Gifted Issues Discussion homepage Forums Learning Environments Help me identify options for DD9

I've seen her work exactly one multiplication-with-decimals problem on her own, so am extrapolating from there. The problem was 7.1 x 3.4

After multiplying 7.1 by 0.4, she put what she called a placeholder decimal between the tenths and hundredths columns (so one place in from the right). Then after she finished multiplying and adding, she ignored the placeholder, counted the places to the right of the decimal in the original problem, correctly arrived at two, counted two places from the right in her answer, and correctly placed the decimal point. And then asked me if you counted from the right or from the left, because she remembered her teacher having told her from the right, but she wasn't completely sure.

So she's capable of getting the mechanics right, but she has no understanding of why you do it that way. (We had a similar mechanics-vs-understanding issue when we were working together on factoring, and she was astonished that every item on the list of numbers that were factors of 30 could be constructed from the prime factors of 30. She was capable of accurately generating a list of factors, and of identifying the prime factors, but didn't "get" how those numbers were related.)

The AOPS pretest tests mechanics, not understanding. The course IMHO requires understanding. OTOH, I'm not sure that the standard public school curriculum cares one bit for understanding.


I think it's likely that we'd do at least some afterschooling. 6th graders can do MathCounts, too.


In our house, algebra is fun.

AFAICT, our district is moving to Common Core. There's a lot more algebra-looking material in the general math classes.

EPGY Math for grade 1 has very simple algebra problems. My 5yo daughter has solved problems such as

n - 3 = 5
n = ?

but I won't say she can do algebra until she can solve

2*n - 3 = 5

I wonder if presenting arithmetic problems as simple algebra problems helps students in a real algebra course later on.

This seems to be a trend in many math programs today, I believe for several reasons:

1. It encourages thinking about arithmetic operations in terms of parts to a whole, as well as in relation to inverse operations, which can have a helpful effect on cementing memorization of math facts as well.

2. It predisposes children not to fear variables and equations.

3. It impresses people, including many parents, when young children can "do algebra". I've seen some parents bragging on the basis of these types of problems.

I don't know how much the first two translate to increased ability when learning algebra later on, but I think lack of fear is probably helpful.

I wouldn't say DD had great understand either, but after a while of working with the mechanics the understanding kicks in. The public school curriculum is more about mechanics. Supplementing at home for more understanding.

I think any holes in their understanding can be quickly filled with some practice and discussion.

I tend to let my kids enjoy the mechanics of math and the understanding will come.

That's very similar to the questions on the end-of-5th test in our district, where it's not called Algebra until 8th or 9th grade. The exact question uses a table of "n"s paired with outputs, and asks for the formula that fits the table, where 2*n +1 is the proper one.

Going a bit off-topic, and IANAn educational theorist, but I think Bostonian's question would, in some circles at least, be considered a lot more challenging than the one you're mentioning. Yours can easily be done without an understanding of the "do the same thing to both sides" procedure (you ask "what's happening?" and it doesn't take much trial and error to see), whereas Bostonian's can't (so easily). All the same, if I took that definition of "can do algebra" then DS could do algebra at 4, before he started school! I'm not sure I really see that being able to do algebra should count as a milestone, however we define it - it depends too much on what algebra you mean!

Yes, it occurred to me after the fact that that was likely the case.