Anonymous wrote:

Anonymous wrote:Even if a 5th grader can handle Algebra I, as sixth graders they will struggle with Geometry (proofs, less so the math), and it gets progressively harder from there. On that track, all the 10th graders will be taking AP Calc BC, Multivariable in 11th, and then what?

I doubt there is a school system on earth where it is common for kids to take calculus in 10th grade, and higher level math thereafter.

Define common. There is one middle school that has 40-50 8th graders taking algebra 2 with trig, and thus on a path to calculus in 10th grade. In Fairfax they could maybe take calculus in 9th if they are taking algebra 1 in 6th grade. There is no requirement of calc AB then Calc BC.

How many kids are in that 8th grade class? That might be 10% of the class, so not common. I would guess that there were 3 MS’s, maybe 4, that have more then 1 class of Algebra 2 in the county. It is more likely that the majority of MS don’t offer Algebra 2. The kids taking Algebra 2 are probably 1-2% of the 8th graders in the County, which would be uncommon or rare.

The HS that those kids attend have classes beyond Calculus BC. Heck, South Lakes has at least one, maybe 2, classes beyond Calculus BC. SLHS has a strong IB cohort with kids placing into Algebra 1 in 7th from Floris and Fox Mill. I know that Fox Mill does not offer Algebra 1 in 6th grade and I have not heard of many kids in the neighborhood taking Algebra 2 in 8th grade. I would imagine that Langley, McLean, and Oakton have more offerings then SLHS does.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:i

Anonymous wrote:Even if a 5th grader can handle Algebra I, as sixth graders they will struggle with Geometry (proofs, less so the math), and it gets progressively harder from there. On that track, all the 10th graders will be taking AP Calc BC, Multivariable in 11th, and then what?

I doubt there is a school system on earth where it is common for kids to take calculus in 10th grade, and higher level math thereafter.

AP Stat would be one class that would be of value for research projects in college. Other options would be differential equations or linear Algebra. Would probably need to be taught DE at local college.

DP. You're not making the case that any student needs to take algebra earlier 7th or 8th on an accelerated track, fyi.

Yes, I am aware starting Algebra 1 in 8th grade will allow a student to take Calculus as a Senior.

My point is that there should not be a cap, they should be allowed to get to Calculus and beyond, and starting Algebra 1 in 7th gives you one addition course such as statistics.

The US needs to do a better job of integrating Algebraic and other concepts from day one. You can solve for X in preschool using marbles. Will every kid get the concept at 4 the first time the teacher does it, no. Does it start to introduce concepts of Algebra, yes. Will they get it eventually, yes.

No different that exposing them to a second language at this age. The earlier they start the better.

Again the accelerated track is not for everyone, and there are off-ramps that can be taken at any time. But why artificially stop the progress at Calculus or Calculus + 1. Why place a ceiling on math or any subject. It makes no sense.

They don’t. There is a small percentage of kids that go well beyond Calc or Calc +1. My daughter knows a kid who did AP Calc BC as a 9th grader. IIRC, one of the Regeneron kids from a couple of years ago did it in 8th grade. Your average HS math teacher is not equipped to handle these kids, so they have to seek other paths to continue their math journey, usually involving DE/college.

This in no way means that most kids should be taking Algebra I in 5th grade.

Anonymous wrote:

Anonymous wrote:i

Anonymous wrote:Even if a 5th grader can handle Algebra I, as sixth graders they will struggle with Geometry (proofs, less so the math), and it gets progressively harder from there. On that track, all the 10th graders will be taking AP Calc BC, Multivariable in 11th, and then what?

I doubt there is a school system on earth where it is common for kids to take calculus in 10th grade, and higher level math thereafter.

AP Stat would be one class that would be of value for research projects in college. Other options would be differential equations or linear Algebra. Would probably need to be taught DE at local college.

DP. You're not making the case that any student needs to take algebra earlier 7th or 8th on an accelerated track, fyi.

Yes, I am aware starting Algebra 1 in 8th grade will allow a student to take Calculus as a Senior.

My point is that there should not be a cap, they should be allowed to get to Calculus and beyond, and starting Algebra 1 in 7th gives you one addition course such as statistics.

The US needs to do a better job of integrating Algebraic and other concepts from day one. You can solve for X in preschool using marbles. Will every kid get the concept at 4 the first time the teacher does it, no. Does it start to introduce concepts of Algebra, yes. Will they get it eventually, yes.

No different that exposing them to a second language at this age. The earlier they start the better.

