Please critique my math acceleration plan.

[Rivka]

Alex (2nd grade, about to turn 8) seems to be in the middle of a big leap forward in math. She just finished MEP 4a, and although she was excited to get Beast Academy 3d now that it's finally out, the phrase "that was insultingly easy" is coming out of her mouth more and more often as we dig into it. She's enjoying Perfectly Perilous Math, a math enrichment book for middle-schoolers, and she's figured out how to do things like long division with a multi-digit divisor and adding fractions with unlike denominators without my help. The struggles we used to have with math motivation and being afraid to be wrong are long gone. Instead, she is restless.

 

Until now, we have been doing almost everything in her math curricula. I have really been afraid to make big jumps. But it seems clear that moving ahead at the rate of one year of math every 180 school days is neither necessary nor sufficient. At the same time, I don't want to just rush her ahead on a linear path - partly because I want to focus on complex math problem-solving rather than just the basics of increasingly-advanced programs, and partly because, at her age, I think most advanced math textbooks would be too dry and "adult" in their presentation.

 

Here's the plan I have tentatively come up with. Please poke holes in it or suggest additions to it.

 

Rest of this spring: Finish Beast Academy 3d, skipping too-easy parts as needed. I think she will benefit from the estimation chapter even if the fractions are way too easy.

 

3rd grade, age 8 (our school year runs June-May, so starting June 2013): MEP 4b-6b, compacted. I've picked out the weeks I think she'll need, and it's about 40 weeks of lessons altogether if we keep to our current pace of about 45 minutes of math 5 days a week.

 

4th grade, age 9: Advanced problem-solving in elementary math. The materials will probably include Zaccaro's books Becoming a Problem Solving Genius and Challenge Math for the Elementary and Middle School Student, as well as MOEMS prep materials like Creative Problem Solving in School Mathematics and books of MOEMS problem sets. (The MOEMS stuff is on the AoPS website.)

 

5th grade, age 10: AoPS pre-algebra.

 

6th grade, age 11: AoPS algebra, possibly going over into 7th grade as well. It seems ridiculous to plan any further ahead than that, so I haven't.

 

How does this look?

[wapiti]

The 4th grade plan seems a little vague to me - an entire year on problem-solving without moving forward with concept instruction - it doesn't sound like enough (from your dd's perspective). Maybe add the problem-solving during 3rd, stretching out the (albeit compacted) MEP with problem-solving at the same time. In other words, join your 3rd and 4th grade plans together and then stretch over two years. Or, more likely, I'd guess, you may find yourself starting the Prealgebra sometime in the middle of 4th, if not earlier.

[jennynd]

If she gonna do all the very challenging.math book at 4th grade, she probably won't need 2 yrs for AOPS preA. Get the AOPS algebra ready at that point.... :)

[Arcadia]

I'll run AOPS pre-algebra concurrently with whatever you plan for 4th.

[Rivka]

Crud, I'm still kind of in denial, aren't I?

 

Thanks for the feedback. My thinking was based on Richard Ruszyck's article "The Calculus Trap," and particularly on this quote:

 

For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer. [...] Developing a broader understanding of mathematics and problem solving forms a foundation upon which knowledge of advanced mathematical and scientific concepts can be built. Curricular classes do not prepare students for the leap from the usual ‘one step and done’ problems to multi-step, multi-discipline problems they will face later on. That transition is smoothed by exposing students to complex problems in simpler areas of study, such as basic number theory or geometry, rather than giving them their first taste of complicated arguments when they’re learning a more advanced subject like group theory or the calculus of complex variables. The primary difference is that the curricular education is designed to give students many tools to apply to straightforward specific problems. Rather than learning more and more tools, avid students are better off learning how to take tools they have and apply them to complex problems. Then later, when they learn the more advanced tools of curricular education, applying them to even more complicated problems will come more easily.

 

That's why I was thinking of spending plenty of time on special topics, puzzles, and extra-tricky problem-solving before moving on to pre-algebra. I also traded e-mail with Jason Batterson, the author of Beast Academy, He's been following along with Alex a little since she's one of the first kids going through BA. He encouraged me to advance her as much as she seems ready for, but he also had this to say: "[Richard Ruszcyk] tells me that generally if we have a 10-year-old in one of the Algebra classes, the kid is either the best or the worst kid in the class. Algebra at 10 or 11 is certainly not unheard of. The best kids I taught (admittedly, they were some of the best in the nation) usually took Algebra in 6th grade (what's that, 11?)"

