Math in the US

[Anonymous]

Anonymous wrote:This is why the US has a math problem. Pedantic arguing of how to place math topics in high school that kids in countries like Turkey master in late elementary and middle school.

Sure let’s copy Turkey’s educational system. I’ll pass.

[Anonymous]

People misunderstand the American education system, particularly immigrants (I’m one) that come from countries with more centralized education.

Other countries have a uniform curriculum across the entire nation, and while rigid, it will cover more advanced topics because it caters to the students that will go to universities.

In US the educational system is more flexible, but if you look at the run of the mill Eureka curriculum it just seems completely inadequate. In reality this is the floor of the curriculum, about 30% of the students are 1 year accelerated and 5% are 2 years accelerated in math. During the high school years there’s even more opportunity to accelerate and specialize with courses like AP Calculus and AP Statistics, that generally are more rigorous than what other countries have, but are only taken by about 5% of all students. Also the community college system is something other country don’t have but allows for enrollment of high school students, where someone with talent and interest can take classes up to differential equations, completing all the lower division courses for a math BS degree while in high school.

For sure US education has its own issues, but just looking at textbooks content is not an apt comparison.

[Anonymous]

Anonymous wrote:This is why the US has a math problem. Pedantic arguing of how to place math topics in high school that kids in countries like Turkey master in late elementary and middle school.

What’s so great about Turkey’s math education?

[Anonymous]

Anonymous wrote:

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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.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Berkeley is not representative of college math classes in general - it's in the top 20 out of 6000, or top one third of a percent.

https://www.mvsu.edu/academics/academic-programs/arts-sciences/departments/mathematics-computer-information-sciences/undergraduate/bs-mathematics/courses

MA 300. CALCULUS II. Differentiation and integration of transcendental functions, techniques of integration

https://kranishapcalculus.weebly.com/uploads/7/0/7/1/70719881/ap_calculus_bc_syllabus.pdf - this BC syllabus covers logs

Yes, Calculus BC covers logs, as it should.

[Anonymous]

Anonymous wrote:People misunderstand the American education system, particularly immigrants (I’m one) that come from countries with more centralized education.

Other countries have a uniform curriculum across the entire nation, and while rigid, it will cover more advanced topics because it caters to the students that will go to universities.

In US the educational system is more flexible, but if you look at the run of the mill Eureka curriculum it just seems completely inadequate. In reality this is the floor of the curriculum, about 30% of the students are 1 year accelerated and 5% are 2 years accelerated in math. During the high school years there’s even more opportunity to accelerate and specialize with courses like AP Calculus and AP Statistics, that generally are more rigorous than what other countries have, but are only taken by about 5% of all students. Also the community college system is something other country don’t have but allows for enrollment of high school students, where someone with talent and interest can take classes up to differential equations, completing all the lower division courses for a math BS degree while in high school.

For sure US education has its own issues, but just looking at textbooks content is not an apt comparison.

How much can students accelerate in your home country?

[Anonymous]

People need to be more specific about what the US math education problems are. It’s far from perfect, but what are we aspiring to? Countries with high stakes national college entrance exams like China, India, Korea aren’t the model either. In many countries parallel tutoring and soul crushing after-school cram-schools are the norm. I do not want this for my child.

[Anonymous]

Anonymous wrote:People misunderstand the American education system, particularly immigrants (I’m one) that come from countries with more centralized education.

Other countries have a uniform curriculum across the entire nation, and while rigid, it will cover more advanced topics because it caters to the students that will go to universities.

In US the educational system is more flexible, but if you look at the run of the mill Eureka curriculum it just seems completely inadequate. In reality this is the floor of the curriculum, about 30% of the students are 1 year accelerated and 5% are 2 years accelerated in math. During the high school years there’s even more opportunity to accelerate and specialize with courses like AP Calculus and AP Statistics, that generally are more rigorous than what other countries have, but are only taken by about 5% of all students. Also the community college system is something other country don’t have but allows for enrollment of high school students, where someone with talent and interest can take classes up to differential equations, completing all the lower division courses for a math BS degree while in high school.

For sure US education has its own issues, but just looking at textbooks content is not an apt comparison.

As much as everyone like to whine about math in US, most countries don’t have courses as in depth as AP Calculus BC and AP Statistics, which are considered the hardest high school math classes. Many students here go beyond that.

