Math in the US

[Anonymous]

Anonymous wrote:

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

What countries are you talking about and by what metric are they much better at teaching math?

[Anonymous]

Anonymous wrote:

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

Often people quote PISA assessments as proof that US math education is really bad. Many of the top countries select who takes the test or have early tracks into vocational training which skew the results.

National curriculums may be good at raising the averages, but not great for the bottom or top students. The top 5% of students in US are not behind other countries, based on coursework completed by end of high school, they are better prepared for college.

Whoever has the patience can read this very thoughtful and interesting article in how Chinese scholars compare the math education with that in US. It may challenge many of the assumptions in the thread.

https://pmc.ncbi.nlm.nih.gov/articles/PMC8291123/

[Anonymous]

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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.

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.

Woosh. There go the goal posts again.

So much butthurt over being corrected again and again.

BS narrative:
"For integrated math there’s no opportunity to accelerate"
"IM classes are not compacted"
"Schools don't offer compacted IM classes"
"Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking"
"When the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM"

Facts:
- BC offers a more "accelerated" path than AB.
- Integrated math can be accelerated (faster) and/or advanced (more depth), just like any other content sequence.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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

Often people quote PISA assessments as proof that US math education is really bad. Many of the top countries select who takes the test or have early tracks into vocational training which skew the results.

National curriculums may be good at raising the averages, but not great for the bottom or top students. The top 5% of students in US are not behind other countries, based on coursework completed by end of high school, they are better prepared for college.

Whoever has the patience can read this very thoughtful and interesting article in how Chinese scholars compare the math education with that in US. It may challenge many of the assumptions in the thread.

https://pmc.ncbi.nlm.nih.gov/articles/PMC8291123/

Interesting.
"Xia: Chinese students are really good at exams. Take the GRE advanced math test as an example. Among applicants to Northwestern University, Chinese students mostly rank at >90% in the exam. But, once the ETS, which administers the exams, changed the styles and inventories of the questions, their test scores mostly fell to 70% and above. Several years after the changes, their test scores came back again to 90% and above. So we can tell that the scores of Chinese students cannot truly reflect their preparedness for math, but rather their preparedness for taking exams. Maybe we should change the styles and types of questions in the Gaokao every year, so that repetitive training would not work."

"Xia: All these factors are relevant. But I think, as we have talked about, the exam-oriented education system is not good at selecting and cultivating innovative talent. Yes, the system is good at cultivating skilled workers conforming to a uniform standard, but not innovative talents with independent thinking."

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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

Often people quote PISA assessments as proof that US math education is really bad. Many of the top countries select who takes the test or have early tracks into vocational training which skew the results.

National curriculums may be good at raising the averages, but not great for the bottom or top students. The top 5% of students in US are not behind other countries, based on coursework completed by end of high school, they are better prepared for college.

Whoever has the patience can read this very thoughtful and interesting article in how Chinese scholars compare the math education with that in US. It may challenge many of the assumptions in the thread.

https://pmc.ncbi.nlm.nih.gov/articles/PMC8291123/

They are just like us! Criticizing the local system they know and imagining that the foreign system they don't know is better.

"Yang: The basic physics and chemical courses in college require mathematical knowledge of calculus and linear algebra. In Chinese universities, most freshmen have no such knowledge so that we have to stop the specialized courses for one or two weeks, during which we supply them with the mathematical knowledge before we can come back to the main course."

Chinese universities teach basic calculus and linear algebra in 2 weeks! Because their students are well-prepared for college.

Intro University science classes in China require calculus and linear algebra! Into US classes do not; they are more mathematically based.

[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.

This is stupid. RSM teaches Geometry over THREE YEARS, alongside Algebra. This is INTEGRATED.

All math from K through "Pre-algebra" (which includes pre-geometry) is INTEGRATED.

It's only in "Algebra" that the integration stops.

AOPS teaches a 4 year "Contest math" class that covers Alegebra, number theory, geometry, and counting, every subject every year, which is INTEGRATED.

