Math in the US

[Anonymous]

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

You’re just persisting in ignorance.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

You’re just persisting in ignorance.

Are you really trying to argue that integrated math (in MS or HS) can’t be compacted?

Cuz people are already doing it.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

[Anonymous]

Anonymous wrote:

Anonymous wrote:The way you were taught is taught in some American schools. If you look for classes labeled Math I, Math II, or Integrated Math I, II they use this model.

Unfortunately, there are two problems with integrated math in the US:

1. It's not the standard track, so if you are halfway through a combo of algebra and geometry, and then, like many Americans, move, you're either going to be slotted ahead or behind where you should be.

2. The subtler problem is that, in the US, it is basically never something like Singapore's hardcore New Syllabus, but rather districts that adopt integrated math like to go with fluffy, inadequate discovery-oriented curricula.

Yes, exactly. Here is why:

Hidden within these progressive approaches to math is always the DEI agenda. Specifically “equity of outcome.” That means: everyone has to arrive at the same place and no one should be ahead of anyone else.

The easiest way to accomplish the “equity of outcome” goal is: lower the bar.

So that is what DEI departments in school districts across the country have been doing.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

Ding dong - did you open the second link?

Integrated math can be compacted, just like any other sequence.

Really, so any math sequence can be compacted?

The regular math sequence is Algebra 1, Geometry, Algebra 2, Precalculus, Calculus, Linear Algebra and Differential Equations, and you might add along the line Statistics and Discrete Math.

You don’t see this sequence compacted especially for the higher level classes unless the class is useless like compacted Algebra 2 and Precalculus or if it’s a magnet high school like Blair Functions but even then the kids come with Algebra 2 done plus a ton of enrichment.

You seem to be more familiar with elementary and middle school compaction classes. It’s done because those classes move very slowly and there’s a lot of repetition, high school math is different.

Thanks for proving my point. Yes, some schools do in fact compact HS-level math. One of my kids is in a compacted path right now. I am plenty aware.

Any sequence can be accelerated. Look at AB vs. BC -- BC is compacted.

Maybe you are stuck on the language? Compacted just means accelerated. They cover more content in less time.

Capiche?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way you were taught is taught in some American schools. If you look for classes labeled Math I, Math II, or Integrated Math I, II they use this model.

Unfortunately, there are two problems with integrated math in the US:

1. It's not the standard track, so if you are halfway through a combo of algebra and geometry, and then, like many Americans, move, you're either going to be slotted ahead or behind where you should be.

2. The subtler problem is that, in the US, it is basically never something like Singapore's hardcore New Syllabus, but rather districts that adopt integrated math like to go with fluffy, inadequate discovery-oriented curricula.

Yes, exactly. Here is why:

Hidden within these progressive approaches to math is always the DEI agenda. Specifically “equity of outcome.” That means: everyone has to arrive at the same place and no one should be ahead of anyone else.

The easiest way to accomplish the “equity of outcome” goal is: lower the bar.

So that is what DEI departments in school districts across the country have been doing.

OMGERD DEI!!! SO SCARY!! AND REAL!!!!

Sounds like your issue is really the DEI boogeyman, not actually the progression of math content.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way you were taught is taught in some American schools. If you look for classes labeled Math I, Math II, or Integrated Math I, II they use this model.

Unfortunately, there are two problems with integrated math in the US:

1. It's not the standard track, so if you are halfway through a combo of algebra and geometry, and then, like many Americans, move, you're either going to be slotted ahead or behind where you should be.

2. The subtler problem is that, in the US, it is basically never something like Singapore's hardcore New Syllabus, but rather districts that adopt integrated math like to go with fluffy, inadequate discovery-oriented curricula.

Yes, exactly. Here is why:

Hidden within these progressive approaches to math is always the DEI agenda. Specifically “equity of outcome.” That means: everyone has to arrive at the same place and no one should be ahead of anyone else.

The easiest way to accomplish the “equity of outcome” goal is: lower the bar.

So that is what DEI departments in school districts across the country have been doing.

OMGERD DEI!!! SO SCARY!! AND REAL!!!!

Sounds like your issue is really the DEI boogeyman, not actually the progression of math content.

When you have kids in school, you'll understand.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Integrated math is taught poorly and doesn’t go in depth. Most district that try it switch back to Algebra and Geometry.

But the question is, why is it taught poorly?

