Not Sure Should Continue with AOPS---Need High School Math Advice

[IrishTiger]

I'm a long-time reader of the board but haven't been much of a poster.  My DS is in 8th grade, and he just finished Ch 16 in AOPS'  Introduction to Algebra.  I'm realizing now, that he's officially finished the Algebra I material, and we were going into Algebra II material.  The end of the chapter on functions , and the next chapter was stuff I'd never seen before.  I consider myself pretty good at math, but AOPS has been a whole other level.  

I'd describe my son as strong in math---we did all of Beast Academy and AOPS pre-algebra.  Although he's good at math, his interests lean toward literature, history, theology, and writing.  I'm not sure continuing on with AOPS makes sense for him.  He's not going to be involved in math competitions, and I don't see a math and science type career in his future.  If we continue on, I'm thinking we might need to look into online classes to take pressure off of me, as well.

We tried Foerster Algebra at the beginning of the year, and it seemed super easy for him.  So, we returned to AOPS.   Not sure if we continue with AOPS because of its rigor, or go with a more typical math book, and if it's easy, than it's easy.  At the end of the day, we want him to know the typical high school math, do well on the ACT and SAT, and get into a good college.  

So, if we switched math, do you have suggestions on what to switch to?  I'd rather a series, so I don't have to research math books every year.  I have three younger children that I homeschool, one has special needs, and another is very precocious and starting Beast in Kindergarten.  My plate is feeling very full.  The only series that comes to mind is Saxon, and it seems like people either love or hate that series.  If a series doesn't make sense, but I have an idea of what book to get, that would be okay.  I definitely like having a teachers manual and/or solutions manual.

Also, would you do geometry next, then Algebra II, pre-calculus/trig, then calculus?  Since we're into the Algebra II part of the Introduction to Algebra, would you rush through/skip portions of the Algebra II text when we come to it?  It seems like a lot of people who use Saxon, don't have a whole year of geometry because it's integrated into the other years of their texts, from what I understand.

If you think we should stay with AOPS, what four books would you do for high school?  

Thanks for reading.  Any advice would be helpful.

 

 

 

 

[EKS]

Derek Owens math is excellent.  

As for what course to do next, I'm a fan of doing geometry between Algebra 1 and 2 to allow them to forget whatever hasn't stuck properly.  

[frankincense]

Second the recommendation for Derek Owens. We've used him for Physical Science, Algebra II, and now Geometry. I'm very impressed with the teaching quality, responsiveness to questions (my daughter emails questions and a TA responds same day, often within an hour or two), and challenge level of the material. 

I had DD take Algebra II immediately following Algebra and wish I'd followed the traditional Algebra, Geometry, Alg II sequence. If you take DO for Geometry, he nicely integrates Algebra review into each chapter so it stays fresh.

[Farrar]

Another vote for Derek Owens as the "math for kids who could do AoPS but probably shouldn't because they don't want their lives consumed by math" program. Keep in mind that while it's an online course, it's totally self-paced so you have to really be on top of it to make sure a student completes it, especially early in high school. It's not a "okay, go, fly now, little high schooler and manage your own coursework" class for the majority of kids, at least not at first, which other classes with deadlines sometimes can be a little more.

Another option would be to consider doing the WTMA AoPS classes. They dial it back and don't use the whole book. So it's AoPS without the full on AoPS approach.

[madteaparty]

My DS did Derek Owens through Precalculus, and it was fine.
I will say I love Forrester. I wanted something that didn’t involve me but I’m a bit wistful that we didn’t get to do Forrester and I won’t get to do it with the next kid either.  I’m also thinking if he found Forrester easy perhaps DO is also not the correct amount of challenge, if that’s what you’re looking for? I never thought of Forrester as easy myself. 

[IrishTiger]

I appreciate all of the responses.  I'm going to look into Derek Owens.  If anyone has any other suggestions, I'm happy to hear them.

[daijobu]

I'll only add that if you only have time for 1-2 AoPS courses, PreAlgebra and Algebra are the ones to study as those are the key topics he'll use for the rest of high school and college.  He's off to a good start already, wherever he ends up.  

[8filltheheart]

If he is strongly interested in other areas, I would only have him continue with AoPS if that is what he wants to do.  While AoPS is a great math program, it isn't the only one that provides students with a solid math education.  I have 2 older kids who are both gifted.  The older one loves all things math and physics.  The younger one loves all things literature and languages.  The older one convinced the younger one to try AoPS bc he loved it so much.  She tried it.  She did perfectly fine with it, but she definitely did not feel the love.  She happily walked away from AoPS and spent her time studying languages and epic poetry.  

FWIW, I'm not sure how far you made it into Foerster's text, but if your ds had completed AoPS pre-alg, then the first several chpts would have all been review.   I have used Foerster's alg 1 and 2 with all of my kids.  My ds who loved AoPS didn't jump into AoPS until intermediate in 8th after finishing Foerster's alg 2.  The transition from Foerster's to AoPS was smooth, so he wasn't lacking any skills to make the transition.  Pt being that other programs can equally prepare kids for complex mathematically thinking.  

In terms of where to go, definitely not Saxon.  A child who is used to big picture teaching would feel like they were being poked to death by a 1000 pokes by Saxon.

[EKS]

3 hours ago, 8filltheheart said:

In terms of where to go, definitely not Saxon.  A child who is used to big picture teaching would feel like they were being poked to death by a 1000 pokes by Saxon.

🤣🤣🤣

[skimomma]

We did AoPS up until dd stalled out in Intermediate Alg. halfway trough 10th grade, at which time we switched to Foerster's to finish 10th grade math. That ended up being mostly review because I did not figure out that Intro to Alg. was more than just typical Algebra I content until that point (whoops).   She moved to DE math after that and completed through Calc II by the end of HS.  AoPS was a real challenge for dd but I am glad we did what we did then switched when it got too consuming.  Dd is strong in math (and now an engineering major) so the challenge of AoPS served her well long term.  But she is also a slow worker so it got to a point where the challenge was just consuming too much time.  

Whatever you choose, I'd go as far in your current book this year as you can.  Solid algebra skills are never a regret and will just make that material easier to digest when you get to it again.

[ResearchMama2]

Hi-

I'm going to piggyback on this post if that's ok :).  

My oldest is a young 9.  He just finished Singapore Math US ed 6B.  

He WANTS to go into math and science (so the opposite of the OP), and he is very interested in the Ivies (due to family members and friends who have attended).  Any recommendations about where to go from here?  He will need to do very well on all of his standardized tests. I am having a really difficult time finding others who are interested in a strong math background, and all of the text reviews I've read talk about how they are great for those not interested in math.  I would be ecstatic if anyone could relate the success story of any homeschoolers who are now in college or have graduated from college having pursued math and science at a high level --even better if they've gone on to medical school or attended an Ivy and done well and what path they used to get there.  

All of the people I know who are currently in the medical field (as physicians) were taught in a public school system.  (I'm tempted to just get some high school texts....is that what I'm reduced to?  They seem so dry for a 9 year old...) 

Thanks for any help you might be able to provide.  🙂

[8filltheheart]

8 hours ago, ResearchMama2 said:

Hi-

I'm going to piggyback on this post if that's ok :).  

My oldest is a young 9.  He just finished Singapore Math US ed 6B.  

He WANTS to go into math and science (so the opposite of the OP), and he is very interested in the Ivies (due to family members and friends who have attended).  Any recommendations about where to go from here?  He will need to do very well on all of his standardized tests. I am having a really difficult time finding others who are interested in a strong math background, and all of the text reviews I've read talk about how they are great for those not interested in math.  I would be ecstatic if anyone could relate the success story of any homeschoolers who are now in college or have graduated from college having pursued math and science at a high level --even better if they've gone on to medical school or attended an Ivy and done well and what path they used to get there.  

