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High school math - need advice - most rigorous?


Guest Melissa Troup
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Guest Melissa Troup

My son recently completed a set of personality tests and ability battery tests (trying to determine possible career interests). We were told by the person conducting the testing that our son needs to be in the “most rigorous math†program we can find. He is currently using Saxon – he is in 9th grade and will complete Algebra 2 in May. I was under the understanding that Saxon was rigorous – help? Am I wrong? Do we need to change directions? If so, what curriculums should I explore? Thanks!

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Most rigorous would be Art of Problem Solving.

BUT:

it is not suitable for every student! It is great for a student who loves, and its good at, math, thrives on a discovery based approach, and is willing to spend more time to go farther and deeper than with a traditional curriculum.

It will be disastrous for a student who does not enjoy math, and it will not be suitable for one who needs direct instruction.

 

As somebody on these boards (I forgot who it was) has once put it succinctly:

xyz program gives you the nuts and bolts. AoPS gives you the nuts and bolts and has you build the Taj Mahal with them.

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Guest Melissa Troup

Great! I will research AoPS - sounds interesting. If he has finished Saxon 2 - do you know which level he should begin with AoPS? I went to website and I'm a little perplexed. Advice?

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Welcome Melissa!

 

When you click on the book links here: http://www.artofprob...tore/index.php?

you will see that each book has a placement test. The diagnostic pre and post tests should give you a clue although I have heard on the grapevine that the pretests are sometimes not an indicator of how challenging the program can be.

 

Do note that the AoPS algebra classification is a little different from how other programs classify algebra. AoPS Introduction to Algebra covers algebra 1 and part of algebra 2. Intermediate Algebra, I believe, covers the rest of algebra 2 and some of the precalculus concepts that appear in traditional precalc texts. Then, they also have a Precalculus text which I imagine will go much deeper into precalc than most other precalc texts (regentrude might be able to advice you better here). If your son has not done geometry, the Introduction to Geometry text is another option.

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Great! I will research AoPS - sounds interesting. If he has finished Saxon 2 - do you know which level he should begin with AoPS? I went to website and I'm a little perplexed. Advice?

 

 

I would have your son complete AoPS Introduction to Geometry and then go on to the Intermediate Algebra book.

 

Your son may want to look at some of the Alcumus problems on the AoPS website to see if he enjoys working with the types of problems he would encounter in the books, since AoPS is much different than Saxon.

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I would have your son complete AoPS Introduction to Geometry and then go on to the Intermediate Algebra book.

 

Your son may want to look at some of the Alcumus problems on the AoPS website to see if he enjoys working with the types of problems he would encounter in the books, since AoPS is much different than Saxon.

 

I would also suggest some significant period of time working through Alcumus problems with the program set to follow the Intro to Algebra book (which covers topics typically covered in Algebra 1 and Algebra 2) just to see if the previous algebra experience has him ready for the level of Intermediate Algebra. I think that the Intro to Algebra book problems are wonderfully complex.

 

 

Or this might be a student for whom the online classes are a good fit. They tend to move rather fast and many people here are using the books only and not trying to keep up with the pace set in the online classes. But for someone who has already done algebra 1 & 2, it might be just the ticket.

 

You might also want to check into the AMC 10 and 12 exams for next year.

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I agree with the above posters.

 

AoPS is the most rigorous progam I know of, but it is certainly not for everyone.

 

I'd encourage him to do as much math as he's capable, but I'd be careful not to push him in over his head. Does HE love math? Does he want to be challenged? Does he get overly frustrated by a complex problem in which he doesn't obviously see the answer?

 

Alcumus is a great way to see what type of problems AoPS has. You can set it to only give algebra problems or other varieties as well.

 

Saxon is a respectable program. Sometimes it is better not to "fix" what isn't broken. I'd do some exploring on the AoPS site and check out alcumus. Just because someone recommends rigourous, doesn't necessarily mean you are doing your son a disservice sticking with what works (which may be plenty rigourous).

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My son recently completed a set of personality tests and ability battery tests (trying to determine possible career interests). We were told by the person conducting the testing that our son needs to be in the “most rigorous math†program we can find.

 

 

Why? Because he is a math whiz who needs a stretch or because he is so behind he needs major intervention?

