I seem to recall reading somewhere that even gifted kids generally shouldn't start algebra before age 10 (maybe in the developing math talent book or on the CTY website).

Curious about other people's perspectives on this.

Cat

I hadn't heard that. I'm kind of inclined to think that like foreign language, anything introduced early is easier. My DS7 is in pre-algebra now, so will have algebra at 8. I'll have to see if I can find any research on it but I can't imagine trying to slow him down.

The hardest part of Algebra is the word problems. If a child can translate the word problem into a solvable set of equations, then they should be fine. This does require verbal abstract reasoning which is a different skill from manipulating symbols.

My DS10 started algebra informally with me around his 8th birthday, and then went into a serious course in school at age 9.

I wouldn't say it's been too difficult for him at all. For example, his total algebra exposure over the summer break was ten days of review right before school started (around an hour-ish per day). He tested into the next level with a high score on the pre-test. So he obviously didn't forget it, which I would have expected if he'd been too young for it.

So, FWIW, that's one anecdote in favor.

Val

My 9 year old is doing algebra right now. The thing I've found is it's a very good thing to be able to write out diagrams and steps to longer problems. And just to have the patience to weed through them. The last few Singapore books really pushed this point. Which made me very glad we used Singapore! Singapore is nice in that it encourages deep problem solving skills, especially if you use their extra materials. So it helped slow us down a bit.

My own kid has understood many algebra concepts for a long time. But now his writing skills and maturity have caught up in such a way that I feel comfortable diving into a "real" written algebra curriculum. Every kid is different, so I guess I'm not comfortable with the 10 and up statement. YMMV. Had we done something like an online curriculum I'm sure we would have gotten here sooner.

I recall hearing this before, and I believe that the reasoning was that children are not developmentally ready for the abstraction of algebra. If I recall correctly this is why my gifted classes didn't present pre-algebra before age 11 (when I was in 6th grade).

However, I know that DD's elementary curriculum specifically exposes kids to some algebra concepts as early as 1st grade.

I'm not sure if the original idea was based on Piaget's developmental stages or not.

Yes, good point.

DS had a harder time with the word problems than the manipulations last year. This year...wow, what a difference. Last year I had to help him a lot. So far this year, the pattern is that I give him a quick explanation of one word problem and he does the rest on his own. So something definitely sank in at age 9.

Val

What I've seen working in middle school is that I think students have not been introduced to algebraic concepts EARLY enough! They're afraid of "x" by the time they get to 8th grade. Algebra looks like a foreign language and they don't realize they've been doing "what plus 5 makes 10?" for many years already.

My own DS is 7 1/2 and I'm teaching a pre-algebra pull out at his school. They're all excited to be free of adding two digit numbers.

My DS finished algebra at 9 and I didn't see any difficulty with abstraction. This kind of argument always seems to imply that kids develop at the same rate, but they don't.

Thanks for all of the insights and the stories of younger kids having no difficulty with algebra. I used to play with my DS with the refrigerator number magnets and make the numbers jump back and forth on either side of the equals sign (we called it "making the numbers do tricks"), showing how they would change and he thought it was hilarious at age 2-3. At 5 he was very comfortable with concept of solving for x in simple equations (x + 2x or x -4 = 5 type things, although we tended to present in word problems around the dinner table) and I just don't see what is so different or difficult about algebra that it would be verboten until he is older.

kimck, did you use the must know Singapore math word problems. I really like them and the fact they are generally compound questions.

He has done Fred decimals and fractions, maybe time to buy the Fred algebra (or is there pre-algebra?) book to introduce the concepts?

Thanks again, Cat

I recall that it is a developmentally ready issue too. I think someone who teaches algebra can test to see if a child is developmentally ready instead of just assuming readiness or not based on age. I think the readiness age could just be used as a typical guideline.

I would look into what criteria concludes they are ready. Let us know if you figure it out.

I think I figured out where I saw it - the author of Life of Fred books says something along those lines on his website.

I'm wondering if that is why he has the "pre-algebra + biology" and "pre-algebra + economics" books now, in order to slow the progression toward algebra?