All of the people I know who are currently in the medical field (as physicians) were taught in a public school system.  (I'm tempted to just get some high school texts....is that what I'm reduced to?  They seem so dry for a 9 year old...) 

Thanks for any help you might be able to provide.  🙂

I responded to your question on the accelerated forum, and my answer is still the same.  🙂  FWIW, I have had multiple kids take their first alg course at age 10 (one is a currently a 6th grader). One is a ds who graduated from high school having completed multivariable, diffEQ 1 and 2, and linear alg as well as university physics 1&2, physical mechanics 1&2, and modern physics.   No, he didn't attend an Ivy.  He attended a very avg state U on full scholarship, had incredible undergrad opportunities with a wonderful research mentor and was accepted to multiple highly competitive REUs every summer, and went on to be accepted to numerous wonderful grad programs and decided to pursue physics at Berkeley.  (One of his closest friends at his UG U is currently in the MD-PhD program at Harvard (they accept only 14 applicants/yr Harvard/MIT MDPhD Program ) My pt in sharing that is that he and his friends were highly academic college kids who could pursue what they wanted without some perceived ceiling.)

My answer as to what to do really remains the same as my response on the accelerated forum. (The ds above is #4 of 8 kids, so I have taken the same approach multiple times now.) It isn't going to be about which textbook.  Any number of math programs will prepare him for standardized tests (a very, very low threshold for testing mathematical reasoning).  It really is far more about what matches his learning style and allows him to master content while being happily challenged (not frustratingly so).  Homeschooling offers the privilege of NOT being like every other applicant.  It allows them to explore areas of interests, to delve deep, to pursue activities that they really want.  For example, my ds decided in 8th grade that while he is gifted in math that physics was his love.  He never took a single "textbook" science before 8th grade.  Science is about exploring topics that interest them and reading books on those topics.  His first "real" (if defined by controlled content with a textbook) was physics in 8th grade.  He ended up graduating high school with 12 science credits (physics, chemistry, AP chemistry, astronomy 1 and 2, a self-designed course on black holes and time warp (using a book written by Kip Thorne and Great Courses lectures), biology, and all of the college physics classes that I listed above.  I have another child who graduated with 15 foreign language credits bc she loves languages and studied 3.  

FWIW, summer camps are an awesome way for gifted kids to explore areas of interests while having fun.  Ds above attended Math Zoom, Astronomy Camp, and the Summer Science Program.   My dd attend foreign language camps.  

But most of all, they were just kids being kids and doing what they were interested in and at their level of ability.  (My entire homeschool philosophy is about nurturing internal motivation and ownership over their learning and futures.) At 9, college was not something we ever even thought about. (Never has been and still isn't until they hit about 10th grade bc we pursue colleges that fit their objectives and cost restraints vs molding our kids to fit a college profile.)  It was all about being a little kid and having fun.  🙂

[EKS]

10 hours ago, ResearchMama2 said:

Any recommendations about where to go from here?

Both of my kids started Algebra 1 at age 10.  One was homeschooled and the other was two years accelerated at a b&m school (three years accelerated in math).  Both did fine.

The great thing about starting algebra early is that it gives you time.  In my older son's case, it gave us time to go as slow as he needed to in Algebra 1 and then find a geometry book that worked for him.  For the younger one, it allowed us to spend longer than a year on Algebra 2 and then at the end it gave him two years after taking AP Calculus BC in tenth grade at the public high school to discover his true love of statistics (see signature).

I honestly don't understand why people are so intent on waiting to do algebra.  In a homeschool setting, if you discover "gaps," you can just fill them.  Also, I've found that doing algebra tends to solidify things that can be shaky.  For example, learning about algebraic fractions has helped all of my students (I also teach high school math to friends' children) understand fractions better.

Some texts to check out are:  AoPS, Jacobs, Foerster, and the Jousting Armadillos series.  If you're not planning to teach the material yourself, you might want to consider Derek Owens, AoPS online classes, and WTMA classes that use AoPS.  

 

[ResearchMama2]

6 hours ago, 8filltheheart said:

I responded to your question on the accelerated forum, and my answer is still the same.  🙂  FWIW, I have had multiple kids take their first alg course at age 10 (one is a currently a 6th grader). One is a ds who graduated from high school having completed multivariable, diffEQ 1 and 2, and linear alg as well as university physics 1&2, physical mechanics 1&2, and modern physics.   No, he didn't attend an Ivy.  He attended a very avg state U on full scholarship, had incredible undergrad opportunities with a wonderful research mentor and was accepted to multiple highly competitive REUs every summer, and went on to be accepted to numerous wonderful grad programs and decided to pursue physics at Berkeley.  (One of his closest friends at his UG U is currently in the MD-PhD program at Harvard (they accept only 14 applicants/yr Harvard/MIT MDPhD Program ) My pt in sharing that is that he and his friends were highly academic college kids who could pursue what they wanted without some perceived ceiling.)

My answer as to what to do really remains the same as my response on the accelerated forum. (The ds above is #4 of 8 kids, so I have taken the same approach multiple times now.) It isn't going to be about which textbook.  Any number of math programs will prepare him for standardized tests (a very, very low threshold for testing mathematical reasoning).  It really is far more about what matches his learning style and allows him to master content while being happily challenged (not frustratingly so).  Homeschooling offers the privilege of NOT being like every other applicant.  It allows them to explore areas of interests, to delve deep, to pursue activities that they really want.  For example, my ds decided in 8th grade that while he is gifted in math that physics was his love.  He never took a single "textbook" science before 8th grade.  Science is about exploring topics that interest them and reading books on those topics.  His first "real" (if defined by controlled content with a textbook) was physics in 8th grade.  He ended up graduating high school with 12 science credits (physics, chemistry, AP chemistry, astronomy 1 and 2, a self-designed course on black holes and time warp (using a book written by Kip Thorne and Great Courses lectures), biology, and all of the college physics classes that I listed above.  I have another child who graduated with 15 foreign language credits bc she loves languages and studied 3.  

FWIW, summer camps are an awesome way for gifted kids to explore areas of interests while having fun.  Ds above attended Math Zoom, Astronomy Camp, and the Summer Science Program.   My dd attend foreign language camps.  

But most of all, they were just kids being kids and doing what they were interested in and at their level of ability.  (My entire homeschool philosophy is about nurturing internal motivation and ownership over their learning and futures.) At 9, college was not something we ever even thought about. (Never has been and still isn't until they hit about 10th grade bc we pursue colleges that fit their objectives and cost restraints vs molding our kids to fit a college profile.)  It was all about being a little kid and having fun.  🙂

Thank you for your thoughts. I noticed that you posted on another commenter’s college bound question in February and that was more in line with the response I was looking for in terms of specifics regarding curricula used. 
 

I have a 26 yos who was similar. He completed MUS alg and geometry at 10. His sequence was to follow that with

• Foerster's alg 1 ((way more complex problems than MUS)
• Geometry (Alexander and Koeberlein)
• Foerster's alg 2/trig and AoPS Intro to Counting and Probability 
• AoPS intermediate alg
• AoPS precal
• AoPS cal

After he took the AP cal BC exam, he dual enrolled  at a 4 yr U for

• multivariable cal
• DiffEQ
• linear alg
• DiffEQ 2

He decided he loved physics more than math. He ended up DEing for

• university physics 1&2
• physical mechanics 1&2
• modern physics.

My current 6th grader is about 3/4 of the way through Foerster's after completing MUS alg and geo last yr. I have no clue whether she will want to pursue math like her brother. They have a sister who was at a similar place but stopped a cal 1. She loved languages and literature and that became her focus. (She ended up with degrees in Russian and French and is currently working on her master's in library and information sciences.)  Only she will decide.

