Math For The Ivy League Bound

[Researchmama1]

My young 9 year old just finished Singapore Math 6B. I am in a real quandary about where to go next. He has his sights set on the Ivy Leagues.

Has anyone in this forum sent their child to any Ivy League school? If so, what trajectory did you follow for math? 

We are open to teaching it ourselves, or to having it taught. 

Thank you so much for your insight.

[Lilaclady]

So many members have done that. You can search for the schools and look up their math requirements to get an idea 

[lewelma]

7 hours ago, Researchmama1 said:

My young 9 year old just finished Singapore Math 6B. I am in a real quandary about where to go next. He has his sights set on the Ivy Leagues.

Has anyone in this forum sent their child to any Ivy League school? If so, what trajectory did you follow for math? 

We are open to teaching it ourselves, or to having it taught. 

Thank you so much for your insight.

AoPS is definitely the program you want for an advanced kid who loves math. They have courses, but the books are written to the student, so the student can self teach.  It is a discovery method approach, and focuses on problem solving and insight rather than just algorithmic skills. 

Edited April 7, 2022 by lewelma

[daijobu]

Not an Ivy, but AoPS to Stanford.  

[UHP]

I know very little about Singapore Math. But I wonder if good answers to "how to get into an Ivy League school?" would obscure and distract from good answers to "what to do after Singapore 6?" 

(Can't deny I'm interested in both kinds of answers.)

I have a first-grader working ahead of first grade math. In May we might finish a 4th grade math textbook ("Connecting Math Concepts Level E"). I often wonder: should her next steps, and the next steps of a 4th grader finishing the same textbook, look any different? My tentative answer is no.

Edited April 7, 2022 by UHP

[8filltheheart]

I think a better question that will lead to better outcomes in all directions is what challenges the student while still meeting individual needs.  There is no such thing as "math that gets a student accepted to an Ivy."

For a 9 yr old completing 6B, I'm not sure if that is advanced enough for Epsilon Camp, but you might look into it.  Epsilon Camp 

I'd look for other ways to encourage math exploration and math fun.

• Local math circles
• Math Kangaroo

[8filltheheart]

1 hour ago, UHP said:

I know very little about Singapore Math. But I wonder if good answers to "how to get into an Ivy League school?" would obscure and distract from good answers to "what to do after Singapore 6?" 

(Can't deny I'm interested in both kinds of answers.)

I have a first-grader working ahead of first grade math. In May we might finish a 4th grade math textbook ("Connecting Math Concepts Level E"). I often wonder: should her next steps, and the next steps of a 4th grader finishing the same textbook, look any different? My tentative answer is no.

Having btdt with different kids, I would say the answer is both yes and no.  In some ways, the next step is similar.  In other ways, young kids want things to be fun and interesting.  Ensuring high levels engagement is slightly different than when older kids hit the same level.

[UHP]

3 minutes ago, 8filltheheart said:

Having btdt with different kids, I would say the answer is both yes and no.  In some ways, the next step is similar.  In other ways, young kids want things to be fun and interesting.  Ensuring high levels engagement is slightly different than when older kids hit the same level.

What are the ingredients for engaging older kids? (not still "fun" and "interesting"?)

I haven't been there yet for the logic stage or for puberty or for some other kind of phase change. But what I've noticed change in my daughter from 5 to 7 is the amount of time she can spend in the mode of a pupil: more minutes per day now than before. But I think her tastes haven't changed.

What does btdt stand for?

[8filltheheart]

5 minutes ago, UHP said:

What are the ingredients for engaging older kids? (not still "fun" and "interesting"?)

I haven't been there yet for the logic stage or for puberty or for some other kind of phase change. But what I've noticed change in my daughter from 5 to 7 is the amount of time she can spend in the mode of a pupil: more minutes per day now than before. But I think her tastes haven't changed.

