DS7 has been homeschooling a year. He's currently working at about a 5th/6th+ level across the board (with the exception of writing, which is probably 2nd/3rd grade). Most other subjects are fine, there are so many ways to go deep in history, science and language arts. But, math is completely confounding me, it seems very linear and once you finish a level you have to move on to the next level.

He's not the kind to self-teach, but when he encounters something new he looks at it and then he projects the concept forward to the end. We've been working on fractions using Life of Fred. At one point, the book explains that fractions just means divide. DS read it and then set out to convert his fractions to decimals. The book meant that fractions represent splitting x number of things, x number of ways- not actual division (he understood both ways). The whole next book is for decimals and we're only half way through the fractions one. He did the same thing with Singapore Math when we started last year, he saw how to add and subtract single numbers, made up his own multi-digit problems, had me work through them with him and in the span of 20 minutes was adding and subtracting with carrying any numbers he wanted.

He sucks up everything that I throw at him. He doesn't particularly enjoy math, it's not something he pursues on his own beyond logic type problems he creates for himself. I'm just not sure that a kid who doesn't *love* math needs to be balancing equations or doing geometry proofs at 7.

But, then my OCD-tendency kicks in and I think "But we *have* to do math. We can't just *not* do math."

We already do lots of real-life math problems, having DS help me mentally compare prices per unit in the grocery store, convert measuring units for cooking. We practice evenly splitting snacks between himself, DS5 and DD2.5 or figuring distances from here to there by converting units. He is great at reading word problems and figuring out what it's asking for and what information is important.

I've heard people mention studying things like geometry to slow the kid down a bit, but I'm not sure how that works. I took geometry in 9th grade after Algebra 1 and it was a lead in to Algebra 2 and Trig/Analytical Geometry. Is there some other way to study it that I'm missing?

So, am I doing something wrong? I just don't understand how in a year he's finished elementary school math. Is there something else we can pursue that will be interesting and useful but not necessarily advancing him forward linearly?

Any insight or ideas would be great! Thanks!

Kimberly

Can you do more to integrate science and math and do more problem-solving? Having him use math in experiments and such or to solve problems will mean that he's getting math thinking without rushing through a linear arithmetic-only curriculum.

Keep in mind that arithmetic is not the sum total of math, though most of what kids usually get in an elementary math curriculum is simple arithmetic. That stuff an HG+ child can often whip through ridiculously fast. But mathematical thinking isn't necessarily a linear path and it is a lot more than just arithmetic.

I'd recommend Singapore Math's "Intensive Practice" workbooks to you. They're really challenging math thinking, though the arithmetic is not hard.

I worked on geometry with DS-then-6 last year. We used Lynette Long's "Painless Geometry," which is a simplified without being dumbed-down version of high school geometry (fewer proofs, more pictures...), and it was good for him. It was light on arithmetic and long on concepts. It was visual. It was challenging and yet not over his head.

And that's how I used geometry with a 6yo.

It wasn't in preparation for anything else. It wasn't on any linear curriculum path of any sort. If anything it was a total deviation from the usual math path! But it was math and it was good for him and it was fun. Does he remember everything he learned? No, I don't think so. I don't consider him to have passed high school geometry. But remember that curriculum tends to cycle through concepts. Kids don't usually get things once and never see it again. So whereas other kids his age were learning "this is a square" (which they'll get again at a higher level in 3rd or 4th grade, and then again in junior high, and so on...), DS-then-6 was already learning how to use a protractor and what angles are congruent in a given set of crossing lines. He needed concepts, so that's what geometry gave him.

So, I guess what I'm saying is that you're not doing anything wrong except perhaps that you're accepting a view of math as linear when it doesn't really have to be. And even that's only "wrong" insofar as it isn't really working for you and your son! Try more problem solving, more real-world applications of math, more graphing on Excel or other software, more computer programming-type math...less focus on arithmetic. You can still do some, of course. But if he's mastering that, do something harder and more fun!

Oh, Dottie. I certainly don't mean it like that. I didn't even mean "typical public school curriculum!" I meant homeschool curriculum!

I'm sorry I wasn't clearer. But I wasn't talking about public schools at all!

And let me just state very clearly that it would never be my intention to belittle your children in any way for any reason! I feel just awful that you thought that!

Go DD6th! Math on, girlfriend!