[ResearchMama2]

4 hours ago, EKS said:

Both of my kids started Algebra 1 at age 10.  One was homeschooled and the other was two years accelerated at a b&m school (three years accelerated in math).  Both did fine.

The great thing about starting algebra early is that it gives you time.  In my older son's case, it gave us time to go as slow as he needed to in Algebra 1 and then find a geometry book that worked for him.  For the younger one, it allowed us to spend longer than a year on Algebra 2 and then at the end it gave him two years after taking AP Calculus BC in tenth grade at the public high school to discover his true love of statistics (see signature).

I honestly don't understand why people are so intent on waiting to do algebra.  In a homeschool setting, if you discover "gaps," you can just fill them.  Also, I've found that doing algebra tends to solidify things that can be shaky.  For example, learning about algebraic fractions has helped all of my students (I also teach high school math to friends' children) understand fractions better.

Some texts to check out are:  AoPS, Jacobs, Foerster, and the Jousting Armadillos series.  If you're not planning to teach the material yourself, you might want to consider Derek Owens, AoPS online classes, and WTMA classes that use AoPS.  

 

Thank you for your specific text recommendations. 

[8filltheheart]

@researchmama2 AoPS was already recommended to you on the accelerated forum.  I personally don't recommend AoPS for most students, even accelerated ones.  It is why I didn't recommend it or any specific program.  There are a few programs I personally wouldn't recommend (Teaching Textbooks, MUS for high school equivalent courses (as you noted I do use MUS alg 1 and geo in a single yr as pre-alg/pre-geo)). I also wouldn't recommend Saxon for a student who intuitively gets math bc Saxon is incredibly repetitive. But, by far, the majority of traditional textbooks when taught will prepare students for "future success. " 

You say you are "looking for concrete recommendations for math programs used by students who continued to excel in math throughout their educations extending to college and beyond."  So far you have received recommendations for MM, Dimensions, Jacobs, AoPS.  In addition, some others would be Foerster, Dolciani, Larson, Sullivan, (these latter 2 authors are used in a lot of U engineering depts).   Then there are less traditional approaches.  Derek Owens I believe doesn't use a textbook for his lower level classes but has created his own materials around his teaching.  There is Video Text which progresses through multiple levels.  I don't have any personal experience with any of those except Jacobs and Foerster at the alg1-alg2 level and Derek Owens at the pre-cal level and Larson/Sullivan for college kids.  But, there have been posters on these forums who have kids who have been successful with all of them.

BUT, there are also posters whose kids have been math and engineering majors who used TT and MUS.  Some kids just get math and it really isn't going to negatively impact them one way or the other what they use.  There are also posters who have regretted using Foersters, AoPS, SM, etc.

It really boils down to what the child needs.  Like a poster shared with you on another thread, sometimes presentation is a big factor.  It is why I use MUS for pre-alg vs. just jumping into Foerster's.  Like that poster shared, my kids aren't ready to go from an elementary format to a high school text.  It really is about finding what meshes with your individual student and your teaching style vs. focusing on long-term objectives at 9.  Teaching is probably key, more than anything else.  Going sideways and exploring concepts from different perspectives or exploring topics outside of regular sequence topics is another way to work with kids that doesn't rely on "the right book."  

[SoCal_Bear]

I have a math accelerated kid who uses AOPS. We stopped doing AOPS on our own during Intermediate Algebra. I will also say that we had to stop and back up and redo ch. 10-13 in Intro to Algebra because it wasn't solid the first time through. We use WTMA's AOPS class for Geometry this year and will do Pre-Calc before stopping AOPS. We plan to do Blue Tent AP Calc. Another alternative is Royal Fireworks online AOPS math classes. The text based AOPS classes were never appealing to my son, and we didn't need to move at that pace.

My alternative plan all along has been Foerster's if AOPS stopped being viable for him.

[SoCal_Bear]

@ResearchMama2

I did do AOPS pre-algebra with my son in 4th grade, so it is definitely possible to do. I originally planned to do it over 18 months or more to give him as much time as he wanted. He ended up doing it in 10 months because that was the pacing he wanted to do. This is definitely possible. I actually delayed starting AOPS algebra after this by doing Harold Jacobs' Mathematics: A Human Endeavor.

At this point, my son will be 8th grade and starting AOPS pre-calc in the fall but we never rushed or felt compelled to do the compacted classes through AOPS. We just have moved at a reasonable pace without overwhelming him or making math too dominant in his day.

Alternatively if he really enjoys Singapore, you could switch over and do Singapore Dimensions 7 & 8 and that would take you through algebra.

[ResearchMama2]

@8filltheheart @calbear

Thank you so much. This was very helpful and I really appreciate you both taking the time to respond. 

[Porridge]

21 hours ago, ResearchMama2 said:

Hi-

I'm going to piggyback on this post if that's ok :).  

My oldest is a young 9.  He just finished Singapore Math US ed 6B.  

He WANTS to go into math and science (so the opposite of the OP), and he is very interested in the Ivies (due to family members and friends who have attended).  Any recommendations about where to go from here?  He will need to do very well on all of his standardized tests. I am having a really difficult time finding others who are interested in a strong math background, and all of the text reviews I've read talk about how they are great for those not interested in math.  I would be ecstatic if anyone could relate the success story of any homeschoolers who are now in college or have graduated from college having pursued math and science at a high level --even better if they've gone on to medical school or attended an Ivy and done well and what path they used to get there.  

All of the people I know who are currently in the medical field (as physicians) were taught in a public school system.  (I'm tempted to just get some high school texts....is that what I'm reduced to?  They seem so dry for a 9 year old...) 

Thanks for any help you might be able to provide.  🙂

Others have made suggestions for solid programs. I’ll echo another poster in saying that one of the most important things to consider is what you are comfortable teaching (if your child isn’t ready for independent  study) or supporting (if your child is going to work independently). Some programs are easier to teach than others. Take a look at the various programs that have been suggested. Which one looks like something you could implement  with your child? If you are the one who will be teaching, which one is easiest for you to understand and explain?

I have one kid doing AOPS, and one doing Singapore dimensions. Both are excellent! FWIW, I don’t teach AOPS - it’s too hard for me. My child works independently or takes the online class. I do teach the kid who is using Singapore dimensions. I find it is pretty user friendly to teach, though IMO it does presuppose that the teacher is pretty comfortable with math.

 

[EKS]

2 hours ago, 8filltheheart said:

Teaching is probably key, more than anything else.

This.  Homeschoolers tend to worry overmuch about resources while at the same time undervaluing the role of teaching.  This is exacerbated by homeschooling gurus like SWB holding up independent learning as an ideal that everyone should aspire to.  It makes me nuts.

[ResearchMama2]

@WTMI have considered Dimensions, but am not certain what to do afterward as I understand it takes you midway through both Geometry and Algebra 2. Do you have a general idea of where you will go from there?

How far into AoPS are you? 

I could not agree more about the importance of teaching. I feel confident in my ability to teach Dimensions. I imagine I would feel the same as you about AoPS in terms of teaching it myself (although without the text I don’t know for sure), but my husband feels he can provide support for that if we go that direction. 
 

 

[SoCal_Bear]

It depends on whether or not you want to 1) have a live class 2) have teaching videos and support that or 3) teach yourself. I would not underestimate how things change with tweens/teens. My son has really desired independence and wanted live classes. He did not want me to teach him anymore. This was a big shift to move to that. He also does not do well with asynchronous learning or live classes without deadlines either so the type of live class mattered a lot. He really needs camera face to face contact with class interaction.

