I am looking for some advice in how to best help my very, very mathy child.

Background: She's 8. In her April Peabody, she scored as a 50th percentile 9th grader, 4th month, in math. (That's how they score you -- which grade/month your child would be 50th % -- the tester said she only started to miss questions when it was clear she had never even seen it before, like exponents. Technically, she hadn't "seen" algebra before either except for reading the Basher book about it, but was apparently able to reason out how to do the single variable stuff on the test.) As of yet, we haven't come across a concept that she hasn't immediately "picked up." The only troubles we have ever had were, for instance, when we were doing multi-digit addition and subtraction -- not because she didn't "get" it, but she was frustrated with having to line up the numbers, etc. (Her handwriting is weak.)

Currently, we are finishing up Singapore 2, we are also halfway through MathUSee Gamma (mastery of single and multi-digit multiplication -- though we're flying through it as fast as she can get her facts memorized), and do daily work in Math Whizz and Dreambox. She reads Life of Fred for fun (and a whole stack of other math books floating around). She's working through Art of Problem Solving's Beast Academy 3A and all of the Critical Thinking Company Math/Logic books. I got her the Hands On Equations iPad game a few days ago and she immediately chewed through it and now is all, "Hey, mom, look at me solve 4x + 5 = 2x + 13; can you find me more algebra stuff?"

So. I'm not 100% sure how I should be handling this. On the one hand, I don't want to hold her back or have her bored, on the other, I want to make sure she's solid on, and doesn't miss any, fundamentals. Right now it feels like I'm throwing stuff at an insatiable math monster and I'm not sure how best to teach this girl. (Ha! Like *I've* actually taught her any math.)

My current strategy is to plod along with our "regular" daily curricula (Singapore and MUS), to ensure proper drill and mastery of her foundational skills-- though I'm trying to stay sensitive to the fine line between useful practice and mindless busywork. (I do let her "test out" of some sections.) And then, after that is done for the day, she can go crazy with whatever else she wants, like the resources I mentioned above. Then I was also looking at the physical Hands-On Equations set if she really wants to do some early algebra. (Challenge math? EPGY? Math contests?) I got her a Khan Academy account and occasionally look in to see that's toodling around with absolute value and symmetry and ray lines or whatever else she stumbled upon.

Any thoughts or recommendations?

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## 35 comments:

I would drop MUS. It's one of the easier homeschool math programs and IMHO a waste of time for a bright kid. If she's using Beast Academy, then I would also drop the Singapore textbook/workbook and just do the

Intensive PracticeandChallenging Word Problemsbooks.What I would add is Edward Zaccaro's

Challenge Mathbook, theVerbal Problems Bookfrom Hands-On Equations, and MEP (which is available free for download here.).I like MUS, but I don't really use it in the way that it is intended. Well, for this child, at least. For her, we pretty much only use the systematic review pages and the tests, never pull out the blocks, but do watch the teacher videos together and talk about them. I know it is notoriously poorly thought of in some circles, but when we struggled with forcing her to confront her not-wanna-do multi-digit addition/subtraction (which I alluded to above), running through MUS Beta at breakneck speed did the trick and she got over that mental hump.

(It's use as intended -- at least in the early years -- works well for my very well-spatially oriented but troubled-reader/writer son so I don't mind having the resources around.)

Art of Problem Solving!!!

http://www.artofproblemsolving.com/

They are awesome. And it is run by math-loving math nerds, every last person on staff.

Also --

* Challenge Math is now sitting in my Amazon shopping cart, looks great!

* AoPS -- Beast Academy is their new elementary curriculum, which I purchased, literally (and I actually mean that literally) on the first day it was available for sale. Heh. I also picked up their new Pre-Algebra set, since that is their "youngest" set of the original curricula so I could get a sense of where we needed to be in order to start using it.

Thanks all for the help and insight -- I just haven't been feeling sure about what the right mix should be of drill vs. letting her fly off and follow her math bliss, so to speak. But then we'll have many a day where she flies through her work ... only to find that she got one or three wrong because she didn't slow down and read the instructions or she made a careless error or somesuch.

