Gifted Issues Discussion homepage Forums Learning Environments Do I buy curriculum two grade levels ahead?

We are afterschooling math, partly out of the Singapore math curriculum, partly from some fun worksheets and partly following questions and interests on her part (and ours). I really like introducing new concepts with guidance from the Singapore math material.

DD has finished most of Singapore math 2B (each year is two books, A and B), so I'm going to buy 3A&B. But looking at their overview some concepts we've been talking about are in 4th or 5th level books. (co-ordinate grid and decimals are in 5th). Each set of textbook and instructor's guide for a year costs $60.

Experienced people, please help. I think I'll get the 4th level books for the geometry, but should I stick to working through the other topics in the suggested order? I've discovered that you do need to know multiplication facts to divide and that you need to be able to divide to manipulate fractions. So I'm inclined to think there's a method to the syllabus. But, with only x number of hours per year, maybe they just distribute things where they'll fit and hold off on some stuff until you need it for more complex things. Like, leave a co-ordinate grid until just before you're plotting x=2y and concentrate on telling time and calculating time intervals earlier because it's so useful. Or does co-ordinate grid mean plot x=2y, and not battleships? After all, they're using decimal notation in 2nd, but supposedly not learning it until 5th? And percentages are just 1/100ths, aren't they? So why are they in 4th or 5th?

I am hesitant to just buy them and jump in for two reasons; cost and my inability to tell when she's bored, tired, needs to apply herself or simply isn't mentally able to do something yet. I don't want to jump in with decimals and percentages if it will turn her off the idea. I'm also not a natural teacher and I get frustrated.

Can anyone help?

I can certainly say you're right in your hypothesis about how syllabi work: there are quite a lot of pre-requisite relationships, but those certainly do not determine everything about the order in which things are presented. You might find it interesting to look at as many syllabi as you can find for examples of different orders, to get a feel for what's uaully done. Another thing to watch out for is that, even when concept X doesn't actually require concept Y, if you're looking at material where Y is taught before X, you may find that X is introduced making use of Y as part of an example, so if you're doing things out of order you have to be alert to that and ready to substitute. (I'm encountering a case of this with DS at the moment in fact; he's doing something which is traditionally considered advanced although it's easy, and I'm having to adjust the material I give him a bit.)

Percentages are just hundredths, yes, but the typical school percentage problem is conceptually harder than the typical school fraction problem because it includes difficulties about what should be done with the fractions. E.g. "after a discount of whatever% the price of the article is whatever - find the original price". The challenge there isn't the manipulation of the fractions, it's the understanding of the world to get to the sum. DS found that hard for a little while, mostly I think because of lack of shopping experience! He got there, but he certainly wouldn't have been ready when he first learned fractions. (I think if I had introduced such problems then, he'd have ended up learning how to do the problem types by rote, which I'm sure is what many children do, but it's surely less good for mathematical development than encountering them at a point where numeracy is ingrained enough that you can confidently solve from first principles.)

I don't think there's any harm (rather the reverse, actually) in meeting things you can't yet understand because you haven't got a prerequisite, but OTOH there probably is harm in having a frustrated parent trying to get you to understand! I tend to offer lots of choices and go on the basis that if it's his choice to work on something it must be OK for him. But I have an easy situation (in maths!); he's very mathy, I'm very mathy, it's easy to keep it fun. Not sure what you should do. Maybe stick to the standard syllabus order for "work" but make lots of recreational maths available, and be prepared to skip lightly over things you encounter in the syllabus if they've already been learned as recreation?

I agree with what ColinsMum wrote. I'd tend to stick to a syllabus ordering, especially for a well-respected program like Singapore Math.

As parents we might feel like the aim is to help our kids maximize their advancement in all areas, because we realize that asynchronous development implies that a child will be ready to do some things well in advance of their normal age-relative development in other areas. But you want your kid to have a good foundation in all important areas and sub-areas, too-- and I think that's easily as important.

