Which AOPS course?

[lisabees]

Ds is about to finish Algebra with Derek Owens. Overall, it was very easy for him. He would like to try AOPS. He's never been stretched in a math class before, but he does love alcumus.

 

Should he repeat algebra or move on? Of course, he hates the idea of repeating algebra when he completed Derek Owens in 5 months with a 98 percent.

 

Thoughts?

[regentrude]

If eh wants a course, have him try the algebra 2 course.

It is the second half of the Intro to Algebra text and covers material not usually included in algebra 1.

 

Alternatively, I would buy just the book and have him look at it; he may find interesting stuff in the first half of the book that his course did not cover in as much depth.

[Kathy in Richmond]

Since both algebra 1 and algebra 2 are in the same AoPS introductory algebra book, you'll need to get that text regardless. What I'd recommend is to have him spend some time working through the end of chapter algebra 1 material (the first 12 or 13 chapters) , just to check for gaps. AoPS has a wider scope than standard courses (I'm not sure how it compares to Derek Owen's class, though). Also have him do a selection of the end of chapter challengers, too. Then he should be ready to tackle one of the other introductory AoPS classes: algebra 2 (= the latter half of the introductory alg textbook), counting & probability, or number theory. Geometry is the most challenging of the bunch, and it's generally a good idea not to start AoPS with that course, but ymmv!

[lisabees]

Thanks to both of you. I will order the textbook. Great idea to work through the end of chapter material!

[redsquirrel]

If he finished Algebra 1, then you might consider having him check out Introduction to Counting and Probability before he moves on to geometry.. He is in the perfect place to spend some time with that book. They also have online classes.

 

Right now my son is taking their Pre-algebra class. The plan (so far) for next year is he will take Intro to Algebra in the first semester and then Counting and Probability in the second.

 

http://www.artofproblemsolving.com/Store/curriculum.php?

[lisabees]

Thanks redsquirrel. Does the AOPS site list the classes in the recommended order? If so, it would be Intro to Counting and Probability after Algebra 1.

 

In fact, what's the general consensus in the math community about taking algebra 2 before geometry? Why do most schools schedule geometry in between? I realize that the AOPS schedule is different; I am just curious.

[Sebastian (a lady)]

Thanks redsquirrel. Does the AOPS site list the classes in the recommended order? If so, it would be Intro to Counting and Probability after Algebra 1.

 

In fact, what's the general consensus in the math community about taking algebra 2 before geometry? Why do most schools schedule geometry in between? I realize that the AOPS schedule is different; I am just curious.

 

I've gotten a couple different answers on the standard Algebra 1, Geometry, Algebra 2 sequencing.

 

Student maturity. Algebra 2 may require more out of the box thinking.

 

Prep for standardized tests. Geometry scheduled so that the student has completed before taking SAT tests junior year.

 

Reduce the time gap between Algebra 2 and Pre-Calc. If you go Algebra 2, Geometry, then Pre-Calc, the student may have forgotten a lot of the algebra needed for the Pre-Calculus class.

 

 

You mentioned that you knew the AoPS schedule was different. I have to keep reminding myself of that, because it felt a little odd to just keep going in the intro to algebra book. But when AoPS says that their Geometry course is challenging, I'm going to take their word for it.

[regentrude]

In fact, what's the general consensus in the math community about taking algebra 2 before geometry? Why do most schools schedule geometry in between? I realize that the AOPS schedule is different; I am just curious.

 

 

I think one major reason is simply the testing schedule. Students need to take the PSAT in October of Junior year. If they start algebra 1 in 9th, they must take geometry in 10th to have the necessary material covered by the time they take the test. Also, many juniors take the SAT/ACT early in their junior year to have time for a retake.

 

I have heard the argument about "maturity", but that would actually be in favor of postponing geometry, because that is more abstract, with formal proofs, wheras algebra 2 is just more algorithmic stuff similar to algebra 1.

 

I do not buy the argument that "students would forget their algebra by the time they get to precalculus" if they took algebra 2 before geometry: if algebra is taught well, with a focus on conceptual understanding and not just rote memorization of procedures, it is impossible to "forget" the material. Ideally, ALL of math should be taught to long-term mastery and retention of concepts. Since the schools teach poorly and most students never actually understand math (and quite a few math teachers don't either), they need to bank on the short term memory. Not what you need to replicate in a home school.

Also, a rigorous geometry program would actually use algebra and thus keep the skills fresh.

 

About AoPS: definitely complete the entire intro to Algebra book (i.e. algebra 1 and 2) before attempting Intro to geometry. The geometry text is pretty tough and does need algebra 2.

[Sebastian (a lady)]

I think one major reason is simply the testing schedule. Students need to take the PSAT in October of Junior year. If they start algebra 1 in 9th, they must take geometry in 10th to have the necessary material covered by the time they take the test. Also, many juniors take the SAT/ACT early in their junior year to have time for a retake.