What does btdt stand for?

btdt means been there, done that.  I have had 4th graders completing alg and 8th graders completing alg.   All of my older kids are pretty much self-driven and focused.  My older kids who have been advanced in math have pursued math related interests during high school in addition to math courses.  (physics, engineering, atmospheric science)  

[Lilaclady]

For older kids- some May like math competitions- my student did a lot of that. Some

may like math research.

[Researchmama1]

Thank you to those who recommended AoPS specifically. If there are any other specific recommendations for texts students have done well with I welcome those as well. 
 

Not all math curricula are of the same caliber. Not all provide adequate preparation for future success. There are those who have expressed regret in this area. 
 

I am looking for concrete recommendations for math programs used by students who continued to excel in math throughout their educations extending to college and beyond. 

[daijobu]

44 minutes ago, Researchmama1 said:

Thank you to those who recommended AoPS specifically. If there are any other specific recommendations for texts students have done well with I welcome those as well. 
 

Not all math curricula are of the same caliber. Not all provide adequate preparation for future success. There are those who have expressed regret in this area. 
 

I am looking for concrete recommendations for math programs used by students who continued to excel in math throughout their educations extending to college and beyond. 

At this point I'm wondering with whom you are acquainted who has expressed regret for using AoPS because it did not provide adequate preparation and did not continue to excel in math?   I'm honestly very surprised that would be the case.  

[UHP]

@Researchmama1 would you tell us about your experience with Singapore and your 8-year-old, so far? Though it's passed for you I would be interested in reading it.

28 minutes ago, Researchmama1 said:

Not all math curricula are of the same caliber. Not all provide adequate preparation for future success. There are those who have expressed regret in this area.

They might be right to regret it if their kids have learned untruths or misrules, or if they have gained a misplaced confidence in spite of serious misunderstandings, or if they have taken a long time to learn something that is not important. I agree that it's important to find out which curricula have flaws that lead to these kinds of regretable outcomes. 

But I think no single curriculum could be "adequate preparation for future success," at least not for far-future success. A curriculum might be excellent preparation for the next day's success, if today it teaches your pupil something important that he didn't already know. But you are left every day with the problem of identifying things he doesn't already know.

2 minutes ago, daijobu said:

At this point I'm wondering with whom you are acquainted who has expressed regret for using AoPS because it did not provide adequate preparation and did not continue to excel in math?   I'm honestly very surprised that would be the case. 

For what it's worth I didn't think Researchmama1 was refering to APS in the second phrase you highlighted.

[Researchmama1]

@daijobu, @UHPwas correct. I was not referring to AoPS. Again, thank you for your recommendation. 
 

@UHPDo you have a specific question or questions about Singapore? We’ve absolutely loved it and I’m happy to help. 

[UHP]

43 minutes ago, Researchmama1 said:

Do you have a specific question or questions about Singapore? We’ve absolutely loved it and I’m happy to help. 

Not very specific. I wondered if you would like to boast about your son finishing it early. You might get useful feedback about what to do next. Where did you start in the program, and what is a days work like? But these might be questions less about the program and more about your own process.

I'm looking at the scope and sequence here. Elsewhere you said (I might have misunderstood) that you used something different with your older kids. Does something about Singapore stand out? Which topics are treated especially well in the program?

[lewelma]

Are you just looking for a program? Or do you want to discuss how we as homeschool parents helped our children become successful at math? Just know that the program you use is not even half of the equation. 

My ds's path was not just AoPS, he also did the competitions (AMO, BMO, APMO, IMO). Not all students like competitions, but for my son it was a way to focus on his problem solving and his proof writing skills. This was successful because he found a community of like-minded students and had material that forced him to think creatively about high school level content rather than just taking in more content at a surface level. This meant that his problem solving skills were off the charts by the time he hit university. This background allowed him to walk into grad level math classes as a freshman at MIT and earn As. He is now heading off to graduate school in Theoretical Condensed Matter Physics, which is basically applied math.  

