Another "early" question- Algebra in 3rd grade??

[I.Dup.]

I am fascinated by starting things so early and wanting to know more. In my other thread about starting college early, a poster shared a link to another starting college early thread where people had their kids in Algebra at age 9. How would one even accomplish this? Do you just "try" them with an Algebra curriculum out of the blue to see if they get it? Surely they couldn't have completed 6+ years of math by age 9?

 

I have one child so far that seems math-inclined. I am wondering what the benefits would be to jumping him ahead and seeing how he does in higher-level math, as I assume that's how you do it? I searched but didn't find any specific threads on this...

[wapiti]

I searched but didn't find any specific threads on this...

 

 

This sort of topic is discussed quite often on the Accelerated Learning board.

 

For the especially capable math student, include some depth and challenge. For some perspective, you might be interested in reading Rusczyk on problem solving.

[I.Dup.]

This sort of topic is discussed quite often on the Accelerated Learning board.

 

For the especially capable math student, include some depth and challenge. For some perspective, you might be interested in reading Rusczyk on problem solving.

 

 

Thank you! I wasn't even aware of that board, should have looked harder!

[kiana]

I (personally) started Algebra at age 9. Here is my math career. I have an early fall birthday, so I have listed my age at start of the school year.

 

3 - ungraded private school (technically enrolled as prek), worked through about 2nd grade curriculum. The teacher just kept giving me worksheets and I went through them very fast to earn lots of gold stars.

4 - changed states, placed in first grade.

5 - changed states again. Due to cutoffs in new state they strongly wanted to put me in kindergarden. They ended up 'compromising' on first grade.

6 - in public school second-grade half of the year, deschooling half of the year.

7 - worked through comprehensive arithmetic textbook in diagnostic-prescriptive manner. Also did hands-on equations.

8 - pre-algebra.

9 - algebra 1 and 2.

10 - geometry and precalculus.

 

As you can see progression in early years was by no means linear due to the fact that my mother was still trying to work with the school system.

 

ETA: If AOPS had been around then I think I would have been much better served by switching to that after the pre-algebra course (so doing their pre-algebra at 9). It would have been 100% right for my learning style and introduced me to more challenging mathematics. But it wasn't. The textbooks that were used were moderately conceptual but nowhere near as challenging.

[EKS]

Both of my kids started algebra at age 10.

 

With a kid who is able and motivated to go faster, it's actually pretty easy to move through elementary math at double speed.

 

But just because a kid starts algebra at age 10 (or whatever), doesn't mean he'll be ready to go to college three years early. My older one ended up taking two years to complete Algebra I, another almost two to finish geometry, then he had a year-long stint at a private school where he did not progress in math at all (because he had to track with his grade), so now, at age 16 he is finishing precalculus this year. He will actually go away to college (he is currently dual enrolled at the CC) a year later than his grade by age (he is very young for his grade so we decided to redshirt him in 11th grade and call him a 10th grader).

 

The younger one is taking Algebra I as a 6th grader at a private school this year. He skipped 5th to enter the school early. I'm not sure how his math education will play out from here. My plan is to keep him at home until he is 18 though he'll probably dual enroll when he is 15. He'll likely end up taking calculus and beyond at the CC (they have several classes that are more advanced than calculus there).

[8filltheheart]

I am fascinated by starting things so early and wanting to know more. In my other thread about starting college early, a poster shared a link to another starting college early thread where people had their kids in Algebra at age 9. How would one even accomplish this? Do you just "try" them with an Algebra curriculum out of the blue to see if they get it? Surely they couldn't have completed 6+ years of math by age 9?

 

I have one child so far that seems math-inclined. I am wondering what the benefits would be to jumping him ahead and seeing how he does in higher-level math, as I assume that's how you do it? I searched but didn't find any specific threads on this...

 

Not by 9, but my current 11th grader finished through Horizons 6 around 10 1/2. By the end of 8th grade, he had completed alg 1, 2, 3, geo, and counting and probability.

 

FWIW, **I** didn't **do** anything. He just absorbs math. By the end of 7th grade, I rarely understood anything he was saying in regards to math. :p

 

ETA: Now I don't understand 1/2 of what he talks about in general. ;)

[beaners]

Surely they couldn't have completed 6+ years of math by age 9?

 

 

Why do you say that?

 

Many kindergartners can skip the year of learning how to write numbers and start with a 1st grade program. You can work through the summer. Within a program with a traditional scope and sequence, there is a lot of repetition at the beginning of most years and as more advanced concepts are taught. There are separate lessons for adding two two-digit numbers, adding three two-digit numbers, adding two three-digit numbers, adding three three-digit numbers, adding two four-digit numbers, etc. If your child understands the concept to begin with, you can move into adding many large numbers immediately and either skip the unnecessary lessons as they come up or use them as review. That's assuming you are strictly following a grade-based program.

 

I'm sure there are students who wouldn't be developmentally ready, but I don't think finishing basic arithmetic in that time frame is beyond most bright kids. That doesn't mean it's a path anyone is required to take either.

[I.Dup.]

Both of my kids started algebra at age 10.

 

With a kid who is able and motivated to go faster, it's actually pretty easy to move through elementary math at double speed.