Again the accelerated track is not for everyone, and there are off-ramps that can be taken at any time. But why artificially stop the progress at Calculus or Calculus + 1. Why place a ceiling on math or any subject. It makes no sense.

Anonymous wrote:

Anonymous wrote:Even if a 5th grader can handle Algebra I, as sixth graders they will struggle with Geometry (proofs, less so the math), and it gets progressively harder from there. On that track, all the 10th graders will be taking AP Calc BC, Multivariable in 11th, and then what?

I doubt there is a school system on earth where it is common for kids to take calculus in 10th grade, and higher level math thereafter.

AP Stat would be one class that would be of value for research projects in college. Other options would be differential equations or linear Algebra. Would probably need to be taught DE at local college.

DP. You're not making the case that any student needs to take algebra earlier 7th or 8th on an accelerated track, fyi.

Anonymous wrote:Even if a 5th grader can handle Algebra I, as sixth graders they will struggle with Geometry (proofs, less so the math), and it gets progressively harder from there. On that track, all the 10th graders will be taking AP Calc BC, Multivariable in 11th, and then what?

I doubt there is a school system on earth where it is common for kids to take calculus in 10th grade, and higher level math thereafter.

AP Stat would be one class that would be of value for research projects in college. Other options would be differential equations or linear Algebra. Would probably need to be taught DE at local college.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:5th grade is ideal if child has proper math education prior to then. But the will require parent participation to accomplish.

Lol

Why by 5th grade the kid has solid abstract thinking skills and can easily work to manipulate equations and solve for x. Math is really just a different language and we all know the earlier you start with a language the easier it is.

It is why the rest of the world speaks English and are way ahead of American students in math.

Laugh if you want but it the reality of the situation, just look at where the US ranks worldwide in math.

That's a generalization which is very optimistic. Are you sure you know what your talking about?

And kids doing well in algebra in 7th don't have to worry about the rest of the world. They'll be fine.

Yes, most people develop abstract thinking skills at 8 or 9 years of age.

No. Kids doing Algebra 1 in 7th grade are behind the rest of the world.

As other posters have touched on, the US concept of math branch based education of doing Algebra 1 - Geometry - Algebra 2 is stupid. Math should be taught as an integrated whole.

Again it is just like a language. Kids don’t take Spanish 1 - German 1 - Spanish 2. But that is the equivalent of
what the US does with math.

I think the problem with American math is happening long before they get to HS. In most other countries, the early years in math are spent focusing on calculations exclusively. By the time they get to different math types in HS or college, they can already calculate really well and work with numbers. In American math, the entire elementary time is spent with math that is maybe half to one third calcuation at best, and the rest is meaningless junk that doesn't even exist as math in other countries. For example, there is a ton of vocabulary (that isn't necessary for calculating), writing paragraphs about how you solved a problem, coming up with your own way to solve a problem and then talking about it in a group, doing number trees and other weird exercises that only exist in elementary school, and so on. Show this to a student from China and they will think we are nuts and say something like "that's not math." Because it isn't math. Americans don't even know what math is.

Research suggests this is not true at all. International comparisons of high performing math countries in Elementary school (e.g., Singapore, Japan, Finland) show that they do fewer calculations, more open-ended problem solving. Americans do far more calculations in elementary school. The problem is they are canned and sorted--you learn a problem type, you practice that problem type and you are told whether it is correct or not.

This is just a confusion of vocabulary. When I said calculations, I meant working with numbers as opposed to writing number sentences and paragraphs and demonstrating your thinking by coloring a piece of paper and talking about it with a friend. You are just talking about, as you said, a different way of working with them. But American elementary students do very little actually working with numbers - a huge amount of time is spent on non-numerical items, including things like estimating the height of a wall in human body lengths or something similar. I know because I was a teacher, and while most kids couldn't solve an equation we still had to stop working on whatever equation it was and start teaching them how many potato sacks a car might weigh, or the definition of a bunch of math vocabulary words that would appear on an SOL test (but not how to actually use the words to solve an equation - just to choose the correct definition on a standardized test).

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:5th grade is ideal if child has proper math education prior to then. But the will require parent participation to accomplish.

Lol

Why by 5th grade the kid has solid abstract thinking skills and can easily work to manipulate equations and solve for x. Math is really just a different language and we all know the earlier you start with a language the easier it is.

It is why the rest of the world speaks English and are way ahead of American students in math.

Laugh if you want but it the reality of the situation, just look at where the US ranks worldwide in math.