Even with Dimensions, Singapore Math Live (misnomer) offers recorded lessons to support Dimensions here: https://singaporemathlive.com/dimensions/

Not WTM, but I would go on to geometry and algebra 2 after Dimensions. 

Other options would be Derek Owens math lectures or Math without Borders lectures which uses Foerster for everything but Geometry. This would allow your husband to support the math studies.

[Porridge]

@ResearchMama2  I emailed Singapore and asked them what they recommend after Dimensions 8. They said the student should move into Geometry. 

My plan with my son is to move to Derek Owens Geometry after Dimensions. I don’t mind if there is some review. My son benefits from periodic review, and we can always move more quickly through topics with which he is familiar. 

My daughter just finished AOPS Intermediate Algebra .
 

[Porridge]

@calbear Math Without Borders is interesting - I had not heard of it. Thank you for the suggestion. Have you used it? 

[SoCal_Bear]

It was going to be my backup plan. I know some  find his lectures boring, but I think they were fine to me. Plenty of samples on his website. I dislike math programs that are built around pure e-delivery so I personally haven't been drawn to Derek Owens ever since he dropped using a textbook. Other e-courses aren't going to fly over here. I'm comfortable enough with supporting using lectures and worked solutions. If you poke around on youtube, there are people who talk about MWB and also on the boards here.

[8filltheheart]

21 minutes ago, calbear said:

It was going to be my backup plan. I know some  find his lectures boring, but I think they were fine to me. Plenty of samples on his website. I dislike math programs that are built around pure e-delivery so I personally haven't been drawn to Derek Owens ever since he dropped using a textbook. Other e-courses aren't going to fly over here. I'm comfortable enough with supporting using lectures and worked solutions. If you poke around on youtube, there are people who talk about MWB and also on the boards here.

My kids have only used his pre-cal class, but they don't use his ebook.  They use the Sullivan text and complete the problems that align with his lectures.

[Frances]

On 4/8/2022 at 8:22 PM, ResearchMama2 said:

Hi-

I'm going to piggyback on this post if that's ok :).  

My oldest is a young 9.  He just finished Singapore Math US ed 6B.  

He WANTS to go into math and science (so the opposite of the OP), and he is very interested in the Ivies (due to family members and friends who have attended).  Any recommendations about where to go from here?  He will need to do very well on all of his standardized tests. I am having a really difficult time finding others who are interested in a strong math background, and all of the text reviews I've read talk about how they are great for those not interested in math.  I would be ecstatic if anyone could relate the success story of any homeschoolers who are now in college or have graduated from college having pursued math and science at a high level --even better if they've gone on to medical school or attended an Ivy and done well and what path they used to get there.  

All of the people I know who are currently in the medical field (as physicians) were taught in a public school system.  (I'm tempted to just get some high school texts....is that what I'm reduced to?  They seem so dry for a 9 year old...) 

Thanks for any help you might be able to provide.  🙂

Getting into medical school does not really require much math, nor does it require attending an Ivy, and you don’t even have to be a science major. So if medical school is your goal for your child, almost any high school math program done well and to completion should be just fine. Just find one that is a good fit for his learning style and your teaching style.

It seems awfully early to be concerned about how he is going to do on standardized tests for college admissions. That was certainly not in our radar at such a young age. Like @8filltheheart, we allowed and encouraged our son to follow his passions and be a kid and did nothing just because it would look good on a college application or increase the chances of acceptance to a certain college tier. My son was accepted to several medical schools, although ultimately he chose not to attend. Having attended an Ivy for grad school myself, I did not encourage him to consider them for undergrad. He was still accepted to some Ivy medical schools despite “only” attending a state university.

[Sebastian (a lady)]

On 4/9/2022 at 9:01 PM, EKS said:

This.  Homeschoolers tend to worry overmuch about resources while at the same time undervaluing the role of teaching.  This is exacerbated by homeschooling gurus like SWB holding up independent learning as an ideal that everyone should aspire to.  It makes me nuts.

It was a SWB workshop that made me realize I'd expected independent learning before my kids were ready for it. I think she described an at the elbow, in the room, then periodic check ins progression. I realized that I'd skipped the intermediate steps.

 

[EKS]

39 minutes ago, Sebastian (a lady) said:

It was a SWB workshop that made me realize I'd expected independent learning before my kids were ready for it. I think she described an at the elbow, in the room, then periodic check ins progression. I realized that I'd skipped the intermediate steps.

Didn't SWB start talking about the elbow thing only after her WWS book intended for fifth graders came out that explicitly stated that the student should be working on their own?    

[Sebastian (a lady)]

2 hours ago, EKS said:

Didn't SWB start talking about the elbow thing only after her WWS book intended for fifth graders came out that explicitly stated that the student should be working on their own?    

I'm not sure about the timing. I listened to the recording sometime around 2011-2013. WWS was in beta testing around the same time.

But WWS has an instructor text (that I remember as being pretty hefty). So I'm not sure how independent it was expected to be. (I think it's way advanced for most middle schoolers to do on their own, btw.)

I've always felt that parents were more pushing students towards independent work than the WTM curriculum outlined. Not sure if that was because they felt overwhelmed or wanted some kids to work alone to allow the parent to work with others or just an idea that independent work was an expected (and good) goal.

I will say that my kid who has the best foundation in math is the one I did every math assignment with from pre-algebra through geometry and algebra 2. His math is solid (he's a mechanical engineering student) and it was good together time. I think it helped for him to see me struggle with and work through complicated problems (we used AoPS).

[EKS]

58 minutes ago, Sebastian (a lady) said:

But WWS has an instructor text (that I remember as being pretty hefty). So I'm not sure how independent it was expected to be. (I think it's way advanced for most middle schoolers to do on their own, btw.)

If you look at the first page of the instructor guide for WWS 1, you'll see that SWB explicitly states that the student is supposed to do the bulk of it on their own.  Here is the sample.  

58 minutes ago, Sebastian (a lady) said:

I will say that my kid who has the best foundation in math is the one I did every math assignment with from pre-algebra through geometry and algebra 2. His math is solid (he's a mechanical engineering student) and it was good together time.

Same here.  I had drunk the independent learning kool aid with the older one and it is my biggest regret of homeschooling.  I changed things with the younger one, and it worked like a charm.

I also looked through my old copy of WTM and found this about "logic" stage students:  "The logic stage student is doing much more independent work than the grammar stage student and is requiring much less one on one attention from you.  Home educated students typically spend an hour in self directed work for every ten minutes of parental tutoring."  I'd like to know which study this was pulled from, because that's not the way it worked around here!

But the main thing in WTM isn't so much that it says specifically that the student should work independently.  It's how everything is presented from grade five on.  For example, the entire science program is the student doing "experiments," researching things, and writing things up on their own.  Just about everything is worded as the student working through something.  There is very little mention of the teacher.  

I know that some people have kids who thrive with independent learning, but I honestly think that they are the exception.

Edited April 11, 2022 by EKS

[Ausmumof3]

On 4/9/2022 at 12:52 PM, ResearchMama2 said:

Hi-

I'm going to piggyback on this post if that's ok :).  

My oldest is a young 9.  He just finished Singapore Math US ed 6B.  

He WANTS to go into math and science (so the opposite of the OP), and he is very interested in the Ivies (due to family members and friends who have attended).  Any recommendations about where to go from here?  He will need to do very well on all of his standardized tests. I am having a really difficult time finding others who are interested in a strong math background, and all of the text reviews I've read talk about how they are great for those not interested in math.  I would be ecstatic if anyone could relate the success story of any homeschoolers who are now in college or have graduated from college having pursued math and science at a high level --even better if they've gone on to medical school or attended an Ivy and done well and what path they used to get there.  