Also, I don't think your child's ability to do, say, coordinate graphs work will be negatively impacted by putting more focus in the short term on areas where your child is relatively weak, in math sub-topics that may be prerequisites for other sub-topics. I think that a lot of math is about the ability to think abstractly and manipulate symbols. While it might seem like focusing more on multiplication and division and fractions, for instance, would delay important abstract development, I don't think it's really the case, especially since you will probably find your child will pick up just about anything very quickly, and you'll be back to coordinate graphing and beyond before you know it.

IIRC Terence Tao's father, of all people, has said publicly that he didn't think it was as important to race ahead with new math concepts, as it was to build a strong, broad foundation in math. His son turned out okay. Math geniuses throughout history have developed in times and with resources that were primitive compared to ours today. So I wouldn't sweat it too much, no matter what your approach turns out to be.

One thing you can do easily, as a parent, is called "curriculum compacting", which includes testing out: you assess your child to see if she's okay to skip a lesson. You will just have to develop with her your ability to do this well. Present it as a valuable option for her-- it gets her out of boring work and you get to do more exciting stuff.

I wouldn't hesitate to add more grade-forward stuff as enrichment, but you will have to keep track of what you've covered, which will lose one of the big benefits of a curriculum. I see it more as an exercise in two things: 1) keeping enough "math stuff" in the pipeline so my child is growing, and 2) not forcing him to do boring work, which also increases the speed at which he can advance. I don't care much any more about the specific order, as long as he's learning well, and will go with a curriculum ordering that seems to make sense.

There is plenty of fun, challenging math work you can use to spice up the curriculum, and might also allow giving early assessments of whether your child can handle a certain grade-forward topic out of order.

I have really liked some workbooks recently that I bought for my son: the FlashKids "Math for the Gifted Student" and the mini-workbook "Problem Solving" series are both fun and interesting for my son. The big ones are around $10 US, the small ones (with still a lot of pages, just in a smaller format) around $4 US. What I did was rip or cut them out of the book and feed them through my printer/scanner, saving them as PDFs, so I can feed them to him out of order, he can look at them on the computer if he prefers, etc. Those workbooks are nice because they're quite inviting visually, no two are alike, and they work on a wide range of problem-solving skills which are important for math.

You might also decide to devote some time each week just to problem-solving or critical thinking skills. That's what I've done, and my grouping of material is a bit hodge-podge at the moment because I took material from such a wide range of sources. It includes a lot of material that is visual-spatial in nature, and hence more "mathy", together with more verbal stuff like analogies.

If you want to explore critical thinking, I recommend checking out the Critical Thinking website (although I'm not hawking their wares and am suggesting this just as a starting point), and Amazon for logic books for kids (although I'm not shilling for them and suggest their website just for its great search engine). Mindware.com is another okay place to start poking around. Critical Thinking offers a bunch of now-classic stuff like the "Building Thinking Skills" series, "mind benders", etc.

Yes, you've hit the point spot on, Colinsmum. The problems they give are so much more complicated.
Our problem is that she's mathy and my husband is mathy, but she and I are very visual-spatial and he thinks that using manipulatives is for non-mathy people. He will do all the teaching in a few years, but I think math-phobic me is better with the basics. It's like fluent readers forgetting they used to use phonics and trying to teach kids with whole-language. For example, she had not caught on to the tricks for mental arithmetic like making tens/fives and estimating. Until I sat down last week and showed her with manipulatives, then we did some problems written down and now she can do them mentally. I think he has forgotten how he got to his feel for numbers.

I was showing her how to simplify fractions the other day using multiplication tables, but I think she was rote learning it.

Luocounu, I know she'll be fine whatever, but she gets such a kick out of new cool tricks!

This completely reminded me of my mother! She is incredibly math-phobic, outsourced our homework questions to my dad when we were kids - but wow, in a department store, she was the queen of the 40% percent off. She could calculate percent off, tax, whether it was worth the sale or use the coupon. It was astounding!

DeHe

There's no harm in skipping around in a curriculum, as long as you teach depended-upon concepts before dependent concepts. That is, you can create your own order as you go.

I also just discard things entirely from the curriculum. For example, I haven't taught my son much about measurements. The NH state standards require teaching about liquid measures, etc. beginning earlier than third grade, IIRC. Though my son has done a lot of work with fractions already, I just didn't think it was important to teach him the relationship between quarts and cups. It wasn't a foundational skill for anything else, and didn't increase his math knowledge, but was rather a real-life skill that tends to be lumped in with math because it uses math, and might provide some concrete examples for practice.

