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Æthelthryth the Texan

s/o Math TED Talk- why is there a race to Calculus?

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The math TED talk was interesting, and made me realize I am old. My high school did not offer Calculus, period, nor did the surrounding schools at that time. The ONE kid in my graduating class who took it was bussed to a local college for the course.  

What changed, and why has it trickled down into high school level in the last 20 or so years? What's the rush? 

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I don't agree that AP cal is something new.  I graduated from high school in 1984 and I took calculus in high school.  

I think that what has changed is the shift in ideology that all students should attend college.  When I was in high school, there were numerous paths within our high school.  There were a whole host trade programs (auto shop, brick laying, horticulture, etc) on the same campus as the college prep and AP courses.  There was 1 section of each AP course offered (and even back then my very rural school offered cal, bio, chem, English, world, and probably a few others that I no longer remember.  I took several of those.)  Most students were not taking APs.  Most were either pursuing trades or in your standard CP courses.

Edited by 8FillTheHeart
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I am not from the US system. I found this Brookings 2008 article which is what I understood as the reason for the push for algebra in 8th grade.

“President Clinton lamented, “Around the world, middle students are learning algebra and geometry. Here at home, just a quarter of all students take algebra before high school.”1 The administration made enrolling all children in an algebra course by eighth grade a national goal. In a handbook offering advice to middle school students on how to plan for college, U.S. Secretary of Education Richard Riley urged, “Take algebra beginning in the eighth grade and build from there.”2 Robert Moses ratcheted up the significance of the issue by labeling algebra “The New Civil Right,” thereby highlighting the social consequences of so many poor and minority students taking remedial and general math courses instead of algebra.3 

The campaign was incredibly successful. Several urban school districts declared a goal of algebra for all eighth graders. In 1996, the District of Columbia led the nation with 53 percent of eighth graders enrolled in algebra. From 1990 to 2000, national enrollment in algebra courses soared from 16 percent to 24 percent of all eighth graders. 

The surge continued into the next decade. Eighth-grade enrollment in algebra hit 31 percent nationally in 2007, a near doubling of the 1990 proportion. Today more U.S. eighth graders take algebra than any other math course.4 In July 2008, the State of California decided to adopt an algebra test as its eighth-grade assessment of student proficiency. The policy in effect mandates that all eighth graders will be enrolled in algebra by 2011.” https://www.brookings.edu/research/the-misplaced-math-student-lost-in-eighth-grade-algebra/

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My small high school did not offer Calculus. My sister and brother took a lot of math in college, and they say they started off behind many of the other students. That was over 20 years ago, so at least some kids were doing Calculus in high school then. My kids who will do Calculus in high school will do it because we are just doing the next thing. I feel like I've failed them in some areas, but my 12 year old is factoring polynomials like a boss right now. We'll repeat Algebra I with a different text, but he'll still likely be ready for Calculus when he is 16 - just like my oldest. As long as they have good understanding, I think it is fine. I am looking at some of the AOPS books like Number Theory, though, for options.

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I took calculus in high school (Canada, graduated 1991).  Medium sized suburban high school in a high SES area.   There were 3 sections IIRC.  It was certainly not expected that everyone would take it.  I'm also from a generation where high school in my province went to grade 13.  It was possible to graduate after grade 12 but that was a rare thing. Almost everyone (and certainly all university bound students) completed grade 13.   So we had 5 years of high school math.  Grade 13 was eliminated in the early 2000's and I think it's too bad.  Most of us really benefited from that extra year - more time for electives, more time to mature.  Gap years were unheard of.  I felt very well prepared for university.

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I graduated in 1996.  Calc wasn't offered at my high school.  In fact, pre-calc was a single class available to seniors only and in order to get into pre-calc you had to have started with Algebra 1 in 8th grade, AND you had to have the recommendation of your trig teacher.  Who was the ONLY trig teacher.  So even if you took Algebra 1 in 8th, if you couldn't get the Trig teacher to agree, No Pre Calc For You!  And, there wasn't an AP option.

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28 minutes ago, Arcadia said:

I am not from the US system. I found this Brookings 2008 article which is what I understood as the reason for the push for algebra in 8th grade.

“President Clinton lamented, “Around the world, middle students are learning algebra and geometry. Here at home, just a quarter of all students take algebra before high school.”1 The administration made enrolling all children in an algebra course by eighth grade a national goal. In a handbook offering advice to middle school students on how to plan for college, U.S. Secretary of Education Richard Riley urged, “Take algebra beginning in the eighth grade and build from there.”2 Robert Moses ratcheted up the significance of the issue by labeling algebra “The New Civil Right,” thereby highlighting the social consequences of so many poor and minority students taking remedial and general math courses instead of algebra.3 

The campaign was incredibly successful. Several urban school districts declared a goal of algebra for all eighth graders. In 1996, the District of Columbia led the nation with 53 percent of eighth graders enrolled in algebra. From 1990 to 2000, national enrollment in algebra courses soared from 16 percent to 24 percent of all eighth graders. 