That's a generalization which is very optimistic. Are you sure you know what your talking about?

And kids doing well in algebra in 7th don't have to worry about the rest of the world. They'll be fine.

Yes, most people develop abstract thinking skills at 8 or 9 years of age.

No. Kids doing Algebra 1 in 7th grade are behind the rest of the world.

As other posters have touched on, the US concept of math branch based education of doing Algebra 1 - Geometry - Algebra 2 is stupid. Math should be taught as an integrated whole.

Again it is just like a language. Kids don’t take Spanish 1 - German 1 - Spanish 2. But that is the equivalent of
what the US does with math.

I think the problem with American math is happening long before they get to HS. In most other countries, the early years in math are spent focusing on calculations exclusively. By the time they get to different math types in HS or college, they can already calculate really well and work with numbers. In American math, the entire elementary time is spent with math that is maybe half to one third calcuation at best, and the rest is meaningless junk that doesn't even exist as math in other countries. For example, there is a ton of vocabulary (that isn't necessary for calculating), writing paragraphs about how you solved a problem, coming up with your own way to solve a problem and then talking about it in a group, doing number trees and other weird exercises that only exist in elementary school, and so on. Show this to a student from China and they will think we are nuts and say something like "that's not math." Because it isn't math. Americans don't even know what math is.

Research suggests this is not true at all. International comparisons of high performing math countries in Elementary school (e.g., Singapore, Japan, Finland) show that they do fewer calculations, more open-ended problem solving. Americans do far more calculations in elementary school. The problem is they are canned and sorted--you learn a problem type, you practice that problem type and you are told whether it is correct or not.

No, not really. Americans do fewer calculations (including missing essential techniques and algorithms), no symbolic manipulation, and little to no logical thinking.
Successful countries do a right amount of calculations, early symbolic manipulation and algebraic techniques, logical thinking and challenging but well-defined problems and they don't do "open-ended" problems at all. We saw during the VMPI discussion what "open-ended" problems meant to some educators here and it more or less falls into the "not math" category. It was laughable.

Anonymous wrote:

Anonymous wrote:Even if a 5th grader can handle Algebra I, as sixth graders they will struggle with Geometry (proofs, less so the math), and it gets progressively harder from there. On that track, all the 10th graders will be taking AP Calc BC, Multivariable in 11th, and then what?

I doubt there is a school system on earth where it is common for kids to take calculus in 10th grade, and higher level math thereafter.

Define common. There is one middle school that has 40-50 8th graders taking algebra 2 with trig, and thus on a path to calculus in 10th grade. In Fairfax they could maybe take calculus in 9th if they are taking algebra 1 in 6th grade. There is no requirement of calc AB then Calc BC.

I was responding to the PP who said that 5th grade is appropriate for kids to take Algebra I, and then went on to imply that American kids are behind in math, and that's how things are done in the rest of the world, where kids have better math education. In their world (wherever that is), the sequencing would lead to taking Multivariable no later than 11th grade. I was challenging that assertion, that there are school systems around the world where this is the sequence for most students.

What you described above is not what I was talking about. This happens in some (former, I guess) TJ feeder schools, where there is a small cohort of kids that take Algebra II in 8th grade.

Anonymous wrote:Even if a 5th grader can handle Algebra I, as sixth graders they will struggle with Geometry (proofs, less so the math), and it gets progressively harder from there. On that track, all the 10th graders will be taking AP Calc BC, Multivariable in 11th, and then what?

I doubt there is a school system on earth where it is common for kids to take calculus in 10th grade, and higher level math thereafter.

Define common. There is one middle school that has 40-50 8th graders taking algebra 2 with trig, and thus on a path to calculus in 10th grade. In Fairfax they could maybe take calculus in 9th if they are taking algebra 1 in 6th grade. There is no requirement of calc AB then Calc BC.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:5th grade is ideal if child has proper math education prior to then. But the will require parent participation to accomplish.

Lol

Why by 5th grade the kid has solid abstract thinking skills and can easily work to manipulate equations and solve for x. Math is really just a different language and we all know the earlier you start with a language the easier it is.

It is why the rest of the world speaks English and are way ahead of American students in math.

Laugh if you want but it the reality of the situation, just look at where the US ranks worldwide in math.

That's a generalization which is very optimistic. Are you sure you know what your talking about?

And kids doing well in algebra in 7th don't have to worry about the rest of the world. They'll be fine.

Yes, most people develop abstract thinking skills at 8 or 9 years of age.

