Math Path for student who wants to be a mathematician?

[MamaSprout]

Is it pretty much AoPS with some contests thrown in? Would love some BTDT experience. This is my 4th kiddo, and I am sure I've never in my life heard a kid say, "I want to be a mathematician when I grow up."

[retiredHSmom]

I would say that a lot depends on your child's interest level.  If he/she wants to do some math contests, do them.  Make sure that he/she has a strong understanding of math.

 

I have a daughter who is a junior in applied mathematics, she planned to be a ballerina.  She loves math now.  She did math research this summer and loved every minute of it.  

 

We used a lesser loved math curriculum. When she showed up at college, she wasn't way ahead in math.  She took pre-calc her first semester. Deciding that she loved it was the turning point.  She has taken 2-3 math classes each semester since then and is now planning a PhD in math.

 

Encourage love, build a strong foundation.

[kiana]

AOPS is not necessary although it would certainly be my first choice unless the student or I hated it. AOPS wasn't around when I was a child and I still managed to become one. I sure wish it had been around, though.

 

A strong, solid, conceptual, and joyous understanding of mathematics at all levels covered would be my goal. There are many programs that can accomplish this. I would also make sure to include just-for-fun math enrichment topics. Here, though, the level is pretty important, so how old is the child, what has s/he done so far, and why does s/he like math?

 

I would consider it useful to include an introduction to programming at some level. More and more careers that involve mathematics involve some level of programming. For my PhD I was required to do a project which involved a significant amount of programming, and the students who had limited experience before the program had to take courses to get there. I also wouldn't stint science -- many students begin university as mathematics majors, and decide that what they liked wasn't the proofs (which is what university mathematics is really about) but solving problems with mathematics. They often switched majors into physics, chemistry, geology, engineering, or computing.

[Mhorai]

what is APOS?

 

 

[HS Mom in NC]

This can help you get an idea of what kinds of options are out there and how to prep for them.

 

The Book of Majors

 

http://www.amazon.com/Book-Majors-2014-All-New-Edition/dp/1457300222/ref=sr_1_1?ie=UTF8&qid=1380231675&sr=8-1&keywords=book+of+majors

 

Each major includes information like:

 

What it's about

Is this for you?

Recommended High School Prep

Did you know (miscellaneous information) 

Typical Courses in this Major

Concentrations

What the study of this major is like

Other majors you might like

Questions to ask colleges

Career Options and Trends

Insider's Viewpoint

Contact Info to learn more

[Spy Car]

what is APOS?

Art of Problem Solving is a small company near San Diego that publishes textbooks for math adept students. They also run a website and offer online classes. they are in process on rolling out an elementary math program called Beast Academy. Third Grade and the first (of 4) 4th Grade levels of BA are out now.

 

Bill

[Luckymama]

I'd also recommend exposure to discrete math topics that aren't covered in the typical math sequence----counting/combinatorics, probability, number theory, game theory, set theory, etc.

[MamaSprout]

AOPS is not necessary although it would certainly be my first choice unless the student or I hated it. AOPS wasn't around when I was a child and I still managed to become one. I sure wish it had been around, though.

 

A strong, solid, conceptual, and joyous understanding of mathematics at all levels covered would be my goal. There are many programs that can accomplish this. I would also make sure to include just-for-fun math enrichment topics. Here, though, the level is pretty important, so how old is the child, what has s/he done so far, and why does s/he like math?

 

I would consider it useful to include an introduction to programming at some level. More and more careers that involve mathematics involve some level of programming. For my PhD I was required to do a project which involved a significant amount of programming, and the students who had limited experience before the program had to take courses to get there. I also wouldn't stint science -- many students begin university as mathematics majors, and decide that what they liked wasn't the proofs (which is what university mathematics is really about) but solving problems with mathematics. They often switched majors into physics, chemistry, geology, engineering, or computing.

 

She's elementary age, and has always passionately wanted to be a scientist "when she grew up" until very recently. She always just tolerated math, so I'm a little startled by this change.

 

There really isn't any elementary math concept she's not solid on, but I'm not yet moving her into algebra because I think she needs a more maturity and more patience with problem solving. She is picking up speed with both, and keeps her own math notebook, for fun.