There was also a parent here, Quark, whose son loved math and did lots of math research while he was at AoPS. He was the top contributor for years to all the research projects they ran. So there are many ways to get really involved in math without it just being textbook knowledge.

In general, I'm not quite clear on what you are asking for. Overlaying math skill with being Ivy League bound is confusing to me because my son did so much math because he loved math not because he was planning to use it to get into an elite university. And in addition, you can't get into an elite university with just great math, holistic admission is complex and elites are very much a lottery. So maybe just focus on doing math because he loves math. AoPS is an excellent choice. Others, though, have used Foresters if I remember correctly.  It is deep but doesn't use the discovery method. 

[UHP]

6 minutes ago, lewelma said:

Others, though, have used Foresters if I remember correctly.  It is deep but doesn't use the discovery method. 

That's intriguing. These titles and authors come up on the forum pretty often, but I'm still not too familiar — my daughter is a ways away. But meanwhile I've grown skeptical of the "discovery method" (or anyway my feelings are mixed) and haven't heard yet the textbooks sorted according to whether they use it.

[lewelma]

2 hours ago, UHP said:

That's intriguing. These titles and authors come up on the forum pretty often, but I'm still not too familiar — my daughter is a ways away. But meanwhile I've grown skeptical of the "discovery method" (or anyway my feelings are mixed) and haven't heard yet the textbooks sorted according to whether they use it.

I think it was 8 who had a kid who used Forester's. 

[Researchmama1]

11 hours ago, UHP said:

Not very specific. I wondered if you would like to boast about your son finishing it early. You might get useful feedback about what to do next. Where did you start in the program, and what is a days work like? But these might be questions less about the program and more about your own process.

I'm looking at the scope and sequence here. Elsewhere you said (I might have misunderstood) that you used something different with your older kids. Does something about Singapore stand out? Which topics are treated especially well in the program?

We began with Kindergarten Standards and then moved on to Primary Math US Ed 1-6.  

Most appreciated aspects as an instructor;

1. Mastery Curriculum 

2. Instructor’s Manual - clear and concise 

3. Regular Review 

4. Written Specifically for Homeschoolers 

Process;

1. Teach from instructor’s manual 

2. Verbally go through the textbook 

3. Assign workbook problems and any textbook reviews as they arise 

4. Upon completion of the unit assign corresponding Intensive Practice (IP) and Challenging Word (CW) problems (these are separate texts)

In the early days the IP & CW problems were completed over the course of about a week with no other instruction. Later, at my son’s request, they were divided up over the course of a week, but new material was taught simultaneously. Finally he moved on to completing IP & CW in a single day (his decision) and moved onto new material the same day. 

I followed his lead in terms of pacing for the most part, although I think he would have completed a whole year in a day if he could have. He has never wanted to stop. He loves math. But he is a child who also just loves learning.  

My greatest desire is to see him move forward in a way that allows him to continue loving what he is doing with another stellar curriculum. I have read reviews by posters who have had similar children who have gone on to hate math. I like to try to learn as much as I can from others to hopefully choose a great option from the start. 

I know that the teacher is very important, but also that the text itself needs to be thorough. 

Someone mentioned Derek Owens and I looked him up and he mentions very specifically that his physics course is not a college level course, although he apparently also has a college level course. This is of particular interest to me because I took IB physics in high school (I was educated in a public school) and I absolutely hated it. I then went on to college and took physics and hated it still. I wonder had I taken some introductory course with a teacher like Mr. Owens and then gone on to more advanced physics if that would be the case. And could I have gone from introductory physics to college physics in a seamless manner, or was college level physics necessary in high school? But I digress, in terms of math it seems people rave about his instruction while also calling it too easy. Is it? Or is he just a stellar teacher? Is there academic rigor missing from his teaching? I excelled in college math because I had excellent teachers using thorough texts. The classes were easy and I suspect that was because my teachers were so excellent. This is precisely why I am not opposed to outside teaching. My husband likes the AoPS approach. We have both excelled in math, but we are very, very different in our approach. 