And my neck is acting up, so I'm on muscle relaxants and probably shouldn't be writing at all! I never did say that I was talking about HSing curriculum. You're good, but you're not a mindreader!

Since I'm thinking about it, I should also state that even my experience with homeschool math curriculums is--of course--limited to what I've seen. Singapore is supposed to be one of the better ones for GT kids. Yet aside from the Intensive Practice workbooks, even it seemed mostly arithmetic to me.

Saxon is supposed to be worse, and from what I've seen and heard about Aleks, it's also pretty much just arithmetic. That's fine for what it is. But it isn't conceptual and problem-solving...

DS7 is now in a homeschool math class for 9-12yos using the "Key to..." series by Rasmussen and Rosekrans. It was going great for a while, but once he got through the fractions and on to decimals, it went back to arithmetic again. And one again we're hitting the wall...the same wall we hit last year when I left Singapore's linear format and moved on to geometry. *sigh*

I have had some good luck with random workbooks picked up for cheap from Didax and Prufrock Press and such. But I've really been cobbling things together out of those. I'm afraid that Singapore's IP workbooks and Art of Problem Solving (when we get there) are about the only common formal curricula that really push problem solving and aren't so linear.

I'd *love* to hear about how wrong I am about that though, how there are all KINDS of options!

I highly recommend Math Olympiad (MOEMS)problems. All the elementary level problems can be solved using elementary school math, but kids have to work hard to solve them - even mathematically gifted kids. The problems provide a level of problem solving found in few if any math curricula (public school or homeschool).

http://www.artofproblemsolving.com/Books/AoPS_B_CP_MOEMS.php

Summer

Hi, Kimberly--

I wonder if he'd be interested in any math history? That might be a way to add breadth/depth without speeding up any more for now. Julie Brennan's Living Math site has lots of great suggestions ( www.livingmath.net ).

People will doubtless be getting tired of me (!) recommending these, but the computational linguistics puzzles at the NACLO site are really fun, and use mathematical thinking in a very different way. ( www.naclo.cs.cmu.edu/index.php )

What about cryptography? There again, lots of math, but a little bit different, and pretty fun, if he's that kind of a kid (one of mine is--he just finished a two month-long unit study on the Enigma machine).

If you're really feeling venturesome, you could jump into some symbolic logic! I had some of my old university logic texts out today for the kids to play with a little bit--symbolic logic is good stuff!

Or another goodie, topology--one place to start might be here:
http://britton.disted.camosun.bc.ca/jbrubbergeom.htm

Anyway, maybe one of these ideas might interest him? Nothing wrong with a little detour...

peace
minnie

And these are always fun.....more critical thinking and real life math(you don't always have to keep going up to the next level):

http://www.criticalthinking.com/sea...ories=bs&subjects=m&gradeLevel=5

http://simplycharlottemason.com/books/your-business-math/your-business-math-ebooks/

http://apps.simplycharlottemason.com/resources/detail/1113

Texas Summer - which of the books do you recommend starting with - Creative Problem SOlving in School Mathematics or Math Olympiad Contest Problems for Elementary and Middle Schools?

The ALEKS program depends on which program you choose. There are programs that just teach arithmetic without anything else and ones that do make a good attempt to add in geometry and algebra beginning with third grade. That is the track that my DD9 is on. They also do a pretty good job with decimals and fractions, much more than she was exposed to in public. They also have middle school geometry to give more of an introduction before high school geometry.

I also like Singapore math.

Math Detective, on the Hoagies Gifted Board might be promising. They are available in computer and book format. They are supposed to combine high order thinking, reading, and writing in mathematicss. Has anyone tried them?

You can still go deep once you hit 4+ grade. Singapore Challenging Word Problems are marvelous. Zaccaro books are really good. Any books about logic, infinity, probability can be a good choice. There are quite a few options before moving onto algebra.

Wow, this is *exactly* the kind of stuff I was hoping to find, different ways to think about what he already knows or completely different paths all together!

Cryptography sounds right up his alley- he's been creating his own codes and cyphers and giving me messages to decode lately.

The Business Math program from Charlotte Mason looks great, too!

I didn't realize that Math Olympiad had elementary level problems, which I think might be exactly the kinds of problems I want him to learn to solve. It uses basic math he already knows, but he has to get creative and manipulate it in new ways.

Using Singapore and Alex to review and take care of gaps is a good idea, so rather than use them as our primary teaching programs (which we've done both in the past), we can use them as needed at or slightly below level.