 

But just because a kid starts algebra at age 10 (or whatever), doesn't mean he'll be ready to go to college three years early. My older one ended up taking two years to complete Algebra I, another almost two to finish geometry, then he had a year-long stint at a private school where he did not progress in math at all (because he had to track with his grade), so now, at age 16 he is finishing precalculus this year. He will actually go away to college (he is currently dual enrolled at the CC) a year later than his grade by age (he is very young for his grade so we decided to redshirt him in 11th grade and call him a 10th grader).

 

The younger one is taking Algebra I as a 6th grader at a private school this year. He skipped 5th to enter the school early. I'm not sure how his math education will play out from here. My plan is to keep him at home until he is 18 though he'll probably dual enroll when he is 15. He'll likely end up taking calculus and beyond at the CC (they have several classes that are more advanced than calculus there).

 

How would one go about doing the bolded? Do I just buy several years' ahead of curriculum and try him with various years and see how quickly he picks it up? Do people just skip entire years?

 

FWIW, **I** didn't **do** anything. He just absorbs math. By the end of 7th grade, I rarely understood anything he was saying in regards to math. :p

 

But you had to keep providing him with more and more advanced curriculum, right? I hadn't even thought about presenting my children with materials that were ahead of their grade level. Sure they're advanced in some levels but I didn't even think about that.

[kiana]

I. Dup, what are you using right now with your kid who seems math-inclined and what indications have led you to believe he's math-inclined? That would enable more specific recommendations.

[8filltheheart]

 

 

How would one go about doing the bolded? Do I just buy several years' ahead of curriculum and try him with various years and see how quickly he picks it up? Do people just skip entire years?

 

 

 

But you had to keep providing him with more and more advanced curriculum, right? I hadn't even thought about presenting my children with materials that were ahead of their grade level. Sure they're advanced in some levels but I didn't even think about that.

 

My ds didn't skip anything. He would just finish one grade level and I would provide the next. I was pretty naive. I didn't realize until he was in 7th grade just how good in math he actually was. All of my children have been strong math students (his oldest brother is a chemical engineer), so I just thought he was great in math. But that is just not an accurate depiction. You can't "make" a student into what he is. It is the way he thinks and processes the world.

 

I think it is a falsity to suggest that students can be taught by just going through the materials faster or skipping ahead. W/ ds, it is what it is.....innate ability. FWIW, my other strong math students, including my oldest, were not accelerated in math like this ds. Our oldest started alg in 8th grade. He has a younger sister that has completed geo this yr as an 8th grader. Even though she is ahead, she does not have any where the "innate mathematician sense" that her older brother does. She can **do** math. But she does not theorize and prove everything mathematically like he does.

 

While I am glad my ds has been able to have access to the classes that he takes b/c he would be bored to tears doing anything else, I do NOT see a benefit for most students. Building an incredibly strong foundation and ensuring that they know exactly what they are doing is going to serve them FAR FAR better than being able to say that they took alg as a 9 yr old. There are just those small % of kids that just need to be.

[I.Dup.]

I. Dup, what are you using right now with your kid who seems math-inclined and what indications have led you to believe he's math-inclined? That would enable more specific recommendations.

 

He's 8yo and just completed 2nd grade Singapore. He got the concepts incredibly quickly with very little instruction from me; however, when I did Singapore grade 1 with my oldest, it was like pulling teeth to get her to understand any of it. It made conceptual leaps that were just far above her head, so I was surprised when he needs very little help or instruction. I'm not sure where to go from here? I was thinking of switching him over to CLE 3rd grade next year. My oldest does CLE and it's a lot easier for me to help them if they need help. I also like the spiral aspect of it. But if he can skip a grade or two, why not? He's the one I would be most interested in early college.

[crazyforlatin]

 

 

He's 8yo and just completed 2nd grade Singapore. He got the concepts incredibly quickly with very little instruction from me; however, when I did Singapore grade 1 with my oldest, it was like pulling teeth to get her to understand any of it. It made conceptual leaps that were just far above her head, so I was surprised when he needs very little help or instruction. I'm not sure where to go from here? I was thinking of switching him over to CLE 3rd grade next year. My oldest does CLE and it's a lot easier for me to help them if they need help. I also like the spiral aspect of it. But if he can skip a grade or two, why not? He's the one I would be most interested in early college.

 

I'm not familiar with CLE, but if you need to accelerate to a point where your son is getting the challenge he needs, I would go with MM due to its cost and layout. The text is in the workbook, which means it could be possible for a child to teach himself with some parental help.

 

ETA: Accelerating is not exactly skipping grades. I would feel uncomfortable with skipping.

[kiana]

I wouldn't switch to CLE with a talented child who gets it with very little teaching. The spiral and the fact that CLE doesn't get to algebra until 9th grade would probably make much less fun.

 

Frankly I would leave him in Singapore. I'd also start using IP (intensive practice) instead of the workbook. If it's too challenging, go back to the workbook. If you need something easier for someone raised with the American way of math education Math Mammoth would be a good choice to switch to. Also if he likes comic books I would look into Beast Academy. I would probably do this after Singapore 3 though.

 

As for "how to accelerate", just keep giving him the next level. For example, you said he just finished Singapore 2 -- start him on Singapore 3 now.

[EKS]

Neither of my kids skipped anything. I would reduce the number of problems they had to do if they showed me they really understood a concept, but we never skipped an entire level.

 

I'd stick with Singapore. It is an excellent program and it is easy to accelerate. It also has supplements (IP and CWP) that I would recommend using.

[Alira]

Surely they couldn't have completed 6+ years of math by age 9?

