It's true.. Singapore's treatment of word problems is better than Saxon's, I think. I plan to supplement with them...

like I said, nothing is perfect.

-- CarolynJohnston - 24 Sep 2005

One more thing: I did every one of the Saxon 6/5 lessons myself. All the problems, everything.

-- CatherineJohnson - 23 Sep 2005

I do trust, strongly the power of overlearning to the poitn of automaticity.

It's not just that automaticity takes a load off working memory, either. At some point automaticity starts to turn into expertise.

I can't think of a good example right now, but some topics that were extremely confusing to me started to 'feel' clear & 'natural' simply because I had done the problems so many times that it felt right to do them that way.

Willingham's textbook talks about this a bit, so I'll get that posted as soon as I can.

Anyway, when a child really can't understand something yet, it pays to have him keep doing & doing it until he's got it down cold, because at some point it can morph into a concept he understands.

I don't know what causes the jump, or why so much overlearned knowledge remains procedural.

But I know it happens.

-- CatherineJohnson - 23 Sep 2005

_If you're a homeschooling parent with a lot of math savvy, I would say to go for Singapore; otherwise opt for Saxon in the elementary and middle grades, and feel good about it, because it really is a good program for elementary and middle school math.

Look at what it did for Christopher._

Well, again, I'm glad to hear it.

Because we REALLY leaned on Saxon.

Obviously I've been putting a lot of work into math, and re-learning it myself, but during the year that he pulled ahead all of my work was spent studying the Saxon 6/5 book myself. I hadn't started RUSSIAN MATH or even SINGAPORE MATH (though I did read Liping Ma's book very closely. I learned a huge amount of elementary mathematics from her book.)

But basically, it was Saxon 6/5 for both Christopher & me.

-- CatherineJohnson - 23 Sep 2005

You know -- a really great teacher can rise above as crummy a curriculum as there is out there. The reason we need good curricula is to support weaker teachers, whether they be parents or professionals, who aren't so sure of themselves. I think Saxon really does that.

Well, as I say: I keep coming back to it.

Also, you're absolutely right that we need good curricula to support the teachers. PERIOD.

The Chinese teachers spend HOURS studying their children's textbooks--and they're GOOD teachers!

-- CatherineJohnson - 23 Sep 2005

I too have read and been concerned about Saxon for the higher grades, but not as concerned as you and the other homeschoolers. I have the picture of math ed across the whole age spectrum in mind, and Saxon is doing the right thing in the early grades.

I'm glad to hear it.

My problem is that I don't have a picture of math ed across the age spectrum, so I am ALWAYS flying blind. I really do mean blind, too.

I'm old enough that I've developed 'instincts' & intuitions about many of the realms I confront; I usually have a 'feeling' about what I should do.

Math ed is completely out of my.....hmm. What's the proper analogy?

Can't think of one at the moment.

Anyways, I have ZERO instincts when it comes to math ed.

No, that's not right. I have a tiny handful of instincts & ZERO sense of whether to trust my instincts or not.

I felt the exact same way about autism FOR YEARS.

People would say, 'trust your instincts' and I would say 'what instincts?'

What are my instincts about raising a severely autistic child?

-- CatherineJohnson - 23 Sep 2005

I had to deal with a good teacher and a pretty-bad text, but nothing hardcore.

Big difference.

-- CatherineJohnson - 23 Sep 2005

I think you wouldn't be sanguine if you faced it. You'd be upset about the foolish make-work and the wasting of precious time, and the dissipation of your kids' energy, which is after all very finite. But Ben and I did it for two years.

You're right.

-- CatherineJohnson - 23 Sep 2005

Thank you, Carolyn & V, but Saxon got there first!

-- CatherineJohnson - 23 Sep 2005

umm. the terms are things that get added, period. thus, in x^3 - 3x^2 + 3x - 1,
the "quadratic" term is "-3x^2" (not "3x^2"):
the sign is part of the coefficient.

thank you and good day.