It’s true that in the early grades the curriculum moves at a slower pace.

[Anonymous]

I am preparing to become a math teacher this year. (Career shift)
I’m so excited. Not that I think I’m the 2nd coming of math. But I think it’s a worthwhile curriculum to assist in teaching to the next generation.
If you knew me in hs and college, you’d see me as a writing teacher. But I’ve had recent (5 years coming) experiences with math and a growing love for it.

[Anonymous]

Anonymous wrote:

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Anonymous wrote:

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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.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Berkeley is not representative of college math classes in general - it's in the top 20 out of 6000, or top one third of a percent.

https://www.mvsu.edu/academics/academic-programs/arts-sciences/departments/mathematics-computer-information-sciences/undergraduate/bs-mathematics/courses

MA 300. CALCULUS II. Differentiation and integration of transcendental functions, techniques of integration

https://kranishapcalculus.weebly.com/uploads/7/0/7/1/70719881/ap_calculus_bc_syllabus.pdf - this BC syllabus covers logs

Ok, got it, you’re a complete idiot.

Berkeley, being part of the largest university system in the nation with standardized transferable courses among University of California, California State, and California Community Colleges, serving a total of 3 million students is not representative, but Mississippi Valley State with its 2000 students is.

You clearly don’t know much about the US educational system or math in general, but you insist on giving your “expert” opinion on it.

The PP isn’t insisting he/she is an “expert” in anything. She seems to understand these concepts more than you though…

To recap:
AB = calc 1 “advanced”
BC = calc 1 + calc 2

Let's look at three students who are starting at Berkeley this fall:
11 - precalculus
12 - ap calc ab (low score)
13.1 - math 1a
13.2 - math 1b

11 - precalculus
12 - ap calc ab (score 5)
13.1 - math 1b
13.2 - math 53

11 - precalculus
12 - ap calc bc (score 5)
13.1 - math 53
13.2 - math 54

https://math.berkeley.edu/courses/overview/high-school-exam-credits

By covering the additional content at a faster pace than AB, kids who take BC and score a 5 may be able to place out of an extra calculus class in college and take higher-level math courses sooner.

BC offers a more "accelerated" path than AB.

My original point stands:
Integrated math can be accelerated/ compacted, just like any other sequence.

[Anonymous]

Anonymous wrote:This isn’t a “why is math so bad in the Us ?” question that I have seen a few times here recently. It’s why is math taught the the way it is here? I mean: why is it taught in separate topics in middle/high school, ending in some form of calculus? I went to school in another country where math each year is a mix of many different topics and the final/hardest math class will have a mix of advanced topics including calculus, statistics, etc. I think it is taught this way in many other places too. I am certainly not assuming that the way I was taught was better (and I never even took the highest level offered in my curriculum), but I am wondering what is the reason for the way it is taught in the US?

Classes that are include a mix of topics are not as in depth as the courses dedicated to a single area. In US, International Baccalaureate is like that but it’s not as good as AP Calculus or AP Statistics.

The US curriculum is more influenced by college classes which explore a single topic in detail. Advanced classes in high school are meant to line up with college classes so the student can take credit or use a prerequisite. It sort of trickles down to Algebra and Geometry and it’s worth noting that colleges in US have classes like Precalculus, College Algebra.

[Anonymous]

Anonymous wrote:

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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.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Berkeley is not representative of college math classes in general - it's in the top 20 out of 6000, or top one third of a percent.

https://www.mvsu.edu/academics/academic-programs/arts-sciences/departments/mathematics-computer-information-sciences/undergraduate/bs-mathematics/courses

MA 300. CALCULUS II. Differentiation and integration of transcendental functions, techniques of integration

https://kranishapcalculus.weebly.com/uploads/7/0/7/1/70719881/ap_calculus_bc_syllabus.pdf - this BC syllabus covers logs

Ok, got it, you’re a complete idiot.

Berkeley, being part of the largest university system in the nation with standardized transferable courses among University of California, California State, and California Community Colleges, serving a total of 3 million students is not representative, but Mississippi Valley State with its 2000 students is.

You clearly don’t know much about the US educational system or math in general, but you insist on giving your “expert” opinion on it.