I have two boys who are accelerated in math, and this is exactly what they did. Ds13 started Singapore 1A at 5 and finished 6B at 8. Ds10 started at 5.5 and finished just before he turned 10. They're very different learners, but both definitely have an innate ability that they didn't get from me. Ds13 just "knows" the concepts before he's taught them, while Ds10 has a great memory for procedures, but needs to work through them to fully understand the concepts. Both boys skipped the workbook for some sections (just did the textbook and CWP), and Ds13 skipped a few sections entirely. We didn't skip any levels.

 

Algebra in elementary school is only appropriate for a very few kids, and accelerated kids are definitely overrepresented on this forum. My Ds11 will start algebra in 8th grade, maybe the second half of 7th, and I'm perfectly happy with where he is.

[Spy Car]

My son is still 8 and we've played around with basic algebra for a time, doing linear equations and using algebra to solve word problems, and things like that. There are a number of sources that can help you play around with algebra while only requiring basic arithematic skills.

 

Among the things I like are:

 

Primary Grade Challenge Math by Zaccaro. It has several chapters introducing algebra in an easy to understand and fun way.

 

The app called "DragonBox" is a game that children may not realize is math (at first) and is learning via "stealth."

 

We enjoyed the Hands On Equations app for iPad, but there is a "non-virtual" version too.

 

And Beast Academy 3D has a nice section on using variables.

 

Bill

 

[AnIslandGirl]

For our dd9, math is just her "thing". She not only gets it, but she is excited by math the way other children get excited to play a video game or play sports. She even begs for extra math problems before bed.

We have used a progressive math approach starting rather early, and one area just leads to the next. We didn't skip anything, but some concepts just come really easy to her, so once she has it mastered, we just move along. At 5, she had her multiplication tables memorized. We don't push her, it just comes organically the way some children can do a back handspring or others can list all of the presidents.

We follow dd's lead, and have been turning through two or three different math topics a year so far. I try to have the next topic ready to start whenever she is ready to move on.

[vonfirmath]

How would one go about doing the bolded? Do I just buy several years' ahead of curriculum and try him with various years and see how quickly he picks it up? Do people just skip entire years?

 

 

 

But you had to keep providing him with more and more advanced curriculum, right? I hadn't even thought about presenting my children with materials that were ahead of their grade level. Sure they're advanced in some levels but I didn't even think about that.

 

 

The one year I was allowed to work at math at my own pace (5th grade) I got through so much math it was 8th grade (Algebra I) before I learned anything new in math. DULL, I'll tell you.

 

The way my teacher did it that year? She gave us a packet of assignments.Do these problems on these pages. Then take a quiz. Pass the quiz and you can continue. These problems, these pages. Another quiz. Etc. All the way through. a whole packet of assignments and you worked at your own pace and time. She was there to help if you had any questions.

 

The assignments were not graded for a grade. But there was the ability to check your answers so you'd know if you needed to work more/or what have you before doing the quiz. She expected the class to get through a particular point in the packet but provided a LOT more work for the "go getters" among us.

[Jen in PA]

My DD is 9 and working through Lial's Introductory Algebra. We didn't start terribly early, and we didn't skip anything, we just kept moving ahead as she finished levels. We started with Singapore EB when she was 4, continued through using SM US edition, adding in CWP and some MEP. When we finished Primary Math, she spent a year playing around with various things -- MM Integers, LoF fractions/decimals, Challenge Math, and various inexpensive workbooks on algebraic reasoning and word problems. I finally decided to just go ahead and start algebra. Now, my DD would never tell you that she likes math, and doesn't seem to think that she is particularly good at it. She doesn't do well with drawn-out lessons and balks at writing pages of problems, so we usually only work on math for no more than an hour, 4 days a week. I think that if she went to school she would realize that math is something that comes naturally for her, but she doesn't have much basis for comparison at the moment.

[lewelma]

My ds didn't skip anything. He would just finish one grade level and I would provide the next. I was pretty naive. I didn't realize until he was in 7th grade just how good in math he actually was. All of my children have been strong math students (his oldest brother is a chemical engineer), so I just thought he was great in math. But that is just not an accurate depiction. You can't "make" a student into what he is. It is the way he thinks and processes the world. He has had a college professor tell him that he is in the top 1% of math students he has ever taught. (ETA: and in reality, ds is just not that great. In the world of great math students, he is near the bottom. This professor sees what he does in ds b/c he is not teaching elite math students at an elite university.)

 

I think it is a falsity to suggest that students can be taught to this level by just going through the materials faster or skipping ahead. W/ ds, it is what it is.....innate ability. FWIW, my other strong math students, including my oldest, were not accelerated in math like this ds. Our oldest started alg in 8th grade. He has a younger sister that has completed geo this yr as an 8th grader. Even though she is ahead, she does not have any where the "innate mathematician sense" that her older brother does. She can **do** math. But she does not theorize and prove everything mathematically like he does.

 

While I am glad my ds has been able to have access to the classes that he takes b/c he would be bored to tears doing anything else, I do NOT see a benefit for 99% of other students. Building an incredibly strong foundation and ensuring that they know exactly what they are doing is going to serve them FAR FAR better than being able to say that they took alg as a 9 yr old. There are just those small % of kids that just need to be.

 

 

This is beautifully said.

