Entries from SaxonMath

They're the same age--both going into 6th grade--and my sense is that math is probably this boy's strong suit.

I just gave him the Saxon placement test, and he placed into Saxon 7/6, which is the 6th grade book.

That would be great, but here's the hitch: he has been taught almost nothing about fractions at all. (He had a good math teacher--he and Christopher were in the same Phase 3 class for the first half of this year--who left to have a baby. So it seems that the subject of fractions & decimals fell through the cracks.)

So.....if anyone has thoughts, I'd like to hear them. I'll probably go ahead with 7/6, but that means I'm starting a 6th grade book with a child who's been taught virtually nothing about fractions and decimals.

update

whose job is it, anyway?

Why should I be the person figuring out that this boy hasn't been taught fractions & decimals?

Why shouldn't the school be figuring this out? (Yes, the school might say he was taught fractions and decimals, but didn't learn them. However, it's clear to me that there are certain topics he simply hasn't even heard of, because with some topics he'll say, 'I kind of remember that.' In other words, he can tell me which topics he failed to learn, or didn't learn well enough to retain, or whatever it is. With topics like adding fractions, he simply doesn't know anything about them, and has no memory of having been taught.)

So, yes, the school might say, 'He was taught, but he didn't learn.'

But so what?

If he was 'taught' and 'didn't learn,' then he wasn't taught as far as I'm concerned. It's the school's job to perform formative assessment to know what students have and have not learned.

Then it is the school's job to re-teach if a child has not learned.

Then, if the child still isn't learning, it's the school's job to figure out what else he needs.

common sense from The Education Wonks

That's one of my major concerns with NCLB. When students don't do their homework or study for exams, or even attempt to do classwork, it's still considered to be the teacher's fault if the students don't achieve their federally-mandated level of proficiency in reading, math, and science.

And yet NCLB doesn't give me, as a teacher, the authority to require student's who aren't even attempting the work to stay after school and complete their assignments. Unless the kid has committed some breach of the school's disciplinary policy, I can't keep them any later than the school regular dismissal time.

The No Child Left Behind Act holds me solely accountable for my students' academic progress but doesn't give me the authority to help make that happen, especially for children that are considered to be "at risk" of failing to meet minimal standards of academic progress.

Sadly, under the law as it is now written, a large number of children are going to be left behind.

But that's not the case with Christopher's friend. This boy has done all of his work; he's a serious student; his parents are serious parents.

It's the school's responsibility to know whether this boy has or has not learned how to add, subtract, multiply, and divide fractions, and to teach or re-teach the subject if he hasn't.

I've been wanting to get this book for a while, but funny -- it's never at our (beloved) local used bookstore. That is usually the sign of a good book -- people are hanging on to their copies. Of course, it's too bad for me. I may have to break down and buy it new. Everything I'm seeing about this book is telling me it's a great read.

I am a fan of the whole concept of Core Knowledge, being (I suppose) an educational traditionalist. Ben went to a Core Knowledge elementary school, and he learned quite a bit in spite of himself.

Thomas/Vorblik writes:

The philosophy behind these movements is often described in the literature as "constructivism''. Thus, Jack Price, President of the NCTM, says in [6]: "the standards are based on research and on a constructivist theory of learning . . . Critics may not agree with the theory, but they cannot say that the standards are not research based.'' But, as The Schools We Need shows, they can and do.

Is it possible that the ideas recommended by the NCTM are the very ideas that already pervade the schools they are supposed to reform?
Such a hypothesis is reinforced by the teaching methods that the NCTM and other reform groups advocate for achieving higher-order thinking skills. These "new'' methods include attention to individual needs and learning styles, discovery learning, and thematic learning. But these teaching techniques are essentially the project-oriented, child-centered methods that have long dominated educational thought and have prevailed for decades in our schools.
--Hirsch p. 132

If Hirsch is right about the entrenchment of constructivism, then we are the radical reformers; and it feels kind of nice for a change.

This supports my feeling that constructivism, in some form, is (like the poor) always with us, at least since Rousseau. And I suspect before Rousseau as well ... perhaps Ed knows what predated Rousseau's ideas, or perhaps Hirsch has even written about it; the reviews say that he treats the historical genesis of constructivism at length.