The PP isn’t insisting he/she is an “expert” in anything. She seems to understand these concepts more than you though…

To recap:
AB = calc 1 “advanced”
BC = calc 1 + calc 2

Let's look at three students who are starting at Berkeley this fall:
11 - precalculus
12 - ap calc ab (low score)
13.1 - math 1a
13.2 - math 1b

11 - precalculus
12 - ap calc ab (score 5)
13.1 - math 1b
13.2 - math 53

11 - precalculus
12 - ap calc bc (score 5)
13.1 - math 53
13.2 - math 54

https://math.berkeley.edu/courses/overview/high-school-exam-credits

By covering the additional content at a faster pace than AB, kids who take BC and score a 5 may be able to place out of an extra calculus class in college and take higher-level math courses sooner.

BC offers a more "accelerated" path than AB.

My original point stands:
Integrated math can be accelerated/ compacted, just like any other sequence.

lol at accelerated/compacted calculus, as a prerequisite for accelerated multivariable, or anything really, like accelerated bachelors degree, since that’s also a sequence, aka a list of major requirements.

Technically you’re not wrong, but you sound dumb, ignorant and embarrassing at the same time.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Berkeley is not representative of college math classes in general - it's in the top 20 out of 6000, or top one third of a percent.

https://www.mvsu.edu/academics/academic-programs/arts-sciences/departments/mathematics-computer-information-sciences/undergraduate/bs-mathematics/courses

MA 300. CALCULUS II. Differentiation and integration of transcendental functions, techniques of integration

https://kranishapcalculus.weebly.com/uploads/7/0/7/1/70719881/ap_calculus_bc_syllabus.pdf - this BC syllabus covers logs

Ok, got it, you’re a complete idiot.

Berkeley, being part of the largest university system in the nation with standardized transferable courses among University of California, California State, and California Community Colleges, serving a total of 3 million students is not representative, but Mississippi Valley State with its 2000 students is.

You clearly don’t know much about the US educational system or math in general, but you insist on giving your “expert” opinion on it.

The PP isn’t insisting he/she is an “expert” in anything. She seems to understand these concepts more than you though…

To recap:
AB = calc 1 “advanced”
BC = calc 1 + calc 2

Let's look at three students who are starting at Berkeley this fall:
11 - precalculus
12 - ap calc ab (low score)
13.1 - math 1a
13.2 - math 1b

11 - precalculus
12 - ap calc ab (score 5)
13.1 - math 1b
13.2 - math 53

11 - precalculus
12 - ap calc bc (score 5)
13.1 - math 53
13.2 - math 54

https://math.berkeley.edu/courses/overview/high-school-exam-credits

By covering the additional content at a faster pace than AB, kids who take BC and score a 5 may be able to place out of an extra calculus class in college and take higher-level math courses sooner.

BC offers a more "accelerated" path than AB.

My original point stands:
Integrated math can be accelerated/ compacted, just like any other sequence.

lol at accelerated/compacted calculus, as a prerequisite for accelerated multivariable, or anything really, like accelerated bachelors degree, since that’s also a sequence, aka a list of major requirements.

Technically you’re not wrong, but you sound dumb, ignorant and embarrassing at the same time.

Project much? And thanks for finally admitting that I’m right.

Integrated math is just the sequence of content. It can be accelerated.

Sorry, MAGAs. Need to find a different narrative.

[Anonymous]

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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.

I’d take the College Board description with a grain of salt because they also have to back up the AP exam course equivalence.

Differential equations and Applications of integration from the description the AP Calculus AB syllabus are usually found in Calculus 2. While contents vary, see if you can find a Calculus 1 college course that covers these topics.

An example from UC Berkeley:

Calculus 1, Math 51
This course is intended for STEM majors. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus 2, Math 52
Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Arguably AP Calculus BC is not as in depth as a college calculus class. Even at the community college where my dual enrollment student took calculus there were many topics not touched in the AP Calculus BC. A few examples: logarithmic differentiation, techniques of integration (ie trig substitution), applications of integration (surface area of revolution, cylindrical shell etc), first order linear differential equations (AP only does exponential and logistic, college classes include integration multiplication factors). As shown in the example from Berkeley on Calculus 2, some classes go in even more depth for differential equations.