All of the people I know who are currently in the medical field (as physicians) were taught in a public school system.  (I'm tempted to just get some high school texts....is that what I'm reduced to?  They seem so dry for a 9 year old...) 

Thanks for any help you might be able to provide.  🙂

I would do AOPS PreA. Some of it will be repetition but will give you a good foundation and you can skim through stuff that’s easy 

 

I find the AOPS texts best in terms of teaching Guidance and the videos available on AOPS site are a great support.

you could try having kid9 watch some of the pre A videos and do a handful of alcumus problems and see if it’s clicking.

Edited April 12, 2022 by Ausmumof3

[ResearchMama2]

On 4/10/2022 at 10:14 PM, Frances said:

Getting into medical school does not really require much math, nor does it require attending an Ivy, and you don’t even have to be a science major. So if medical school is your goal for your child, almost any high school math program done well and to completion should be just fine. Just find one that is a good fit for his learning style and your teaching style.

It seems awfully early to be concerned about how he is going to do on standardized tests for college admissions. That was certainly not in our radar at such a young age. Like @8filltheheart, we allowed and encouraged our son to follow his passions and be a kid and did nothing just because it would look good on a college application or increase the chances of acceptance to a certain college tier. My son was accepted to several medical schools, although ultimately he chose not to attend. Having attended an Ivy for grad school myself, I did not encourage him to consider them for undergrad. He was still accepted to some Ivy medical schools despite “only” attending a state university.

I would be really interested in knowing why you did not encourage your son to attend an Ivy for undergrad. 
 

Did you find attending an Ivy for graduate school useful? 
 

I am also curious what field you are in and what your son ended up doing. 
 

You clearly raised a bright student who excelled, do you have any words of wisdom? 
 

What math trajectory did you follow?
 

My ultimate goal with my children is to prepare them well so that they can pursue their passions and take advantage of any opportunities that come their way. I don’t want them to be inhibited by lack of adequate preparation.
 

I was underprepared for my course of study in graduate school following my undergraduate studies at a small liberal arts college, which made my graduate studies much more difficult. Unfortunately my college did not even offer the classes necessary for proper preparation. 
 

One of my dearest friends attended Princeton and enrolled in Calculus II as a freshman and did not do well. She had aspirations to become a physician, but she said that she was advised that grade alone would preclude her from doing so because so many other students had excelled. I retook Calculus I in college before moving on to Calculus II and excelled in both, but I have always thought that perhaps the degree of difficulty at Princeton was higher than at my small liberal arts college, and I definitely do not want my son to be underprepared if that is the case.
 

Thank you for your post and any further thoughts you might have. 

[ResearchMama2]

21 hours ago, Sebastian (a lady) said:

I'm not sure about the timing. I listened to the recording sometime around 2011-2013. WWS was in beta testing around the same time.

But WWS has an instructor text (that I remember as being pretty hefty). So I'm not sure how independent it was expected to be. (I think it's way advanced for most middle schoolers to do on their own, btw.)

I've always felt that parents were more pushing students towards independent work than the WTM curriculum outlined. Not sure if that was because they felt overwhelmed or wanted some kids to work alone to allow the parent to work with others or just an idea that independent work was an expected (and good) goal.

I will say that my kid who has the best foundation in math is the one I did every math assignment with from pre-algebra through geometry and algebra 2. His math is solid (he's a mechanical engineering student) and it was good together time. I think it helped for him to see me struggle with and work through complicated problems (we used AoPS).

Thank you for that last paragraph in particular. Immensely helpful, and my son and I were just discussing this a couple days ago. We really enjoy working together and I definitely feel at his age that ideally we should continue. Somehow I was gathering the impression that working with your student is like AoPS sacrilege, so I greatly appreciate this. 

[ResearchMama2]

20 hours ago, EKS said:

If you look at the first page of the instructor guide for WWS 1, you'll see that SWB explicitly states that the student is supposed to do the bulk of it on their own.  Here is the sample.  

Same here.  I had drunk the independent learning kool aid with the older one and it is my biggest regret of homeschooling.  I changed things with the younger one, and it worked like a charm.

I also looked through my old copy of WTM and found this about "logic" stage students:  "The logic stage student is doing much more independent work than the grammar stage student and is requiring much less one on one attention from you.  Home educated students typically spend an hour in self directed work for every ten minutes of parental tutoring."  I'd like to know which study this was pulled from, because that's not the way it worked around here!

But the main thing in WTM isn't so much that it says specifically that the student should work independently.  It's how everything is presented from grade five on.  For example, the entire science program is the student doing "experiments," researching things, and writing things up on their own.  Just about everything is worded as the student working through something.  There is very little mention of the teacher.  

I know that some people have kids who thrive with independent learning, but I honestly think that they are the exception.

What kinds of things did you change after your older student? 
 

I would also be interested in knowing why you feel the regret with the first one? Did it have a negative impact on that child in the future? 
 

(Being very familiar with regret myself, I’d like to try to avoid it with my kids as much as possible…)

 

21 hours ago, Sebastian (a lady) said:

I'm not sure about the timing. I listened to the recording sometime around 2011-2013. WWS was in beta testing around the same time.

But WWS has an instructor text (that I remember as being pretty hefty). So I'm not sure how independent it was expected to be. (I think it's way advanced for most middle schoolers to do on their own, btw.)

I've always felt that parents were more pushing students towards independent work than the WTM curriculum outlined. Not sure if that was because they felt overwhelmed or wanted some kids to work alone to allow the parent to work with others or just an idea that independent work was an expected (and good) goal.

I will say that my kid who has the best foundation in math is the one I did every math assignment with from pre-algebra through geometry and algebra 2. His math is solid (he's a mechanical engineering student) and it was good together time. I think it helped for him to see me struggle with and work through complicated problems (we used AoPS).

 

[EKS]

On 4/12/2022 at 6:23 AM, ResearchMama2 said:

What kinds of things did you change after your older student? 

I stopped trying to get him to work independently and made practically everything into a conversation.  This was for all subjects.  Even when he was doing practice problems independently in math, for example, I sat across the room and had him tell me the answers he was getting as he was getting them.  If he missed one, I had him tell me from across the room what he did step by step.  He was usually able to find his error himself that way, but if not, I'd give him a hint. 

When it came to writing instruction, the conversations we had were really amazing.  I went from thinking that writing was something to be learned and done alone to it being the manifestation of ideas that, especially for students, become fully formed through conversation (otherwise known as "discussion" in educational circles).  So instead of giving him something to read, say, and then telling him to write two paragraphs to answer a particular question, we would read the thing together and then discuss several questions.  He would then choose one to write about.  And part of that process was even more conversation during the writing itself.  This last part morphed into having him write a draft on his own which we then made better during yet another conversation.

This process really opened my eyes to the real possibilities of one-to-one instruction.  Most homeschoolers seem to be so intent on moving their kids along to the independent learning stage that they never even consider that there might be something better.

On 4/12/2022 at 6:23 AM, ResearchMama2 said:

I would also be interested in knowing why you feel the regret with the first one? Did it have a negative impact on that child in the future?

I regret trying to get him to work independently at the expense of his actual education.  The two areas where this had the most negative impact were math and writing.  It stalled his progress in both when he was in high school.  That said, you can see from my signature that he was able to be successful in a math intensive field.  What the signature doesn't say is that he also has something resembling a minor in writing and rhetoric.  But honestly, he achieved these things in spite of my pushing for independence, and certainly not because of it.

Edited May 22, 2022 by EKS

[8filltheheart]

1 hour ago, EKS said:

I stopped trying to get him to work independently and made practically everything into a conversation.  This was for all subjects.  Even when he was doing practice problems independently in math, for example, I sat across the room and had him tell me the answers he was getting as he was getting them.  If he missed one, I had him tell me from across the room what he did step by step.  He was usually able to find his error himself that way, but if not, I'd give him a hint. 

