lower ratio's the point remains, you need to hand hold the kids, and we don't give our teachers the time or flexibility to do that.
- csa 5y ago
  > but even very young children can learn these concepts if you would just spend some time teaching it to them. Many decades of cognitive science disagree with you. See Piaget for one of the earlier researchers on this topic. Even though his original ideas have been refuted or refined, the basic premises of his ideas are still prominent among the large group of modern researchers that some people dub neo-Piagetians.
  - dkhenry 5y ago
    Many decades of the lived experiences of children in other countries disagrees with that research. Children in eastern European countries learn advanced concepts from as early as second grade. In asian countries they are introducing Algebra in 6th grade or earlier. This is the problem California finds its self in. They have wonderful "research" showing that kids pick up the concepts better if you wait till they are older, but they ignore the lived reality of the rest of the world, that with the correct teaching you could actually have them doing this work at a much younger age. Even here in America, tutoring schools such as Russian Math or Kumon are successfully teaching advanced topics to children at much younger ages than the public schools. I know the temptation is to just say its its high aptitude kids that are being sent to these after school programs, but it's not. It is just rich kids whose parents want to give their children a leg up. Almost all children could learn the topics, but we won't put in the effort
nostrademons 5y ago
Counting and arithmetic are themselves abstractions. The concrete reality is "this is a raspberry. this is another raspberry" etc, and that's about where my kid was at 2 (his loveys are named "Owl" and "Another owl"). Then we learn that there can be 5 raspberries just like there might be 5 ducks or 5 bricks, and that taking away 1 raspberry is like taking away 1 duck or 1 brick. I could believe that the ability to abstract develops at different times in different kids. But I'd caution about taking Western research and generalizing it across all cultures, or generally assuming that kids are less adaptable than they are. There are existence proofs for kids learning algebra at much younger ages than most American schools do (3rd and 4th graders do in eastern Europe, as do Americans who participate in RSM).

threatofrain 5y ago

It's notable that Cupertino has some remarkable public schools, with high schools that have about half of their math faculty as Calculus teachers, and half of the students incoming from junior high are on track to finish Calculus by their junior year. Some students continue their math education at local colleges. Part of the success is most certainly the student culture, which pushes far harder than the faculty. It's one thing for a school to offer opportunity for advanced math (and in that sense Khan Academy already offers this); it's quite another for peer pressure to demand it.

chrisseaton 5y ago
> with high schools that have about half of their math faculty as Calculus teachers What does this mean? Is there some special qualification or licence to be allowed to teach calculus?
- anonAndOn 5y ago
  Most of the student body is taking/has taken some level of Calculus.
- sokoloff 5y ago
  Both my parents were public school math teachers. There are gradations of teaching qualifications* in some districts and, even where there aren’t, the math department head usually knows which teachers are incapable of teaching beyond Algebra II or incapable of teaching specifically Calculus. Presumably, if a teacher has ever been assigned to teach a Calculus class, they are a Calculus teacher. * Concrete example: our district had a shortage of high school qualified teachers. Middle school teachers were invited to apply with the understanding that they’d teach only general math, pre-Algebra, Algebra I, and Geometry.
  - chrisseaton 5y ago
    I don't really get how you can be a mathematics teacher and not know enough to be able to teach calculus? Like surely you've done calculus yourself?

unanswered 5y ago

I hate to be that guy, but... it's not irony. In this case, it's design. Increasing social injustice is the whole point, because that ensures increased political power for those who campaign on social justice.

lacker 5y ago

I've heard a good argument that algebra specifically should be moved the other way: teach it in elementary school, when kids are first exposed to arithmetic. I think the core problem here is trying to teach all kids math in the same way. Not all kids are equally capable of learning math. Some smart kids can learn algebra in elementary school. There are plenty of students capable of going through the standard curriculum and finishing calculus by the time they are 13 or 14. For these students, the faster the better. Go into even a "good" second-grade math class and you will find some of these students, acing tests and completely bored with everything taught in class. On the other hand, some students will never be able to have a good understanding of pre-calculus. It doesn't matter if they take it when they are 17 or in college, they will never really get it. Or at least, there is no known teaching method capable of doing it. How can you possibly design an education program that takes this into account? You just can't teach all 15-year-olds the same math curriculum without wasting the time of many of the students, either it's too hard or too easy.

mixmastamyk 5y ago
It's not really a problem that not everyone will get it the first time. There's always the second, or third attempt. The latter handled by differing levels thru high-school math.

bcrosby95 5y ago

Seems like it's already part of the California standard for 1st grade: https://www.ixl.com/standards/california/math/grade-1 https://www.ixl.com/standards/california/math/grade-1 E.g. "Find the missing number: _ + 1 = 5". Same thing with subtraction. Based upon my experience with my 6 year old (in a public California elementary school), they actually seem to teach math in a huge variety of ways in 1st grade. Word problems, number problems, relationships between plus and minus, and boatloads of ways to solve any given problem. I think they introduced it in Kindergarten too. But it was way beyond her at the time.

deleted 5y ago

[deleted]