Because there’s not enough time to go in depth, so the teacher does a quick review of a small number of topics each year.

As mentioned in the thread, other integrated math classes like IB are not very good. High level classes like AP Calculus and Statistics are focused on an overarching theme. For building connections it’s easy to set a few hours to study for example applications of algebra in geometry.

For integrated math there’s no opportunity to accelerate, which dissuades top students from following that route.

In which school district?

Integrated math is sequential so one has to do them in order, eg IM 1, IM 2, IM 3. Algebra and Geometry courses can be taken concurrently and students can double up in math in a given year.

School districts can still offer compacted versions of the courses. Which is how most kids are accelerated today.

Schools don't offer compacted IM classes, or compacted Algebra/Geometry, sometimes there’s a summer version. They do occasionally offer compacted IM3 and precalculus, which is a complete disaster.

That’s not how kids are accelerated today. That happens through outside classes like AOPS and once they know the material well they double up during the school year or take the summer version.

RSM especially, and also AoPS, will reach algebra 1/2 and Geometry concurrently for first exposure classes. RSM will do it for both the basic track and the enrichment track.
(AoPS only has one track.)

[Anonymous]

Anonymous wrote:I went to high school in a state with a traditional math curriculum, but I went to college at an engineering school in New York state, so my classmates were mostly from New York State public schools which offered an integrated math curriculum.

From years of study groups and my now DH, I have a strong impression that the integrated curriculum was a whole lot weaker and less rigorous than what I learned, but also that the students who had taken a mixed up curriculum had no idea what they knew and didn't know. They couldn't identify something as algebra, statistics, trigonometry, geometry, or any particular type of math. They knew lots of random bits of stuff without knowing how it fit together or how it built on itself. Given that experience, I have a strong preference for a curriculum that builds linearly instead of jumping all over the place at random.

You're confused.
"algebra, statistics, trigonometry, geometry, or any particular type of math." is an artificial invention that hampers learning. Real math blends these all together.

Look at a college course catalog, and you'll see classes with names like

Algebraic Geometry
Differential Geometry
Geometric Algebra
Linear Algebra

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I went to high school in a state with a traditional math curriculum, but I went to college at an engineering school in New York state, so my classmates were mostly from New York State public schools which offered an integrated math curriculum.

From years of study groups and my now DH, I have a strong impression that the integrated curriculum was a whole lot weaker and less rigorous than what I learned, but also that the students who had taken a mixed up curriculum had no idea what they knew and didn't know. They couldn't identify something as algebra, statistics, trigonometry, geometry, or any particular type of math. They knew lots of random bits of stuff without knowing how it fit together or how it built on itself. Given that experience, I have a strong preference for a curriculum that builds linearly instead of jumping all over the place at random.

This is definitely true for me and how I learned math in the UK - I didn’t really know what anything was called. But the math in my math A Level (the exam taken at age 18) was generally much harder than the math I see in high school here, except for calculus which there seems to be much more of.

There's not really a standard level of math coming out of US high schools. The tops students will have taken Calc 3 and Differential Equations, so a full two years of college math. Struggling math students may have taken "Algebra concepts" and classes titled something like "math for every day". That's a huge span.

UK is essentially the same. A-Level is their version of AP. It's not the standard for every student.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Examples of compacted integrated math:
https://elm.sweetwaterschools.org/compacted-integrated-math-integrated-math-course-i-placement/

https://rdmcounseling.weebly.com/7th-grade-course-selection.html

You don’t seem to be familiar with the US curriculum, and just posted the first Google hits you could find.

Integrated math I, II, III refers to a mix of three years of algebra and geometry taught instead of the Algebra 1, Geometry, Algebra 2 sequence.

Integrated compacted math 6/7/8 doesn’t really mean much it’s the same curriculum but compacted so kids can accelerate.

In California schools there’s a push for integrated math which originates with social justice champions like Jo Boaler, whose initiative received a lot of criticism.

A feature of CA math pathways is the compacted IM 3 with precalculus which is disastrous. Also they make AP Calculus AB a prerequisite for BC which is ill advised.

IM I is compacted with middle school math, as IM 3 is compacted with Precalculus. That leaves only IM 2 not compacted.