[Anonymous]

Anonymous wrote:

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.

This is stupid. RSM teaches Geometry over THREE YEARS, alongside Algebra. This is INTEGRATED.

All math from K through "Pre-algebra" (which includes pre-geometry) is INTEGRATED.

It's only in "Algebra" that the integration stops.

AOPS teaches a 4 year "Contest math" class that covers Alegebra, number theory, geometry, and counting, every subject every year, which is INTEGRATED.

Oh no! Are the MAGAs going to boycott RSM now?!

[Anonymous]

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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.

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.

Some issues with integrated math
"For integrated math there’s no opportunity to accelerate"
"IM classes are not compacted"
"Schools don't offer compacted IM classes"
"Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking"
"When the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM"

Fixed it for you, these are not absolute, maximalist statements, it’s what many parents run into related to integrated math education of their kids. Exceptions do exist. I can’t help you further if you’re too dumb to understand the nuance. Parents had these gripes with integrated math since forever.

https://talk.collegeconfidential.com/t/how-to-accelerate-within-high-school-integrated-math/

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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

What countries are you talking about and by what metric are they much better at teaching math?

Just looking at PISA really. Obviously I don’t know the curricula of every country. Poland, Estonia, Netherlands are all countries with very high levels of math education that is integrated. And just anecdotally, the last 2 tech companies I have worked at have huge portions of their software engineer teams based in Poland. Something is being done well in their STEM education

[Anonymous]

Anonymous wrote:

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.

This is stupid. RSM teaches Geometry over THREE YEARS, alongside Algebra. This is INTEGRATED.

All math from K through "Pre-algebra" (which includes pre-geometry) is INTEGRATED.

It's only in "Algebra" that the integration stops.

AOPS teaches a 4 year "Contest math" class that covers Alegebra, number theory, geometry, and counting, every subject every year, which is INTEGRATED.

AOPS teaches something like 10 classes by subject, but because they teach Prealgebra and contest math in your mind it proves they subscribe to integrated math teaching methods. Or that the fact that RSM teaches classes called Geometry or Algebra proves they teach integrated math. Astonishing! You really need to take your meds, sorry won’t respond anymore, it feels wrong to mock you.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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

Often people quote PISA assessments as proof that US math education is really bad. Many of the top countries select who takes the test or have early tracks into vocational training which skew the results.

National curriculums may be good at raising the averages, but not great for the bottom or top students. The top 5% of students in US are not behind other countries, based on coursework completed by end of high school, they are better prepared for college.

Whoever has the patience can read this very thoughtful and interesting article in how Chinese scholars compare the math education with that in US. It may challenge many of the assumptions in the thread.

https://pmc.ncbi.nlm.nih.gov/articles/PMC8291123/

They are just like us! Criticizing the local system they know and imagining that the foreign system they don't know is better.

"Yang: The basic physics and chemical courses in college require mathematical knowledge of calculus and linear algebra. In Chinese universities, most freshmen have no such knowledge so that we have to stop the specialized courses for one or two weeks, during which we supply them with the mathematical knowledge before we can come back to the main course."

Chinese universities teach basic calculus and linear algebra in 2 weeks! Because their students are well-prepared for college.

Intro University science classes in China require calculus and linear algebra! Into US classes do not; they are more mathematically based.

That’s not what they said though. They highlighted some issues related to math education in China, namely that the focus on exam preparation takes a toll on creativity, students waste a full year preparing for Gaokao and advanced US students generally have more high level coursework done in high school.

Intro physics classes for stem majors in US are calculus based.

[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.