 

My ds started AoPS algebra at 9, and worked through it independently. I am only coming to realize now that he is pretty special when it comes to math. He was *ready* at 9 -- I definitely did not push him into it. And his foundation is secure given that it took him 2.5 years to get through the AoPS book. Normal kids just don't start Algebra at 9 and if they are pushed into it, they end up using a very simple program. If a child is truly ready at 9, by 12 he is not just doing the 'next thing' in traditional math, his math program will look unlike anything you have seen. Here is an example of what age 12 looks like if algebra is done at age 9 and I promise you that I am having a very difficult time keeping up (read the whole thread, because the answer is at the bottom!): http://forums.welltr...ut-huge-for-us/

 

Ruth in NZ

[Wheres Toto]

My son is doing 4th grade math at 7 years old. I'm not sure exactly the pace we are finishing grades since we do MM in a bit of a scattered way but I think we are doing 1 1/2 a year. We haven't skipped any grade, but we do skip problems if it's a concept he already knows. I could see him starting algebra at 9 or 10 years old. He is working through "Algebra Readiness" workbooks from Scholastic.

 

Edited to add: I bought all 6 years of MM when it was on sale through the co-op so we just keep moving up in a topic as he finishes a level.

[Clear Creek]

My oldest is accelerated in math, but that didn't involve skipping anything. In our house that meant introducing the math lesson for the day, and if she knew the concept we would turn to the next lesson and see if that taught her anything, and continue until we found a lesson that taught her something she didn't already know. Like another poster mentioned, this type of student just intuits many math concepts, ones that have not been covered in their math books yet. R&S is very, very easy to accelerate with - chapters are divided by topic. We went through the 4th & 5th grade book her 4th grade year, and this year (after a brief foray into LOF and the Key to... series) we have been working through the 6th & 7th grade books. They both cover similar topics, so I introduce it using lessons from the 6th grade book and then go deeper/harder with the 7th grade book. We have just about gone through all she needs to learn from those books before beginning AOPS Pre-Algebra (I skipped Biblical measurement and all the reviews).

[quark]

How would one even accomplish this?

 

DS started with Dolciani (the 1990s Classic series) Algebra at 8 years 3 months and finished it a few weeks before turning 9. We didn't set out trying to accomplish this. The best description/ explanation I can offer is that with each grade level curriculum that I tried, he lost a little bit of his love of math each time until it finally dawned on me to try a grade level higher. Another level higher. Another level. And yet another until his eyes started lighting up and he was excited about math again.

 

So in this way, we did "skip" several years of math until he was about midway through harder fractions and decimals problems at 7+. He had not mastered his multiplication tables when he began Algebra but you know what, he did not need to. He finally mastered his multiplication facts when he found that mastering them would help him solve for x much quicker. By the time he was about halfway through Algebra 1, he was very confident with multiplication.

 

Do you just "try" them with an Algebra curriculum out of the blue to see if they get it? Surely they couldn't have completed 6+ years of math by age 9?

 

Not really. What happened was that DS was making some connections on his own. You see, I used to work with him using a whiteboard and we didn't always get to every single problem in the arithmetic books when he was younger. There was no need as I could see for myself that after 4 or 5 problems, he could understand any new concept quite well. And he has always been a patterns-loving kid.

 

One day, around the time he turned 8, DS started using variables and equations to communicate his observations of patterns. It went something like this: he would spend hours in the shower and I used to get really irritated when one day I lost it and yelled at him, "what on earth are you doing in there, laying eggs?" or something like that. So he came downstairs all wet, teary eyed that I was mad at him, and to explain himself he took a marker and drew a rectangle and started explaining to me that if one side of the rectangle was x units long and the other was x+1 units long, the area would be x(x+1) units squared. And that he was trying different combinations of variables to see what would come of it and that's why he's showering so long every day. That shut me up. A little while later, he figured out a formula to predict triangle numbers. I was still having him work on fractions at that time and could see that he was on an obvious roll here: loving the use of variables to come up with equations. So I started looking for someone to mentor him on number theory. The tutor I found did a demo session with DS, found that DS could understand FOIL after just a few seconds of explanation and told me he was going to work with DS on Algebra 1. My husband and I were surprised but we quickly agreed because we could see that DS was ready. I did insist that we finish up our fractions and decimals curriculum on the side lol. After that, we just went along with whatever the tutor suggested because he really seems to have DS's best interests at heart.

 

DS is now 10, has finished most of high school geometry (ETA: proof heavy, using the Jurgensen Brown text) and is working on whatever college level geometry he can with his tutor that doesn't yet require knowledge of calculus. He also works on number theory and precalculus books/ programs in his leisure time and a bunch of AoPS books that we have laying around. Because he loves math. Period. I don't require him to do this extra work. I expect that he will finally slow down when he hits calculus in about a year...then again, he could surprise me as he has done in the past.

 

So no, he didn't finish 6+ years of math. But he didn't have to. Honestly, I don't think DS is amazing or exceptional in that sense. He is definitely math gifted but above all a very hardworking and persistent kid who is adamant that he wants math all the time. Even as I type this (we are having a free day) he is watching math videos on Numberphile on YouTube (videos he has already watched multiple times).

 

I also feel that the system just makes it seem like you need 6+ years. We didn't need prealgebra at all for example. With a mathy kid, it just wasn't necessary. Why repeat so much math year in year out when we're homeschooling and doing things differently anyway?

[Arcadia]

If a child is truly ready at 9, by 12 he is not just doing the 'next thing' in traditional math, his math program will look unlike anything you have seen.

