Math in the US

[Anonymous]

Anonymous wrote:

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.

+1

Unfortunately a lot of bizarre ideas in math teaching come from the left. Like ethno-mathematics, de-tracking, representation etc, While they may have some place in math history they are completely counterproductive when it comes to teaching math.

Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking.

[Anonymous]

Anonymous wrote:

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?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

[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.

I was about to say the same things. Also geometric algebra is some form of Linear Algebra by other name.

There’s not a lot of “blending” in higher math. Sure there are connections and spiraling but courses are organized by overarching themes, techniques and applications, not studying everything at once.

[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.

“Equity” ended this program, along with similar programs in Seattle, most of California, etc:

https://www.cnn.com/2021/10/08/us/new-york-gifted-and-talented-education-program/index.html

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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.

+1

Unfortunately a lot of bizarre ideas in math teaching come from the left. Like ethno-mathematics, de-tracking, representation etc, While they may have some place in math history they are completely counterproductive when it comes to teaching math.

Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking.

Only because Republicans whipped up some hysteria around these topics and irrational people get confused easily.

If people actually took a moment to understand what integrated math is then they'd realize that it really doesn't have anything to do with detracking.

Trust me that I know what’s in the integrated math and what’s best for my child.

Integrated math is used as a detracking tool in several ways. First, when the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM. Second, it’s not possible to take concurrent algebra and geometry which was one way to move to the upper track. Third, integrated math is a little bit of everything without going into depth because there not enough time, which hurts the top students the most.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

[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.

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.

I was about to say the same things. Also geometric algebra is some form of Linear Algebra by other name.

There’s not a lot of “blending” in higher math. Sure there are connections and spiraling but courses are organized by overarching themes, techniques and applications, not studying everything at once.

Geometric algebra is actually a generalization of linear algebra
https://youtu.be/60z_hpEAtD8?si=dKh8caDIgLK4u043

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

What do you consider to be compacted, or accelerated, then?

[Anonymous]

Teacher Math. 15 minute to grade one paper, 25 papers per class, 5 classes= 1875 min. 1875÷60 min = 31 hours. Now teachers only gets 5 hours per week to grade and much of our contracted planning hrs are taken by (un)paid subbing covering for the severe teacher shortage. So this makes the review and appraisal system arbitrary, corrupted, and retaliatory. So when admin write negative reviews on new teachers to get them ousted it really means that they weren't able to play ball with the corruption, mismanagement, and violence that happen everyday. This is why teachers go bye bye and naive warm bodies will be the ones for you to mismanage and retaliate against in the future.

[Anonymous]

Opinion only, but I think numeracy needs to be taught intentionally and frequently at a very young age.

Traditional Singapore math in Elementary School.

Developmental readiness is critical- we had our son re-take Algebra in 8th (he got a C+ in 7th). I thought he was struggling too much with the homework load, and wasn't ready to follow the necessary process of solving equations (was still in the mindset of doing things in his head).

Relating math to another class or practical use helped- DS took AP physics and AP calc the same year. We thought it would be a challenge, but he said that the classes complement each other.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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.

+1

Unfortunately a lot of bizarre ideas in math teaching come from the left. Like ethno-mathematics, de-tracking, representation etc, While they may have some place in math history they are completely counterproductive when it comes to teaching math.

Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking.

Only because Republicans whipped up some hysteria around these topics and irrational people get confused easily.

If people actually took a moment to understand what integrated math is then they'd realize that it really doesn't have anything to do with detracking.

Trust me that I know what’s in the integrated math and what’s best for my child.

Integrated math is used as a detracking tool in several ways. First, when the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM. Second, it’s not possible to take concurrent algebra and geometry which was one way to move to the upper track. Third, integrated math is a little bit of everything without going into depth because there not enough time, which hurts the top students the most.

Integrated math can be taught accelerated and/or advanced. It's just the sequencing of the topics. It's how they do math in many other countries.

You are conflating the topics and make baseless assumptions.

[Anonymous]

^making

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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?

Not sure why you insist on this as you’re clearly out of your depth. Calculus BC is not compacted, it covers Calculus 1 and 2, typically taught over one semester each in college, or one year in high school. You can say Calculus AB is more fluffy or equivalent to a lower level calculus like college equivalent of Calculus for life sciences and business majors.

LOL. Again, thanks for proving my point.

https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc
"In other words, AP Calculus BC covers more content than AP Calculus AB"

"All topics in the eight units of AP Calculus AB are also included in AP Calculus BC. However, AP Calculus BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6─8."

"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

AB = Calc 1
BC = Calc 1 + 2

More content covered in less time = accelerated = compacted.

It must be hard for you to struggle so much with math and language.

You can call whatever you want accelerated or compacted, that doesn’t mean the rest of the world agrees. I had a good laugh at “compacted” and “accelerated” calculus.

While class contents vary, AP Calculus AB is more than just Calculus 1. Applications of integration and differential equations are usually Calculus 2 along with series and parametric functions. Other topics from Calculus 2, ie techniques of integration, and some integration applications like moments are missing from AP Calculus BC. That doesn’t mean college calculus is doubly accelerated and compacted compared to already accelerated and compacted BC. It’s just that there are different classes, students, majors, and graduation requirements.

By this silly argument Honors Precalculus would also be compacted and accelerated compared to regular Precalculus because it includes additional topics of vector algebra and conics. It’s not, it’s a different class that go into more depth and more topics.

Semantics aside, your entire point is finding some snippets online that you think validate your word choices. Try to contribute with something more substantive.

I'm sorry you are struggling with the definitions of these words. Maybe pick up a dictionary?

As for the content covered by AB/BC, I trust the College Board on this:
"AP Calculus AB focuses on topics that are taught in the college-equivalent first-semester calculus class. AP Calculus BC focuses on topics covered in both first- and second-semester calculus classes."

"The two courses cover content and skills that are introduced in a first-semester calculus course at the college level. All topics in the eight units of AP Calculus AB are included in AP Calculus BC."
https://blog.collegeboard.org/difference-between-ap-calculus-ab-and-bc

Integrated math is just the sequencing of content. Integrated math courses can be designed to be accelerated/compacted or advanced, just like any other sequence.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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.

+1

Unfortunately a lot of bizarre ideas in math teaching come from the left. Like ethno-mathematics, de-tracking, representation etc, While they may have some place in math history they are completely counterproductive when it comes to teaching math.

Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking.

+1