 

I did pick up some kids to tutor and we've been doing a daily math circle. She's my last kiddo at home, so math has always been a solo pursuit up until now. I think that may be the spark, she is a bit competitive. I've just been using bits from Singapore IP, Zaccarro, and Beast Academy. I'm not sure what to buy next. I wish I could see some of the math contest books before I buy them. There are so many to choose from, and yes, I think one can have too many math books...

 

She would enjoy programming. "physics, chemistry, geology, engineering" Those, at the kid level, are pretty much her hobbies (and nature stuff like playing in the woods plus creating miniatures for American Girl dolls).

 

I'm really conscious of her path, because we goofed with an older sibling on a couple of math classes (let him move into college algebra before taking high school calc.) He decided to be an engineer, and has been playing catch up.

 

Thanks for the great info!

[mathmarm]

Its all in the attitude. From what I have seen of AoPS, I don't like their PreAlgebra which feels "klunky" to me, but the program looks genuinely solid and is unlike any other math curricula I've seen in the US in all my years of teaching, however it is not necessary in the least to be a good math student or to train a mathematician, though it is an excellent program, from what I can tell. I'm still perusing and I haven't gotten through all of the text. I am toying with the idea of buying the collection for my own personal use, seeing as how my son is only a couple of weeks old.

 

I had started to write about what math studies were like in my household when I was growing up, but it quickly became a really, really long reply so I cut it out. But suffice it to say we didn't have any special curriculum/math program. I honestly don't even think that my mom set out to accelerate us in math or make us "math smart" or anything. She was a math teacher and we were poor, she made up games and gave us tasks to do that were within her personal scope and budget, many of which were very math centric. It probably helped tremendously that my mom was a very well rounded mathematician, though she only taught high school she self studied a few other math courses from the undergraduate catalog she was only certified to teach highschool math.

 

If your son was serious then I'd say your halfway there, no matter what curriculum you go with. I will advise you get him a math mentor as he gets into highschool mathematics though. Sometimes a mentor is invaluable.

[Arcadia]

. I wish I could see some of the math contest books before I buy them. There are so many to choose from, and yes, I think one can have too many math books...

 

My libraries has the contest books by MAA.

 

Canada's Math Kangaroo (1st - 12th grade)  past contest problems and solutions page

More downloadable contest problems links in this thread

http://forums.welltrainedmind.com/topic/190273-middle-school-math-contest-problems/

[FairProspects]

Subbing. My ds alternates between wanting to be a physicist, aeronautical engineer, and mathematician. We just started private tutoring and math circles, but other than that I don't really know where to go with it.

[kiana]

I think your plan sounds pretty good and I like the resources you're using. You might also consider Hands on Equations if she's not quite ready for algebra -- I used it myself the year before pre-algebra and I really think it helped with the rock-solid understanding I've always had of basic algebra.

 

Here's another cute book: http://www.amazon.com/Alien-Math-Marya-Washington-Tyler/dp/188266471X -- doing arithmetic in different bases is fun and imo deepens our understanding of base 10. Math for Smarty Pants is another fun intro to a lot of different topics that I didn't see again until much more advanced courses. Both of these are really enrichment books.

 

You might also look at the Elements of Mathematics -- the books are (I believe) available from IMACS -- and the courses are also offered online at www.elementsofmathematics.com. I have gotten these books from the library and consider them excellent -- they were written for advanced students of 5th grade and up (note that this is advanced 5th graders, not younger students advanced to 5th grade), so if she is not quite there yet, it may be something to keep in mind. They have an online aptitude test.

 

Finding her a mentor once she gets to high school age (if she is still interested) would be a wonderful idea. Perhaps if you have a local university they would have a professor who was interested in mentoring young, gifted students? I know that I would be if anyone in my area contacted me.

[quark]

I have some math stuff linked in my siggy if you are interested in more resources, Bean. I do believe one can NEVER have too many math books though. :D

Good luck!