I know he already doesn't love math and I would think that if I push him forward, it's not going to help any. The Life of Fred: Fractions has been great, he actually enjoys it a lot and I want to do the next book LOF: Decimals, too. But that's only maybe 6 months worth of work before the 3rd book which is Algebra. So, I'm hoping that we can fill in with other things and get a year or 18mo between the lower level LOF books and the problem solving type resources you guys have suggested.

And I'm still confused on how a not-PG kid is running through math like this? I didn't really believe we were this far ahead until he did an online assessment (Let's Go Learning) and it put him at Grade 5.25 and the test only goes to end of 5th grade. I'm just not *that* fabulous of a teacher, lol!

I'm feeling a lot calmer about this now though, I can see there are a lot more resources out there than what I had found before and they definitely add some depth and breadth to what we've already done.

Thank you all (and if anyone has more suggestions, I'll take all I can get)!

Kimberly

One more thought, Kimberly, given that he likes Fred--I read on another board that Stan Schmidt is writing another book to slide in between Decimals and Algebra--maybe it will be done in time for you? You could always email him and see how far along it is--he's very approachable.

peace
minnie

Two other thoughts..... My DS does a lot of math while working on Astronomy. Charting and so forth. Another thing would be to do mapping, you could even map your own yard and he can learn coordinates etc.

Sort of OT but following along the arithmetic and various curricula....

I've been using Rightstart math with my boys. It's similar conceptually to Singapore Math but differs in scope and sequence. The entry levels A and B (you can start in B w/ a 1st grader or A with a Ker) goes all the way to 4 digit addition. Every so often RIghtstart includes some conceptual tidbit which goes beyond arithmetic. I'm always surprised when my boys make that leap and it's easy as pie. It offers things like tangrams and lots of geometry. The drawing tools are fun to play with. It includes a drawing board, 30-60 triangle, 45-triangle, and a T-square. It's first introduced in level C. Level E begins w/ several lessons on magic squares. Tessellations come up at some point. It also uses check numbers for checking answers to add/sub/multi/div which I've never seen in any other program. It's in Singapore Math but it's one of the supplement problem solving books. the last level, the Geometric approach has units on Koch snowflake, Pythagorean theorem, Fibonacci spiral, Escher, reflections, symmetry etc. I don't have that level yet but it looks intriguing!

the issue I've had w/ RS is that it moves a bit slow. ALthough I think that's b/c I've always been trying to catch up to my son. THe way RS is written, it's not easy to compact or skip around like SM. But I love how it gives a problem that the child has to use all available knowledge to figure out - the strategy wasn't taught explicitly.

Oooh! That is nice!

What is nice?

This:

OH that's what I assumed but wanted to make sure lol. Yes, I think she made the distinction at some point about exercises vs problem solving...which I just read again in AoPS website.

I agree with Dottie's recommendation.

I'm glad to read you agree with Dottie since I already ordered the Creative PRoblem solving (the first book)!

I think almost all my favorites have already been named... but there's one more -- Bletchley Park (British codebreaking center for WWII) has a set of excellent cryptography lesson plans on their website.

Ooooo! Thanks, Erica! That's one I haven't seen before. Next year we have more access to the Internet during school days, so I'll use that one.

Yes, the Bletchley stuff is fun--Harpo spent a lot of time on those lessons this year (they're printable, by the way, Kriston, so if you wanted to, you could print some off to use on days when you didn't have Internet access). Budding cryptanalysts might also like Simon Singh's "The Code Book," which is an excellent read, and has some codes to crack at the back of the book.

peace
minnie

Thank you for the heads up, Minnie! I emailed Stan and he confirmed that there is another book coming, probably by the end of summer. It's one of 3 pre-algebra books he's planning, all from different angles (Biology, Economics and Physics). I think that might help us hold off Algebra for quite a while!

Thank you, Kimberly, for the update--not only one, but three, new Freds! Harpo will be thrilled! And it sounds like your son will be, too!

peace
minnie

OH OH OH, I thought Stan was a year away from publishing the Physics book. I'm happy to hear it might be out by the end of the summer!!! GO Stan GO!!!!

No, it's the Biology one that he expects by the end of the summer, there wasn't an ETA for the other two. I'm sorry for the confusion (and sorry that we'll have to wait longer for the physics one- DS will *love* that)!

OH well, I'm sure biology will be great too!!! WOOHOO!!!