The surge continued into the next decade. Eighth-grade enrollment in algebra hit 31 percent nationally in 2007, a near doubling of the 1990 proportion. Today more U.S. eighth graders take algebra than any other math course.4 In July 2008, the State of California decided to adopt an algebra test as its eighth-grade assessment of student proficiency. The policy in effect mandates that all eighth graders will be enrolled in algebra by 2011.” https://www.brookings.edu/research/the-misplaced-math-student-lost-in-eighth-grade-algebra/

This is interesting.

It is true the middle school age students are learning some algebra in many countries, but almost always it is within the context of integrated math courses--not an entire year spent on algebra.

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Calculus is included as part of a standard high school curriculum in other countries, but successful implementation relies on tracking, which is a difficult topic here in the U.S.

If we look at German school systems, we would see that children are placed in academic vs. trades tracks around middle school age and sometimes earlier. Kids in the trade track study "normal" subjects such as history, math, science, etc., but they also study their trade so that they can get jobs upon graduation. I have an acquaintance in Germany, and the way it was explained to me (if Regentrude reads this - it would be lovely if she could elaborate) is that each of my acquaintance's children knew their future profession and was working on skills by the time they were 14 years old. So, one of the kids was training to make wood furniture.

A more academic track would include more years of math, science, foreign language, and prepare students to go to university. The key understanding is that not everyone needs to go to university in order to have a good job and a nice life. Students in this track would begin algebra and geometry in middle school and continue to study both through high school - algebra, geometry, trigonometry, all the way through calculus and beginnings of analysis. 

One reason it doesn't work well here is that not everyone is ready and not everyone needs calculus in high school (or ever), but since there is no tracking as it exists in Germany and other countries, it is not possible to teach each class at their instruction need/level. You have kids who are more than ready, kids who are lost, kids who need individual attention, kids with behavior issues - all in the same classroom. Couple that with teachers who sometimes have math phobia themselves and whose own preparation was not done by a math department but by an education department, and, well, things don't work very well.

 

 

 

Edited by RosemaryAndThyme
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5 minutes ago, RosemaryAndThyme said:

Calculus is included as part of a standard high school curriculum in other countries, but successful implementation relies on tracking, which is a difficult topic here in the U.S.

 

 

 

We definitely had what was called "streaming" - tracks for basic, general, advanced and enriched.  Started in grade 9.  Calculus was only possible for those in the advanced or enriched streams.

 

Edited by wathe
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2 minutes ago, wathe said:

We definitely had what was called "streaming" - tracks for basic, general, advanced and enriched.  Started in grade 9.  Calculus was only possible for those in the advanced or enriched streams.

  

That was the case when I was in high school in rural farmland USA.  But it wasn't as if we had no flexibility, either.  I didn't have to take APs if I didn't want to. There was the ability to sign up or down based on our grades (not like we hit 6th grade and our course sequence in the future was sealed.)

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I did Calculus in high school. I graduated in 1985 from an urban high school. Dh graduated a few years later from a rural high school with Calculus. I am actually surprised that the percent doing Algebra in 8th grade was so low in 1990. It wasn’t extraordinary in my world. 

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On 2/17/2019 at 3:18 PM, 8FillTheHeart said:

I don't agree that AP cal is something new.  I graduated from high school in 1984 and I took calculus in high school.  

I think that what has changed is the shift in ideology that all students should attend college.  When I was in high school, there were numerous paths within our high school.  There were a whole host trade programs (auto shop, brick laying, horticulture, etc) on the same campus as the college prep and AP courses.  There was 1 section of each AP course offered (and even back then my very rural school offered cal, bio, chem, English, world, and probably a few others that I no longer remember.  I took several of those.)  Most students were not taking APs.  Most were either pursuing trades or in your standard CP courses.

 

I recently read a very interesting article in The NY Times magazine about the history of women in programming. Women used to represent a much larger percentage of those in computer science and this started to change just when I graduated from high school and went to college. Carnegie Mellon was one of the leaders in trying to reverse the trend. And one of their solutions was two tracks at the beginning of the major, one for those with programming experience and one for those without. By junior year there was really no difference in the students from the different tracks and their retention rates for the CS major were much higher.

 

 

 

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2 hours ago, 8FillTheHeart said:

That was the case when I was in high school in rural farmland USA.  But it wasn't as if we had no flexibility, either.  I didn't have to take APs if I didn't want to. There was the ability to sign up or down based on our grades (not like we hit 6th grade and our course sequence in the future was sealed.)

We definitely had some flexibility.  No-one was locked into their stream - but it would have been difficult to move up to a more academically challenging level.  There was a lot of flexibility in course choice - students could focus on more arts courses vs science and math for example.  Or take an advanced math/science sequence concurrently with a general level humanities sequence.  It was really quite ideal.

