I recently had a discussion about the order in which math should be taken. Way back when I took Algebra I, then Geometry, then Algebra II. Apparently some schools do Algebra I, II, then Geometry. Does it matter? Is any particular order recommended? I have DS in Algebra 1 now and assumed I would have him take Geometry next, now I'm not so sure.

(homeschoolers included - what order are you following)

My kids are too young to have this discussion yet, but I had no acceleration opportunities before high school. So I took Geometry and Algebra 2 the same year. If I remember correctly, it was totally fine to do them together and it would have been fine to do them in either order as well. I went on to get a BS in math (and comp sci) so I wasn't too scarred from that experience (I am a bit scarred by my whole elementary school experience, but that's another story!)

We're not even trying to go in the "right" order, so take this with a grain of salt, but the geometry we've done so far (and what I remember from my own education) requires only the most minimal of algebraic skills. I mean that it is of the 2x+1 sort that most HG+ kids understand innately, without any real teaching, even from a very young age. DS7 has had no trouble with the algebraic parts of the geometry we've done so far.

Theorems and proofs require logic and problem-solving skills that algebra might help to develop, but I don't think there's any general necessity to have algebra 2 before geometry. I think that's just a personal choice or the choice of the school system.

I freely admit that I could be wrong, however!

Another caveat: I'm sure it is possible to introduce more algebra into geometry, especially in terms of area, circumference, etc. So if your school suggests taking alg 2 before geometry, I think I would respect that unless you have a good reason not to. Better safe than sorry.

Well, I'm pretty sure this meandering post doesn't help you at all. Sorry!

kriston: what geometry have you done so far? have you put this together or are you using a currciulum?

Dazey

Like Kriston, we're not even trying to do the standard math order... so maybe two grains of salt

To start with, the curriculum we're using (as a "spine" -- not as our be-all-end-all), is Singapore NEM. The pattern they follow is two years of alternating Algebra and Geometry (approximately a half-year of each, each year), such that at the end of the two years you've finished Geometry and something close to Algebra 1 (their algebra sequence isn't quite the same either... so there's a little Algebra 2 in there, and also a little Algebra 1 missing). Then we complicate it by supplementing with a bunch of other stuff and messing about with whatever we feel like, so our sequence so far has been:

2007-08 Algebra 1 (using three different sources - eek! and skipping around in NEM 1 & 2), a little geometry (reading Euclid, playing with Zome), and dabbling in statistics and programming.

2008-09 Statistics (and some SAS programming), a little geometry (Zome with a group), and dabbling in Algebra 2. Wish us luck on this one -- he's been playing around with Statistics long enough and he's solid enough in the rest of his math that I think we can do it, but it sounds ridiculous, even to me.

2009-10 (subject to change of course!) finish formal Geometry and Algebra 2, and maybe do a little more with the Stats depending on what he thinks of it all at the end of next year, or maybe a little programming.

2010-11 ...uh.... good question. Probably something that would count as Algebra 3/ Trig/ Precalc. Maybe some more Geometry too...

All this is colored by his being ridiculously young for any of it, and IMO too young to "specialize" for a whole year in a single topic. (Not that there's a magic age for that, just that I think he's not ready yet.) So we dabble. And although Statistics isn't traditionally part of the whole curriculum (and definitely not usually done before Algebra 2), the "dabbling" contingency means anything that turns up in Statistics that he can't do with what he already knows (and my recollection is that there isn't a ton...) we can remedy on the side.

It's not something that I would necessarily recommend if I weren't homeschooling, just because of the dozen ways it could go wrong if you're not on top of it to anticipate issues. For instance I would hate for him to find himself adrift in Statistics because there was one little quibbly point, formula, or vocabulary that didn't make sense because of a gap in his earlier math education. But because we have the flexibility to change courses mid-stream, or to take a week off and remedy a gap, this way has been great fun in a flying-by-the-seat-of-your-pants kind of way

I've already shared specifics with CFK, but in short, our higher two "tracks" do algebra 1, algebra 2 and then geometry, while the lower two tracks do algebra 1, geometry and then algebra 2. I think the reasoning might be tied to the PSAT/SAT testing. Order doesn't necessarily matter for the higher tracks, but this allows the lower tracks some of each subject before the big tests. (The lower tracks don't start algebra until 9th, and the lowest track does algebra 1 over the course of two full years.)

I really don't think the order matters, as geometry seems pretty stand alone to me. FWIW, our elementary kids get a very heavy dose, and I'm looking forward to learning what more the high school level has to offer. DS in particular seems incredibly strong there already.