When it came to writing instruction, the conversations we had were really amazing.  I went from thinking that writing was something to be learned and done alone to it being the manifestation of ideas that, especially for students, become fully formed through conversation (otherwise known as "discussion" in educational circles).  So instead of giving him something to read, say, and then telling him to write two paragraphs to answer a particular question, we would read the thing together and then discuss several questions.  He would then choose one to write about.  And part of that process was even more conversation even during the writing itself.  This last part morphed into having him write a draft on his own which we then made better during yet another conversation.

This process really opened my eyes to the actual possibilities of one-to-one instruction.  Most homeschoolers seem to be so intent on moving their kids along to the independent learning stage that they never even consider that there might be something better.

I regret trying to get him to work independently at the expense of his actual education.  The two areas where this had the most negative impact were math and writing.  It stalled his progress in both when he was in high school.  That said, you can see from my signature that he was able to be successful in a math intensive field.  What the signature doesn't say is that he also has something resembling a minor in writing and rhetoric.  But honestly, he achieved these things in spite of my pushing for independence, and certainly not because of it.

I love your post. It sums up my educational philosophy and why I named my homeschool business Treasured Conversations.  From my perspective, homeschoolers who outsource everything or have their kids working independently are missing the best part of homeschooling.

[regentrude]

On 4/8/2022 at 5:41 AM, 8filltheheart said:

In terms of where to go, definitely not Saxon.  A child who is used to big picture teaching would feel like they were being poked to death by a 1000 pokes by Saxon.

So much this. Our misguided foray into Saxon right when I started homeschooling was an excrutiatingly painful mistake

[regentrude]

On 4/8/2022 at 10:22 PM, ResearchMama2 said:

I am having a really difficult time finding others who are interested in a strong math background, and all of the text reviews I've read talk about how they are great for those not interested in math.  I would be ecstatic if anyone could relate the success story of any homeschoolers who are now in college or have graduated from college having pursued math and science at a high level --even better if they've gone on to medical school or attended an Ivy and done well and what path they used to get there.  

I responded to your post on the Accelerated forum. We used AoPS. (which is only suitable for students interested in math, LOL)

My kids both went on to earn their BS in physics and graduated with honors. Is that a sufficient success story for you?
My DD's school was not strictly an Ivy, but an extremely selective, high ranking college (U Chicago).

ETA: You don't need a lot of math for med school. Much much less than for physics.
 

Edited April 12, 2022 by regentrude

[regentrude]

4 hours ago, ResearchMama2 said:

 Somehow I was gathering the impression that working with your student is like AoPS sacrilege, so I greatly appreciate this. 

No. There's no issue with working with your student. AoPS uses the discovery method, so that would be lost of the parent were explicitly teaching the new concept before the student had the opportunity to work the introductory problems. It would rob the student of the chance to discover the new idea.
I did a mix with my kids; I was next to them while they were doing math, and we did the hard problems together; however, I gave them the gift of first wrestling with the problem without my help.

The only text for which we did explicit teaching was calculus which is very different in style and much more theoretical. 

[ResearchMama2]

27 minutes ago, regentrude said:

I responded to your post on the Accelerated forum. We used AoPS. (which is only suitable for students interested in math, LOL)

My kids both went on to earn their BS in physics and graduated with honors. Is that a sufficient success story for you?
My DD's school was not strictly an Ivy, but an extremely selective, high ranking college (U Chicago).

ETA: You don't need a lot of math for med school. Much much less than for physics.
 

Thank you for this. Yes, this is exactly the kind of success story I was interested in. 

[Frances]

5 hours ago, ResearchMama2 said:

I would be really interested in knowing why you did not encourage your son to attend an Ivy for undergrad. 
 

Did you find attending an Ivy for graduate school useful? 
 

I am also curious what field you are in and what your son ended up doing. 
 

You clearly raised a bright student who excelled, do you have any words of wisdom? 
 

What math trajectory did you follow?
 

My ultimate goal with my children is to prepare them well so that they can pursue their passions and take advantage of any opportunities that come their way. I don’t want them to be inhibited by lack of adequate preparation.
 

I was underprepared for my course of study in graduate school following my undergraduate studies at a small liberal arts college, which made my graduate studies much more difficult. Unfortunately my college did not even offer the classes necessary for proper preparation. 
 

One of my dearest friends attended Princeton and enrolled in Calculus II as a freshman and did not do well. She had aspirations to become a physician, but she said that she was advised that grade alone would preclude her from doing so because so many other students had excelled. I retook Calculus I in college before moving on to Calculus II and excelled in both, but I have always thought that perhaps the degree of difficulty at Princeton was higher than at my small liberal arts college, and I definitely do not want my son to be underprepared if that is the case.
 

Thank you for your post and any further thoughts you might have. 

I did not encourage my son to attend an Ivy based on his goals at the time (medical school), planned STEM major, and my experience as a grad student at an Ivy. Like you, I attended a small LAC for undergrad. The classes were small, there were no TAs, and I developed very close relationships with my professors that continue to this day. Next month my husband and I will be flying out of state to spend a week with one of his profs from the same college. In grad school, it was primarily only the graduate students that experienced what I did as an undergrad, small classes, close relationships with professors, classes primarily taught by professors, etc. Unlike you, my husband and I both felt very well prepared for grad school coming out of a LAC and have three advanced STEM degrees between us.

As I posted in the recent thread on MIT going back to using test scores for admission, I actually felt sorry for the undergrads at my Ivy, as did my husband’s two students who went from a LAC to the Ivy League for STEM PhDs and @8filltheheartnoted her son felt the same at Berkeley. My SIL who did her grad work at an Ivy (not STEM) and attended the same LAC as me and my husband for undergrad, actually forbade her daughter to consider them for undergrad. She instead went to an elite LAC and then got her STEM PhD from an Ivy. By going from a LAC to an Ivy, I felt like I got the best of both worlds. Even though my husband and I were both top students at our LAC, we never lacked peers at our level and some of our profs were among our closest friends and still are to this day. We also had no problem getting research experience at both our LAC and during the summers at research universities.
 

My son was initially interested in LACs and primarily applied to them, but ultimately chose the humanities focused honors college of a state school after doing DE at our local LAC for the last two years of high school. Although it wasn’t really a consideration, this was also the best financial option, as he had a full tuition scholarship plus a few other small ones, while most of the elite LACs where he was accepted give no merit aid. In many respects, his undergrad experience was very similar to ours with small classes, close relationships with and great mentoring from professors, research experiences directly with professors (not working for a grad student), very few classes with TAs, etc. Ironically, after doing chemistry research and German study in Germany on a scholarship and then graduate work in a non-STEM field at the London School of Economics, he ended up in one of the few careers for which I would actually recommend an Ivy undergrad, consulting. Investment banking is the other one, as students for these two careers are most commonly recruited from elite schools. But he certainly wouldn’t trade the many and varied experiences on the path he followed for going directly into his current career with an Ivy undergrad degree.

While my son loved science and ultimately completed a science major in college, his real area of giftedness was verbal skills. So my goal with math was to find a program that was a good match for him and do it well and to completion, so as to lay a strong foundation and keep all doors open. All of the resources we used have already been mentioned here or in your other thread. The most important thing is to find a good match for your son’s learning style and your teaching style (unless of course you choose something taught by someone else).

At your son’s age, I would just allow him to be a kid and follow his interests and passions. Personally, I would not encourage talk about Ivies, as I would not want him to get the idea that they are the only acceptable options for undergrad or the only places he can fulfill his learning and career goals. It’s great to have goals and dreams, but realistically, at age nine he doesn’t even understand what he’s aiming for by saying he wants to attend an Ivy.