I attended a lycee in France on exchange in 1989.  Their tracks were very rigid.  A class took all the same courses together with no flexibility or electives. The academic track class I was placed in took French, English, Latin, German, Math, Social Studies, Science, Phys-Ed.  My exchange partner had the time of her life at during her time at my Canadian high school - she took all the electives that she wouldn't have been able to take in her rigid academic french track at home:  fine arts, home-ec (dress-making), auto-shop etc.

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I didn't feel rushed into calc in high school but had the option to take AP- AB and BC at a suburban school in Arkansas circa 1994.

Edited by Sneezyone
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4 hours ago, Æthelthryth the Texan said:

The math TED talk was interesting, and made me realize I am old. My high school did not offer Calculus, period, nor did the surrounding schools at that time. The ONE kid in my graduating class who took it was bussed to a local college for the course.  

What changed, and why has it trickled down into high school level in the last 20 or so years? What's the rush? 

 

Class of 87 here from a high SES midwestern suburban high school that offered AP Calc AB and BC.  You needed to have taken algebra in 8th grade in order to get the timing right to take calculus senior year.  

I think AP normalized high school calculus for future STEM students as a marker for math achievement.  I think admissions committees at competitive colleges use AP calc that way, a quick way to check that a future STEM student is prepared (provided the school offers the class).   

And I scratch my head at the idea that there is a "rush" to calculus.  It didn't seem like a rush to me, just the natural pace of learning.  If anything, I spent most of elementary math waiting to learn something new.  

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I don't think offering Calculus is what has changed. I think it is the number of students who are trying to get to Calculus in high school that has changed. I took it in high school 20-some years ago, but my class was comprised of 7 seniors out of 244 and we were all college bound in a subject that required Calculus. What I see happening now is average math students trying to take Algebra in 8th grade so they can get to Calculus in high school. This is not a good idea ... seen far too many students struggle with Calculus because of insufficient algebra skills.

 

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9 minutes ago, RenaInTexas said:

I don't think offering Calculus is what has changed. I think it is the number of students who are trying to get to Calculus in high school that has changed. I took it in high school 20-some years ago, but my class was comprised of 7 seniors out of 244 and we were all college bound in a subject that required Calculus. What I see happening now is average math students trying to take Algebra in 8th grade so they can get to Calculus in high school. This is not a good idea ... seen far too many students struggle with Calculus because of insufficient algebra skills.

 

That may be the case but isn't what I experienced. There was a full class of 30 juniors in my AB class and another full class of 30 seniors in BC. My DD's algebra class seems to have a lot of struggling students in it but I attribute that to parents not wanting their kids to be with the unwashed masses in Math 8. Most of them won't ultimately take calc because their foundations aren't strong enough.

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I think it’s a competitive desire to have more AP classes.

No, not for everybody.  But for some.  

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I’m not sure there truly is a race to Calculus. How I’ve seen it work is that yes, most college-bound students take Algebra 1 in eighth grade. That was the case even back in the eighties, although now it is many more kids that do and back then it wasn’t like you couldn’t get into a selective college if you were a year behind that track. But now that more kids do, it seems like the ones who are more humanities minded take AP Stats rather than calculus their senior year, and statistics is a good course for a high school student to take. 

I think the argument for going deeper and including other math topics rather than focusing on calculus in high school is a conversation that educators should be having. I don’t think eighth graders should be pushed into math they aren’t ready for, but if they are ready they should not be held back. If our country could figure out how to do integrated math successfully on a national scale rather than state by state, perhaps that is the best way. More topics could be added into the algebra-geometry-Precalculus sequence and it could be stretched out rather than trying to cram as much as possible into four years. There is also nothing wrong with beginning calculus in high school, but the conversation there might be about whether the AP math courses are the best way to introduce kids to college level math, when some college professors are saying they hinder rather than help students’ conceptual understanding of calculus. 

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In my area, there is a race. With Algebra 1 in 8th grade being standard for California previously, students on accelerated math track takes Algebra 1 in 7th or 6th grade. Some parents are going to push their kids into the accelerated track for multiple reasons.

Then there is college admissions saying to take the most rigorous courses offered. My neighboring school districts offers Multivariable Calculus and Linear Algebra in high school for those who finish AP Calculus BC by 11th grade. My district is going to offer as well, now in planning stage. So the pressure on parents and students is there.

My kids favorite summer school provider (private micro school) has many students taking geometry or algebra 2 during summer to accelerate math. 

Public schools want to attract parents too for a strong PTA and having accelerated math tracks is an incentive.

It might not be the intention of former President Bill Clinton but the race is there.

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16 hours ago, RosemaryAndThyme said:

Calculus is included as part of a standard high school curriculum in other countries, but successful implementation relies on tracking, which is a difficult topic here in the U.S.

If we look at German school systems, we would see that children are placed in academic vs. trades tracks around middle school age and sometimes earlier. Kids in the trade track study "normal" subjects such as history, math, science, etc., but they also study their trade so that they can get jobs upon graduation. I have an acquaintance in Germany, and the way it was explained to me (if Regentrude reads this - it would be lovely if she could elaborate) is that each of my acquaintance's children knew their future profession and was working on skills by the time they were 14 years old. So, one of the kids was training to make wood furniture.