I get torn between the recognition that, sure, it's not that she didn't know how to do it and, hey, bridges fall down because someone counted the sloppily carried 1 into the wrong column, you know?

We always called our son a sponge for knowledge. I used to leave out math practice sheets when he was in Kindergarten and he would sit down and do them. I think his Kindergarten teacher thought that was a form of child abuse. However, he had no "problem".

The school had a problem because they used MathLand. We, his parents, had a problem. Our son was not challenged, but that didn't translate into an issue of boredom for him. We were very conscious of not translating our frustrations to him. We didn't speak badly of the school in front of him (most of the time).

We moved him to a private school, but that used Everyday Math. I used Singapore Math at home. It wasn't difficult to keep him up to speed so that he could make the transition to the AP calculus track in high school. It was, however, rather difficult to get him to focus on speed on the times table and in doing mental calculations. They just don't emphasize that at school, and that was not fun for him. That problem has resolved itself with some work, but at the time, I wasn't so sure. I do remember how surprised he was when he realized how well his parents could do something like multiply 12 X 17 quickly in their heads.

Then, in sixth grade we brought him back to the public school which now also used Everyday Math. The principal was very happy to see a few kids come back, rather than go away, and bent over backwards to accomodate him. We got the school to allow him to skip 6th grade math and go into 7th grade pre-algebra that used a proper textbook. NOW, there were problems, but they had nothing to do with math. He was "the baby" according to some 7th graders even though he was getting the highest grades. It was not a happy year. Also, the teachers did not like the special special schedule accomodations that were made for him. The math teacher ended up not liking him. Some teachers just seem to not like smart kids. BTW, other kids could be that smart if given the chance.

So, because of schedule issues and student issues, the school allowed me to teach him algebra and geometry at home the next two years so that he started with algebra II as a freshman. In high school, there is no problem with being ahead a year, but it was an issue in middle school.

In general, we never thought it was a race. We had him skip a year in math because it was an opportunity to skip what would be a very boring 6th grade of Everyday Math. However, next year he gets to AP calculus as a junior with nothing left for his senior year. Community college? No, it's too far and the schedule won't work. Online course? The high school is not set up for that and he would still have to take a math course. AP statistics? The only real choice, AND it's higher weight helps his weighted GPA.

At this point, he has other ways to satisfy his "math bliss". Last year we got him a copy of Mathematica. (He started with the free version of GeoGebra before that. You HAVE to get that. Our son loved it. We had talked about Fourier Analysis and he used sines and cosines to create a saw-tooth function. He used it to create functions for all sorts of shapes.) A while ago, he derived the formula for the summation of i^4 from 1 to n. He now takes care of math bliss all by himself. He likes to leave problems for me to do.

One thing he has never done (somewhat of a concern to me) is that he has shown no interest in math competitions. I don't care about the actual competitions, but the problems they solve seem to be a way to separate students. He has done OK on the AMC/10 test, but we have never focused on those questions. That's a special skill. He would rather move on to learning things like calculus and Fourier Analysis. I have gotten AoPS books, but he does not want to follow a text for his math bliss. School is for that.

Then there is the SAT. The questions are not hard for him, but if he wants a score that puts him into the same bucket as his peers, he will have to practice on speed and become familiar with the problems. With just a few wrong answers, you can drop below 700.

In general, he thinks that school classes are for book learning, and outside of school is only for his own math bliss. It's a challenge to get him to do something outside of school at his level that systematically follows a text or curriculum. Our middle school didn't have anything like MathCounts. That might have helped. Now that he is in high school, he has shown no interest in their Math League team, even though they have asked him to join.

In terms of dumb math mistakes, this was also a problem for him, even when he got to pre-algebra. I was concerned. I worked with him on it, but the problem soon disappeared, and I don't think I had much to do with it. I don't know why it disappeared. Maybe he just didn't like making dumb mistakes. Maybe it's because he slowed down on tests. One interesting thing I've noticed is that he makes more dumb mistakes when the test is easy. He can get a hundred when the median is 75, but a 90 when the median is 90. He always had a tendency to overthink some problems.