[MamaSprout]

I think your plan sounds pretty good and I like the resources you're using. You might also consider Hands on Equations if she's not quite ready for algebra -- I used it myself the year before pre-algebra and I really think it helped with the rock-solid understanding I've always had of basic algebra.

 

Here's another cute book: http://www.amazon.com/Alien-Math-Marya-Washington-Tyler/dp/188266471X -- doing arithmetic in different bases is fun and imo deepens our understanding of base 10. Math for Smarty Pants is another fun intro to a lot of different topics that I didn't see again until much more advanced courses. Both of these are really enrichment books.

 

You might also look at the Elements of Mathematics -- the books are (I believe) available from IMACS -- and the courses are also offered online at www.elementsofmathematics.com. I have gotten these books from the library and consider them excellent -- they were written for advanced students of 5th grade and up (note that this is advanced 5th graders, not younger students advanced to 5th grade), so if she is not quite there yet, it may be something to keep in mind. They have an online aptitude test.

 

 

 

The alien book is cute. I can see her liking it. We do have DragonBox 2, and she easily translates that to math, but the Hands On Equations could be done with other kids. I'll look at the Elements of Mathematics.

 

Thanks!

[Crimson Wife]

There is a good chapter on math in the book "What High Schools Won't Tell You" by Elizabeth Wissner-Gross.

 

I would highly encourage you to see if there is a math circle close to you. http://www.mathcircles.org/FindAMathCircleNearYou_USMap

[crazyforlatin]

Agreeing with CW that a math circle for an interested math kid can be an awesome experience. DD joined one and absolutely loves it. Parents are not allowed to attend, so I'm not sure exactly what goes on in there (except for the paperwork that I see after class). The teachers are either math grad students or PhD mathematicians. They seem to be making the kids very excited to be part of the circle.

[MamaSprout]

There is a good chapter on math in the book "What High Schools Won't Tell You" by Elizabeth Wissner-Gross.

 

I would highly encourage you to see if there is a math circle close to you. http://www.mathcircles.org/FindAMathCircleNearYou_USMap

 

Nope, in a black hole. I actually already checked at a local university. If there is a real math circle, it would be me running it (and I was not a math major.) I haven't heard of the Wissner-Gross book, I'll take a look.

 

ETA- I know this is going to sound terrible, but we are not really shooting for aggressive admissions for undergrad for this dd. Two of her older siblings have had shockingly bad experiences at nameless Selective Engineering University, and this kiddo is grade skipped, so would be starting college around 17. I was thinking maybe semi-selective liberal arts college less than 3 hours from home, knowing she'll probably do grad school eventually somewhere Big and Scary. I'll still check out the book.

 

Thanks!

[Crimson Wife]

I was thinking maybe semi-selective liberal arts college less than 3 hours from home, knowing she'll probably do grad school eventually somewhere Big and Scary. I'll still check out the book.

 

Thanks!

The advice in the book would help the student on scholarship applications as well. LAC's often have fairly generous merit aid because they're trying to lure kids away from the "name brand" schools. So even if you don't think your child would be a good "fit" at an elite school for undergrad, the stronger the application, the better position for getting merit scholarships.

[daijobu]

ETA- I know this is going to sound terrible, but we are not really shooting for aggressive admissions for undergrad for this dd. Two of her older siblings have had shockingly bad experiences at nameless Selective Engineering University, and this kiddo is grade skipped, so 

 

Doesn't sound terrible to me at all, and maybe this is a topic for another thread, but I for one am very interested to know more about your kids' bad experiences at this SEU's.  

[MamaSprout]

Doesn't sound terrible to me at all, and maybe this is a topic for another thread, but I for one am very interested to know more about your kids' bad experiences at this SEU's.  

 

Housing and student life were the issues- bad beyond imagination. I really don't want to start a whole topic. If you have a specific University kiddo is looking at, send me a PM, and I'll let you know if it's the same (or what I know- with 4 kids, I know a bit about most of them in the Midwest.

[Hunter]

OP, I'm not addressing you with this, but more the many lurkers who are reading this thread and not posting, but being influenced by it.