[Researchmama1]

*I should clarify that I excelled in college math because I had excellent teachers in high school using thorough texts who prepared me well for the rigors of college math. My college professors were also good, but it was the solid foundation I had in high school that was critical. I remember students struggling precisely because they did not have that foundation. I noticed this most greatly in math and chemistry and I am grateful for those teachers to this day, 

[EKS]

I think that the better question to ask is "What math text is best for this student/teacher combination right now?"  

[Ting Tang]

I've looked at AOPS pre-algebra a bit for my 10 year old (eventually).  I don't think it would be the right fit for us.  But the company itself has great resources for those interested in math.  

I've looked a bit at the Archi-Bulgarian math.  It is in part written by the woman who created the Berkeley Math Circles.  However, I have found numerous "typos" throughout the samples, and the support is TERRIBLE for people looking for information on the materials.  It is an integrated math, and so far she has levels 6-9.  I've been unable to determine if one completes level 8 or 9 if one would have covered the content in a typical Algebra I course.  I've tried and tried to reach out, but the few messages I've gotten back have been incomplete.

AOPS on the other hand has great customer service.

I think math, reading, and writing are the most important subjects to prepare students for high school and then college level science.  I think that is the classical method.  I don't care what kind of science my kids do now so much as they have a good math foundation, gifted or not.  Without it, they won't do well in science later.

[purpleowl]

AOPS is a wonderful fit for my particular kids. My girls started it at ages 10 and 8, I believe, and they thrive with it. And AOPS certainly provides a solid foundation for future math study for kids who do well with it.

There are plenty of kids who thrive with other programs and also get a great foundation. And no one is guaranteed admission to a particular school on the basis of their math curriculum. So while I do suggest looking at AOPS, I also want to encourage you not to think that you have to pick The Perfect Program right now or your kid won't get into his desired school. 

(As an aside, I noticed that you're using two different usernames, which is not allowed on this board - you can contact support@welltrainedmind.com to ask for the accounts to be merged.)

[regentrude]

Another AoPS family here.

DD went to U Chicago, DS to SLU. Both (after graduating with their physics degrees) have recently expressed how grateful they are we did AoPS because they noticed that they had a significant edge over their classmates not merely in terms of coverage but of attitude: they had learned to wrestle with hard problems, something they noticed other students did not know how to do.

Btw, you don't "send" your kid to an Ivy; a kid is lucky if they win the acceptance lottery with schools that reject 95% of their applicants. 
A better goal is solid math mastery that prepares the student well for a STEM major at a rigorous college. There are several paths.

[Clemsondana]

I've got a kid of the sort that might have a shot at ivy league schools, except that kid has no interest in attending one, so take this with a grain of salt.  There are reasons to choose a challenging program like AoPS - you can end up with a deeper understanding, learn to deal with challenge, see some concepts that aren't in most other programs, etc.  But, most colleges aren't going to be looking at what math you use at age 10.  For that matter, I'd expect that they will look at a high school transcript and see  'AP Calculus' or 'Dual Enrollment math x' and not really care how a student got to that point.  They might care about some of the other classes that you could also have on a transcript - number theory, probability, etc - but I'd expect it to be incredibly rare for them to be choosing students based on which program that they used to learn algebra. 