Yes, they recommend 2-year Calculus as standard, but they also document Calc BC as an option for juniors. Considering how most students retake calculus in college currently, the slower pace replacing the fake learning of Calc BC isn't a step backward.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I went to high school in a state with a traditional math curriculum, but I went to college at an engineering school in New York state, so my classmates were mostly from New York State public schools which offered an integrated math curriculum.

From years of study groups and my now DH, I have a strong impression that the integrated curriculum was a whole lot weaker and less rigorous than what I learned, but also that the students who had taken a mixed up curriculum had no idea what they knew and didn't know. They couldn't identify something as algebra, statistics, trigonometry, geometry, or any particular type of math. They knew lots of random bits of stuff without knowing how it fit together or how it built on itself. Given that experience, I have a strong preference for a curriculum that builds linearly instead of jumping all over the place at random.

This is definitely true for me and how I learned math in the UK - I didn’t really know what anything was called. But the math in my math A Level (the exam taken at age 18) was generally much harder than the math I see in high school here, except for calculus which there seems to be much more of.

There's not really a standard level of math coming out of US high schools. The tops students will have taken Calc 3 and Differential Equations, so a full two years of college math. Struggling math students may have taken "Algebra concepts" and classes titled something like "math for every day". That's a huge span.

This.

People that are new to math education in US are misinformed and rehash cliches of how bad the system is. The truth is there’s a huge variation and the system allows for the very top students to go very far up to second year of undergrad through community colleges. That’s impossible in other countries with a more uniform and rigid educational framework.

I’ll take the US system any day and I’m coming from a country that did the integrated route.

In other countries, students from the top track high schools don't have to retake calculus and linear algebra in university after doing a shoddy imitation in high school.

[Anonymous]

Anonymous wrote:

Anonymous wrote:I went to high school in a state with a traditional math curriculum, but I went to college at an engineering school in New York state, so my classmates were mostly from New York State public schools which offered an integrated math curriculum.

From years of study groups and my now DH, I have a strong impression that the integrated curriculum was a whole lot weaker and less rigorous than what I learned, but also that the students who had taken a mixed up curriculum had no idea what they knew and didn't know. They couldn't identify something as algebra, statistics, trigonometry, geometry, or any particular type of math. They knew lots of random bits of stuff without knowing how it fit together or how it built on itself. Given that experience, I have a strong preference for a curriculum that builds linearly instead of jumping all over the place at random.

You're confused.
"algebra, statistics, trigonometry, geometry, or any particular type of math." is an artificial invention that hampers learning. Real math blends these all together.

Look at a college course catalog, and you'll see classes with names like

Algebraic Geometry
Differential Geometry
Geometric Algebra
Linear Algebra

I would call these blending.

Algebraic geometry shows you that algebraic solutions are equivalent to geometric solutions. Different mathematical methods that arrive at the same answer.

Differental geometry isn't exactly geometry in the traditional "you can draw it" sense. It's how to handle multidimensional spaces with calculus.

Geometric algebra is an abstract algebra. There's no geometry except for vector spaces.

Linear algebra extends algebra from a single variable to matrices. It's another level of algebra and not a combination of things.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I went to high school in a state with a traditional math curriculum, but I went to college at an engineering school in New York state, so my classmates were mostly from New York State public schools which offered an integrated math curriculum.

From years of study groups and my now DH, I have a strong impression that the integrated curriculum was a whole lot weaker and less rigorous than what I learned, but also that the students who had taken a mixed up curriculum had no idea what they knew and didn't know. They couldn't identify something as algebra, statistics, trigonometry, geometry, or any particular type of math. They knew lots of random bits of stuff without knowing how it fit together or how it built on itself. Given that experience, I have a strong preference for a curriculum that builds linearly instead of jumping all over the place at random.

You're confused.
"algebra, statistics, trigonometry, geometry, or any particular type of math." is an artificial invention that hampers learning. Real math blends these all together.

Look at a college course catalog, and you'll see classes with names like

Algebraic Geometry
Differential Geometry
Geometric Algebra
Linear Algebra

I would call these blending.

Algebraic geometry shows you that algebraic solutions are equivalent to geometric solutions. Different mathematical methods that arrive at the same answer.

Differental geometry isn't exactly geometry in the traditional "you can draw it" sense. It's how to handle multidimensional spaces with calculus.

Geometric algebra is an abstract algebra. There's no geometry except for vector spaces.

Linear algebra extends algebra from a single variable to matrices. It's another level of algebra and not a combination of things.

Sorry , I would NOT call...