-- VlorbikDotCom - 23 Sep 2005

Hey C,

the terms are things that get added to or subtracted from the expression.

Coefficients are constant numbers (like 3) that multiply unknowns (like ab).

-- CarolynJohnston - 23 Sep 2005

I've been semi-sanguine about the possibility of having two math curricula in your child's life, a fuzzy one at school & a non-fuzzy one at home.....but the fact is, I haven't (really) had to face that situation.

I think you wouldn't be sanguine if you faced it. You'd be upset about the foolish make-work and the wasting of precious time, and the dissipation of your kids' energy, which is after all very finite. But Ben and I did it for two years.

I too have read and been concerned about Saxon for the higher grades, but not as concerned as you and the other homeschoolers. I have the picture of math ed across the whole age spectrum in mind, and Saxon is doing the right thing in the early grades. Remember those cognitive psychology principles that E.D. Hirsch outlined? Saxon is intelligently applying most of them (especially the distributed practice one), and I think those principles are the best guidance we have.

You know -- a really great teacher can rise above as crummy a curriculum as there is out there. The reason we need good curricula is to support weaker teachers, whether they be parents or professionals, who aren't so sure of themselves. I think Saxon really does that.

It's not an ideal world, and there's no ideal curriculum. I think the two best ones out there are Saxon and Singapore. If you're a homeschooling parent with a lot of math savvy, I would say to go for Singapore; otherwise opt for Saxon in the elementary and middle grades, and feel good about it, because it really is a good program for elementary and middle school math.

Look at what it did for Christopher.

-- CarolynJohnston - 23 Sep 2005

congratulations, Carolyn!

way to go--

I'm relieved, I have to say. I've been semi-sanguine about the possibility of having two math curricula in your child's life, a fuzzy one at school & a non-fuzzy one at home.....but the fact is, I haven't (really) had to face that situation.

Last year, in 5th grade, Christopher had SRA Math at school, and Saxon Math 6/5 at home. SRA Math is a very tough textbook to teach from (impossible for me, and experienced teachers have told me the same). But it's not hardcore fuzzy.

David Klein points out that most U.S. textbooks are fuzzy to some degree. That was certainly the case with SRA. Time and again I'd read a passage--this was when I was just setting out to reacquaint myself with math--and not have a clue what it meant. Invariably this was because the text would lay out a couple of observations and then pose a question to the student, who was supposed to draw the appropriate conclusion.

I remember one day I was trying to figure out how to find the equation for the slope of a line, and there was just no way. Finally my neighbor came over, read the passage, and said, 'You'd have to know how to do it to understand this explanation.' Then she showed me how.

Still and all, SRA Math wasn't a b*s book. Not at all. The math was real, and Christopher had two good teachers who'd had plenty of experience getting math into kids' heads in spite of the problems.

I'm pretty sure that in Christopher's case it was a net plus that he had two separate math curricula. He had far more time-on-task, and he had the benefit of seeing the same subjects from slightly different vantage points (which always helps me, and is probably good for everyone).

But I wasn't having that feeling about Ben at all. SRA & Saxon, OK. Connected Math & Saxon? Blech.

So, long story short, I was getting worried about Ben. I'm glad Connected Math is gone.

Saxon into the breach

I've now read quite a few negative assessments of Saxon, by people whose judgment I respect. These are folks on the web--a couple of obviously intelligent homeschoolers, as well as Robert, who writes the brightMystery blog. Robert told me he wants to like Saxon, but just does not--and that students who come to his college courses having been homeschooled in Saxon aren't ready. (That's a paraphrase, so take it with a grain of salt.)

I have misgivings myself. Sometimes I worry Saxon is TOO 'structured'; I worry about pattern training--that Christopher is going to be a Saxon Boy who can only do Saxon Problems typed in Saxon Font.

Thus far that has not been the case. As far as I can tell, all of Christopher's Saxon knowledge has transferred to SRA (and, now, to Prentice Hall).