I hope my comments help. In general, I would advise keeping parent angst hidden from kids, and I would advise not leaving everything (after school) up to the kids and their math bliss. If I got to do it over, I would have focused more on a coverage of AoPS and AMC questions.

My 8 yo is also very interested in math. Between chronic bullying problems and deadening boredom, I pulled him out of school in 1st grade. We went through the Singapore books through 3B this year (2nd grade), and he spent so much time on Khan Academy that every time I thought something was new he knew it already. He's now turned 8 and is super-thrilled to be starting AOPS pre-algebra. I heartily recommend it. It's very much the math book I wish I had when I was a kid, challenging and through-provoking. My wife stays up late reading it. It's the shiznit.

Doing the more fun math makes it all the clearer to the wee nipper how important it is to develop fast fluency in basic arithmetic like multiplication.

Art of Problem Solving pre-algebra. Go there because it's interesting. If she needs something she'll go back and pick it up in a flash.

Zaccarro also has an algebra book that's good.

Mathcounts is a middle school competition. The website probably has sample questions. Those could be fun for her at some point.

Kangaroo Math is an international contest for K-12. My son had a tutor who won it one year.

I do think the competition problems help alleviate boredom for the mathy kid.

It sounds like you're handling it well. The only problems we had were missing a few middle school topics because of the jump to pre-algebra and algebra in the 4th/5th grades. He missed out on all of the probability topics that get covered a lot these days. He also managed to miss learning about the Pythagorean Theorem, but he was able to teach himself about it, and it comes up in a lot of problem solving questions.

SusanS

I'll give another vote in favor of Zaccaro's Challenge Math . . . I had two kids who enjoyed it. It seemed to me that it was a great combination of new concepts plus harder applications of basic concepts. One thing that I liked about it was that it was good for us to work on together, unlike a lot of stuff on the computer that works better for the child to do alone.

Another book that was very popular around here was The Number Devil. I think the story and language would appeal quite a bit to an 8-year-old. It's not a book of problems or lessons -- it's more of a fun introduction to more advanced mathematical concepts that rely mostly on arithmetic.

As for school, we found elementary school and early middle school hard to manage, because there wasn't much room for appropriate advancement. Once my kids hit 7th grade they were permitted to start Algebra a year ahead of the typical honors track. One kid will end up doing Calculus in 11th grade, the other did Calculus this year as a 10th grader. We are lucky in that we live in a college town, so there are good opportunities for math life after calculus, but not everyone is in that situation.

Things for now:

Math Olympiads for Elementary and Middle School. It's a contest (moems.org) and they have books, too. The books are available through AoPS. It's another way for him to find fun, challenging problems. I heard Richard Rusczyk (of AoPS) talk at MathPrize for Girls one year and he mentioned the richness of the MOEMS problems -- there are usually several ways to solve each one. So, that could be a challenge, too.

Another source for problems and a contest is Grace Church School's Abacus contest (it's not about using the abacus). http://www.gcschool.org/program/abacus/index.aspx It's an untimed contest and it's not multiple choice.

I'll second or third AoPS, Singapore Math, Beast Academy, and Edward Zaccaro.

We made sure to separate arithmetic fluency from advancing in math. There were times when she had to do some arithmetic practice (like multiplication facts) each day as well as some math. I feel like this was the best of both worlds and she didn't come to dread math because it included fun new stuff as well as practice for improvement.

Do you have a bunch of books to read about math? Books by Theoni Pappas are always fun. The Phantom Tollbooth by Norman Juster was a favorite of my daughter. The Murderous Maths books (published in the UK by the Horrible Histories people -- can buy in the US at www.horriblebooks.com) are fun. My daughter also liked The Number Devil by Enzensberger. More books are listed at www.livingmath.net in the Math Reader section.

There's a summer camp just for crazy math kids, although it requires a parent to attend, too. This year is the second year. It's the younger sibling of MathPath for middle schoolers. www.epsiloncamp.org

Check and see if there are Math Circles in your area and what ages they are for.

For the future:

Besides AoPS, my daughter also did coursework through eIMACS (www.eimacs.org). They have great mathematical logic classes and computer science classes.

Math Circles!