 

.I also feel that the system just makes it seem like you need 6+ years. We didn't need prealgebra at all for example. With a mathy kid, it just wasn't necessary. Why repeat so much math year in year out when we're homeschooling and doing things differently anyway?

 

 

:iagree: my kids are making me hit the books. I think I need to budget for a tutor for proofs in a few years time :leaving:

[Crimson Wife]

If I switched my DS to an easy math like TT or MUS, he could probably finish the rest of the series and be in algebra by 9. However, I am much more concerned about building a solid foundation in math than I am about bragging rights. So I am deliberately slowing him down by using harder programs (Singapore with IP + Beast Academy). He's still accelerated (in 3B of SM and will start BA 3C after that) but he won't be doing algebra 1 at 9.

[jennynd]

DS finished AOPS algebra 1 part (ch1-13) when it was 1 week past his 9th birthday. We didn't do any formal math until he started 1st grade age wise. But at that time he already mastered multi-digit multiplication and division with 2 advisor as well as fraction operations. It was just here and there get taught by me on different occasions. We started with SM 3/4 and we went through it in 4 month since he already master the concepts and operation. We really just check if there are holes needed to be filled.. He started with SM 5 second semister at 1st grade, and we added IP somewhere there. He finished SM 6 in the middle of second grade. And we finish all IP and CWP as well as key to algebra before the end of second grade year and we treated the combination as pre algebra and he started algebra at 3rd Grade. I did not plan it. It just happened. And I don't think many of us planned to have kids to do algebra at 3rd grade. It really just sort happened

[quark]

Thanks for quoting Ruth, Arcadia. I hadn't taken the time to read the whole thread prior to my reply above.

 

My ds started AoPS algebra at 9, and worked through it independently. I am only coming to realize now that he is pretty special when it comes to math. He was *ready* at 9 -- I definitely did not push him into it. And his foundation is secure given that it took him 2.5 years to get through the AoPS book. Normal kids just don't start Algebra at 9 and if they are pushed into it, they end up using a very simple program. If a child is truly ready at 9, by 12 he is not just doing the 'next thing' in traditional math, his math program will look unlike anything you have seen.

 

Hee hee, I see Ruth's post above and now feel that I need to explain why I don't think my DS is exceptional. Perhaps he is. But I live in an area where there are lots of math and science professionals and lots of math accelerated kids with younger kids doing much more than DS is now. So looking at it from that PoV, DS is just another math-loving, accelerated kiddo. But I do see that his hard work sets him apart. He doesn't complain about work and I'm very grateful that this is so.

 

Definitely adding my agreement about things not looking like the usual progression when the child is truly ready for higher math at a younger age.

 

[Edited out a few paragraphs as they could be considered as bragging/ too much info and that was not my intention. Apologies for that!]

 

I am thanking the heavens for AoPS's challenging problems. And thanking Kathy in Richmond each time she suggests a math book on these boards because she is giving me more tools to throw at him. He is not very interested in competitions so I haven't pushed him that way but I hoard math documentary links and mass market math books. And I no longer look at math curriculum other than AoPS. I have instead been looking up math books from Dover publications because they are cheap and go up to a sufficiently high level. The moment you realize that you can no longer count on the usual homeschool math curriculum providers (other than AoPS) for long, you know that the path is going to be significantly different for your child.

[Mommy22alyns]

On the not exceptional kid side, you can easily start Hands on Equations with a bright third grader once most multiplication is down.

[Hunter]

I am much more concerned about building a solid foundation in math than I am about bragging rights.

 

:iagree:

 

In the mid 90s I really didn't know what I was doing. While afterschooling I introduced Algebra to my 9 year old and finished up his elementary education with adult ed materials from the library and the local bookstore. When I pulled him out of school in December of the year he was 10, I started Saxon Algebra 1 with him. He also did some of the old High school CLE math, some integrated math from New York, Some of the old Dolciani math with American School, some Aufmann math (junior college texts) and more Saxon.

 

If I had to do it over again I'd worry less about math, and spend less time on it. I think I should have spent more time on his math handwriting and memorization of basic facts. I think I spent the right amount of time teaching him to read math texts and how to use random math books as reference books when stuck on a problem.

 

As I said, I really didn't know what I was doing. There were pros and cons to all I did.

[I.Dup.]

Thank you all for the specific suggestions, I will look into those!

 

So if they complete Algebra in 3rd or 4th grade, that would put them on track to potentially finish your run of the mill high school math courses by the time they complete middle school, right? So in high school, what would they do? Are those of you doing things this way planning on enrolling them in college early?

[Hunter]

Most children are not developmentally ready to do Algebra at 9 or 10, and even less ready to do calculus in middle school. Even if developmentally ready for the texts, they simply might not be ready to complete such a thick text each year.

 

I really suggest you read Simply Charlotte Mason math to hear a contrast of why math should not be over emphasized.

 

In contrast to my younger son, my older son graduated college without ever completing Algebra 1 at all, and has had a very successful career in business management. He built a house and paid for a wedding when he was just 24 years old.

 

Examine carefully your reasons for accelerating and be aware of what the child will miss out on because of your choice to do this.

[kiana]

Just because they start algebra early doesn't mean they need to move forward at one year per grade. They can take 2 years or even 3 to do algebra and enjoy themselves with something that's an appropriate challenge level.