A more academic track would include more years of math, science, foreign language, and prepare students to go to university. The key understanding is that not everyone needs to go to university in order to have a good job and a nice life. Students in this track would begin algebra and geometry in middle school and continue to study both through high school - algebra, geometry, trigonometry, all the way through calculus and beginnings of analysis. 

One reason it doesn't work well here is that not everyone is ready and not everyone needs calculus in high school (or ever), but since there is no tracking as it exists in Germany and other countries, it is not possible to teach each class at their instruction need/level. You have kids who are more than ready, kids who are lost, kids who need individual attention, kids with behavior issues - all in the same classroom. Couple that with teachers who sometimes have math phobia themselves and whose own preparation was not done by a math department but by an education department, and, well, things don't work very well.

 

 

 

This is how it is here, at least in my state.  The only difference is that the kids go to a separate trade school to concentrate on their trade rather than the regular public high school.  There are so many vocational opportunities but students graduating from these high schools still often have the opportunity to go to college upon graduation if that is what they desire.

I graduated in 87 from a small suburban high school and took Calculus.  It was a full sized class (maybe 25).  We had a variety of classes at every level and in my dc's small suburban high school I see even more choices and levels including remedial classes (which are double block period of math, not actually called remedial), CP classes, honors classes and APs..  Sometimes you do see students doubling up on math to reach Calculus if they never took Algebra in 8th and feel ready to do so.  The thing that always feels very different to me when reading threads like this is that as a  student you could take, and can take, any class you like unless you are missing a pre-requisite.  Schools just suggest levels and placements they do not mandate them.  

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I was in high school in the early to mid nineties. I went to a very large urban high school in the southwestern us in 9th grade, a tiny rural high school on the east coast in 10th grade that had fewer students in the entire school that I had in my 9th grade class at my previous high school and then a mid-sized high school in the same district for 11th and 12th grade. All the schools had more or less the same setup for math and graduation requirements. The standard college prep track math classes were Algebra I, Geometry and then Algebra II. If you completed Algebra I in eighth grade then You started with geometry in 9th grade and took trigonometry as your 3rd math credit for graduation. There was also a track for those who were not college bound or just plain not good at math. You took algebra IA, algebra IB (basically algebra I over two years instead of one )and then consumer math or geometry to get 3 math credits to graduate.

If you wanted to pursue a math related major in college, then you also took Calculus your senior year and things like discrete math and statistics as electives. If you wanted to pursue a humanities or liberal arts degree in college, then the standard math track was considered fine. Provided your test scores and grades were good enough, you started in College Algebra I your first year in college which was essentially a semester long review of high school algebra I and II. Many kids however needed to take remedial algebra which taught the same things as College Algebra but at a slower pace over two semesters. 

One thing I haven't seen mentioned as a motive to push taking Calculus in high school is the cost of extra college classes. If you have to take remedial math classes to place into your required math classes for your degree, that's extra money spent on tuition for classes that don't even count for your degree. If you don't have a lot of math requirements for your degree, then it is possible that you could place out of your math requirements if you take calculus before college and that's classes you don't have to pay for and possibly graduate quicker. I don't see that working out very well for many, if not most students, but I have heard people talk about wanting their kids to get calculus in before college while their education is still "free".

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14 hours ago, wathe said:

We definitely had some flexibility.  No-one was locked into their stream - but it would have been difficult to move up to a more academically challenging level.  There was a lot of flexibility in course choice - students could focus on more arts courses vs science and math for example.  Or take an advanced math/science sequence concurrently with a general level humanities sequence.  It was really quite ideal.

I attended a lycee in France on exchange in 1989.  Their tracks were very rigid.  A class took all the same courses together with no flexibility or electives. The academic track class I was placed in took French, English, Latin, German, Math, Social Studies, Science, Phys-Ed.  My exchange partner had the time of her life at during her time at my Canadian high school - she took all the electives that she wouldn't have been able to take in her rigid academic french track at home:  fine arts, home-ec (dress-making), auto-shop etc.

I also attended French schools and this description is accurate with the exception that at our school we had a choice of foreign languages--for example, I was in a Russian class, while others from my core class were studying German or English.

Tracks were determined by which bac exam you planned to take.

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No race to Calculus here, but there is a push to get into 8th algebra due to scheduling as it gets one out of fully included core classes that aren't operating on grade level.  That goal requires 7th prealgebra and its just too much for any pushed student - the pushed usually end up in a review course after Alg. II, where they can fill in all the gaps they didn't fill in during tutoring and retake their Regents' Exams.   12th Calc is  very very easy for a student who is interested and did the 'enrichment' all along ie the robust curriculum that was offered before Common Core and NCLB.  Students going into 12th gr Calc 1 and II are the top 5% here and they usually think K,  2nd, 5th, and 6th grade are dull as dishwater review -- this is a district that wants multiplication facts mastered by the time grade 6 starts.  Students going into Calc 1 only as a 2 semester course are the next 5% and usually have had a tutor for the whole ride...their motive is to get that box checked cheaply as its a Community College course and it completes all the math they need for their intended degree. Students taking Calc I and II as 11th or earlier are very math interested, some do take precalc some don't. Course placement is a matter of fit and interest.  