Fun summer math camps. They start beginning in middle school, but some are only for high schoolers. Some are pure math (Math Path, MathCamp, Ross, Texas MathWorks, Promys, HCSSiM) and others are more competition math focused (AwesomeMath, Math Links, Math Zoom, etc.). Some have a very structured programs and others give the students lots of choices. My daughter attended AwesomeMath and MathCamp. Everyone we know who has attended MathPath loved it.

Some of these camps have school year programs, too, either in-person or via correspondence.

Set theory and problem solving are excellent additions. We used an older text out of the library for set theory. We used HM's Problem of the Day collection for problem solving. Other fun challenges are in games..for ex. in Zoo Tycoon on PC - can she max her zoo objectives? In Pit Droids on PC, can she make her own puzzles?

HM POD example

We borrowed from school. There are also collections on line.

It would also be good if you could find a "mentor" who was really into math. At some point, having someone to discuss things with (e.g. can you have a negative base number system?) would be good.

-Mark Roulo

In addition to reading the replies here, I suggest that the OP also browse the Davidson Gifted Forum, where questions similar to hers have been asked dozens of times. Another forum to browse is the Parents' Forum Accelerated Learner Board at the Well-Trained Mind forum.

Wow, thanks for all of the fantastic suggestions and leads.

My biggest waffle right now is still trying to assess how to handle/balance the having to practice/master the stuff she "gets" -- once she has the "aha" moment, how much practice should there be to solidify it before letting her scamper off. (Because, at this stage, the "aha" moment is immediate.) And then once we've completed that for the day, she can go off and do whatever tickles her fancy. Or, perhaps a section of fundamental drill, a section of something above and beyond, and then do whatever she wants after that.

Again, thanks all for insights and things to check out.

Ed Zaccaro's material will help you with the waffle, as will the IP challenge problems. Enjoy.

Terri, you should teach her to admin a Linux box, then the two of you can go into business together.

But she'll still have to do math, so here are some thoughts. It seems to me that you are talking about three issues:

1) drill for fluency

2) conceptual understanding

3) the fun of exploring math

I don't think you have to worry about #1 as long as you have #3. Kids need to drill a skill to the point that it becomes useful, at which point they can move on and continue their practice by using the skill. Fluency can come from repeated use as well as from drill (but only if it is usable). If you occasionally move on too soon, you'll fix it easily later. There just isn't much risk of under-drilling here. (I'm only talking about YOUR situation not, say, an inner city classroom.)

But that's fluency, not understanding. It's possible to fake understanding with fluent pattern recognition. I have two techniques for reducing this problem. The first is to increase the variety of problems my kids work on. It's easy to solve problems by pattern matching when all the problems follow the same pattern. That's one weakness with most drills. I give my kids a lot of one-off problems: a Singapore bar model, an SAT ratio, a Russian puzzle, a many-digit long division problem, etc. They can't deal with that kind of surface variety without developing deeper abstractions (eventually).

The second technique is to ask, "Why?" repeatedly. It's hard for them to fake understanding when they have to justify every step of their process.

Although the risk of leaving a misunderstanding is somewhat greater than the risk of under-drilling, if you keep feeding her a varied diet of problems and asking why, why, why, you won't miss much.

As for the last issue, the fun of exploring math, don't spoil it by worrying too much about doing math properly. (Allison is going to have kittens if she sees this.) In your case, it will be a lot easier to polish dysfluencies and straighten out misunderstandings than to rekindle her passion for math if she ever loses it.

Terri, in addition to agreeing with the comments above, what I have found is that the problem difficulty and/or complexity needs to be pushed up well above where you may think it should be. The contest problems are helpful in that respect, plus they are a mix rather than all the same type of problem.

Also, my son has been enjoying an Imacs class this spring - I think this is the same organization that does eImacs, but these are once a week physical class meetings rather than being on-line. The classes seem to be largely a series of math games and the presentation and material is quite different from that usually seen in school.

I've not read all the comments here yet, but felt I had to jump in.

1) Don't do the Intensive Practice book from Singapore—that's for kids who need "intensive practice", not for those who get it quickly.

2) Do use the Challenging Word Problems, though they get too repetitive in 6th grade.