 

I would be the last person to advocate early algebra for all. I absolutely agree that most aren't developmentally ready. But the kids who are ready should have the opportunity instead of re-doing arithmetic until they hit some arbitrary age marker. Isn't that part of homeschooling -- to give an education that's customized to the child?

[Spy Car]

Most children are not developmentally ready to do Algebra at 9 or 10...

 

 

Depends what you're calling "algebra." All the algebra resources I listed above are highly appropriate to 9 or 10 or 8 year olds, and easily can serve as fun suppliments to a core math program.

 

Personally I think it is a mistake not to introduce the basics of algebraic thinking early. The "wait till they have hair under their armpits" agruement strikes me as wrong-headed.

 

If you mean doing AoPS Algebra (or similar) at 9 or 10, then I'd agree that relatively few children would be there. But some.

 

Bill

 

 

 

 

[kiana]

Thank you all for the specific suggestions, I will look into those!

 

So if they complete Algebra in 3rd or 4th grade, that would put them on track to potentially finish your run of the mill high school math courses by the time they complete middle school, right? So in high school, what would they do? Are those of you doing things this way planning on enrolling them in college early?

 

 

With a young, gifted child there's no reason to head straight for the run of the mill high school math program. There are many electives that can be done after only algebra 1. AOPS does a counting and probability course and a number theory course, and there are other courses that could be done early if the parent, tutor, or mentor is capable. IMACS has books in mathematical logic and set theory that could be completed even prior to algebra and definitely after algebra 1. Once geometry is completed there are more advanced courses in geometry which could be completed. After algebra 2 some more advanced courses in counting and probability (aops), number theory (many elementary textbooks would now be accessible to someone who completed the AOPS introductory course and a solid algebra 2 course), statistics, graph theory, etc. After precalculus it opens still more and after calculus still more. Specific courses chosen could depend on the child's interests -- for example, a kid primarily interested in biology could, after algebra 2, self-study some matrix algebra and then do a basic course on game theory w/evolutionary/ecological applications (I find this fascinating myself), while a kid interested in physics would want to head more towards calculus and then afterwards look at subjects like differential equations, linear algebra, mathematical statistics.

 

I would also recommend reading The Calculus Trap (an online article) about why you shouldn't just rush a gifted kid through the standard curriculum on the way to calculus.

[lewelma]

So if they complete Algebra in 3rd or 4th grade, that would put them on track to potentially finish your run of the mill high school math courses by the time they complete middle school, right?

 

No, not in my ds's case. Like so many of the others, we are following Kathy in Richmond's advice. She suggested that we look into the competitions as a way of extending my son. So we are studying the International Math Olympiad material, none of which is in traditional high school math courses -- it is all proofs. And like the one that I linked to in my pp, these proofs are NOT straightforward and often require an hour of investigation before the writing of the proof can even begin (I am not talking standard geometry proofs). The book that Kathy recommended has enough material to keep my ds occupied for 4 more years, AND this material can be working through concurrently with the more traditional high school material (at the AoPS challenge level). It is not faster; it is deeper.

 

Today, my son did 5 problems in math, and spent 4 hours. These problems took so long because they are not just exercises -- here is how you do it, now go do some. Instead, each one takes 30 minutes of investigation, 15 minutes of trialling different tactics and proof styles, and then 15 minutes to write up the proof. Point being, we are not accelerating through traditional math, we are going broader and deeper. I know the list in my siggy looks like we are rushing through the material, but is just a one time thing for 4 months to get him to the level he needs to be for the exam in July; then he will be back to a balanced schedule.

 

And my ds cannot do run of the mill math courses. He just can't. His eyes glaze over, he lacks motivation, and gets many problems wrong. I tell people it is like being asked to proof read a phone book. You might have good intentions, but you just. can't. do. it.

 

Ruth in NZ

[ebunny]

I am fascinated by starting things so early and wanting to know more. In my other thread about starting college early, a poster shared a link to another starting college early thread where people had their kids in Algebra at age 9. How would one even accomplish this? Do you just "try" them with an Algebra curriculum out of the blue to see if they get it? Surely they couldn't have completed 6+ years of math by age 9?

 

I have one child so far that seems math-inclined. I am wondering what the benefits would be to jumping him ahead and seeing how he does in higher-level math, as I assume that's how you do it? I searched but didn't find any specific threads on this...

 

 

I am late to the discussion (different time zone), nevertheless.....

 

Just to give you a different perspective....II'll share math progression in Indian schools.

 

All Indian school kids hit Basic algebra and Gemoetry by 6th grade (11 yrs). Quadratic equations are added in 7th grade. Trignometry the year later. By the 10th grade, *all* kids (excluding those in IGCSE schools) are working on Algebra+ geometry+Trignometry. No separation Algebra into I and II.

 

What I really want to say is, children (average and up) are on the *same* trajectory in Math in India.

 

Factor in innate math ability and you will see some children itching to start Algebra by 3/4/5 grade. Or at 8/9/10 yrs, if you will.

 

Until you introduce Basic equations to your child, and check for his/her interest, Algebra at 8 seems unconventional. But the kids who learn Algebra at that age are *math loving* children who want more. It is the child who demands more and the path deviates from the norm.

[quark]

I would say it all depends on the child and what his and your motivations are. There is a lot of math left for him to do and I can't somehow see us just going for "run-of-the-mill" stuff kwim? But that's because he is serious about a math/STEM career. It may be different for a family who just wants to get the math out of the way for some other major.