 

That really gave me pause. Do I think that Alex is one of the best math students in the nation? I can't imagine that she would be. And I wouldn't feel like I could assume that she'd be that 10-year-old who was best in an AoPS algebra class full of the best, most advanced math students around the country, either. That fed into my thinking that it would be better to give extra time for her complex problem-solving skills to mature.

[wapiti]

That fed into my thinking that it would be better to give extra time for her complex problem-solving skills to mature.

 

If you want to go more slowly, I'd add something to the 3rd grade plan where you're planning to compact MEP 4b-6b. That might stretch that plan into 4th somewhat. The Prealgebra book seems to take my kids around a whole school year, though I can easily imagine a young student getting through it faster - or, alternatively, much slower - depending on their individual pace *and also* whether and when you schedule working with Alcumus, how many challenge problems you assign, etc.

 

I'm not sure about the relevance of RR's comments on students in the AoPS Alg 1 on-line class. The class moves very fast, and many younger students might find that using the book without the class, at a much slower pace, may be just fine and much more appropriate for them than the class. In other words, not being ready to complete AoPS alg 1 in a 16-week on-line class doesn't mean a student isn't ready for algebra with AoPS.

[Lilaclady]

I will say it is better to stretch out Mep 4-6over 2 years. I have found mep to be very solid and it is very hard to rush through it.

 

One thing you might want to consider that will help is getting her into a math circle or math club for elementary and doing math competitions. I think it really helps the kids to start thinking about math as they are encountering different questions on the same topics that they have covered.

 

My ds1 has just finished Mep 5 and will be doing Mep 6 and aops prealgebra concurrently so I am not sure when she will fish. Se loves math but also find it sometimes challenging. It is definitely note easy but not frustrating.

[jennynd]

But I will much rather spend time in algebra and geometry or calculus than elementary math. The abstract thinking accelerate his maturity in problem solving. I will rather spend 2 year in algebra than 2 years in preA.

[Arcadia]

"rushing through the standard curriculum" or hothousing is different from letting your child set the pace. Both my kids don't like Zaccaro's style of books so it makes life harder for me :p Algebra don't have an upper bound though. Your child can go as deep as she likes beyond what testing requires.

[kiana]

But I will much rather spend time in algebra and geometry or calculus than elementary math. The abstract thinking accelerate his maturity in problem solving. I will rather spend 2 year in algebra than 2 years in preA.

 

 

 

Yes, this, exactly. There are so many interesting places to go even after Algebra 1, and even more that are accessible after Geometry.

[Barbara H]

I understand the desire to have the sense of control that comes from long range planning. But, and I say this gently, it is really just a false sense of control. You can't really predict how she is going to learn and you are probably going to need to take it semester by semester, year by year, and just see how it goes. As you do that I would encourage you to let go of the fear. I don't understand exactly why but there does seem to be a lot of gloom and doom fear mongering around young gifted kids and math. There are all these warnings kids don't really understand what they are doing or they will "hit the wall" or that there is some kind of magical "developmentally ready" brain for algebra. Yes, that maybe is all a concern if your child had to proceed on a set schedule in school lockstep to the beat of a curriculum that doesn't fit. But, at home you don't have that problem because you can always adapt to where your child is. For what it is worth, I know a number of gifted kids who started algebra younger than 10 and none of them had a problem with it nor did they have trouble later. Try not to be scared!

[kiwik]

Even if you do hit a wall so what? Take six months to go over or round the wall - take a year to do something else then try the wall again. It seems silly to risk boring a child to death just in case they hit a wall in five years time.

 

I know nothing about it personally but I have read time and time again the the AoPS online courses are very fast.