3) Get the Art of Problem Solving books that are

notin the standard curriculum—the contest math books and the counting books.4) Look for math circles and math contests in your area.

No, the EXTRA practice books are the ones that bright kids should avoid as it is at the same level as the workbook. The INTENSIVE practice books are quite challenging. Many of the problems at the 4th grade level & up are similar to ones I remember being on the SAT. The IP books are harder than the CWP books.

Look at the AMC-8 contest. It's for 8th graders and below. My daughter participated for the first time in 5th grade, but younger students can (and do) participate. It's a relatively short (I think 45 minute) multiple choice exam in November. It's the younger sibling of the AMC-10 and AMC-12 which are used for USAJMO and USAMO qualification. AMC-8 doesn't qualify you for anything other than AMC-8 awards, but it does give you a chance to practice problem solving.

Singapore Primary Math level 6 is focused on preparing Singapore students for the Primary School Leaving Exam, so much of it is solidification of existing knowledge/review. If you're going to do a good pre-algebra book/class (like AoPS Pre-Algebra), then you could probably skip level 6.

If your child likes mathy things, then be sure to look at fun mathy games like Set. 3D tic-tac-toe is fun (we had one with multiple levels of clear plastic boards, but I see there are also versions where you stack pieces) and chess is always good to learn. Dominos are a great way to practice basic facts (use double-9s or double-12s and change the scoring from multiples of 5s to some other multiple to make things more challenging).

Zome can be fun to play with, too (and is currently on sale through the Homeschool Buyer's Co-op).

lots of good practical advice, so this is on a different take.

What are the big goals you are trying to achieve? Bigger than math, I mean.

Some big goals are discipline, perseverance, and humility.

By discipline I mean the fortitude to do the interesting and the boring as necessary, by perseverance I mean the ability to tackle difficult and

intimidating work without fear of failure or giving up, and by humility mean knowing you aren't the smartest and/or hardest working person in the world.

So then asking how can you make choices locally on in the near term here to help

those big goals can guide what to do next.

Balancing the conceptual side and procedural side speaks to the discipline issue.

Her mathematical nutrition should be balanced. Not necessarily every day, but over the course of the week , and she needs to eat her mathematical vegetables, too. That means practicing written on mental computations until they, over time are perfect and automatic.

Forcing her not to ignore math that she can't immediately grok speaks to the perseverance. She needs to learn to tackle her fear of failing, and doing it little by little,

and by just pushing that boundary some few minutes every week, she gains practice at not just giving up. the issue of asking why is about perseverance.

Most mathy kids figure out the procedural side so quickly, and don't spend the effort on the conceptual side. It may not even seem separable to them. the "why" of place Value is just the hundreds, tens, etc. column.

The why of manipulative algebraic statements is because you can do the "same to both sides." But the real whys are deeper. (what of it's an inequality? How dons that " same to both sides" things work for you?

Can you successfully count in base 12 or add in base 16?

Math competitions or math teams can help with the humility, and

somewhat help the perseverance and discipline, if she has a good coach. locally, I'd look into Karl Bunday's classes at ECAE, Edina Center for Academic Excellence. I know they are trying to expand to the North metro. I'd also look at District 287's enrichment offerings.

We do their Fermi off the Wall math League.

Put a big X on your long term parenting map, and use that to inform your decisions as to should you buy another curriculum, or do this other enrichment. keep a handle on what the big goals are.

--the fun of exploring math, don't spoil it by worrying too much about doing math properly. (Allison is going to have kittens if she sees this.) In your case, it will be a lot easier to polish dysfluencies and straighten out misunderstandings than to rekindle her passion for math if she ever loses it.

well, yes and no. i have now seen so many youngsters, including those who tested highly or profoundly gifted, with the most disturbing gaps. ex: no ability to do 2 digit by 2 digit addition mentally, (yet supposedly ready for Primary math 4a), others who are sure fractions can't be bigger than 1, other who are sure you can't divide 6 candy bars among 7 people (even when they could divide 1 among 7), and the bright child who thinks "8+3=11, but the answer can;t be greater than 9."

and then i've met highly gifted kids who figured things out for themselves and filled in all of those gaps for themselves as necessary.

i think the answer is temperament. some temperaments are curious and yet fearful, others are curious and not fearful. (the big 5 personality traits fit this: OCEAN says you can be open to new experiences and still highly neurotic). So some kids find those gaps and dive in to figure out what it means, and others find those gaps and get afraid that it undermines what they know. so i think for some, having errors is more problematic than others. i would try to think about how she might react to realizing she has been getting something wrong. big deal, or little? if big, take much more care in the first place.