Some issues with integrated math
"For integrated math there’s no opportunity to accelerate"
"IM classes are not compacted"
"Schools don't offer compacted IM classes"
"Integrated math falls into this category because it’s associated with removal of honors classes, so it’s a way to implement de-tracking"
"When the switch is made from AGA to IM they eliminate honors classes and offer only one level of IM"

Fixed it for you, these are not absolute, maximalist statements, it’s what many parents run into related to integrated math education of their kids. Exceptions do exist. I can’t help you further if you’re too dumb to understand the nuance. Parents had these gripes with integrated math since forever.

https://talk.collegeconfidential.com/t/how-to-accelerate-within-high-school-integrated-math/

No, people are pushing these limited experiences as universal "truths" to push some BS RWNJ narrative.

Again, integrated math absolutely can be accelerated (faster) and/or advanced (more depth), just like any other content sequence.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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.

This is stupid. RSM teaches Geometry over THREE YEARS, alongside Algebra. This is INTEGRATED.

All math from K through "Pre-algebra" (which includes pre-geometry) is INTEGRATED.

It's only in "Algebra" that the integration stops.

AOPS teaches a 4 year "Contest math" class that covers Alegebra, number theory, geometry, and counting, every subject every year, which is INTEGRATED.

AOPS teaches something like 10 classes by subject, but because they teach Prealgebra and contest math in your mind it proves they subscribe to integrated math teaching methods. Or that the fact that RSM teaches classes called Geometry or Algebra proves they teach integrated math. Astonishing! You really need to take your meds, sorry won’t respond anymore, it feels wrong to mock you.

Oh no. Were you triggered by the facts posted by the PP? Poor RWNJ can't handle definitions or facts. Life must be tough for you.

Interesting point from RSM:
"Most public schools offer geometry over one year at most while some even less than that, but is impossible to fully learn geometry in less than three years. "

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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

What countries are you talking about and by what metric are they much better at teaching math?

Just looking at PISA really. Obviously I don’t know the curricula of every country. Poland, Estonia, Netherlands are all countries with very high levels of math education that is integrated. And just anecdotally, the last 2 tech companies I have worked at have huge portions of their software engineer teams based in Poland. Something is being done well in their STEM education

I don’t think PISA is the right way to look at it. There are many ways to measure success. I come from an Eastern European country like the ones you listed and I think the American education is actually quite good because it’s flexible and students have the opportunity to succeed at many points along the way.

Presumably the companies you worked at were American so something must be done right in our STEM education.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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

Often people quote PISA assessments as proof that US math education is really bad. Many of the top countries select who takes the test or have early tracks into vocational training which skew the results.

National curriculums may be good at raising the averages, but not great for the bottom or top students. The top 5% of students in US are not behind other countries, based on coursework completed by end of high school, they are better prepared for college.

Whoever has the patience can read this very thoughtful and interesting article in how Chinese scholars compare the math education with that in US. It may challenge many of the assumptions in the thread.

https://pmc.ncbi.nlm.nih.gov/articles/PMC8291123/

They are just like us! Criticizing the local system they know and imagining that the foreign system they don't know is better.

"Yang: The basic physics and chemical courses in college require mathematical knowledge of calculus and linear algebra. In Chinese universities, most freshmen have no such knowledge so that we have to stop the specialized courses for one or two weeks, during which we supply them with the mathematical knowledge before we can come back to the main course."

Chinese universities teach basic calculus and linear algebra in 2 weeks! Because their students are well-prepared for college.

Intro University science classes in China require calculus and linear algebra! Into US classes do not; they are more mathematically based.

You can’t seriously say the two week intro to calculus and linear algebra compare to taking AP Calculus BC over one year and one semester of linear algebra. A few of the interviewed people taught in US universities, one of them coached the Chinese national math Olympiad team, they are not the average Joe on DCUM.

The point they were making was that Chinese students are being less prepared for university courses than the American students because of outsized emphasis put on university entrance examination. For example sophomore undergrad American students often take graduate level courses, something that’s impossible for Chinese students.

American university stem courses are math based and use calculus and linear algebra, likely they are more rigorous than Chinese equivalent classes, just look through MIT open courseware. You’ll probably say that MIT is not representative, but note that there’s no Chinese university like MIT and most students going there are the product of American math education, faulty as it may be.