No. Kids doing Algebra 1 in 7th grade are behind the rest of the world.

As other posters have touched on, the US concept of math branch based education of doing Algebra 1 - Geometry - Algebra 2 is stupid. Math should be taught as an integrated whole.

Again it is just like a language. Kids don’t take Spanish 1 - German 1 - Spanish 2. But that is the equivalent of
what the US does with math.

I think the problem with American math is happening long before they get to HS. In most other countries, the early years in math are spent focusing on calculations exclusively. By the time they get to different math types in HS or college, they can already calculate really well and work with numbers. In American math, the entire elementary time is spent with math that is maybe half to one third calcuation at best, and the rest is meaningless junk that doesn't even exist as math in other countries. For example, there is a ton of vocabulary (that isn't necessary for calculating), writing paragraphs about how you solved a problem, coming up with your own way to solve a problem and then talking about it in a group, doing number trees and other weird exercises that only exist in elementary school, and so on. Show this to a student from China and they will think we are nuts and say something like "that's not math." Because it isn't math. Americans don't even know what math is.

Research suggests this is not true at all. International comparisons of high performing math countries in Elementary school (e.g., Singapore, Japan, Finland) show that they do fewer calculations, more open-ended problem solving. Americans do far more calculations in elementary school. The problem is they are canned and sorted--you learn a problem type, you practice that problem type and you are told whether it is correct or not.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:5th grade is ideal if child has proper math education prior to then. But the will require parent participation to accomplish.

Lol

Why by 5th grade the kid has solid abstract thinking skills and can easily work to manipulate equations and solve for x. Math is really just a different language and we all know the earlier you start with a language the easier it is.

It is why the rest of the world speaks English and are way ahead of American students in math.

Laugh if you want but it the reality of the situation, just look at where the US ranks worldwide in math.

That's a generalization which is very optimistic. Are you sure you know what your talking about?

And kids doing well in algebra in 7th don't have to worry about the rest of the world. They'll be fine.

Yes, most people develop abstract thinking skills at 8 or 9 years of age.

No. Kids doing Algebra 1 in 7th grade are behind the rest of the world.

As other posters have touched on, the US concept of math branch based education of doing Algebra 1 - Geometry - Algebra 2 is stupid. Math should be taught as an integrated whole.

Again it is just like a language. Kids don’t take Spanish 1 - German 1 - Spanish 2. But that is the equivalent of
what the US does with math.

I think the problem with American math is happening long before they get to HS. In most other countries, the early years in math are spent focusing on calculations exclusively. By the time they get to different math types in HS or college, they can already calculate really well and work with numbers. In American math, the entire elementary time is spent with math that is maybe half to one third calcuation at best, and the rest is meaningless junk that doesn't even exist as math in other countries. For example, there is a ton of vocabulary (that isn't necessary for calculating), writing paragraphs about how you solved a problem, coming up with your own way to solve a problem and then talking about it in a group, doing number trees and other weird exercises that only exist in elementary school, and so on. Show this to a student from China and they will think we are nuts and say something like "that's not math." Because it isn't math. Americans don't even know what math is.

It's not entirely true that most other countries spend the early years solely on calculations. On the contrary. I went back to my own math worksheets and tests in the 1970s and saw that it was solid calculation + elementary symbolic manipulation, practical geometry (applied, projections, etc.) going back to 1st grade. For instance: "Determine all natural numbers x for which x + 7 < 9" was literally a question posed on a 1st grade test I saw - yes, 1st grade - age 6/7. Compare this to the VA SOL which doesn't allow the use of variables until 5th grade (this is true). Before then, students are expected to make up stuff (can you say "number sentence") that as you correctly point out isn't really math. Similarly, the positional number system was introduced in 3rd grade using actual powers of ten, writing 3124 = 3*10^3 + 1*10^2 + 2*10^1 + 4 for instance. My 4th math book had actual definitions that used variables.
There was none of this irrational fear of abstraction, detail, and rigor you see today. And yes, we did do long division, even in timed tests. And there were always challenge problems that were difficult (there are none today in school).

On the other hand, though, the subjects taught in today's Algebra I (quadratics, linear systems in 2 variables) weren't taught until 8th/9th/10th grade to the GenEd population, and only 1-2 years earlier than that to advanced kids, and there were fewer of those. So my Algebra I 6th grader is actually probably 2 years ahead of where I was at the time. Good thing we're working in a field related to math and supplemented in elementary and didn't rely on the state curriculum. Plus, there are so many more easily accessible resources today than there were back then.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:5th grade is ideal if child has proper math education prior to then. But the will require parent participation to accomplish.