I just think that you shouldn't let the fun looking-ahead stuff take up too much time, since it will be to the detriment of other stuff that might need more time to absorb and is holding up whole areas of development.

BTW I probably misused the term "relative weakness". I think that some things are inherently much easier to understand and learn quickly, especially for an abstract thinker, and that the ease of picking these things up might bear no relationship to their place in the curriculum. It might be that coordinate graphing appears so late in some curricula just because the authors didn't find a way to stick it in earlier, and/or didn't think it would be hard to pick up quickly, and/or didn't see the need to introduce it until just before dependent concepts.

So failure to come up to speed as quickly in other areas might be quite natural, and even in line with the intent of the curriculum; they include that stuff earlier and spend more time on it because it takes time.

I really think you should check out those workbooks. They're really fun, and you can find plenty in them to stimulate your daughter. And I guess I wouldn't shy away from teaching her whatever she wants to learn either (for the record, I let my son zip ahead on a range of different graphing too). You just have to realize that you're maybe creating a bit of a mess for yourself in keeping track of what's been done and what hasn't, but it shouldn't be insurmountable at this stage.

FWIW I think that's the greatest benefit of an online learning website: it can record your progress in different areas. That's how I use IXL: I can look around and see what we've done, and what hasn't been done, which lets us skip around to our heart's content.

As to rote learning, I am actually spending a few days focusing on that. We initially sped through the times tables in a couple of nights, which left my son with a lot of math facts which he started knitting together, but without the instant facility that would speed up doing other math work. Now we're going back and painstakingly doing each number using a couple of "Math Mammoth" techniques (thanks La Texican), noting interesting number relationships, etc. and not going on until he's rock solid.

So we did one night on 8, then one night on 7 and 8 (with the latter just sped through super-quickly for reinforcement), then one night on 6, 7 and 8 (with the latter two sped through). Tonight we do 5, 6, 7, 8, and 9; then tomorrow, 4-9; then Sunday, 0-12. He has never had trouble remembering any of the facts for 3 and below.

I usually don't encourage my son to rote-learn anything, but for multiplication I just think it will increase his processing speed a good deal on a range of problems. So far the plan is working: we spent about 25 minutes last night doing 6-8, and tonight anticipate spending about 30 minutes on 5-9. He is enjoying it because he knows he's working towards a goal of being flawless on multiplication, to the point that he will never have to memorize it again. Then we're back to the mega-fun stuff.

No help to your question but if you purchase the books from Rainbow Resource before 12/16, you will get free shipping (on orders $25 or more). RR has very low prices.

Thanks, mamja, that's an awesome deal.

Iioconu, I posted about those workbooks on here, we love them.

OMG. You were the one that got me hooked on those. Disregard... and you should be ashamed of yourself. I'm like an addict for those things now, never mind DS5.

I thought about your issues some more, and realized they are the same ones I'm facing right now, partly. How do you order activities for an asynchronous little one, while letting them pursue their interests too? I think that's why I started scanning everything in, so I could easily change the ordering on things.

I have a file-system folder of gigabytes of electronic documents, and they're organized by area, level, source, and description. I can pick and choose certain things out of their natural sequence, and move them so that I don't hit them again later, and move things out of the way that I think he'd find boring too. I can also put things aside in a "skipped" place to revisit later (I may not actually ever use them, in which case I put them in the "done" place).

So if you were to do something like that, it would take cutting out the sheets from the Singapore Math books, but you could combine them in one place with material from other sources and reorganize to your heart's content, and keep track in a less messy way, maybe, than shuffling paper or keeping notes.

In any event I hope I didn't come off as lecturing before. I think it'd be wrong to deny your daughter the chance to do what she likes best, and I can think of plenty of avenues of investigation her interest in coordinates and geometry, for example, could open up for her.

Ioucounu, that's dedication. We just leaf through the worksheet books and pull out one that looks fun/interesting. With the curriculum I'll ask her what she feels like doing that day and take up where we last left that topic. She needs to practise her writing, like most five year olds, so I like having her write answers.