As for your friend at Princeton, my former college prof husband would say she got terrible advising. One bad grade should not deter you from applying to medical school. While very good students, neither my husband (who was also accepted to but did not attend medical school) nor son were straight A students. But they were passionate learners who strongly pursued their goals and interests and both had strong skills and interests outside of the sciences.

Edited April 12, 2022 by Frances

[daijobu]

8 hours ago, ResearchMama2 said:

One of my dearest friends attended Princeton and enrolled in Calculus II as a freshman and did not do well. She had aspirations to become a physician, but she said that she was advised that grade alone would preclude her from doing so because so many other students had excelled. I retook Calculus I in college before moving on to Calculus II and excelled in both, but I have always thought that perhaps the degree of difficulty at Princeton was higher than at my small liberal arts college, and I definitely do not want my son to be underprepared if that is the case.
 

Thank you for your post and any further thoughts you might have. 

What a funny coincidence that you mentioned Princeton math specifically.  One of my favorite slides from Richard Rusczyk was from a talk he presented at Math Prize for Girls.  (One of my dd's attended for a few years before the pandemic.)  I've added RR's comments below.  It seems like Princeton is in the habit of admitted unprepared students.  

And why would anyone tell this person not to apply to medical school just because of one lousy math grade?  That's just so... weird.  Heck, I got a C in chemistry the first time around and I was admitted to UCSF.  Not exactly Ivy League, but still.  

2014 MPG video

 

 

Right after I started Art of Problem Solving I received an email from someone who attended Princeton who attended right around the time I did.  

 

I want you think for a minute what this student’s middle school and high school teachers thought when he went off to Princeton.  They thought, “We succeeded.  He went off to Princeton; we’re awesome.”  They never saw this.  I’m sure he didn’t go back to his middle school teachers and say, “Yeah what’s up?!?  You didn’t prepare me for this.”

 

So they didn’t get this feedback, and this happens a lot.  I saw this a lot at Princeton, this happens a lot now.  Kids go through school, some very good schools, they get perfect scores on everything, and then they come to place like MIT, a place like Princeton, they walk into that first year math class, and they see something they’ve never seen before: problems they don’t know how to solve.  And they completely freak out.  And that’s a bad time to have these first experiences.  Having to overcome initial failure. 

[regentrude]

21 minutes ago, daijobu said:

Kids go through school, some very good schools, they get perfect scores on everything, and then they come to place like MIT, a place like Princeton, they walk into that first year math class, and they see something they’ve never seen before: problems they don’t know how to solve.  And they completely freak out.  And that’s a bad time to have these first experiences.  Having to overcome initial failure. 

And that is not the fault of Princeton or any of the receiving schools, but solely the fault of a school system that does not challenge its strong students! And Ap tests and whatnot are not designed to find out who can think, but just who has trained best to jump through a hoop that hangs precisely where you expect it to hang.

This is exactly why I homeschooled my gifted kids: to give them the gift of a challenge.

As I said in another post, both my kids expressed independent from another that it was exactly this: having encountered hard problems they didn't know how to solve and having the confidence and strategies to just go in and wrestle with the problem which set their math education apart from their college classmates.

Edited April 12, 2022 by regentrude

[Clemsondana]

15 hours ago, regentrude said:

And that is not the fault of Princeton or any of the receiving schools, but solely the fault of a school system that does not challenge its strong students! And Ap tests and whatnot are not designed to find out who can think, but just who has trained best to jump through a hoop that hangs precisely where you expect it to hang.

This is exactly why I homeschooled my gifted kids: to give them the gift of a challenge.

As I said in another post, both my kids expressed independent from another that it was exactly this: having encountered hard problems they didn't know how to solve and having the confidence and strategies to just go in and wrestle with the problem which set their math education apart from their college classmates.

I'd add to this that it doesn't specifically have to be AoPS math, or math at all.  Many of the Science Olympiad kids that I know credit that experience with teaching them to cope with a lot of college challenges.  The idea is that students study a set of topics and take tests or build something to specifications.  But, every year we get to competitions and somebody wrote a test over completely different topics - for Ecology it may be that it was supposed to focus on aquatic environments but they get a test on deserts, for instance.  The kids learn to think on their feet, logic through things, stand up for themseleves if a proctor gives instructions that don't follow the rules, etc.  The kids learn to research unknown topics on their own, know when to ask for help, and know how to handle both disappointment and triumph gracefully.  Kids can learn those things through sports, music, academic competitions, challenging study groups, volunteer work, advanced classes, or probably a host of other areas.  How much challenge a kid can manage to get stronger without 'breaking' - struggling emotionally, avoiding the activity, etc - is going to depend on the kid, their circumstances, their maturity, and the activity.  That's why people can't give one-size-fits-all advice. 

[8filltheheart]

2 hours ago, Clemsondana said:

I'd add to this that it doesn't specifically have to be AoPS math, or math at all.  Many of the Science Olympiad kids that I know credit that experience with teaching them to cope with a lot of college challenges.  The idea is that students study a set of topics and take tests or build something to specifications.  But, every year we get to competitions and somebody wrote a test over completely different topics - for Ecology it may be that it was supposed to focus on aquatic environments but they get a test on deserts, for instance.  The kids learn to think on their feet, logic through things, stand up for themseleves if a proctor gives instructions that don't follow the rules, etc.  The kids learn to research unknown topics on their own, know when to ask for help, and know how to handle both disappointment and triumph gracefully.  Kids can learn those things through sports, music, academic competitions, challenging study groups, volunteer work, advanced classes, or probably a host of other areas.  How much challenge a kid can manage to get stronger without 'breaking' - struggling emotionally, avoiding the activity, etc - is going to depend on the kid, their circumstances, their maturity, and the activity.  That's why people can't give one-size-fits-all advice. 

I agree.  I think that is one of the strengths of homeschooling and having a mom who doesn't know 1/2 of the answers!  My kids have learned how to research things that we don't know the answer to and then study until understood.  That has given them an advantage in college.  When their peers have not understood what has been discussed in class, they have floundered like there was no way to understand.  When my kids haven't understood, they have simply looked for resources to help them understand better.  In our house, we call it the spoonfed defeat vs. the initiative to learn understand.

Edited April 13, 2022 by 8filltheheart

[ResearchMama2]

19 hours ago, daijobu said:

What a funny coincidence that you mentioned Princeton math specifically.  One of my favorite slides from Richard Rusczyk was from a talk he presented at Math Prize for Girls.  (One of my dd's attended for a few years before the pandemic.)  I've added RR's comments below.  It seems like Princeton is in the habit of admitted unprepared students.  

And why would anyone tell this person not to apply to medical school just because of one lousy math grade?  That's just so... weird.  Heck, I got a C in chemistry the first time around and I was admitted to UCSF.  Not exactly Ivy League, but still.  

2014 MPG video

 

 

Right after I started Art of Problem Solving I received an email from someone who attended Princeton who attended right around the time I did.  

 

I want you think for a minute what this student’s middle school and high school teachers thought when he went off to Princeton.  They thought, “We succeeded.  He went off to Princeton; we’re awesome.”  They never saw this.  I’m sure he didn’t go back to his middle school teachers and say, “Yeah what’s up?!?  You didn’t prepare me for this.”

 

So they didn’t get this feedback, and this happens a lot.  I saw this a lot at Princeton, this happens a lot now.  Kids go through school, some very good schools, they get perfect scores on everything, and then they come to place like MIT, a place like Princeton, they walk into that first year math class, and they see something they’ve never seen before: problems they don’t know how to solve.  And they completely freak out.  And that’s a bad time to have these first experiences.  Having to overcome initial failure. 