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My son recently completed a set of personality tests and ability battery tests (trying to determine possible career interests). We were told by the person conducting the testing that our son needs to be in the “most rigorous math†program we can find. He is currently using Saxon – he is in 9th grade and will complete Algebra 2 in May. I was under the understanding that Saxon was rigorous – help? Am I wrong? Do we need to change directions? If so, what curriculums should I explore? Thanks!

 

I am also curious about what tests they gave him? Personality or aptitude? Personality will only take you so far.

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My son recently completed a set of personality tests and ability battery tests (trying to determine possible career interests). We were told by the person conducting the testing that our son needs to be in the “most rigorous math†program we can find. He is currently using Saxon – he is in 9th grade and will complete Algebra 2 in May. I was under the understanding that Saxon was rigorous – help? Am I wrong? Do we need to change directions? If so, what curriculums should I explore? Thanks!

 

Personally, I wouldn't necessarily take the advice of the person conducting the test, unless I absolutely agreed with what he or she said. Your ds may not "need" to be in "the most rigorous math program" at all. I assume that the tester doesn't know your ds, but is basing the recommendations solely on test results -- and while that recommendation may be helpful, it may also be entirely worthless if your ds doesn't love math. I hate it when people tell me I "need" to do something -- go ahead and tell me why it would be a good idea, and how it would be beneficial, but don't tell me what I "need" to do, because quite frankly, they don't know for sure, based on a few test results.

 

All of us have strengths and abilities, but just because we're very good at something doesn't mean we enjoy it, and in that case, we don't "need" to do it to its fullest extent. In this case, if your ds's career interests will all require a strong math background, well then, he does "need" to be in a rigorous math program so he's prepared -- and that's probably what the tester meant -- but if this is just "he tested well in math, so he needs the most rigorous program," I don't necessarily agree with that.

 

I think you should base your decision on what you already know about your son. If he's great in math, you didn't need a test to tell you that. If he loves math, again, you probably already knew it.

 

I'm not saying that you should discount test results, just that your own common sense as your ds's mom, combined with your ds's own feelings and future ambitions, should ultimately be what leads to a decision about math curriculum (or anything else, for that matter.)

 

As far as specific math programs go, I think you should look at several options and see which one "clicks" with your ds. The most important thing is to find a curriculum he likes and that he understands, rather than simply choosing the one that's supposed to be the most challenging.

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My guess is that the "most rigorous" math suggestion was made because he's doing math "above" his grade level and doing very well. To me, that says keep doing what you're doing as it's obviously working. Saxon is rigorous. You can add in more challenge in a variety of ways with supplementing - math competitions, Alcumus, SAT test prep, etc.. If she didn't clarify why she made that suggestion, I'd call and ask.

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"Rigorous" is almost a word without meaning when it comes to math programs. It is a wax nose, shaping itself to fit whatever the person using it wants it to be. Almost every math program will claim to be rigorous in one way or another. I would not worry about trying to decide which is the "most rigorous", but which will best fit your son and his interests.

 

If your son likes and enjoys Saxon, then keep using it. But also supplement it with other resources (Alcumus is wonderful!) which have a different sort of "rigor" --- perhaps it would be better to say, a different emphasis? Every program has strengths and weaknesses, so by balancing them you may end up with something even better.

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"Rigorous" is almost a word without meaning when it comes to math programs. It is a wax nose, shaping itself to fit whatever the person using it wants it to be. Almost every math program will claim to be rigorous in one way or another.

 

Actually, if the word "rigorous" has meaning anywhere at all, it is in the realm of mathematics, and there it is clear:

mathematical rigor means that all statements are proved. There is no "one way or other".

 

Different math programs may be great, useful, solid, get good outcomes - but a rigorous math program, by the very use of the term in math, would have to be proof centered, and the degree of rigor, in a mathematical sense, can be determined independent of personal preferences.

 

(To be clear: the most mathematically rigorous program may not be the best fit for any particular student. But the meaning of the word is clear when pertaining to math.)

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I also have a 9th grader finishing Saxon Alg. 2 in May. If your son likes Saxon, stick with it. He can choose to challenge himself to do Advanced Math in one year versus 3 semesters. If your son is gaining confidence and competence he will be well served.

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Actually, if the word "rigorous" has meaning anywhere at all, it is in the realm of mathematics, and there it is clear:

mathematical rigor means that all statements are proved. There is no "one way or other".