 

[StephanieZ]

I like your plan. :)

 

I'd consider adding in Patty Paper Geometry in 4th grade or so. It is really fun, and very low stress, and introduces a LOT of helpful vocabulary and geometry concepts, so when they do a full geo course later on, it'll be smoother sailing. Anyway, it is interesting and fun! I think it is a wonderful pre-geometry course. I've been doing it this year with my 10 yo (who did AoPS PreA last year, and is reviewing/perfecting it this year), and I just think it is a super side-project for a student who is doing fairly intense math. Do PPG once or twice a week for a year, and regular AoPS or similar intense math the other days. It's groovy.

 

And, it helps slow the boogers down, lol, which is one of the reasons I added it to dd's schedule this year. I just didn't feel like starting Algebra with my 10 yo. :) So, we spent this year really nailing AoPS PreA (she is doing 95% of the challenge problems w/o any help now) as well as a new, interesting, but low-stress challenge with the PPG. It's been delightful. Highly recommended to fit in somewhere in the PreA years.

 

We'll head in to AoPS Algebra in the coming fall fully confident and after having had a very solid PreA and PreGeo program. :)

 

FWIW, the AoPS classes DO go very fast. My dd took the PreA classes last year, when she was 9, and she did just fine in the challenge sets, etc, but the courses moved too fast for me to have her do ALL the text problems. She did enough of them to succeed in the course, but not as much as *I* want her to have done in order to be fully competent in all the materials. I want complete mastery and comfort with all PreA before heading into Algebra. I want pretty much PreA perfection before plunging on the Algebra, *especially* considering how young she is.

 

This is why I took this second PreA year to review (doing all the end of chapter summary sets and challenge sets) before beginning Algebra. She'll be totally ready for AoPS Algebra in the fall, when she'll be in 5th grade. (Yoikes.) However, having seen how fast the courses go, I'm planning on doing Algebra myself with my dd instead of having her take the class. The classes are wonderful, but I don't want to swamp her, and she's not really old enough to enjoy the social/competitive nature of the classes. She still probably prefers the Mom-time of working 1-1 with me. So, we'll do the Algebra book together next year. I'll consider having her take an AoPS class again AFTER Algebra. (Maybe Counting & Probabilti -- that's a fun one . . .)

 

Enjoy!

[quark]

NM

[kiana]

One of the big issues with accelerating too young with PS'd kids is that they HAVE to be ready for all the subsequent courses in the sequence. If they take Algebra in 5th grade, they NEED to be ready for Calculus in 9th. Happily, this needn't be true at home -- if someone really needs 3 semesters for Geometry, they can DO that.

 

I would really recommend thinking sequentially rather than 'We will do this in THIS year and then we will do that in THAT year' etc.

[Luckymama]

I understand the desire to have the sense of control that comes from long range planning. But, and I say this gently, it is really just a false sense of control. You can't really predict how she is going to learn and you are probably going to need to take it semester by semester, year by year, and just see how it goes. As you do that I would encourage you to let go of the fear. I don't understand exactly why but there does seem to be a lot of gloom and doom fear mongering around young gifted kids and math. There are all these warnings kids don't really understand what they are doing or they will "hit the wall" or that there is some kind of magical "developmentally ready" brain for algebra. Yes, that maybe is all a concern if your child had to proceed on a set schedule in school lockstep to the beat of a curriculum that doesn't fit. But, at home you don't have that problem because you can always adapt to where your child is. For what it is worth, I know a number of gifted kids who started algebra younger than 10 and none of them had a problem with it nor did they have trouble later. Try not to be scared!

 

I agree.

 

When we started homeschooling dd in fifth grade, I had NO IDEA she'd be where she is now in math before the end of seventh grade. I've given up planning math courses and just let her go as she wishes. Thank goodness for all the non-traditional AoPS books!

[mom2bee]

I wouldn't plan by year and grade but by topic. Some things she may just swallow in one sit-down, others she may need to grind between her molars for a bit and still floss afterwards! (Can you tell I'm going for a dental cleaning next week?)

 

I have heard only great things about Zacarros books, so I would look into them. Its a pity that BA probably won't be out when you need it.