This is absolutely invaluable. Thank you for sharing!! 

[ResearchMama2]

23 hours ago, Frances said:

I did not encourage my son to attend an Ivy based on his goals at the time (medical school), planned STEM major, and my experience as a grad student at an Ivy. Like you, I attended a small LAC for undergrad. The classes were small, there were no TAs, and I developed very close relationships with my professors that continue to this day. Next month my husband and I will be flying out of state to spend a week with one of his profs from the same college. In grad school, it was primarily only the graduate students that experienced what I did as an undergrad, small classes, close relationships with professors, classes primarily taught by professors, etc. Unlike you, my husband and I both felt very well prepared for grad school coming out of a LAC and have three advanced STEM degrees between us.

As I posted in the recent thread on MIT going back to using test scores for admission, I actually felt sorry for the undergrads at my Ivy, as did my husband’s two students who went from a LAC to the Ivy League for STEM PhDs and @8filltheheartnoted her son felt the same at Berkeley. My SIL who did her grad work at an Ivy (not STEM) and attended the same LAC as me and my husband for undergrad, actually forbade her daughter to consider them for undergrad. She instead went to an elite LAC and then got her STEM PhD from an Ivy. By going from a LAC to an Ivy, I felt like I got the best of both worlds. Even though my husband and I were both top students at our LAC, we never lacked peers at our level and some of our profs were among our closest friends and still are to this day. We also had no problem getting research experience at both our LAC and during the summers at research universities.
 

My son was initially interested in LACs and primarily applied to them, but ultimately chose the humanities focused honors college of a state school after doing DE at our local LAC for the last two years of high school. Although it wasn’t really a consideration, this was also the best financial option, as he had a full tuition scholarship plus a few other small ones, while most of the elite LACs where he was accepted give no merit aid. In many respects, his undergrad experience was very similar to ours with small classes, close relationships with and great mentoring from professors, research experiences directly with professors (not working for a grad student), very few classes with TAs, etc. Ironically, after doing chemistry research and German study in Germany on a scholarship and then graduate work in a non-STEM field at the London School of Economics, he ended up in one of the few careers for which I would actually recommend an Ivy undergrad, consulting. Investment banking is the other one, as students for these two careers are most commonly recruited from elite schools. But he certainly wouldn’t trade the many and varied experiences on the path he followed for going directly into his current career with an Ivy undergrad degree.

While my son loved science and ultimately completed a science major in college, his real area of giftedness was verbal skills. So my goal with math was to find a program that was a good match for him and do it well and to completion, so as to lay a strong foundation and keep all doors open. All of the resources we used have already been mentioned here or in your other thread. The most important thing is to find a good match for your son’s learning style and your teaching style (unless of course you choose something taught by someone else).

At your son’s age, I would just allow him to be a kid and follow his interests and passions. Personally, I would not encourage talk about Ivies, as I would not want him to get the idea that they are the only acceptable options for undergrad or the only places he can fulfill his learning and career goals. It’s great to have goals and dreams, but realistically, at age nine he doesn’t even understand what he’s aiming for by saying he wants to attend an Ivy.

As for your friend at Princeton, my former college prof husband would say she got terrible advising. One bad grade should not deter you from applying to medical school. While very good students, neither my husband (who was also accepted to but did not attend medical school) nor son were straight A students. But they were passionate learners who strongly pursued their goals and interests and both had strong skills and interests outside of the sciences.

Thank you for taking the time to provide your thoughts, I sincerely appreciate it. 

In terms of determining a course of action in terms of math, this really resonated with me, and is exactly my own sentiment, “So my goal with math was to find a program that was a good match for him and do it well and to completion, so as to lay a strong foundation and keep all doors open.” 

You mentioned having already provided your resources used, but I had difficulty finding that information. Is there any chance you have a link? 
 

Thank you again for your wisdom and insight. My husband is where he is today because of some advice I received from a more seasoned professional in his field about a course he should pursue following graduate school to provide him the greatest number of opportunities in the future. At the time my husband was convinced that it was unnecessary, but now he is grateful every day for that advice and the unexpected doors it opened. 

[lewelma]

Sorry OP, this is answering Researchmama's request for high school sequence and texts, and does not answer your OP.

Researchmama2: So it looks like you are interested in the actually progression and materials used for advanced math students. This is what my older boy did in highschool. With this background, he was able to walk into graduate level math classes as a freshman at MIT. He is graduating in May with a double major in Math and Physics and has been accepted into the #1 ranked graduate school in his subfield of physics.   

Formatting is a bit off, but I bolded the courses so you could see which resources went with which courses.

Things to note: 1) he did Introductory Algebra over 3 years. Back then the preA book was not printed, and he did every. single. problem. in the entire Intro Algebra AoPS book. My biggest advice to you is to make Algebra rock solid. Three FULL years for this very advanced boy and it was sooooo worth it. 2) He did number theory and combinatorics over many years because he was studying for the competitions -- I simply split into two half courses and gave him a full credit each. 3) He was *very* underwhelmed by the university courses he took, which is one of the reasons he decided to leave NZ and go to the USA for his education. He earned 98% with a course median of 64%, and he was 5 years their junior. We were told that this level of math is what we would find throughout NZ universities.  4) He did Calculus twice, once theoretically and once practically. 

HTH

Ruth

                                                                       9th           10th       11th      12th

Also Multivariate Calc in summer after 12th grade so he could test out.

Algebra 1. 4th-7th (self study with text)
Textbook: Introduction to Algebra (Art of Problem Solving), by Richard Rusczyk

Geometry. 8th (Self study with text)

Textbook: Introduction to Geometry (Art of Problem Solving), by Richard Rusczyk

Algebra 2. 8th (self study with text)
Textbook: Intermediate Algebra (Art of Problem Solving), by Richard Rusczyk

Precalculus. 9th (AoPS online class, 1 credit)
Textbook: Precalculus (Art of Problem Solving), by Richard Rusczyk and Mathew Crawford

Olympiad Geometry. 9th (AoPS online class, 0.5 credits)
Textbook: material provided in the course

Combinatorics and Probability. 9th and 11th grade (Blended class: AoPS online class and self-study, 1.0 credit)

Textbooks: Introduction to Counting and Probability (Art of Problem Solving), by David Patrick
Intermediate Counting and Probability (Art of Problem Solving), by David Patrick
Problem Solving Tactics, by Angelo Di Pasquale et al.
Selected readings were provided for advanced topics

Calculus 1 – 10th (AoPS online class - 1 credit)
Textbooks: Calculus (Art of Problem Solving), by David Patrick
 

Calculus 2. 10th grade (1 credit) (blended class, AoPS online class and self study using Anton which has a practical physics/engineering approach)

Textbooks: Calculus (Art of Problem Solving), by David Patrick
Calculus, by Howard Anton and Irl Bivens

Number Theory. 9th and 10th grade (Blended course: AoPS online class and self-study, 1 credit)
Textbooks: Introduction to Number Theory (Art of Problem Solving), by David Patrick

Problem Solving Tactics, by Angelo Di Pasquale et al.

Selected readings were provided for intermediate and advanced topics

Linear Algebra. 11th grade (local university)
Textbook: Elementary Linear Algebra: Applications Version, by Howard Anton

Foundations of Algebra, Analysis, and Topology.  11th grade (local university)
Textbook: Materials produced by professor

Real Analysis. 12th grade (self-study -1 credit)
Textbook: Principles of Mathematical Analysis, by Walter Rudin
Lecture Series: Real Analysis, MIT OpenCourseWare

Multivariate Calculus 12th grade (self study )

MIT opencourseware

Edited April 13, 2022 by lewelma