Math at two levels?

[dovey]

I have another question about my 7 year old son. He loves math which is way above his grade level, and he understands it. He wants to do fractions, algebra, geometry, trigonometry, physics, logic etc. I show him new concepts and he eats it up. But at the same time, he has only memorized his multiplication up to the 3x tables. Not so popular. Right now, what we do (we homeschool), is do a little grade level math each day, which is pretty tedious for him. And then we do whatever other more advanced math that he is interested in. It's kind of odd, that having arithmetic memorized is not really necessary for the more advanced math, but I know that it's very important for him to know how to do this stuff. Do you think that this is going to be less helpful to him in the long run than just powering through the arithmetic, and waiting for the advanced math?

[insidevoice]

DD approached math the same way.  Honestly, I didn't push the tedious stuff, but as she used it with more 'interesting' problems she saw the value in it and decided to at least remember it.

[Roar]

This is similar to what we did and it worked out great. It is that exclusive forced focus on arithmetic that makes some kids turn off math. The memorization will improve in time and there are always other ways to practice that with games and so forth. Down the road he does need to work on learning to formally write out proofs and show his work but there is plenty of time for that when he's older.

If you haven't already done so you may want to look at the Challenge Math books. https://smartmall.net-smart.net/challengemath/index.cfm

[ollyoxenfree]

I think it's fairly common. For the tedious multiplication, if he understands the concepts but can't be bothered to memorize just yet, he may like learning some of the shortcuts, eg. the rule of 9's, finger math tricks etc. If he hasn't tried them, perhaps that's something that can take the place of the daily grade level math for a little while. 

[hergrace]

This is exactly what DS1 (7) is like.

For multiplication speed drills, we have been using Timez Attack on the computer - http://www.bigbrainz.com/

We also use KenKen for arithmetic practice.

Embedding the drill in a more complex activity definitely helps him stay focused and he is learning the facts by using them.

HTH

[moominmamma]

I kind of thought that was normal. That's what I was like as a kid and all my children have been the same way. I think schools often kill enthusiasm for mathematics by focusing exclusively on the sequential mastery and memorization of arithmetic and failing to feed an interest in higher math concepts. One of the great beauties of homeschooling is in being able to constantly shift the focus back and forth in keeping with your child's readiness and interest. My middle dd was graphing conic-section functions and exploring calculus concepts at age 9-10, but still hadn't mastered converting decimals and fractions. My youngest dd was solving linear algebra equations at 5-6 but still hadn't memorized her timestables. For us algebra, trig and calculus are the carrots that keep the kids interested in math while they gradually, on their own sometimes-seemingly-glacial timetable, master and memorize basic arithmetic builds. When that readiness for the arithmetic work comes, it tends to come quickly, and it tends to be fueled by motivation that is the result of seeing the point of all that arithmetic -- ease with calculations while solving truly interesting higher-level problems. 

Miranda

[FarmerBeth]

Stuff like times tables is more of a memorization skill than a math skill.  Many kids who are great at language arts and memory skills can get good at things like times tables, but higher level math is about having the ability to conceptualize the abstract language of math.  DH is now quite happily in a second career as a nurse, but started out his adult career as a computer engineer.  He's great at creating and working with complex formulas, and slow as molasses with some basic arithmetic (like I don't think he'd want to be a waiter in a busy pub!).  Your son will probably just have to work extra hard at the memorization bit.  You can use tricks like seeing if he is better at memorizing visually or chanting them out loud.  My oldest son (who has great conceptual math skills, but a poor memory) practiced hes times tables while playing catch with me.  Whatever works!

[rachelsmama]

Memorizing multiplication tables isn't really mathematics, it's memorization.  Sure, it can be useful for speed, and so on, but it's not vital.  The idea that all that memorization is hugely important always makes me giggle a little because my mother uses my lack of memorization as proof that I'm bad at math, despite the fact that I did just fine in university level calculus and statistics.

[Aufilia]

My DD is the same way; I'm glad to hear she isn't alone.  DD hasn't memorized most addition or subtraction tables, but she can always figure them out if she wants to.  It drives me a bit nuts that she needs to sit and figure the same problems over and over but she can't be bothered to memorize them so I guess that's what works for her. This is the child who can tell me the title of every single children's song on any CD we own just based on the track number ("Oh, number 13... that's Kookaburra.") so she's certainly capable of memorizing completely random number-related information.  I bought her some flashcards thinking she might be mildly entertained by them in the car, but she never looks at them so... whatever, I guess...

[heatherdeg]

Add us to the list... and mine is 7-1/2yo.  What are you guys using to teach the higher level math?    I'm woefully low on resources for that.