 

Have you considered some fun but lengthy side tracks, since you are going for broader strokes across math and not narrow some of the moms here maybe able to help you pick the best supplements from among all the ones out there, things like Hands on Equations, Calculus without Tears, Patty Paper Geometry, Life of Fred (sounds like she'd get the most out of the books starting at Pre-Algebra vol1 and 2, but others will know more), Secrets of Mental Math, Zaccaro books, Murderous Maths,and a book on symbolic logic. She is plenty young and so she has lots of time to explore math. You may want to get her an account on KhanAcademy though that is good for practicing the mechanics of solving a problem and does'nt have the indepth questions that Alcumus asks.

 

 

I have seen it recommended that students be exposed to many different math ideas, even as they blaze through arithmetic and algebra. You can explore some cool things with graphs and graphing too. Getting a college level "Math for Non-majors" math book may be a good idea. Those text tend to explore a great range of mathematical ideas in a fairly easy to understand way and you could get years of use out of it. I have two in mind in particular, though others may know of much better ones.

Mathematics for the Modern World by Dale Hathaway and another one by Blitzer, I can't think of the title, but its kind of generic sounding, (Thinking Mathematically, though this one is a little wordy.) This type of text can be a neat reference to have on hand over the next several years and they show-case the many real world uses of math. Buy them used or a previous edition and you can get them nice and cheap.

 

One skill that I would say is extremely important is making sure that she learns how to read a math book well. I hope that doesn't sound stupid, but its a skill I still haven't mastered, but I work on it daily.

[Dmmetler]

You also might want to look at some of the various talent search math classes and other topics math classes. NUMATS and TIPS both have classes that I think would keep my DD happy for at least a month or two, and I figure that running some of those in parallel with Fred might just give her hands a little time to mature (right now, her biggest bar in math isn't doing the math-it's writing it down, and I suspect most of that problem is being a young 8 yr old.)

 

I will also say this-accelerating last year about this time was the right move. It was terrifying to take that jump, but DD has been much happier now that she's at a level that she has problems she really has to sink her teeth into, both in her "core" math (Pre-Algebra/Beginning Algebra) and her enrichment stuff (Calculus for young people, Math competition stuff, etc, the EIMACS free class...)

[Wildiris]

You might want to read through this old thread, particularly lewelma's response concerning AoPS Pre Algebra. It seems to me in math there is on the one hand "creative" problem solving, Then on the other hand there is knowing the operations with ease, and knowing when and how to apply them with simpler word problems or outright drilling of math facts without calculator. Developing both strands is important.

 

About your plans: If it were my child, I would spread MEP out over 3rd and 4th grade. I would include activities such as MathPack: Quest from Duke TIP, and play with the ideas presented in Go Figure. The rest of your plan is my plan too.

[kohlby]

"[Richard Ruszcyk] tells me that generally if we have a 10-year-old in one of the Algebra classes, the kid is either the best or the worst kid in the class. Algebra at 10 or 11 is certainly not unheard of. The best kids I taught (admittedly, they were some of the best in the nation) usually took Algebra in 6th grade (what's that, 11?)"

 

I'm wondering if he's not talking about using the AoPS books, but taking the online classes. The pace of the online classes can be too fast for some students, especially the youngest students. My oldest did finish what I consider to be Alg I from the AoPS book in 4th grade. (I use the first 12 chapters of AoPS Intro to Alg). At the start, I had to sit by his side. It took a few months for him to get into that style more indendently. He did wonderfully with it. However, had I signed him up for it online, it could have easily been a disaster. There are many kids who don't have the math maturity for Alg I in 5th grade- espeically when you're talking about AoPS. But there's far less who have the overall maturty for the online AoPS classes at that point. I did write to Ruszcyk asking him about trying out Intro to Alg since I was worried my oldest was too young - this was two months after he turned 9. He told me that he did have students that young use the book and that as long as my child did well on the pre-test, that it was worth the try. (And if not, then to do the pre-Algebra even though my son had taken a different pre-Alg course. That one was much less difficult, but there was only small gap that was easy to overcome).