Our school allows alg 1 in 7th, geo in 8th and then alg 2 in 9th. This is for kids who pass a test in 6th to be able to start this sequence in 7th. That is the class order they always go in no matter when the sequence is started. I think Dottie is right that geometry seems pretty stand alone, so I'm not sure it matters where it comes in.

We usually have Alg 1 in 8th or 9th, Alg 2 in 9th or 10th, Geometry in 10th or 11th. I like E&C Mom's earlier start order.

I'm using Painless Geometry by Lynette Long. I have no idea if it's hated or well-respected or what; it's just a book I found on the library shelves among lots of other books when I was looking for geometry materials. I flipped through the armful of stuff that I found, and I liked this better than the other stuff. It seemed to fit where we are.

It is more experiment-based than the other materials I found, so DS7 can see that what the book is teaching is true. I like this problem-solving approach. It is real geometry, not the "this is a triangle" stuff that passes for grade-school geometry. It uses theorems and even proofs, but it doesn't get bogged down with them, as I remember geometry doing in my jr. high class. It's more gentle. (And BTW, I liked proofs, but I can't imagine asking a 7yo to slave away over them!) It moves at a fairly easy pace. It doesn't have much arithmetic or algebra (we're on page 95 of 300 or so), so I don't have to require that he memorize his times tables yet. If there is a workbook, I didn't get it, so it doesn't require that DS7 do workbook problems. That's a plus right now. It has challenge problems fairly regularly spaced through the chapters that stretch logic and make him really think about how the figures work, what the rules are.

I'm babbling a bit, but for a 7yo visual-spatial kid who is ripe for math but not loving arithmetic right now, it's been an astonishingly good fit.

And I'm with Erica: I like that we can jump around and follow our noses, weird though it may seem. I know we'll have some gaps as we go along, given that we're doing geometry before we do long division. (!) But we have plenty of time to spiral back around and fill the gaps in as we need to. I'm not worried about it. Heaven knows, DS7 is learning and loving to learn! What more can I ask for, really?

Does that answer your question, Dazey? I feel like I'm just rambling incoherently...

We have an "integrated" curriculum where they do some of each every year. So my son is in the first year of the 4 year high school sequence and he has done some algebra, some geometry, some statistics, some probability, some trig. They will go into more depth on each of these and add other topics for each year. In some ways it isn't a bad idea, except it really causes problems if you move in our out of the district because the kids are way out of sync with the rest of the world!

My dd's school offers the following sequence after lower school math: pre-algebra, algebra I, algebra II, geometry, pre-calculus, calculus (the pre-calculus and calculus are usually a class of one or two students that are really advanced in math) in that order. We have excellent math teachers in the middle school and are getting a math specialist in the lower school for next year. Kids are also allowed to choose Math as their LEAP class (Every wednesday children decide what subjects to study and they spend 4 or 5 hours of the day in their chosen subject).

DOK, bianca!

You know, sometimes I think you're just making that school up to haze the rest of us. :p

Hi Kriston,

You will just have to come and visit!!

It's kind of a long commute...LOL!

If I was building my dream school I would have every day like this. Each day could be a different subject so you could really go into depth.

As far as math order, it sounds like it doesn't really matter what order DS progresses in. He's is enrolled in the AoPS Intro to Algebra class in which we just heard from the instructor that it is supposed to cover Algebra I AND II, so I guess my dilemma is solved anyway.

I just heard another "order" for math. As a child, I had official trigonometry after both algebras and geometry. For us, it was an 11th grade course (fast track) called "precalculus". The local schools seem to have a similar lineup, though they specifically call it precalc/trig. I've also heard it labelled algebra3/trig.

Well, a friend just told me her school offered trig with algebra 2. DD13's text does have some intro trig in it, but I think they only touch on that, if they get to it at all.

So...is my assumption that "late" trig is the norm off base? Or is my friend's school the unusual setup?

All said and done, it probably doesn't matter all that much, but I would think trig the way I know it would depend on a nice strong algebra foundation, including that "precalc" stuff.

I'm also wondering if The Almighty Spiral wasn't around for longer than we think, LOL!

Algebra 1
Geometry
Algebra 2/Trig ?
Pre-Calc/Trig ?