Lol

Why by 5th grade the kid has solid abstract thinking skills and can easily work to manipulate equations and solve for x. Math is really just a different language and we all know the earlier you start with a language the easier it is.

It is why the rest of the world speaks English and are way ahead of American students in math.

Laugh if you want but it the reality of the situation, just look at where the US ranks worldwide in math.

That's a generalization which is very optimistic. Are you sure you know what your talking about?

And kids doing well in algebra in 7th don't have to worry about the rest of the world. They'll be fine.

Yes, most people develop abstract thinking skills at 8 or 9 years of age.

No. Kids doing Algebra 1 in 7th grade are behind the rest of the world.

As other posters have touched on, the US concept of math branch based education of doing Algebra 1 - Geometry - Algebra 2 is stupid. Math should be taught as an integrated whole.

Again it is just like a language. Kids don’t take Spanish 1 - German 1 - Spanish 2. But that is the equivalent of
what the US does with math.

I think the problem with American math is happening long before they get to HS. In most other countries, the early years in math are spent focusing on calculations exclusively. By the time they get to different math types in HS or college, they can already calculate really well and work with numbers. In American math, the entire elementary time is spent with math that is maybe half to one third calcuation at best, and the rest is meaningless junk that doesn't even exist as math in other countries. For example, there is a ton of vocabulary (that isn't necessary for calculating), writing paragraphs about how you solved a problem, coming up with your own way to solve a problem and then talking about it in a group, doing number trees and other weird exercises that only exist in elementary school, and so on. Show this to a student from China and they will think we are nuts and say something like "that's not math." Because it isn't math. Americans don't even know what math is.

Agree Americans not only don't get math, they by and large fear it. Many educators are trying to dumb it down (tried to do it in VA), local school districts are not going to change, so it will be up to individual families to set the pace that the feel is best for their kids.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:5th grade is ideal if child has proper math education prior to then. But the will require parent participation to accomplish.

Lol

Why by 5th grade the kid has solid abstract thinking skills and can easily work to manipulate equations and solve for x. Math is really just a different language and we all know the earlier you start with a language the easier it is.

It is why the rest of the world speaks English and are way ahead of American students in math.

Laugh if you want but it the reality of the situation, just look at where the US ranks worldwide in math.

That's a generalization which is very optimistic. Are you sure you know what your talking about?

And kids doing well in algebra in 7th don't have to worry about the rest of the world. They'll be fine.

Yes, most people develop abstract thinking skills at 8 or 9 years of age.

No. Kids doing Algebra 1 in 7th grade are behind the rest of the world.

As other posters have touched on, the US concept of math branch based education of doing Algebra 1 - Geometry - Algebra 2 is stupid. Math should be taught as an integrated whole.

Again it is just like a language. Kids don’t take Spanish 1 - German 1 - Spanish 2. But that is the equivalent of
what the US does with math.

I think the problem with American math is happening long before they get to HS. In most other countries, the early years in math are spent focusing on calculations exclusively. By the time they get to different math types in HS or college, they can already calculate really well and work with numbers. In American math, the entire elementary time is spent with math that is maybe half to one third calcuation at best, and the rest is meaningless junk that doesn't even exist as math in other countries. For example, there is a ton of vocabulary (that isn't necessary for calculating), writing paragraphs about how you solved a problem, coming up with your own way to solve a problem and then talking about it in a group, doing number trees and other weird exercises that only exist in elementary school, and so on. Show this to a student from China and they will think we are nuts and say something like "that's not math." Because it isn't math. Americans don't even know what math is.

Anonymous wrote:My future STEM kid did algebra in 8th and will do geometry in 9th. If you get too caught up in the dcum AP rat race then you will think your kid will be a complete failure if they don't take algebra early, but actually most kids don't. FCPS limits who can take algebra in 7th pretty severely, at least in our school. I think either is fine. I know kids who have graduated and gone on to great colleges and they didn't take algebra in 7th.

DCUM has multiple school systems. MCPS generally starts in 7th, rare occasion 6th.

My future STEM kid did algebra in 8th and will do geometry in 9th. If you get too caught up in the dcum AP rat race then you will think your kid will be a complete failure if they don't take algebra early, but actually most kids don't. FCPS limits who can take algebra in 7th pretty severely, at least in our school. I think either is fine. I know kids who have graduated and gone on to great colleges and they didn't take algebra in 7th.