I didn't realize you were in MN. If so, then I'll definitely second the suggestion of at least TALKING to Karl Bunday about what the options are in your area. Whatever he tells you will be exhaustively researched.

Early on, we had the issue of knowing how much to push mastery of the basics. In our son's case, it seemed to fix itself without getting weird about it. This took through most of middle school to get him to be as good as his parents in mental math.

Another was the dumb mistakes on timed tests. This was a big worry for me. I pushed him to slow down and write out every step. That helped, along with the fact that he didn't like losing points on tests. Now, the issue is speeding him up to get ready for the SAT. This is after telling him that math is never a race.

Then there is the issue of whether school math (even at the top level) is enough. There is a conflict between the "game" and what might be best for his mathematical development. The big game tests are SAT, SAT II, and the AMC/12.

My son had nothing like MathCounts in middle school. I think it would have been good for him, but we had nothing. He could have done something on his own, but it's a whole lot easier to do this as part of a group. Now that he is in high school, he has many things going on and the Math League is not high on his list. After school math would help with speed on the tests, and tests (for better or worse) open or close doors based on very slight differences. He loves to explore math, but he doesn't love to methodically cover specific topics and problems - that's what class is for, and he does it very well. Unfortunately, the time has come to methodically prepare for the SAT tests.

Once you get into college (through the door), everything changes. You don't have to worry about competition math and door-opening math. My issue now is that my son might do (relatively) poorly on the SAT. He can no longer focus on things like calculus, he has to get very fast at things like solving odd/even math questions.

The other day, we were talking about how some functions reduce to zero if you differentiate them enough (like polynomials), and how some never reduce (like sines and cosines). We talked about what that means. Now we have to drop all of that and methodically go through the types of questions and tricks he will see on the SAT. Just getting a few questions wrong can make a huge difference in your score.

I've noticed that my son does best on methodical coverage if it gets right to the point and doesn't waste time. I'm trying to figure out how to do that for SAT math. I think the best technique is to have him take real tests and let that drive the learning.

Generally, I've given up on having him optimize his AMC score, although his current AMC/10 scores are not bad. SAT comes first, but I resent having him play this game. It's not the best use of his time mathematically.

Steve H said "Once you get into college (through the door), everything changes. You don't have to worry about competition math and door-opening math."

Not quite true. How well you do in math classes can make a big difference in what majors you are allowed to declare, so "door-opening math" is still present. And the Putnam math prize exam is a pretty prestigious math contest for undergrads.

Someone who is good at math and who has seen all the topics of SAT I math and who is progressing through the algebra/trigonometry/calculus sequence should not need to spend a lot of time on SAT practice to get a score that reflects his abilities.

The SAT likes to include a lot of "trick" problems in the math section, much more so than the ACT. I would say that it is far easier for a student to get an ACT math score that accurately reflects his/her math skills than a SAT math score that does.

Crimson Wife said "it is far easier for a student to get an ACT math score that accurately reflects his/her math skills than a SAT math score that does."

That depends on how you define "math skills". The SAT questions are perfectly reasonable math questions—they are not weird "tricks". It may be that the ACT tests lower-level cognitive skills than the SAT (memory and procedural skills rather than problem-solving skills)—that doesn't mean that it more accurately reflects a student's math skills.

Aye. Doing SAT prep with my rising senior now. Haven't met a problem that I can't easily ID the concept being tested. The major issue is that Regent's classes tend to ignore concept in favor of procedure for Gr. 6 - Algebra 1 and certain teachers will omit part of the curriculum in the attempt to get enough time in on major topics such that fully included students get a 'pass', which shorts everyone else. Afterschooling in a district that doesn't offer honours math is a must.