I was concerned about lack of depth in 7th up as I wasn't seeing any challenge problems, and was seeing too many exercises,   but pulling out my old Dolciani's showed me the courses were deep enough for my dc to do all the Dolciani challenge problems easily, so no complaints other than a unit or two that I felt should be included.   The dc that accelerated had no trouble in college either and rather enjoyed discussing points with math profs; has TA'd Calc 3 and Diff Eq. 

I agree with the presenter that the courses need to be more robust.  I had math daily in elementary school; here is 3 times a week.  Way too much time spent on remediating LA and math; my dc used that time to do math POD or work on SM at their level since the school dropped the robust curriculum but left the books in the rooms. 3rd grade for my dc didn't even get to multiplication until June, that's how much remediation is going on with all the transfer students.

 

Edited by HeighHo

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When I was a kid (graduated in 1983), Calculus was 5th year math in our high school.  So you either had to do a double year of math (usually combining Algebra II with either Geometry or Trig/Pre-Calc), or you had to be one of the brilliant prodigies allowed to take algebra in 8th grade.  (In retrospect, I would have been fine taking algebra in 8th, but I had just switched school districts and they told me it was "really hard" and discouraged it.)

I only got through 3 years (Algebra I & II and Geometry), but I got a 28 on the ACT math section (without studying - few studied for ACT/SAT in those days), so I'm not sure what that means.  I have never regretted not taking the higher math classes in high school.  I did take a series in college that went through Calculus, and I found it interesting and did well.  But the fact is that most people have little use for Calculus in their lives - even many highly paid professionals.  I venture to say that some of the professionals I deal with may not have ever passed Algebra I.

My older brother took HS Calc, and I think one or two of my sisters did.  More power to them.  They were more interested in that stuff than I was.  On the other hand, my younger brother (who is a nurse practitioner, maybe has a MS?) chose to re-take Algebra I because it was over his head the first time.  Not sure whether he ended up taking Calc or not.

As for today, I think it's fine for kids to be offered Calculus.  Some are ready and will enjoy that.  I don't think it's right to make kids feel like they have to take Calc or they'll have no future.  I can honestly say that there has never ever been a time in my life when I needed to know the area under the curve, other than in Calculus class.  In a time when you can get through life not even knowing your own mother's phone number, or how to read a map, or how to cook on a stove top, I really doubt my kids are going to need Calculus in order to survive - unless they aspire to a professional field that actually uses that.

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Integrated maths here in NZ.  8th, 9th, and 10th grade for Algebra/Geometry/Statistics - so 3 high school math courses completed by end of 10th grade for everyone. What is nice about this approach: 1) the content is reviewed each year which helps retention and 2) in 8th grade only the easy algebra/geometry/stats content is taught, then moderate content in 9th, and advanced content in 10th. This leads to a stronger foundation in all three.  

Ruth in NZ

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I went to more than one high school in more than one state, graduated in , cough, ‘79 (though skipping some grades so not quite quite as old as that sounds🤫

   Some had calculus, some not.   (Actually some went beyond Calculus, and some couldn’t teach even geometry adequately, but I digress.) 

Here’s an article recommending 12th grade calculus back in what looks like the 30s.  

https://www.jstor.org/stable/30173543

I had had Algebra 1 in 8th, in a plan that would have led to Calculus in 12th presumably— but then my first high school made everyone take Algebra 1 for 9th, so I fell off the math track.  

In college most of my calculus classmates had already taken it in high school.  And were retaking it.  Made it much easier for them, I expect.

Edited by Pen

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Adding:  Jaime Escalante started teaching in ‘74, and AP Calculus was already a “thing” in “better” schools.  I wonder if when Stand and Deliver came out as a popular movie that helped popularize the idea of calculus for high school?

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3 hours ago, lewelma said:

Integrated maths here in NZ.  8th, 9th, and 10th grade for Algebra/Geometry/Statistics - so 3 high school math courses completed by end of 10th grade for everyone. What is nice about this approach: 1) the content is reviewed each year which helps retention and 2) in 8th grade only the easy algebra/geometry/stats content is taught, then moderate content in 9th, and advanced content in 10th. This leads to a stronger foundation in all three.  

Ruth in NZ

Sounds like a beautiful approach.