DS has been a lab rat for the past three years as he is always in the class that the school has just added. Last year in ALG 2 was a disester. Teacher teaching it for the first time, not all the kids up the the level, change in state curriculum etc. As the result, they did not cover half of the material.
This year, DS is supposed to have a totally new, level IV teacher for his pre-calc class and rumor has it there will only be two students in that class. If this is true, they will be able to cover both Algebra 2 again and Pre-calc. I have a feeling though that the school won't let that happen . We will see.
Have alook at this:
http://www.artofproblemsolving.com/Resources/NCTM08talk.pdf

My daughter’s school has placed her in Advanced Algebra 1 for next year. The three possible placements for freshman include Algebra 1, Advanced Algebra 1 or Advanced Geometry. The projected progression for her is;

Advanced Algebra 1
Advanced Geometry
Advanced Algebra 2/ Trig
AP Calculus

We were a bit concerned about her having to repeat Alg 1, but since our son has been participating in the online Introductory Algebra class through AoPs, we realize that she hasn’t yet been trained in depth for the problem solving aspect of algebra despite her computational proficiency.

It's all in the name Delbows! I was "shocked" at first to find your regular progression for high school starting in just algebra 1, but then realized you end up at the same place, LOL! I imagine there's a good bit of overlap in our (yours and mine) freshman algebras and junior trig/precalc.

Here's our projected progression for DD13, a rising freshman...

Honors Algebra 2
Honors Geometry
Honors Precalc (trig)
AP Calculus

And you are so right about classes like AoPS having more depth! Hopefully both your "advanced" A1 and our "honors" A2 will give some similar depth.

I'm still nervous about AP Stats with DS next year, and those AOPS books are my "plan B" -- especially the counting/ probability book, since it would fit well with the subject. I'm on the verge of just buying it anyway.

My DH took her to the placement exam which sounds as if it had lots of AoPs type questions. DH said more than half the kids left the exam within 15 minutes with explanations to their parents that the test was brutal. DD at least stuck it out and didn’t seem traumatized.

The AoPs class has really put it in perspective and given the school’s stated purpose of providing fast pace and problem solving depth in Advanced Alg 1, I believe the math dept made the right call!

I agree with you, Dottie. I guess this class name issue is why most schools rely on their own placement test for math, in particular!

KAR,
Why are you nervous about AP Stats for your DS?

Well.... part of it is his age (still just 8!) although that's not a really good reason.... Part of it is that we're heading that way on his suggestion and I wonder if he really knows what he's asking for... and part of it is of the half dozen or so books I have, only one of them looks like "fun" -- I'm a little nervous that he'll find it tedious even as it's within his mathematical grasp. I just think it might take a lot of tweaking on my part to keep the pace, workload and interest all doable, just because they're aiming for nearly-adult college freshmen here... not little boys, no matter how good at math.

On the plus side, if we're throwing in SAS (and I think we are...) that really cuts down the tedium quite a bit and picks up the pace, while giving us a side-track in programming that we can switch back and forth to without completely derailing... The AOPS stuff I think might be more interesting too (again without slowing us down really, or losing our train of thought), so I'm thinking that we might dabble in that along the way. And then I can throw in some database programming on the side, which contributes in a slightly different way.

Basically I'm nervous of how much work it's going to be for me to make it all go together, and I'm tempted to just chuck it all and go with the AOPS book as-is. I think if we can swing it we'll do much more and have more fun with the whole statistics shebang, but if we can't swing it, I'm nervous of it just collapsing around us. kwim?

Erica,

My son is 3 years older and will begin Alg 1 next year in 7th grade, so it is hard for me to imagine an eight year old near the end of the high school math sequence! He is lucky that you are so well qualified to home-school him in that subject. Will he begin college within the next couple of years?

The Introductory Algebra class is so impressive that we plan to have ds11 do the Counting and Probability courses with AoPs next, assuming his new school schedule allows it. You could probably get through it extremely fast given your son’s ability and your home-schooling flexibility.

Hi Erica, My DS9 is in the exact situation--almost. We are planning AoPS Counting and/or Number Theory this year, and DS is taking Stats (because the middle school cannot guarantee High School credit for other course so they decided to offer something the HS's don't offer). I have a little concern because I've always thought of Stats as dull. My backup is that if after the first month DS isn't thriving, we might have to switch to online course or something else.

delbows, it does intimidate me to forge ahead when they're so young (I think of how much info I forgot from age 8 or 9 versus 12 or 13). But, I have to believe that moving forward is the right thing, right?

My DS is taking that course and we are equally impressed. It's not like any Algebra I class I remember taking! We're undecided about which course to take next. Right now we are considering the Intro to Geometry class. According to the AoPS founder it is supposed to be the more diffifcult of the Intro classes. After watching the Albegra class whiz through the material I can't imagine what "more difficult" could be! We intend to enroll DS in all of the Intro courses.

Cym- are you homeschooling the AoPS courses or is your DC online also?

Well, what's the alternative? I honestly don't see one! If you're doing problem-solving type stuff, you're already going deeper, not just faster. Short of not doing math for a while, you don't really have an option, do you?