 

Some talented children are not able to self-educate. They sometimes broadcast high goals and everyone expects mom to make them happen. Mom is not always equipped to make these goals happen. If a child has some talent, and expresses a high goal, that is above what a mom can provide without sacrificing herself and the other children, the child needs to be capable of some self-education and have the type of personality to reach out to other talented people online and in the community.

 

I had a 2E kid that everyone expected me to spoon feed. It became increasingly difficult for me to do this. I neglected myself and my other child to pour myself into this child, who was never able to use this education anyway, as I couldn't follow him to college, or hire a tutor.

 

When students talk big talk now, I say, "Show me the money". I want to see that they are truly equipped to really get where they say they want to go.

 

There are moms with talented children that need to pick a slower and easier curriculum, if the child will need to be spoon fed all the way through. It needs to be the curriculum that works for MOM if she will be the one doing the most work. To be a good mom she doesn't need to bite off more than she can chew. HOMEschooling is first about the home and the all the "normal" children are as important the little star. And mom is important too.

 

Now, I think everyone here knows how important education is to me, and there is no excuse for educational neglect. If the parents have the resources to provide a top notch education to a talent child, then it is an injustice not to provide that. But there are low income moms, with just a high school diploma, and multiple children, who have their little star waltz in one day and make a pronouncement, that tips their life upside down. We do not owe our children to tip our lives upside down, or to overextend ourselves. We get to keep the FAMILY and ourselves on track. When the pain starts we are practicing self-neglect and all neglect is wrong. Our "best" doesn't hurt.

 

OP, sorry for this, but I just worry about the guilt ridden lurkers. Good luck! And have fun!

[regentrude]

. If a child has some talent, and expresses a high goal, that is above what a mom can provide without sacrificing herself and the other children, the child needs to be capable of some self-education and have the type of personality to reach out to other talented people online and in the community.

...

There are moms with talented children that need to pick a slower and easier curriculum, if the child will need to be spoon fed all the way through. It needs to be the curriculum that works for MOM if she will be the one doing the most work. To be a good mom she doesn't need to bite off more than she can chew. HOMEschooling is first about the home and the all the "normal" children are as important the little star. And mom is important too.

 

. If the parents have the resources to provide a top notch education to a talent child, then it is an injustice not to provide that. But there are low income moms, with just a high school diploma, and multiple children, who have their little star waltz in one day and make a pronouncement, that tips their life upside down. We do not owe our children to tip our lives upside down, or to overextend ourselves. We get to keep the FAMILY and ourselves on track.

 

I respect your opinion, but I disagree that it is a child's responsibility to seek out an education. It is the parent's responsibility to provide one.

A parent who is unable to provide the education at home that meets a specific child's needs has to evaluate the choice to homeschool. If I, as a parent, can not provide the education my talented child needs, it is my responsibility to seek outside help and possibly enroll my student in school, instead of depriving the child just because I am set on homeschooling at all cost. Wasting a special talent is a terrible thing.

[MamaSprout]

OP, I'm not addressing you with this, but more the many lurkers who are reading this thread and not posting, but being influenced by it.

 

Some talented children are not able to self-educate. They sometimes broadcast high goals and everyone expects mom to make them happen. Mom is not always equipped to make these goals happen. If a child has some talent, and expresses a high goal, that is above what a mom can provide without sacrificing herself and the other children, the child needs to be capable of some self-education and have the type of personality to reach out to other talented people online and in the community.

 

I had a 2E kid that everyone expected me to spoon feed. It became increasingly difficult for me to do this. I neglected myself and my other child to pour myself into this child, who was never able to use this education anyway, as I couldn't follow him to college, or hire a tutor.

 

When students talk big talk now, I say, "Show me the money". I want to see that they are truly equipped to really get where they say they want to go.

 

There are moms with talented children that need to pick a slower and easier curriculum, if the child will need to be spoon fed all the way through. It needs to be the curriculum that works for MOM if she will be the one doing the most work. To be a good mom she doesn't need to bite off more than she can chew. HOMEschooling is first about the home and the all the "normal" children are as important the little star. And mom is important too.