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1 hour ago, Pen said:

Adding:  Jaime Escalante started teaching in ‘74, and AP Calculus was already a “thing” in “better” schools.  I wonder if when Stand and Deliver came out as a popular movie that helped popularize the idea of calculus for high school?

http://www.ams.sunysb.edu/~tucker/MathHistory.pdf

http://jwilson.coe.uga.edu/EMAT7050/HistoryWeggener.html

Edited by HeighHo

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I meant to add - I think it is actually unrealistic to assume all college-bound kids are ready for Calculus in 12th grade.  The pace of math instruction is not one size fits all.  I would rather kids have time to actually grasp Algebra II than rush through 5 levels of high school math by age 17-18.  Of course for those who absorb it readily, go for it.  But don't track it that way for everyone so the ones who need more time feel stupid.  I suspect that the average comprehensive math scores of kids who are pushed through the courses (ready or not) are no better than comparably bright kids who take quality courses but are encouraged to progress at a pace that matches their comfort level.

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Well, when I was in hs in the mid-90's in Canada, most kids did not take calculus.  Our program was semestered, and the grade 12 honours math students took two math credits - semester one regular academic math, and then the same group in second semester did a separate calculus course.  Ir wasn't required or expected by universities, all you needed to get into a science program was grade 12 academic math (science).  There was also academic arts math.

As far as I can tell this is still the case, and in fact it seems that compared to American math programs, middle school kids here are about a year behind - I think algebra may be toward the end of grade 8 or in grade 9.  Although - they also seem to mix the topics up a lot more every year in middle and hs - there is no separate geometry year or anything like that.  Universities don't seem to expect kids to have learned it, in any case.

Now, that middle school approach was a change, up until the year I began, the normal approach was to do algebra in grades 7, 8, and 9, bt cover it pretty slowly. My jr high math teacher dd that with us, though he wasn't supposed to really - he though kids did a lot better if they had time to get used to working with math in that way.

 

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18 hours ago, Pen said:

I went to more than one high school in more than one state, graduated in , cough, ‘79 (though skipping some grades so not quite quite as old as that sounds🤫

  

2

In '72 (wheeze, wheeze, creak, creak), trig was the highest math at a regular h.s, and that was not required for U.C.admission. Calculus was usually in the jr. year of college, and combined with organic chem at the same time, was the gatekeeper to medical school. I did not become a serious student until my jr. year.   I would have had to redo math from alg 2 on,  if I wanted to sit for the MCAT.

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On 2/17/2019 at 5:27 PM, Meriwether said:

My small high school did not offer Calculus. My sister and brother took a lot of math in college, and they say they started off behind many of the other students. That was over 20 years ago, so at least some kids were doing Calculus in high school then. My kids who will do Calculus in high school will do it because we are just doing the next thing. I feel like I've failed them in some areas, but my 12 year old is factoring polynomials like a boss right now. We'll repeat Algebra I with a different text, but he'll still likely be ready for Calculus when he is 16 - just like my oldest. As long as they have good understanding, I think it is fine. I am looking at some of the AOPS books like Number Theory, though, for options.

 

I graduated in 1991.

AS a junior in high school I took AP Calculus BC -- and then ran out of math in the local school (This was a BIG issue when I got to college)

We were Texas A&M land but my parents could not afford to send me to take a course there or Blinn so I went a year without math.

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1 hour ago, gstharr said:

In '72 (wheeze, wheeze, creak, creak), trig was the highest math at a regular h.s, and that was not required for U.C.admission. Calculus was usually in the jr. year of college, and combined with organic chem at the same time, was the gatekeeper to medical school. I did not become a serious student until my jr. year.   I would have had to redo math from alg 2 on,  if I wanted to sit for the MCAT.

 

Calculus wasn’t required for admission to anyplace other than possibly CalTech or MIT (or similar type places) in “my day,” nor do I think it is now either so far as I can tell as my son is starting to explore colleges.   

But Calculus was the lowest level of math available for Freshmen to take at my uni, and while more options might have been available, it also was what friend/peers at UC schools were taking, often as Freshmen.  

After “suffering” at my uni from the problem that calculus was new for me while a repeat for most classmates, I think anyone who like me wishes they too had had an intro to calculus before hitting it in college is going to try to get dc to have that if the dc are able to.  

Parent generation hadn’t taken calculus at all though going into medical field where it’s now a prerequisite so far as I know.  My grandmother who was a mathematician and worked fairly early in the then young computer programming field didn’t have calculus until uni, and I think later than a freshman, but she’s dead so I cannot ask for sure.

Sounds like perhaps a lot of change between ‘72 and ‘79, in addition to region.  My first high school was in Calif and like yours didn’t offer Calculus.  But one Calif HS I was at and NYC high schools I was at or had significant experience with did.  

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FYI: MIT currently offers a stretch univariate Calculus course for incoming freshman.  It lasts autumn term plus the additional 1 month January term (IAP). So not all freshman getting into MIT are strong in their calculus foundation, and need an extra month to get through the content beyond a standard university-length term. 