We started AoPS when kid was young because kid was smart and it's what everybody recommended.  It is still one of the 2 things in our homeschool that I have some amount of regret about.  Kid was not ready to deal with that level of frustration at that age, due to maturity and other life things, and it killed their interest in math for several years.  I made choices to slow down, use other programs in addition, and skip challenge problems to find the right balance.  Kid was entirely capable of doing the work, but didn't want to invest that kind of time in math.  But, by the time I had realized the extent of the problem, kid was expressing an interest in a field of engineering where that type of problem solving would be very useful (spouse is in that field and was the one advising about it).  Kid is now in high school and will do calc next year, and I think that the combo of math that we've done has ultimately worked for them and their goals.  However, my other child is not going ot do AoPS ever, unless we decide to do Number Theory.  This kid isn't interested in a field that requires above-and-beyond mathmatical thinking, and kid doesn't particularly like math.  So, kid will use standard programs and likely do quite well on standardized tests like the SAT, which don't test beyond standard use of math.  Neither of my kids has chosen math competitions as an extracurricular (both do Science Olympiad, though), so it's not likely that anything that colleges see will discriminate between the different levels of depth of their math programs.  

[rzberrymom]

On 4/9/2022 at 7:55 PM, lewelma said:

you can't get into an elite university with just great math, holistic admission is complex and elites are very much a lottery. So maybe just focus on doing math because he loves math.

There is a lot of wisdom here. I would listen to these mamas.

[East Coast Sue]

Mine was accepted at three Ivies and picked Yale. Yes, she did a few early AOPs courses but I agree with lewelma. Go for the math that suits your child, their interests and their abilities- but mainly I picked curriculum that kept my kids interested and curious about learning. FTR, my kid took AP Statistics her senior year, and didn’t take AP calculus. She did have nearly perfect SAT scores but I think her essays and recommendations probably earned her admission not her transcript. 

Edited May 9, 2022 by East Coast Sue

[Alice Lamb]

I've never seen Archi-Bulagarian math, but just looking at the table of contents for the 6-8 grade books, it appears that these more than cover a typical algebra 1 course with most of geometry and some algebra 2 as well. I can't tell if it uses geometric 2-column proofs. Some of the functions chapters almost belong in a pre-calculus class.

 

If you can find tables of contents for two or three algebra 1 texts and compare, that would answer your question.  Of course, seeing the complete book to examine lots of actual problems would give a more reliable impression.

 

[Ting Tang]

13 hours ago, Alice Lamb said:

I've never seen Archi-Bulagarian math, but just looking at the table of contents for the 6-8 grade books, it appears that these more than cover a typical algebra 1 course with most of geometry and some algebra 2 as well. I can't tell if it uses geometric 2-column proofs. Some of the functions chapters almost belong in a pre-calculus class.

 

If you can find tables of contents for two or three algebra 1 texts and compare, that would answer your question.  Of course, seeing the complete book to examine lots of actual problems would give a more reliable impression.

 

Oh wow! I got little assistance from the publisher, despite phone calls and emails. At a glance, do you think it’s beyond the scope of Singapore Dimensions? I gave up on this one because of the lack of help. Also, I found errors in the samples. Spelling, mostly, but it made me wonder about the math. 

[Alice Lamb]

Ting Tang,

I would suggest comparing the tables of contents for Archi-Bulgarian math, Dimensions and several tradition US series such as Dolciani and Forrester (pre-algebra, algebra 1, geometry and algebra 2) side by side. Also, find samples of actual pages of instruction and problem sets and let your student look at them before you buy. If either you or the kid truly dislikes the approach or appearance, it will become drudgery. 

The first two are "integrated math" sequences which should easily leave you the option to moving directly to either algebra 2 or geometry after grade 8 and probably accelerating through geometry fairly quickly.  Dimensions looks a bit more "kid-friendly" for a student who will be starting young and doesn't seem interested in the struggle-with-it-first/discovery approach of AoPS.  It would also avoid the spelling errors and such which probably come from the translation in Archi-Bulgarian.

[Green Bean]

Dimensions 6-8, then SingaporeLive's honors high school course for kids who complete DM 6-8. Then college classes.

