Gifted Issues Discussion homepage Forums General Discussion algebra question--> really really dumb

forgive me I am not mathy and this may be quite laughable to many of you but humour me

are these examples of algebra?
9 + 8 = ?
5 + x = 10
my understanding is that algebra is the use of symbols to solve an unknown (in these cases the use of a question mark or an x)

I was trying to have a conversation with DDs' teacher about progressing them in algebra and her response was "but we don't do algebra in Kindy and unlikley to do it for many many years yet". Yet isn't using a question mark or an empty box to denote a numerical value that needs a solution algebra? isn't the teacher already doing algreba with them (albeit in it's most basic form?). If DD6s' read a math problem and then simplify it to 5 + empty box = 10 and then solve the empty box are they not using algebra?

OK, I'm ready to be laughed at now

I think most would classify it as either "elementary algebra" or "pre-algebra". Technically single-variable equations do fit within the definition of algebra, but I guess I agree with Dottie it is misleading to say that a kid doing such stuff is "doing algebra", unless one explains what one means. Since you and the teacher both knew the context, I think you were technically in the right, but the teacher was also in the right going by the normal idea of what algebra entails.

thanks guys
and thanks for not laughing too much

so, in order for one to quote "junior is doing algebra" can you give me the most simplest example of what would be accepted as algebra (hides head under blanket feeling very embarassed for previously saying my DD's can do basic algebra"). I guess what I mean by it is if DDs' read a math problem such as "Penny has 4 flowers but needs 12 to make a bunch, how many more flowers does Penny need?" and the child choses to solve it by doing
4 + x = 12
x = 12 - 4
x = 8
as opposed to how some children would solve the problem by drawing pictures or using their fingers
then I call that "Junior can do algebra"

ok, ready for more laughing

I would call that "elementary algebra" or "pre-algebra", maybe. Google, Wikipedia etc. have definitions of algebra, elementary algebra, and pre-algebra so you can see the rough types of activities that would fall in each (and like ColinsMum posted below, the divisions are context-dependent and may not always make sense). The issue, and I suspect the sticking point for most people on calling this full-blown algebra, is that this is just a simple sum problem that kids can solve without algebra. I guess if your daughter uses a calculus method to solve it, though, you could fairly say she's using calculus!

It sounds like the teacher may have decided that you're simply a pushy parent, and that you're getting some push-back as a result. That's a tough one. If you want differentiation for your daughter, you may have to go over her teacher's head, get some testing done to support your case, consider switching schools, consider teaching your daughter the advanced materials she may need, etc. I am currently in the middle of trying to get some acceleration for my five-year-old son who's enrolled in public kindergarten, and it is slow going.

ETA: By the way, I made the same mistake a while back. I understand that it is exciting when you see your kid learning such things for the first time. I think ColinsMum's advice is entirely sensible, that it's better to talk about the types of things your child can do than to get hung up on labels.

It's terribly context-dependent - in my native context "algebra" starts with group theory, but that's not a context relevant to you... As I understand it "algebra" in a US high school context starts with "Algebra 1" which follows on from a thing called "pre-algebra" which is not itself considered to be algebra (although what the qualitative difference is, do not ask me :-)

Art of Problem solving has useful pre- and post-tests for its courses, which include Algebra 1. Here are a couple of questions from their *pre*-test for Algebra 1 - that is, these are questions you are supposed to be able to do before you are ready to begin what the US calls algebra (they themselves count as "pre-algebra").

2. Solving linear equations.
(a) Find x: 31x + 24 = 365.
(b) Find n: 7n - 4 = 2n + 16.
(c) Find y: 3(10 + y) = 81.
3. Working with variables.
(a) Expand the product 9(3x + 7).
(b) Simplify: 7a - 5b + 3(6a + b).
(c) Simplify: a - (-7a - 3).

At any rate, these are basic enough that I think it's fair to say that if Junior *cannot* do these easily, you should *not* be saying that Junior can do algebra. Really I'd suggest that it's probably not useful ever to say "Junior can do algebra" - much better to say specifically what Junior can do, either by specific skills or by reference to a particular syllabus.

This may help with referencing specific skills. It's information from the MAP test which shows different algebra concepts for different RIT levels. If you click the boxes for Math RIT levels 151-160, 181-190, 221-230, and 261-270 you can see the different skills for the different levels under the 2nd major heading "Patterns, Functions, and Algebra."
http://www.powayusd.com/projects/EdTechCentral/lladder/RITScore.asp

Don't worry, allpink - I'm not mathy at all, so all this jargon makes me befuddled at times, too. Ds7 is working on EPGY, and they were talking about lines, rays and segments - I swear these things didn't exist when I was in school Thankfully, it all seems to make perfect sense to him. When I was in school (in the 70's in England), we did "maths" - it wasn't split into different components, it was all just "maths" - life was so much easier back then
On another note - he does "Hands on Equations" through the gifted program at school - would that be a form of algebra ??

At my middle school, our textbooks would consider x+7=12 to be "pre-Algebra" because it is easily and quickly calculated without any rearranging of the equation, does not require advanced calculation. Many kids could do it in their heads if they weren't worried about that elusive x in there.

Algebra would be problems like ColinsMum has posted. We also include fractions in there where the variable is the denominator or where there is a variable on both sides of the equation. We also consider graphing equations and graphing inequalities to be Algebra.

See - I am so dumb, I don't even know what calculus is. Like I said before - when I did math, math was math, nothing was split into different definitions. I have a whole lot of leanring to do to keep up with ds

For me, algebra connotes the solving of a system of equations, such as 3x+9=y and 2y-5=7... I guess that the question marks or letters are some "pre-algebra" thing so that kids are used to seeing that form of problem before algebra? I've also heard about "differential equations" in seventh grade math, but it has not referred to solving a system of equations with more than one derivative present.

As for calculus, the way I learned it as "independent-study math" was that it dealt with analyzing the behavior of functions and families of functions (limits, derivatives, integrals, sequences and series...).