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I"m wondering if the phrase 'race to calculus' is the euphemism or eduspeak for "stripped down curriculum".  It is very easy for a dilligent student here to reach Calc in 12th, simply because most of the material was declared 'enrichment' and removed from the lower classes. When the NCLB dumbdown was done, my district hadn't bought new books, so the first year was just four chapters of the twelve normally done per grade level in  K to 6, and the enrichment materials that covered number theory, problem of the day, word problems and so forth were eliminated. Common Core moved a lot of content to later grades....the intent there is to be ready for College Algebra as a college freshman, so a two year delay for those not accelerated in middle school.   It became very easy to memorize a test bank and 'do well' until DE College Algebra (or DE Calc if they had a photographic memory).  DE Calc II is the first class here where accelerated students who normally earn a 98-102 land in the 70s..all of that is due to memorizing procedure over a limited number of units as well as moving units to later in the curriculum rather than learning to understand and to show solutions all along. 

 

Also, when I first looked at gifted offerings, for example math from JHU-CTY, it was the same as my growing up, and that was offered to all except special ed.  All of that robust material was ejected when NCLB started. This is the situation of buying a house, and having the contractor who removed the topsoil want to sell it back to you at a luxury price.

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1 hour ago, HeighHo said:

Also, when I first looked at gifted offerings, for example math from JHU-CTY, it was the same as my growing up, and that was offered to all except special ed.  All of that robust material was ejected when NCLB started. 

 

CTY math isn’t that rigorous either. The free MEP math which goes up to 12th grade is actually quite a good integrated math curriculum for foundation (and the student can just go deeper using other resources on whatever they like).

“The branches of mathematics covered by the course are Pure/Core Mathematics, Mechanics, Statistics and Decision Mathematics.” https://www.cimt.org.uk/projects/mep/index.htm

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Calculus was a university class and not offered in high schools at all. Our schools were 11 years. It didn’t matter what/how you did in school because you applied to a specific university department and had to take exams for it. If you wanted to major in English, a set of entrance exams was different than if you wanted to major in engineering. 

Our local PS offers Calculus. My problem is the math program they use prior doesn’t provide good foundation and only the very few bright kids do well in calculus. Most suffer. There wasn’t much rush and pressure on school before but we are starting to see some Bay Area residents move locally and attemp to bring the crazy here. I don’t know how it will all end, but I see no point in rushing when what they really need to be fixing is weak algebra. 

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I agree that when they push down material in name, they also water it down, because the fact is that most kids can't or won't absorb all of the material faster.

I've seen a lot of it in my kids' school (and I don't blame the school, I think it is just how things are done nowadays).  A high % of material covered (in all academic subjects) is not retained and needs to be re-taught year after year.  When will they figure this out and stop trying to beat water out of a stone?

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We did have calculus in my high school.  There was one class for seniors interested in pursuing an engineering degree or similar.  We did not have pre-calc however and I think some of that material was included in Alg 2.    I finished my math at Alg 2 in 11th.  The only problem was restarting in college after a year off, but I only had to take one math class for my major so just suffered through.   There were a lot more social science classes in my high school such as psych, sociology, family development and that sort of thing.  The Vo-Tech students spent half a day on campus and then were bused to the vo-tech campus.  There may have been one or two AP classes towards the end of my time in high school, but I was past the grades they were offered.

We had algebra in 8th, but only one class and it was by recommendation from the teacher.  I was offered the opportunity, but turned it down and I'm glad.  Especially since they said I just met the requirements so it would have probably been too hard.

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2 hours ago, Arcadia said:

 

CTY math isn’t that rigorous either. The free MEP math which goes up to 12th grade is actually quite a good integrated math curriculum for foundation (and the student can just go deeper using other resources on whatever they like).

“The branches of mathematics covered by the course are Pure/Core Mathematics, Mechanics, Statistics and Decision Mathematics.” https://www.cimt.org.uk/projects/mep/index.htm

 

When I first looked at CTY math, they were using Dolciani. In my day, Dolciani was for every mainstreamed student in jr high, not for 'the gifted'.  The 'gifted' did do the entire book in less than 180 days, while others did a few units less in same time frame, but people weren't denied what is now called 'enrichment'.  

 

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1 hour ago, SKL said:

I agree that when they push down material in name, they also water it down, because the fact is that most kids can't or won't absorb all of the material faster.

I've seen a lot of it in my kids' school (and I don't blame the school, I think it is just how things are done nowadays).  A high % of material covered (in all academic subjects) is not retained and needs to be re-taught year after year.  When will they figure this out and stop trying to beat water out of a stone?

 

Its a jobs program.  Every 'remedial' child needs a period of individual or group tutoring daily, every study hall now has a math teacher assigned to tutor individually, every math class in our middle school is double period (second period is remediation for those with gaps), algebra 1 is now a two year course. There are no textbooks, no access to any instruction outside of what is heard in class or tutoring.    If they went back to the time before NCLB and grouped by instructional need, students would progress thru the complete enriched curriciulum rather than just bits and pieces, and the teacher: student ratio would actually be affordable. The work around of course is doing one's own enriched curriculum on one's own time, and that is why so many are getting to Calc by 10th grade -- their time has not been wasted with their private tutor.