[Ting Tang]

7 hours ago, Alice Lamb said:

Ting Tang,

I would suggest comparing the tables of contents for Archi-Bulgarian math, Dimensions and several tradition US series such as Dolciani and Forrester (pre-algebra, algebra 1, geometry and algebra 2) side by side. Also, find samples of actual pages of instruction and problem sets and let your student look at them before you buy. If either you or the kid truly dislikes the approach or appearance, it will become drudgery. 

The first two are "integrated math" sequences which should easily leave you the option to moving directly to either algebra 2 or geometry after grade 8 and probably accelerating through geometry fairly quickly.  Dimensions looks a bit more "kid-friendly" for a student who will be starting young and doesn't seem interested in the struggle-with-it-first/discovery approach of AoPS.  It would also avoid the spelling errors and such which probably come from the translation in Archi-Bulgarian.

Thanks!  I am actually just learning towards putting him into 5th grade Dimensions if we homeschool him next year.  The 6th grade curriculum he did this year was eh, light, even though it did cover a lot of 6th grade topics.  So I guess then it would make sense just to stick with Dimensions if it was working out. I love the idea behind the Archi-Bulgarian math, but I don't they have the staffing yet to assist a lot of people.

[Malam]

On 4/9/2022 at 10:55 PM, lewelma said:

My ds's path was not just AoPS, he also did the competitions (AMO, BMO, APMO, IMO). Not all students like competitions, but for my son it was a way to focus on his problem solving and his proof writing skills. This was successful because he found a community of like-minded students and had material that forced him to think creatively about high school level content rather than just taking in more content at a surface level. This meant that his problem solving skills were off the charts by the time he hit university. This background allowed him to walk into grad level math classes as a freshman at MIT and earn As. 

I'm a little confused here - even if the contests gave him the skills, wouldn't he still have to take an advanced undergrad course as a prerequisite for the graduate course?

Edited May 14, 2022 by Malam

[lewelma]

32 minutes ago, Malam said:

I'm a little confused here - even if the contests gave him the skills, wouldn't he still have to take an advanced undergrad course as a prerequisite for the graduate course?

He placed out of univariate calculus by exam

He earned proper credit by taking the final exam for multivariate stat and differential eq (which he had self studied in high school)

He took and transferred linear algebra from the local uni.

He already knew freshman and sophomore number theory and combinatorics from self study for the competitions. (no credit exams available)

He took his freshman year 2 classes of algebra and one class of analysis.

So second semester freshman year he signed up for a graduate level combinatorics class. And ever after just took grad level classes. 

So basically at the end of freshman year he had: 2 semesters of calc, 1 diff eq, 1 linear algebra, 2 classes combinatorics, 2 classes number theory, 2 classes algebra, and 1 class of analysis. So at the end of freshman year: 11 university math classes of knowledge + his first grad class. They didn't count all his self study for actual credit, but let him choose his level. So his undergraduate degree is with 4 undergraduate classes and 6 grad classes for maths.

Edited May 14, 2022 by lewelma

[Malam]

6 minutes ago, lewelma said:

He took his freshman year 2 classes of algebra and one class of analysis.

So those two algebra classes could be taken simultaneously? And he only needed 10 math classes to graduate? I guess that makes sense considering what I've heard of MIT's flexibility.

Edited May 14, 2022 by Malam

[lewelma]

Just now, Malam said:

So those two algebra classes could be taken simultaneously? And he only needed 10 math classes to graduate? I guess that makes sense considering what I've heard of MIT's flexibility.

No he took Algebra 1 and analysis freshman fall, and Algebra 2 and grad level combinatorics freshman spring. MIT let's students choose the level they want to work at with the professor's permission. So he simply talked to the combinatorics instructor, who evaluated his level of knowledge by just a chit chat, and let him enter the grad level class. 

I think it was 10 math classes for a major, but not super sure. 

[lewelma]

MIT is maybe 

8 core science classes

8 HASS (humanities, Arts, Social Science)

10 classes per major (my son is a double major so 20 classes here, which required an overload)

32 classes expected for graduation.