 

Now, I think everyone here knows how important education is to me, and there is no excuse for educational neglect. If the parents have the resources to provide a top notch education to a talent child, then it is an injustice not to provide that. But there are low income moms, with just a high school diploma, and multiple children, who have their little star waltz in one day and make a pronouncement, that tips their life upside down. We do not owe our children to tip our lives upside down, or to overextend ourselves. We get to keep the FAMILY and ourselves on track. When the pain starts we are practicing self-neglect and all neglect is wrong. Our "best" doesn't hurt.

 

OP, sorry for this, but I just worry about the guilt ridden lurkers. Good luck! And have fun!

I'm not at all offended. When we had this kiddo tested, the tester made it very clear with this kid that teaching her how to work would be more important than what we teach her. He basically said she needs AoPS because if she never has to struggle with anything she'll never reach her potential. I'm still unsure about AoPS, but I see exactly what he means. It's fun to watch your 7 year old do middle school math, but I've learned to take a step back and let her fail when she won't tackle a problem, not because she doesn't know how, but because she doesn't have the maturity jump in and give it a try. She loves Beast but she has 10 pages left in the practice book we are on, and I'm not buying the next set until she takes the initiative to finish up this level.

 

I like that you address the guilt factor on this board. We see all of the 8 year old AoPS algebra students (or whatever- I'm exaggerating) and think, "gee I thought I had a gifted kid, but maybe not."

[Hunter]

I respect your opinion, but I disagree that it is a child's responsibility to seek out an education. It is the parent's responsibility to provide one.

A parent who is unable to provide the education at home that meets a specific child's needs has to evaluate the choice to homeschool. If I, as a parent, can not provide the education my talented child needs, it is my responsibility to seek outside help and possibly enroll my student in school, instead of depriving the child just because I am set on homeschooling at all cost. Wasting a special talent is a terrible thing.

I agree that wasting a special talent is a terrible thing!

 

The first issue, though is that PS is not always the fix. The moms who are struggling the most, often live in areas with the worst schools. It's just not that simple. I wish it was. I don't see more little stars actually make it through PS to the places they say they want to go.

 

Secondly, students need to take SOME responsibility and make SOME sacrifices if they want something special. The child who sits like a baby bird, with a wide open mouth, but makes NO effort WHATSOEVER to self-educate and seek out ANYTHING on their own time, is a student that is not prepared for the places they sometimes say they want to go. The student that says I want to go to Harvard, but at 3:00 heads upstairs to play video games for 5 hours while mom spends those same hours poring over a textbook, isn't doing their part, and isn't going to make it through Harvard even if they get in.

 

Over the decades I've seen many kids do their little star act, telling mom and relatives and neighbors what they want to be, and I've seen the moms cry in fear and guilt and confusion. There needs to be balance. Balance between the child's safety, spiritual, physical, and mental needs. Balance between the child and families needs. Just balance.

 

"I want to be..." and "I want to go..." doesn't ALWAYS need to be granted. We don't owe our children horses and designer clothing and trips and the other things they wish for. Yes, education IS different, but we don't owe them EVERYTHING they ask for JUST because it's education. Especially if they are doing nothing, or very little, to reach that goal themselves. Mom shouldn't be the ONE to make ALL dreams happen.

[regentrude]

Secondly, students need to take SOME responsibility and make SOME sacrifices if they want something special. The child who sits like a baby bird, with a wide open mouth, but makes NO effort WHATSOEVER to self-educate and seek out ANYTHING on their own time, is a student that is not prepared for the places they sometimes say they want to go

The student that says I want to go to Harvard, but at 3:00 heads upstairs to play video games for 5 hours while mom spends those same hours poring over a textbook, isn't doing their part, and isn't going to make it through Harvard even if they get in.

 

 

I agree with you if you are thinking about a teenager.

The OP was asking about an elementary age student.I do not think it is reasonable to expect this from a young child.

I think a 7 year old should most definitely be allowed to be done with school at 3 and not be expected to self educate in the afternoon.