Aside:  Monday was a holiday here.  Went to Chinese buffet for lunch.  Elementary kids of the hostess were doing long division problems in their spare time as mom was not allowing her children to lag behind cousins back home. I don't know what district her dc were in, but in mine long division is not taught in elementary beyond double digit divided by single digit.  They were working on 5 digit divided by 2 and 3..very similar to math in my day.

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3 hours ago, HeighHo said:

 

Its a jobs program.  Every 'remedial' child needs a period of individual or group tutoring daily, every study hall now has a math teacher assigned to tutor individually, every math class in our middle school is double period (second period is remediation for those with gaps), algebra 1 is now a two year course. There are no textbooks, no access to any instruction outside of what is heard in class or tutoring.    If they went back to the time before NCLB and grouped by instructional need, students would progress thru the complete enriched curriciulum rather than just bits and pieces, and the teacher: student ratio would actually be affordable. The work around of course is doing one's own enriched curriculum on one's own time, and that is why so many are getting to Calc by 10th grade -- their time has not been wasted with their private tutor.

Aside:  Monday was a holiday here.  Went to Chinese buffet for lunch.  Elementary kids of the hostess were doing long division problems in their spare time as mom was not allowing her children to lag behind cousins back home. I don't know what district her dc were in, but in mine long division is not taught in elementary beyond double digit divided by single digit.  They were working on 5 digit divided by 2 and 3..very similar to math in my day.

 

This is either 5th grade or 6th grade regular math in Texas.

5th grade is divide 4 digits by 2 digits. 6th grade is to be fluent in all integer operations, and all positive rational number operations.

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I don't understand why it takes kids 8-9 years to master arithmetic.  Is it really that complicated?

And this thing about algebra being "abstract" and that being some sort of developmental barrier.  Really?

So I don't see how getting to calculus in high school would be characterized as some sort of rushed experience.  

What I *do* think should be changed is the lack of statistics in the curriculum.

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2 hours ago, EKS said:

I don't understand why it takes kids 8-9 years to master arithmetic.  Is it really that complicated?

And this thing about algebra being "abstract" and that being some sort of developmental barrier.  Really?

So I don't see how getting to calculus in high school would be characterized as some sort of rushed experience.  

What I *do* think should be changed is the lack of statistics in the curriculum.

The rush to calculus means many kids aren't given enough time to master the lower level classes.  Maybe if we spent more hours on math in the lower grades, it would be different, but we put those hours into other things for whatever reason.  And of course not all teachers are good at teaching math.  So we don't invest enough into building a foundation, and then somehow expect the higher math to click.  And I know it does for some, but most kids need more time IMO.

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Statistically speaking, more American kids just are taking calculus now than before. And the expectation that all college bound students really have to do it is definitely newer. I certainly went to a school that offered it in the early 90's - in fact, my school offered differential equations for after calculus. And I had algebra in 8th grade. But I didn't take it - I took what was basically a statistics class instead. And that was considered okay because I wasn't headed to a STEM field. I loaded up on the hardest lit and history courses my school offered instead - things like Psychology and Literature and AP Euro History. I think now, I wouldn't have been "allowed" to do that. That's different.

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Well, this is something I wonder about.  One of my kids is unlikely to be successful at calculus in 12th, at least not without a ton of support.  She aspires to be a veterinarian.  I doubt that vets require a working knowledge of calculus in order to do their jobs, but is this going to be a barrier to her getting into a vet program in college?  Should it?

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1 hour ago, SKL said:

Well, this is something I wonder about.  One of my kids is unlikely to be successful at calculus in 12th, at least not without a ton of support.  She aspires to be a veterinarian.  I doubt that vets require a working knowledge of calculus in order to do their jobs, but is this going to be a barrier to her getting into a vet program in college?  Should it?

Calculus is not required for either vet school or medical school. That’s not to say that some don’t still take it as part of their major or just because they want to, but it’s not a requirement.

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4 hours ago, EKS said:

I don't understand why it takes kids 8-9 years to master arithmetic.  Is it really that complicated?

And this thing about algebra being "abstract" and that being some sort of developmental barrier.  Really?

So I don't see how getting to calculus in high school would be characterized as some sort of rushed experience.  

What I *do* think should be changed is the lack of statistics in the curriculum.

 

My take on this is how things are structured. So I had geometry in school for the duration of 2 or 3 years. It wasn’t integrated, but a separate class. So twice a week it was “geometry” and 3 time a week “math” which was basically Algebra all starting in 7th grade. So our classes started algebra/geometry early but really went slowly with enough repetition that material soaked in. 

It seems to me they do very little in middle school and then cram and rush through material in order to get to Calculus in high school as opposed to going deeper.

I think Common Core fixed the issue with statistics and actually a lot of it is now included in math curriculum. 

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