 

There are so many factors to consider about college and I'm uncomfortable making a decision based on math ability alone. I'm not sure if early college is the right path for a kid who wants to major in math, do math research and also possibly go into academia. I'm not saying no. I'm just not sure what the right path is for him.

 

Currently, we are able to afford the college level math instruction through his tutor as well as some online high school level courses for other subjects and will continue doing this for as long as we can afford it. We will explore auditing or enrolling in one or two courses at a local uni if the opportunity presents itself and then take it from there.

 

I won't stand in his way if *he* decides he really needs to go early (as in go away to 4yr uni early) and can convince me he is ready for all the other factors necessary as well. One of those factors, depending on our finances, may involve paying for a part of his fees himself or at least winning a good scholarship.

[NASDAQ]

I did proper algebra at nine.

 

My first grade daughter is not advanced or unusual (definitely not "mathy") and is finishing SM 2b . . . well, next week, G-d willing. We're year-rounders, so she will probably, at the current rate, be finishing 3B at the end of the summer. Of course, she could stall out. Who knows. She started counting to five after her fifth birthday, so she's moving fast right now.

 

There are lots of algebraic resources that are written to smaller kids. I think it's wise to use a curriculum that at least sets the children up for algebra from the earliest stages.

[quark]

And my ds cannot do run of the mill math courses. He just can't. His eyes glaze over, he lacks motivation, and gets many problems wrong. I tell people it is like being asked to proof read a phone book. You might have good intentions, but you just. can't. do. it.

Ruth in NZ

 

 

Exactly!

 

There's some stuff I don't mention on these boards just to safeguard DS's privacy as much as I can. It's not just that DS can't do the mundane stuff. There was another reason that forced our hand to accelerate him. It was heart-breaking to watch DS when he wasn't being sufficiently challenged. Acceleration for us was not really an option for that reason...he needed it. I agree with everyone who says it has to come from the child. It's just not the same if it is planned and structured by the parent.

[Arcadia]

So if they complete Algebra in 3rd or 4th grade, that would put them on track to potentially finish your run of the mill high school math courses by the time they complete middle school, right?

 

 

My older might finish his Algebra in 5th. He sets his pace so I'm not going to predict. Both my boys have topics in math that they are interested in which are not in the standard scope so that will stretch out the years. They are more interested in science than math so I'll rather they max out their school years and go deeper in science. Besides they will have their plates full with other subjects. I'm not planning on early college entry for them. After all there is more than math to consider for early college entry. There is also foreign languages, fine arts, literature and all the other requirements.

[kiana]

I would say it all depends on the child and what his and your motivations are. There is a lot of math left for him to do and I can't somehow see us just going for "run-of-the-mill" stuff kwim? But that's because he is serious about a math/STEM career. It may be different for a family who just wants to get the math out of the way for some other major.

 

There are so many factors to consider about college and I'm uncomfortable making a decision based on math ability alone. I'm not sure if early college is the right path for a kid who wants to major in math, do math research and also possibly go into academia. I'm not saying no. I'm just not sure what the right path is for him.

 

Two things:

 

I know this is not your child, but I would recommend very strongly against 'getting math out of the way' if it means doing AP calc at 12 and then never touching math again. I think a kid who is talented but totally uninterested would be better served by going through a standard, honors sequence (which, if they are talented enough to pass AP calc at 12, they could do the standard sequence with very little effort). Even for one who was originally interested but is no longer, I would recommend decelerating by doing half-courses (so, for example, someone who completes algebra 2 in 8th grade but really doesn't want to do more could do half of precalc each in 9th and 10th, half of calc each in 10th and 11th, and legitimately transcript it as college algebra, precalculus, calc 1, calc 2) instead of just stopping.

 

As for yours, there is a student in graduate school with me who finished his undergraduate at 18. There is another one who entered university at 17 but had already taken 8 courses (4 years) of university-level math. Both of these are very strong students and doing well. But they waited to enter university full-time until they were on university level in ALL subjects, not just math. It sounds like your mentor is outstanding so you have some wiggle room. :)

[kiana]

And my ds cannot do run of the mill math courses. He just can't. His eyes glaze over, he lacks motivation, and gets many problems wrong. I tell people it is like being asked to proof read a phone book. You might have good intentions, but you just. can't. do. it.

 

FWIW, this is what happened to me in PS. They wanted me to do page after page of single-digit addition problems and it was so damn boring. I had no motivation whatsoever. Then they wanted me medicated for ADD because I spent all my time staring out the window instead of doing math. They also wanted to keep me back a year because I was young for grade and 'failing math'. Yeah.

[lewelma]

FWIW, this is what happened to me in PS. They wanted me to do page after page of single-digit addition problems and it was so damn boring. I had no motivation whatsoever. Then they wanted me medicated for ADD because I spent all my time staring out the window instead of doing math. They also wanted to keep me back a year because I was young for grade and 'failing math'. Yeah.

 

:sad: I'm so sorry. I am sure this would have been my son if he had been in school.

[quark]

As for yours, there is a student in graduate school with me who finished his undergraduate at 18. There is another one who entered university at 17 but had already taken 8 courses (4 years) of university-level math. Both of these are very strong students and doing well. But they waited to enter university full-time until they were on university level in ALL subjects, not just math. It sounds like your mentor is outstanding so you have some wiggle room. :)

 

Good to know about these students, kiana! It is something we've discussed (doing undergrad from home and going away to grad school is plan A prime I think, have to check with DS, lol). We do have an outstanding mentor. I want to hug him each time they meet online just for the smile he brings to DS's face. He offers math beyond calc so we are indeed very grateful for him.