Other times I've felt the Saxon books are too scattered & fragmented. The fragmentation of topics is a deliberate strategy on Saxon's part, the intention being to use the principles of spaced repetition and distributed practice. That makes sense, but when I taught the Primary Mathematics Grade 3 chapter on fractions to Christopher and his friend Greg it was so much more satisfying and rich, or seemed so.

So.....I've been a heavy-duty Saxon user; I owe Christopher's move to Phase 4 math to Saxon 6/5. And I know the knowledge he's gained from Saxon is conceptual as well as procedural.

But in spite of all these good things, I have Nagging Doubts.

Usually I pay attention to Nagging Doubts. But in this case I think my doubts are either wrong or, more likely, misdirected. Because I keep coming back to Saxon every time I'm in trouble, and Saxon keeps bailing me out.

Saxon vs Dolciani

Christopher has another quiz today, on algebraic expressions.

I was reading along in Prentice Hall, which said that in an expression like x + 7 the x and the 7 are terms.

In an expression like 2x + 7, 2x and 7 are terms, and 2 is the coefficient.

Well, right away I was confused.

Does a term mean you're either adding or subtracting?

Does multiplication mean you don't have a term, you have a coefficient?

That seemed wrong.

So I got out my copy of Mary Dolciani's Pre-Algebra: An Accelerated Course.

I'd been thinking, OK, I'm done with Saxon. There are just too many negative opinions out there, Mary Dolciani's a genius, my neighbor's son liked Dolciani's book, it's shorter than Saxon & we're pressed for time......this year I'm going with Dolciani.

She was no help at all:

In the expression 9 + a, 9 and a are called the terms of the expression because they are the parts that are separated by the +. In an expression such as 3ab, the number 3 is called the numerical coefficient of ab.

Saxon on coefficients

Saxon 8/7 has an entire lesson on algebraic terms. Lesson 84, page 571. I haven't read it yet--I've skimmed--but it's obvious that when I do, my question will be answered.

Here's how he opens:

We have used the word term in arithmetic to refer to the numerator or denominator of a fraction.

Right off the bat, he's made the smart metacognitive move. We have used the word 'term' to refer to numerators and denominators, and it's a good thing to point this out to the student, because otherwise, at some point (probably not now, but later on, when it will really ball things up) the student is going to think, Wait! Doesn't TERM mean DIVISION? Does it mean FRACTION? Does it mean NUMERATOR & DENOMINATOR?

OR WHATTTTTTT?????????

I'm going to go out on a limb and say that Saxon Math is the most metacognitively aware textbook I've encountered to date. Constantly, the books remind you of what you have learned, and point out to you that you are now learning an extension of that concept or you are learning a new and possibly quite different meaning of the same word.

Back to Lesson 84.

Next the book has a table of monomial, binomial, and trinomial algebraic expressions. Wonderful.

THEN the text says:

Terms are separated from one another in an expression by plus or minus signs that are not within symbols of inclusion.

Thank you, John Saxon. I needed that.

More examples follow, and eventually we get to this:

Each term contains a signed number and may contain one or more variables (letters). Sometimes the signed-number part is understood and not written. For instance, the understood signed-number part of a^2 is +1 since a^2 = +1a^2. When a term is written without a number, it is understood that the number is 1. When a term is written without a sign, it is understood that the sign if positive.

Perfect.

At least, perfect for me. What do you think?

deer in the grass

So I looked out, too, and sure enough: the young deer grazing in our lawn is darker than the young deer who was living here a month ago.

But Martine thinks it's the same one. She thinks they get dark in the fall.

It's probably time to give him a name.


(a^2 means a squared - right?)

update

The story problems!

Barry reminded me: they're dreadful. They're just wildly too-easy.

I had meant to put that in the original post, and forgot.

However, the story problems aren't the reason for my 'nagging doubts'.....the story problems are an obvious problem you can remediate easily through supplementation.

It's the other stuff.....

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• Posted by: CatherineJohnson
• LogDate: Sep 23, 2005 @ 12:46

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