[domesticidyll]

We're using Life of Fred, Khan Academy, and just started Art of Problem Solving Pre-algebra. I am loving AoPS, but DS doesn't have the... stamina? to sit and read through, so I give him the problems (sometimes writing them out on paper so there is less clutter and only one thing to look at), and he does a few at a time. And more informal, living math, coop. I have also heard good things about Hands On Equations, but DS doesn't like manipulatives.

Heather

ETA, I am also hoping to start up Calculus for Young People. Other formal resources: Challenge Math, Math around the World, some of the Lawrence Hall of Science stuff. 

[heatherdeg]

LOVE Life of Fred, but they've only put out the first 4 books (which mine promptly ripped through) and there's still a 6-8 book gap before Fractions (which requires you to be able to do long division).  They're supposed to fill the gap by next summer (with the first one or two done by Christmas) but still...

I'll have to check those others out.  Thanks!

[captain optimism]

My son is in public school and he is a math fiend. He does love the arithmetic, even though it's the higher math that really floats his boat. He knows his multiplication tables, but I'm not sure how he learned them. 

Lately, he's been passionately interested in www.khanacademy.org, where he listens to the videos about the more advanced math subjects but performs the arithmetic exercises. The funny thing about these lessons, which have created such a splash around the internet, is that they're just chalk and talk lectures! The teacher is very friendly and pleasant, the lectures are broken into clever sequences and units of meaning, and the student can choose how much to do at a time--I think that's why they work. That would be a good way to integrate the "math facts" arithmetic memorization with the higher math. 

We've done a lot of different kinds of experimental things to enrich math for him. He is not an advanced reader, as many gifted children are, so I've had the opportunity (!) to read him a lot of math books. The book I recommend the most highly is The Number Devil. I read it to him in kindergarten several times, and he has revisited it. (Finally he can read it to himself! Whew!) We also liked the picture books of Mitsumasa Anno. They are so beautiful and creative. My son loved The Math Curse, which isn't such advanced math content, but he liked it. We've also read several books in Cindy Neuschwander's Sir Cumference series. 

We've also attempted a few adult books for general audiences, just to see whether they will work for him. The one I recommend most highly is The Math Book by Clifford Pickover

http://www.amazon.com/Math-Book-Pythagoras-Milestones-Mathematics/dp/1402757964

It's too expensive to buy--just reserve it at the public library. My son leafed through it and got me to read individual pages to him, according to whether they looked interesting. It's a gorgeous book--really interesting. (It's in chronological order like a giant timeline and I am trained as a historian, so of course I liked that! Also timelines are great for children learning historical thinking.) 

We also got a book on M.C. Escher and then followed up by looking up more about his work online. We also (OMG this was insane) read a book on the history of topology--which was a huge success and proved to me that I need to think of my kid as gifted. (Or just nuts!  ) It was called Euler's Gem. It was another chronological book, full of math I could not understand at all, but my son porpoised around in it and had a great time.  I also tried a book on the history of zero called The Nothing That Is, by Robert Kaplan, but it was so larded with literary allusion and historical context that we didn't get through more than two chapters before we fizzled out. 

We got the Challenge Math book, and at first he seemed excited by it, but it doesn't seem to be as big a hit with him as some other things. Remember, I'm not homeschooling so I don't have to provide insurance that he's on grade level or achieving, or whatever. I'm mostly doing all of this to help him stay interested and to compensate for how dull school math is. Mainly I'm along for the ride, and learning as much as I can. 

[dovey]

Thanks for all the recommendations.  Very helpful!

[moominmamma]

If you provide your child with a math-facts table it's possible to use almost any curriculum or program at the conceptual level that challenges your child without the facts learned by rote memory. You just allow him to do the computation with the aid of a printed reference table of multiplication facts. So if he's doing a unit on long division, he just refers to the printed multiplication table to help him multiply 7 x 8 and 7 x 9 to figure out how many 7's to fit into the first digit of 6140. If he's working out an algebra problem and he's left with x = 240/4, you direct him to the printed table to help him find the quotient. 

There are a bunch of neat resources that encourage exploration of concepts without doing any much computation at all. Theoni Pappas' books, "the Number Devil" book, Hands-on-Equations from borenson.com, Calculus By and For Young People ... those are some I recall that we've used. But for my late-memorizing kids, our mainstay approach was just to continue with the Singapore Primary Math that they enjoyed, but with a crib card of multiplication facts that they were free to refer to if they needed. Eventually they no longer needed to bother with the crib card much ... and then not at all. In the meantime they had continued to enjoy math and to learn plenty.

Miranda