 

I have heard the argument about "maturity", but that would actually be in favor of postponing geometry, because that is more abstract, with formal proofs, wheras algebra 2 is just more algorithmic stuff similar to algebra 1.

 

I do not buy the argument that "students would forget their algebra by the time they get to precalculus" if they took algebra 2 before geometry: if algebra is taught well, with a focus on conceptual understanding and not just rote memorization of procedures, it is impossible to "forget" the material. Ideally, ALL of math should be taught to long-term mastery and retention of concepts. Since the schools teach poorly and most students never actually understand math (and quite a few math teachers don't either), they need to bank on the short term memory. Not what you need to replicate in a home school.

Also, a rigorous geometry program would actually use algebra and thus keep the skills fresh.

 

About AoPS: definitely complete the entire intro to Algebra book (i.e. algebra 1 and 2) before attempting Intro to geometry. The geometry text is pretty tough and does need algebra 2.

 

I wonder if the maturity question partly reflects a view of geometry instruction that is light on proofs.

 

It may also be an issue that students who struggled through Algebra 1 can get through Geometry with a passing grade and graduate with the requisite number of credits, where Algebra 2 might not be a course they would suceed in (at least not having just gotten a C or D in Algebra 1).

[lisabees]

Thank you for the insights. Ds is only in 7th grade and will be done with Algebra by next week. He will likely go into a STEM field - physics is his passion. So - let me think out loud here. If he takes AOPS algebra 2 now and geometry and algebra 3 next year (online classes), where does that leave him in the sequence? Can he be too far ahead? Also, are there any concerns with going through these classes too quickly, leaving gaps?

 

This schedule, of course, depends on whether he likes the online AOPS courses vs a more traditional course. That would change the conversation.

[Kathy in Richmond]

HI Lisa,

 

It really doesn't matter whether you do algebra 2 or geometry first with a young student. I did it both ways with my two kids & didn't see different results. I just let them pick which to do first. You could even do both simultaneously over two years (in fact, I'd probably do that if I had a third child :) With AoPS, though, the geometry is particularly challenging, so keep that in mind, too. It wasn't out in time for us, so we used Jacobs geometry instead.

 

For now, why not move into algebra 2 (second half of AoPS intro algebra text) and see how he likes it. I think he'd really enjoy the counting and prob class or text, too. Those Rubiks cubing kids usually love discrete math. :D Lol, he could count all the possible permutations of the cube...

 

I would take it year by year after that. The Algebra 3 course covers the thick Intermediate Algebra text & gets through the advanced algebra part of precalculus (their precalc class picks up from there & covers trig, complex, linear algebra, and beyond). It's a rich and challenging book/course. Whether it's do-able in the same year as AoPS geometry depends on the kid, but it might be too much to squeeze into one year w/o trimming out the good parts.

 

hth!

[Luckymama]

Thank you for the insights. Ds is only in 7th grade and will be done with Algebra by next week. He will likely go into a STEM field - physics is his passion. So - let me think out loud here. If he takes AOPS algebra 2 now and geometry and algebra 3 next year (online classes), where does that leave him in the sequence? Can he be too far ahead? Also, are there any concerns with going through these classes too quickly, leaving gaps?

 

This schedule, of course, depends on whether he likes the online AOPS courses vs a more traditional course. That would change the conversation.

 

Dd is in seventh grade and has recently moved into the algebra 2 portion of AoPS Intro to Calculus (the book only). In the fall she worked through about 2/3 of AoPS Intro to Counting and Probability while studying algebra 1. I stopped her at that point as I felt she needed to get through more algebra.

 

She will be taking the AoPS Intro to Geometry online class (her choice) from the end of March through mid-September (it's their longest class btw). Depending on how the workload is in the summer, she may or may not continue with algebra 2 at the same time.

 

The plan for next year is to finish algebra 2, finish Counting and Probability, and do all of AoPS Intro to Number Theory. She will be taking an entrance exam for a highly-competitive math and science charter school in early December. If she is accepted (she will be subject to a lottery of qualified out-of-district students) she will sit a series of math placement exams that will cover algebra 1 and 2, geometry, probability, statistics, and number theory. She wants to be as prepared as possible!

 

Detouring into Counting and Probability and Number Theory will slow down the race to calculus and broaden dd's mathematical understanding (see "The Calculus Trap" by Richard Rusczyx http://www.artofproblemsolving.com/Resources/Papers/CalculusTrap.pdf ). She has spent a lot of time this year reading math course descriptions on various university websites :)

[lisabees]

 

For now, why not move into algebra 2 (second half of AoPS intro algebra text) and see how he likes it. I think he'd really enjoy the counting and prob class or text, too. Those Rubiks cubing kids usually love discrete math. :D Lol, he could count all the possible permutations of the cube...

 

 

Oh Kathy - it would be fun to watch him count the 43 quintillion ways to solve the cube!

 

Luckymama, thanks for sharing your dd's sequence and for providing the link. It puts things into perspective for me. I ordered the Algebra book, so we'll start with the Algebra 2 class and go from there. Good luck to your dd with her entrance exam.