[Hunter]

I'm not at all offended. When we had this kiddo tested, the tester made it very clear with this kid that teaching her how to work would be more important than what we teach her. He basically said she needs AoPS because if she never has to struggle with anything she'll never reach her potential. I'm still unsure about AoPS, but I see exactly what he means. It's fun to watch your 7 year old do middle school math, but I've learned to take a step back and let her fail when she won't tackle a problem, not because she doesn't know how, but because she doesn't have the maturity jump in and give it a try. She loves Beast but she has 10 pages left in the practice book we are on, and I'm not buying the next set until she takes the initiative to finish up this level.

 

I like that you address the guilt factor on this board. We see all of the 8 year old AoPS algebra students (or whatever- I'm exaggerating) and think, "gee I thought I had a gifted kid, but maybe not."

You sound like you are very grounded and prepared for this. That's why I wanted to make sure you knew this wasn't directed at you.

 

It helps so much to deal with some things, when already having been through it with olders, doesn't it? And knowing in detail the realities of what it's like to have olders in secondary education.

 

I at least had my experience with my older "normal" child, while going through things with my little star. I tried to draw off those experiences, but people kept telling me how "special" the star was and what he "deserved". I got confused. I lost my way. He wasn't more intrinsically worthy than myself and other son. No one stressed that my "normal" son reach his FULL potential in EVERY area. No one cared that I was okay and had needs of my own. It was black and white that the star has all these "rights" but no responsibilities whatsover as long as he kept swallowing. How much a student can swallow is not indicative of how far they can go.

[Hunter]

I agree with you if you are thinking about a teenager.

The OP was asking about an elementary age student.I do not think it is reasonable to expect this from a young child.

I think a 7 year old should most definitely be allowed to be done with school at 3 and not be expected to self educate in the afternoon.

As I said, my comments were not directed to the OP. And in the blink of an eye the 7 year old turns into the teen. When moms pick math curriculum they almost ALWAYS are looking ahead to the teen years when they choose. They are often looking at samples of all grades, and even asking how college students are doing after using the curriculum.

 

This is just for ME, but even with a 7 year old, I'd be looking for some SPARK of desire to self-educate in the child. If they NEVER picked up ANYTHING to do with math on their own time, but announced they wanted to be a mathematician, I would not disrupt my current plans I had already set. If my 7 year old said they wanted to be a writer, but NEVER wrote ANYTHING on their own time, I wouldn't disrupt my current plans.

 

Homeschooling is a marathon. Even for the little stars, comfortable and steady is often okay. The pronouncements don't ALWAYS need to me met with immediate and expensive and disruptive action. They need to be taken NOTE of, yes!! If they are lasting, and the child is taking ANY initiative, then changes can gradually be incorporated as the FAMILY is ABLE.

[regentrude]

This is just for ME, but even with a 7 year old, I'd be looking for some SPARK of desire to self-educate in the child. If they NEVER picked up ANYTHING to do with math on their own time, but announced they wanted to be a mathematician, I would not disrupt my current plans I had already set. If my 7 year old said they wanted to be a writer, but NEVER wrote ANYTHING on their own time, I wouldn't disrupt my current plans.

 

I completely agree.

I was thinking of a child who clearly displays a special talent and is doing something with it.

[Crimson Wife]

He basically said she needs AoPS because if she never has to struggle with anything she'll never reach her potential.

There are other math programs that are intellectually rigorous and will challenge a bright child. AOPS is certain a good option but so is Singapore Discovering Math with the workbook, eIMACS, EPGY, etc. Just because something is popular does not mean that it is right for everyone.

[EKS]

 

I'm really conscious of her path, because we goofed with an older sibling on a couple of math classes (let him move into college algebra before taking high school calc.)

 

Just an aside--I thought college algebra was the algebra part of precalculus.

[Crimson Wife]

Just an aside--I thought college algebra was the algebra part of precalculus.

I'm guessing this was supposed to be Linear Algebra, which does come after calculus. Many colleges do not offer anything below Calc 1 because they do not accept applicants who have not passed pre-calculus (either at a high school or CC).

[MamaSprout]

I'm guessing this was supposed to be Linear Algebra, which does come after calculus. Many colleges do not offer anything below Calc 1 because they do not accept applicants who have not passed pre-calculus (either at a high school or CC).

I think you are correct. To my understanding, it wasn't technically wrong, just less than ideal for an engineering student.