 

Different math programs may be great, useful, solid, get good outcomes - but a rigorous math program, by the very use of the term in math, would have to be proof centered, and the degree of rigor, in a mathematical sense, can be determined independent of personal preferences.

 

(To be clear: the most mathematically rigorous program may not be the best fit for any particular student. But the meaning of the word is clear when pertaining to math.)

 

 

I agree with your definition of "rigorous" when applied to a specific mathematical proof, and that may be the way that you mean it when applied to a math program in general, but you are wrong to say there is any agreement among the general populace (or even among homeschoolers) about what makes a math program "rigorous". I have seen the word used by different people in various contexts to mean any of the following statements -- and in general, what it tends to mean is, "this is a math program I like."

 

A "rigorous" math program:

  • has plenty of practice problems

  • has a few practice problems, but they require many steps

  • has lots of word problems

  • has fewer word problems, but heavy emphasis on algebraic manipulation

  • requires a significant level of independent thinking by the student

  • requires plenty of memorization

  • requires proofs

  • is designed for gifted students

  • is designed to reach all students

  • covers more topics than competing programs

  • covers fewer topics, because competing programs are "only an inch deep"

  • focuses on developing skills

  • focuses on developing understanding

  • focuses on both skills and understanding

  • focuses on whatever areas the competing programs are supposedly slackers in

  • ...

 

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Actually, if the word "rigorous" has meaning anywhere at all, it is in the realm of mathematics, and there it is clear:

mathematical rigor means that all statements are proved. There is no "one way or other".

 

Different math programs may be great, useful, solid, get good outcomes - but a rigorous math program, by the very use of the term in math, would have to be proof centered, and the degree of rigor, in a mathematical sense, can be determined independent of personal preferences.

 

(To be clear: the most mathematically rigorous program may not be the best fit for any particular student. But the meaning of the word is clear when pertaining to math.)

 

I've posted about this before. The problem is that even if you accept your definition of proof-centered that such a program is not obvious to home school parents.

 

I've always said Singapore's upper level program is a rigorous program and certainly international testing holds that up. Not only do their top students score highest, they lift up the top 40% of their students to be in the top 5% (or is it 1%, I forget) in the world. That means to my little statistic based mind that they are lifting average students above gifted students in many countries.

 

Further my anecdotal experience is that my child walked from the last of Singapore's program to AoPS's pre-calculus book with no problems.He's not a math oriented child at all. I'd say the two programs are about equal. Or given my current evidence AoPS is easier. I'd have to do the reverse to find out for sure if they are equal.

 

However, when you look at Singapore's books, you will see no obvious proofs. It wasn't until another thread that I realized that they do walk the student through a real world sort of proof for most of the rules you learn in math. They often do this in what are called class room exercises where students work many problems that represent each step of the proof. However, even they can't prove everything, I recently read with my second son in the NEM 2 book "we can't prove this without calculus." So not everything can be proved to middle school and high school students.

 

My points here are:

  • that just because a parent doesn't see proofs doesn't mean they aren't there.
  • the proof of a math program's rigor can be in the pudding.

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I agree with your definition of "rigorous" when applied to a specific mathematical proof, and that may be the way that you mean it when applied to a math program in general, but you are wrong to say there is any agreement among the general populace (or even among homeschoolers) about what makes a math program "rigorous". I have seen the word used by different people in various contexts to mean any of the following statements -- and in general, what it tends to mean is, "this is a math program I like."

 

A "rigorous" math program:

  • has plenty of practice problems
  • has a few practice problems, but they require many steps
  • has lots of word problems
  • has fewer word problems, but heavy emphasis on algebraic manipulation
  • requires a significant level of independent thinking by the student
  • requires plenty of memorization
  • requires proofs
  • is designed for gifted students
  • is designed to reach all students
  • covers more topics than competing programs
  • covers fewer topics, because competing programs are "only an inch deep"
  • focuses on developing skills
  • focuses on developing understanding
  • focuses on both skills and understanding
  • focuses on whatever areas the competing programs are supposedly slackers in
  • ...

 

But I'm not jumping up and down about this definition either. I am sure that I could find folks who would think just about any program is rigorous. AT some point it would be nice to have a definition.

 

The problem, of course, is that most of such standards are anecdotal and don't mean much. You'd have to test students prior to entering a program and then test them again at completion. They'd all have to have the same teacher or no teacher. It wouldn't be easy.

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