Does anyone have any experience with either of these two pre-algebra books.

And just what the heck is pre-algebra technically? I guess I better start studying our school's curriculum again.

Cat

We used Hands on Equation last year and ds8 had a blast! It explains algebra by using pawns and dice. We also got the word problem book, which posted some challenge for him

Exactly, I've never understood that either. One of DS6's favourite games when he was 4 was "secret number sums", e.g. "The secret number is called x and the clue is that x - 4 = 5". He's actually found algebra one of the easier aspects of maths to absorb, e.g., when I look at syllabuses I tend to find that he's done much more of the algebra on the syllabus than of, say, the data handling. And it's a great area to be really secure on. E.g., he's been filling in a percentages gap just recently. The textbook (presumably because the author thinks of algebra as something that might scare readers off) presents each type of percentage problem separately - so that someone following that method has to keep remembering what number goes where in this particular problem type - but DS tends just to write an equation with an unknown for the thing he's looking for and then solve it, which means he only has to know what a percentage is, what the words of the question mean, and how to solve the equation, IYSWIM.

This is a great question. I had a hard time figuring out if we needed pre-alg after Singapore 6B. With LOF, I felt like we could have jumped right into algebra. I have LOF Algebra here, but DS was balking at the format. He really likes the Singapore format. So that led to us starting Singapore new elementary math series (after looking at a bunch of curriculum).

We did use some Singapore word problem books, and sometimes I'd have DS do the problem and I'd set it up more algebraically on the side. At this point, he can do some algebra set up and certainly understands it.

My dad and I went through algebra when I was pretty young, and I understood most of the concepts and operations. I didn't go through prealgebra first, and, frankly, pre-algebra still doesn't make much sense to me in the context of learning algebra. I think the guidelines are just a rough estimate and can be considered your-mileage-may-vary with gifted kids (especially hg or pg)...

My son started learning algebra at age 4, even before starting to learn multiplication and division. I don't believe in the idea that children aren't able to think abstractly enough to learn algebra until roughly age 10. Once you get over a few basic concepts (what a variable is, what an equation is, etc.) you are ready to begin in earnest.

EDIT: OP, I agree with BWBShari, CAMom, and ColinsMum (and you). I think that thinking abstractly is actually one of the most important things to introduce early in any course of study. I want my kids to have an instant reflex for abstraction when they encounter something new.

Just a quick chime-in because I agree that you don't have to wait for a PG child who understands abstract thinking....

DS6 is only at GL 3.5 on EPGY, but I love that they have him practicing algebraic equations and teaching how to substitute equations and solve for the variables. When he started a few weeks ago, he was at 3.0, and it took him all of 5 minutes to figure out that using letters to solve was the same thing as spaces, question marks, part-whole equations, and everything you'd see in other math programs. Now that he's having to solve with multi-step equations, he thinks it's just a fun puzzle. He is having so much fun with the problems that "algebra" is now his favorite part of math!

For elem. children who like mind benders and that sort of thing, algebra seems like a natural extension.

I really don't see a reason why there should be an age limit for starting algebra. DS8 could solve simple algebraic equations at the age 5 without ever being taught the material. A year later he could understand logarithms.

We moved from Singapore directly to AoPS. I originally planned on doing NEM first, but AoPS Intro to Number Theory seemed like such a perfect match for DS8 that we started that instead. It's exactly the type of math he loves. At one of the DYS parent seminars I asked Richard Rusczyk about doing Intro to Number Theory immediately after Singapore and before Algebra and he had no objections.

So far we've been very happy with the AoPS material. DS8 doesn't take the class, but we cover the material as part of our homeschooling curriculum. We will probably start Intro to Algebra next.

One of my kids did high school geometry at eight (per his request) and then algebra at nine. He did exceptionally well on the SAT math portion at 12, and started college math/science courses at 12. He might have been more radically accelerated, but we chose not to have him rush through the typical math sequence. He spent a lot of time doing things like watching Teaching Company lectures and playing around casually with Life of Fred rather than working in a more linear fashion.