"How well you do in math classes can make a big difference in what majors you are allowed to declare, so "door-opening math" is still present"

That's at a more basic level than what I am talking about.

"Someone who is good at math and who has seen all the topics of SAT I math and who is progressing through the algebra/trigonometry/calculus sequence should not need to spend a lot of time on SAT practice to get a score that reflects his abilities."

NOT at the 700+ level. It takes more specific work. I'll be able to calibrate this better after I work with my son.

"I would say that it is far easier for a student to get an ACT math score that accurately reflects his/her math skills than a SAT math score that does."

Exactly.

"The SAT questions are perfectly reasonable math questions—they are not weird "tricks". "

Who said anything about "weird"?

They are tricky especially with the time constraint. My son can look at any SAT math problem and know that he can solve it. Since the SAT covers only a limited range of material, they go out of their way to find unusual variations. This all relates to the issue of having to take time away from exploring advanced math material to focus on optimizing the fast solution to any possible variation of a limited set of material. They do this because they have to force a reasonable bell-shape curve at the top end.

This thread is about "mathy" kids and how best to develop their talents. We are not talking about kids who will get 600-650 on the SAT. We are talking about top-level kids and the consequences of ignoring the specific preparation needs of the SAT to focus on more advanced topics.

In an older thread, I showed the difference in SAT score between getting 2 or 3 math problems wrong. People talk about "three strikes and your out." With 4 of 5errors, you can easily go below 700.

You have to have seen the problems before. You have to practice the timing and the pressure of the test. I always tell my son to be methodical. That's not good enough. It's not a matter of being mathematically prepared in a general sense. It has to do with being prepared for the specifics of the SAT, because that defines where you end up on the top end of the bell curve, and a few mistakes can make a huge difference.

I disagree, Steve. I offer myself as anectdotal evidence -- didn't spend a minute on prep, traveled over an hour to get to the exam site, and got my 700+. I know teens now who have done the same, and others who have slaved away to get the score. I think the amt of prep is going to depend on the teen and how well he studied and absorbed the topics, as well as the connections he made. I know I didn't see the problem types beforehand. I had only had Dolciani from gr. 7 - SAT test time.

How long ago was that?

The requirement for specific SAT preparation goes up nonlinearly at about 700. In that range, it's not just a matter of whether you have absorbed the material. Top students study old tests. The College Board has to work hard to maintain the shape of the top end of the bell curve. It's a game that has little to do with how well you know math. It's a test of preparation, not aptitude.

I've been studying all of the recent tests I can get my hands on. Time is a huge factor and whether you've seen some variation of the problem before. You have no time to go down a wrong path. Below 700, this effect drops off very quickly. However, look at the 25/75 percent math SAT scores for many colleges and see if getting a 700 is just fine and dandy anymore if you consider yourself a top student.

SteveH, a student's SAT score depends on aptitude and preparation, but after a certain amount of preparation, the score will plateau. "Dr. John Chung's SAT Math" appears to be a book used by some high-scoring students. It has 20 practice tests, tilted toward hard problems. A student could graphs his successive scores on the practice tests. If the score on the 10th test is the same as that on the 5th, that's a sign that SAT preparation time should be spent in some other way.

"... but after a certain amount of preparation, the score will plateau."

Look at it from a different viewpoint. Given a student, what kind of effort will produce the best results? in you are in the average range, then doing practice tests will only help so much. You need to learn more math and fix your gaps in understanding. As you go up the scale, doing specific test prep will pay off more. If you are starting at the high 600 level, then specific SAT math prep will help the most. My son doesn't need to learn more math. If he wants to get SAT scores that are comparable to his peer group, he has to play the preparation game. His competition is practicing and it works. It may not take a lot of preparation for him (I'll find out within the next year), but in a thread from a while back, I calibrated exactly how quickly SAT scores drop with just a few slips. It may take general knowledge to get close to 700, but after that, it's a completely different ballgame.

I have Dr. Chung's SAT Math book and don't like it. You really have to use copies of actual tests. You have to practice with real validated questions and timing.

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