 

I'm also not so sure about an entire year on just problem solving. I agree it's not about racing through, but meeting the specific needs. With my oldest, he was usually able to get through his math curriculum fast. We switched to AoPS when the other curriculum wasn't meeting his needs anymore and it has been wonderful. However, he still hit his bumps in the other curriculum - due to maturity, not intelligence. What I did then was to take some time out of the book. That's when we did all the extra fun problem solving enrichment. With my second child, her math curiculum was working well for her and she was speeding along - doing three years worth so far this year - when all in a sudden, it caused too much stress. She's a perfectionist and was no longer having fun. So, we're taking a Life of Fred break and then we'll go back into our normal curriculum for three days of our school week and LoF for one. Both my older two kids do try to race through and both are advanced kids. So, sometimes I do need to slow them down by adding in extra enrichment.

 

I agree with not planning year by year but by topic by topic - but knowing that can change! We end one math and then go into the next. It doesn't matter what the school year calendar says. Also, the child's learning style and interests can change over time.

 

*I'm a former middle/high school math teacher. Math maturity is very real and has nothing to do with intelligence. The place I saw the biggest issue was not in Alg I, though public school's courses are nothing like AoPS, but Geometry proofs. I could water down the proofs, and wasn't even required to teach proofs to anyone but the honors students, but I feel proofs are a very important part of math with its reasoning and should not be skipped. With my son, I did see math maturity influencing two sections of his Alg I, but it was just two sections and I was able to work through it with him. Had we waited a year, there would be a little less struggling, but the struggling wasn't met with tears but with growth.

[mathwonk]

Just 2 cents. As I read that article, it was mostly about the need for gifted kids to be challenged by being around other gifted kids. So he suggested it is a mistake to put them in college calculus classes with less gifted older kids, and just continue the pattern of a gifted kid always being the best student in each non honors oriented class she takes.

 

So he does suggest challenging the student at each level rather than accelerating them without that challenge. I agree wit that 100%, but it isn't so easy to achieve. I myself used to suggest that if the child is accelerated, she be placed into honors classes rather than non honors ones. A 12 or 15 year old prodigy in an honors college class will likely be challenged, even if not in a non honors one.

 

Later on in the article, he suggests as a solution to the problem of finding gifted peers, having them join a community of other gifted students, such as the online one he is forming at AOPS. I took a brief look at a couple of those threads but I did not find a lot of supportive interchange. More like one ups man ship run rampant. But have you tried that?

 

And maybe some summer camps where the kids are supervised well and make friends could help, like epsilon camp.

[boscopup]

"rushing through the standard curriculum" or hothousing is different from letting your child set the pace.

 

 

Agreed. Also, if you're planning to use AoPS, you aren't rushing through standard curriculum. :D

 

My current plan is to give AoPS Prealgebra a try next year in 4th grade. If all goes well, my son *could* use AoPS books all the way through calculus, hitting it no earlier than 11th grade (if he did one year per level - Algebra 1, Algebra 2, Geometry, etc., plus a semester for each of the probability and number theory books). In reality, we may go slower! We'll see what happens when we try it. But even though we would possibly be doing Algebra in 5th grade as a young 10 year old (our school year starts right around his birthday), we wouldn't be racing to calculus. RR is cautioning against starting Algebra 1 in 5th and doing Calculus in 9th, having no where to go after that. In my area, the community college doesn't allow dual enrollment until 11th grade, and the university (with the better math classes) doesn't allow it until 12th grade! So I don't want my son hitting calculus before 11th, because I'd like him to take calc3/diff.eq. at the local university. I don't think the community college math courses would be sufficient.

 

Also, you *may* find out that your DD slows down some in MEP 4-6. I know my son had a definite slowdown once we hit about 4th grade math. There was a lot more to learn, and it got a lot more complicated. Grades 1-3 were really quite simple, mostly learning basic addition/subtraction/multiplication/division. Easy peasy. We aren't going as slow as one grade level = one year, but it's slower than we were going our first year of homeschool. :) YMMV, of course. Some kids leap ahead to algebra, and some kids need to spend a bit more time on elementary math. My son isn't asking for algebra at this point, so I'm ok going a bit slower, taking our time. We do math every day, and I try to keep the challenge level up, but some days are easy breather days. ;) Since Singapore doesn't have a gazillion problems, my son hasn't been bored with it. I imagine MEP would be similar, since there aren't a gazillion problems.

 

We're finishing Singapore 5B soon, and I plan to have DS work on Life of Fred Decimals & Percents the rest of the school year before he starts AoPS this summer.