[kiana]

 

:sad: I'm so sorry. I am sure this would have been my son if he had been in school.

 

Well, in a way it was a good thing. I doubt my parents would ever have looked into homeschooling if the school had not been so resistant :)

[wapiti]

.

Edited September 15, 2016 by wapiti

[lewelma]

We do have an outstanding mentor. I want to hug him each time they meet online just for the smile he brings to DS's face. He offers math beyond calc so we are indeed very grateful for him.

 

Ah, to have a tutor/mentor. Ours is lined up for September, but seems very far away indeed. For the last 2 months while working through the IMO material, I'm like :huh: and :confused1: and some of :crying: and a whole lot of :willy_nilly: :blink: :ack2: . And I *was* a high school math teacher!

[kiana]

Good to know about these students, kiana! It is something we've discussed (doing undergrad from home and going away to grad school is plan A prime I think, have to check with DS, lol). We do have an outstanding mentor. I want to hug him each time they meet online just for the smile he brings to DS's face. He offers math beyond calc so we are indeed very grateful for him.

 

Obviously he is young now. I'm not sure how good the local university is, but unless it's quite good (flagship state university or something) he would probably be better off to only do math courses there, and when he's maxed them out (which he probably will, again, unless they're really good), then apply to somewhere really good to take 4 years of math electives while doing research etc. This also preserves options longest should he change his mind and decide something else is his true love.

 

I would also look at (once calc is passed) doing mandatory major courses at the university and post-calculus electives with the mentor. For example, linear algebra is a required course and will probably be rather boring to someone who has already self-studied the class. Something like game theory or graph theory or who knows what will be an elective that will strengthen his transcript for university admission and provide a fun and interesting challenge yet not put him in the rather awkward place of having to sit through a class he has already taken.

[Donna]

My dd10 started Alg.1 in the fall. It wasn't anything I did purposefully. She simply learned math quickly especially early on when I started a formal math program with her. At 5yo, she had already mastered K-2nd grade math skills just by playing math games with me when she was interested. So when I started a program, she already knew most of the material and I had her brush up on anything she had missed (mostly measurement type stuff). Then we just kept on moving from there. Math has never been her favorite subject so we did it 3-4 days a week and when she finished a level, we moved on. I schooled year round for a number of years and she tended to complete about 1.5 to 2 levels a year.

 

Now she is doing Alg. 1 but we are going through the book slowly 2 lessons a week and I added in Life of Fred for her more verbal thinking mind (fun math for her) another 2 days a week. It will take us almost about 18 months to finish, judging by where we are now and how long it has taken us to get there, and because I don't plan on schooling her this summer. My middle ds had Alg 1 in school this past year and she has already learned more material than he did in his public school Alg. 1 class.

[8filltheheart]

 

 

Obviously he is young now. I'm not sure how good the local university is, but unless it's quite good (flagship state university or something) he would probably be better off to only do math courses there, and when he's maxed them out (which he probably will, again, unless they're really good), then apply to somewhere really good to take 4 years of math electives while doing research etc. This also preserves options longest should he change his mind and decide something else is his true love.

 

I would also look at (once calc is passed) doing mandatory major courses at the university and post-calculus electives with the mentor. For example, linear algebra is a required course and will probably be rather boring to someone who has already self-studied the class. Something like game theory or graph theory or who knows what will be an elective that will strengthen his transcript for university admission and provide a fun and interesting challenge yet not put him in the rather awkward place of having to sit through a class he has already taken.

 

 

Keeping in mind that I don't understand anything my ds says about math anymore, I can share what he has experienced based on what I think he has shared. (how is that for clarity ;) )

 

His 1st semester of math at a university was multivarible cal. The first several weeks of class were all review of (I think I remember him saying) spherical coordinate system. Whatever it was, he had learned in AoPS alg 3 or pre-cal at a much deeper level than he was getting out of his uni class. He didn't really learn much new in that course that challenged him and told his professor that he was disappointed that they didn't spend more time on proofs.

 

This semester he is studying diffEQ. He hasn't stated that it is review (like last semester), but it certainly has not been a challenging class.

 

I think this is where "the where" the classes are taken and how they are approached really matters. For kids that love math and want that mathematician proof-driven/theory-oriented experience, your typical university is probably not going to meet those needs. Whereas schools like Stanford/MIT, etc those are going to offer theory-oriented classes starting at the freshman level and those classes are going to be filled with great math students that love that sort of challenge. (those are the classes that are going to have the kids that are doing Math Prize for Girls or attending Math Camp, etc......kids like Kathy's that have been doing theory type math like Ruth and Quark describe with their sons.) The regular university math courses will "fall flat" for them. (Kathy's kids, and Ruth's and Quark's kids are in a totally different league than our ds. While our ds isn't really challenged, their kids would be mind-numbingly bored.)

 

Our ds's passion is not math. His is physics, so he immerses himself in that. For kids that want to be mathematicians, sending them to the local CC would be imo a disaster. Sending them to a typical university will be jumping back into traditional textbook problem-solving with students that are being taught how to solve problems and then solving the problems, etc and all that goes with that approach.