Berkeley is not representative of college math classes in general - it's in the top 20 out of 6000, or top one third of a percent.

https://www.mvsu.edu/academics/academic-programs/arts-sciences/departments/mathematics-computer-information-sciences/undergraduate/bs-mathematics/courses

MA 300. CALCULUS II. Differentiation and integration of transcendental functions, techniques of integration

https://kranishapcalculus.weebly.com/uploads/7/0/7/1/70719881/ap_calculus_bc_syllabus.pdf - this BC syllabus covers logs

Ok, got it, you’re a complete idiot.

Berkeley, being part of the largest university system in the nation with standardized transferable courses among University of California, California State, and California Community Colleges, serving a total of 3 million students is not representative, but Mississippi Valley State with its 2000 students is.

You clearly don’t know much about the US educational system or math in general, but you insist on giving your “expert” opinion on it.

The PP isn’t insisting he/she is an “expert” in anything. She seems to understand these concepts more than you though…

To recap:
AB = calc 1 “advanced”
BC = calc 1 + calc 2

Let's look at three students who are starting at Berkeley this fall:
11 - precalculus
12 - ap calc ab (low score)
13.1 - math 1a
13.2 - math 1b

11 - precalculus
12 - ap calc ab (score 5)
13.1 - math 1b
13.2 - math 53

11 - precalculus
12 - ap calc bc (score 5)
13.1 - math 53
13.2 - math 54

https://math.berkeley.edu/courses/overview/high-school-exam-credits

By covering the additional content at a faster pace than AB, kids who take BC and score a 5 may be able to place out of an extra calculus class in college and take higher-level math courses sooner.

BC offers a more "accelerated" path than AB.

My original point stands:
Integrated math can be accelerated/ compacted, just like any other sequence.

lol at accelerated/compacted calculus, as a prerequisite for accelerated multivariable, or anything really, like accelerated bachelors degree, since that’s also a sequence, aka a list of major requirements.

Technically you’re not wrong, but you sound dumb, ignorant and embarrassing at the same time.

Project much? And thanks for finally admitting that I’m right.

Integrated math is just the sequence of content. It can be accelerated.

Sorry, MAGAs. Need to find a different narrative.

Just because a handful of schools accelerate integrated math doesn’t mean it’s done wherever it’s offered, that it’s representative, that it’s done well or it’s good for the students.

Your whole contribution to the thread is googling “integrated math accelerated compacted” and posting the few schools you found in the first five pages of search. Literally that’s all you did. If you think that proves something and you somehow made a fine argument, you’re are quite dumb.

[Anonymous]

Integrated math is usually done very poorly. When I looked at after school programs the best of them like AOPS and RSM do algebra and geometry classes. The worst are integrated math like Kumon and Mathnasium, which are more a random collection of worksheets. I can see how in a class setting integrated math is going to be a sprinkling of everything while barely scratching the surface before moving on to something else.

We prefer the traditional approach and went with AOPS. It’s not only algebra and geometry but other courses as well, number theory, counting and probability, precalculus etc. I don’t see how anyone could do all of them at the same time or why even attempt it. How would that even work? Like a week each of geometry, algebra, number theory, statistics trigonometry, precalculus. The topics would be so spaced out that the poor kids will forget half before getting to the next topic.

Integrated math is one of those educational fads that end up going nowhere.

[Anonymous]

Anonymous wrote:Integrated math is usually done very poorly. When I looked at after school programs the best of them like AOPS and RSM do algebra and geometry classes. The worst are integrated math like Kumon and Mathnasium, which are more a random collection of worksheets. I can see how in a class setting integrated math is going to be a sprinkling of everything while barely scratching the surface before moving on to something else.

We prefer the traditional approach and went with AOPS. It’s not only algebra and geometry but other courses as well, number theory, counting and probability, precalculus etc. I don’t see how anyone could do all of them at the same time or why even attempt it. How would that even work? Like a week each of geometry, algebra, number theory, statistics trigonometry, precalculus. The topics would be so spaced out that the poor kids will forget half before getting to the next topic.

Integrated math is one of those educational fads that end up going nowhere.

I don’t know anything about the after school programs but I think it’s odd to call integrated math a fad when the whole point of this thread is that it’s extremely common in other countries, some of whom are known to be much better at teaching math than the US