It's scary--just thinking about it makes me nervous--but if you're sticking even a little to the traditional math path, I don't see any other option.

I agree that forging ahead is the best option for many of our kids. If they enter a mainstream high school in the future, some courses may have to be repeated for credit, but the subject familiarity from their earlier exposure will serve them well in earning top grades.

I have been reading the book, “What High Schools Don’t Tell You” by Elizabeth Wissner-Gross. I am interested in the math and science talent development information rather than some of the more contrived tips. The advice for math seems like the next steps following “Developing Math Talent”. Essentially, I now understand that excelling in the school math sequence in never enough for distinction beyond a very small area! My son is learning this lesson well with his AoPs class- he is defiantly not the smartest in that class! Obviously to some it is still too easy, but many of the fastest students have “trained” for math similar to our summer swim schedule which has meant up to three times in the pool on some days!

Hey Delbows, did Grinity hit you up too or did you find that book on your own? I'm reading it myself, though not with great haste. The math stuff was a little "scary" in many ways. DS is going to go down as a legend in our small town, but does he have what it takes to play with the Big Boys?

I found it online and purchased it primarily because it listed specific science competitions which I would never have heard of other-wise.

Well thanks for the reminder Delbows....my library copy is probably due any day now, and I've been meaning to order a permanent copy, as it is full of great info that I haven't yet gotten through.

Dottie, I know I told you before, but you've really, really got to have your son try one of the AOPS courses when you think he's ready for the "online" portion of it. (or when you've run out of math in the high school!) They really are great for math loving kids. And AoPS lives for competitions if that's the direction you're headed in.

Thanks....we're strongly considering the October Algebra class!

Well... I don't think of him as being really that close to the end of the high school sequence... He's finishing Algebra 1 as we speak, and everything above that is dabbling and not solid courses. Algebra was dabbling at first too, but this summer I finally put my foot down and said he needed to finish the book so we could get on with it. LOL So... he can handle random stuff up to Precalculus-level questions thrown at him, but he doesn't have the vocabulary or the standard formulas memorized or anything, and there are gaping holes in his post-algebra-1 knowledge.

Introductory Statistics is mathematically pretty straightforward (no calculus), and fortunately I find it fascinating (geek that I am... LOL) so it's more of a rabbit-trail off from the standard sequence rather than a neat linear progression. And honestly I prefer it that way -- we've got the time and there are plenty of roses to smell here, so I think we'll take the long way around.

My only real concern is the age-appropriateness of the texts. How they take such an interesting topic and suck all the life out of it... He did catch sight of my Cartoon Guide to Statistics and wanted to start immediately, so maybe there's hope through that! LOL Or maybe I should write my own curriculum... you know... in my vast quantities of spare time...

I want to put a plug in for mathematical browsing and studying the same material through different courses and texts. Karl Bunday introduced me to the idea of repeating material this way, and his son is very, very strong in math. I've been doing this with my kids, so our linear progression doesn't sound all that impressive, but my 11 year old has a very solid foundation in math. He took geometry as an eight year old, because he had an interest, and just retook geometry this year as an 11 year old. He's done a lot of tangential learning in math, which has enhanced his enjoyment of the topic. His math scores are consistently in the top rank for our state. So don't feel that you have to push your kid through the typical progression asap. It isn't a bad thing, if that's what your child wants, but there are benefits to wandering along the garden path!

Oh, I SOOOOOO agree, Lorel! I love, love, LOVE this way of thinking! I suspect it's what the spiral curriculum aspires to be, but doesn't usually quite reach. It's why we're doing calculus and physics this year, with our highly conceptual but not very arithmetic-y 7yo.

Give 'em a real challenge, let 'em get what they can, then give it to 'em again a little harder in 2 or 3 years. I think it's brilliant!

Thanks, Kriston. It's nice to have such distinguished company!

Awww...

Of course, given that you're one of my mentors in homeschooling, holding my hand more than once through some drama or another, it's not surprising I'd agree with you!

I like the rabbit trail approach just because DS and I are both so distractable. We homeschool with the "ooh look something shiny" method.

ROFL! I hear that!

It's so nice to be able to shift gears like that though, y'know? (And I know you do!)

LOL, we seem to live our lives that way.

There are worse ways to live! Shiny things are pretty!

My uncle used to call it the follow-your-nose method of learning. It allowed you to start the day in one area of the library and finish it in some apparently unrelated area, even though each connection along the way seemed to make sense. Like Kriston said, there are worse ways to live...

BB

I tried to get highly organized for this year, and Lorel had to talk me down from a near-nervous-breakdown. Too much planning is not a good thing for some of us/me. I function better with a little serendipity, a little laziness built into the system.