Fie on Rousseau, anyway. One reason I tend toward educational traditionalism is that, deep down, I believe mankind has not evolved or changed that much since we were all tribesmen. I really do feel that civilization is precariously thin, and not to be taken for granted. I guess Lord of the Flies made a big impression on me (either that, or I'm just paranoid).

Hirsch recommends a math curriculum which he says is "reasonably close to what research is telling us about how students learn". Surprise: it's Saxon math.

The new Saxon Math is here.

In place of the Winner Homeschooling Family from Oklahoma or wherever it was, standing in their yard beaming because they got picked for Homeschooling Family of the Year, we have Out-of-the-box Beaming Learners from Hemera Technologies or some such. The site takes hours and hours to load, and when it finally does load, you can't see any books.

I'm trying to remain calm.




I take it back.

I am not calm.

This is a horror.

We've also worked through the entire PRIMARY MATHEMATICS 3A & B lessons on fractions, and we've done all the workbook problems. Now we've started on the fraction lesson in PRIMARY MATHEMATICS 4A. I've been planning to post something about this, because we're doing the Singapore lessons with a friend of Christopher's.

We also did one bar model story problem from Primary Mathematics 3A almost every day, and we'll carry on doing one a day for good. As simple as the early 3rd grade problems are, there were plenty Christopher couldn't do.

When I say 'couldn't do' I mean that he specifically couldn't conceive of or draw the bar model.

He could do the problem alone, without the bar model. He could set it up and solve it. But he couldn't represent it visually or spatially at all.

Interestingly, he also can't even come close to doing perimeter problems of figures like this:



Asking him to figure an L-shaped perimeter is like asking him to do calculus. Completely beyond his capacities.

This is a kid whose one adult aspiration is to be an architect.

So we're gonna keep working on geometry. Nets are next!

does geometry predict math ability?

I think I'm noticing the same pattern in the 4 children whose math work I know best.

Two of these kids are Christopher & Lew. Lew lives next door and is one of Christopher's good friends. Christopher and Lew both seem to be strongest in verbal skills, and both are befuddled by perimeter problems once you get past finding the perimeter of a square or a rectangle.

Meanwhile, the two other boys I know & have worked with--I'll use their initials, 'G' and 'P'--are the exact opposite.

These two boys may have real math talent. I don't know how to spot Real Math Talent, but that's what I think I see in them.

Both G & P, when I showed them a more-complicated perimeter problem, instantly got it. They SAW it; it 'popped' for them, the way a hidden figure in a hidden figures test 'pops' for Temple (Grandin).

I think that's pretty interesting.

Anyways...this is one of the reasons I love the bar models. I'm pretty sure bar models develop visual-spatial 'seeing' or 'understanding' in verbal kids (& in verbal adults like me).

I've mentioned before that the first girl ever to win an international Olympiad was a Singapore student brought up on Singapore bar models. Singapore, as far as I can tell, is the only country to use bar models systematically throughout the first 6 years of elementary school math.

using bar models to teach fractions in Saxon 8/7

Christopher spent the whole summer complaining about his daily bar model. Then, yesterday, when we used a bar model to find If 2/5 of the the 270 fans wore green to the game, how many fans wore green? he said, 'These bar models do help!'

They really do.

Here's an example of a Saxon bar model used to solve a diferent fraction-of-a-group problem:






From now on I'm going to have him draw the model and link it to the computation. I'm going to have him explain to me why & how 2/3 x 270 is the same thing as dividing 270 by 3 and then multiplying 90 by 2, as the bar model has you do.

Then we're going to keep doing that until it makes sense.

I am happy to say that I was wrong when I wrote that there was no evidence supporting Saxon. There was a large study done in California, in which some pilot schools adopted Saxon math and saw their scores take off relative to those from other schools, which stuck by their existing curricular choice (Everyday Math). Apparently this study was not covered in the What Works Clearinghouse Middle School Math study, probably because it addressed not middle school but elementary school math.

The results are summarized here. -- Carolyn, October 3, 2005.

Original post

Apropos of the analysis of the research on Connected Math I did yesterday...

in the interest of fairness in reporting, it doesn't appear the evidence is overwhelmingly in favor of Saxon Math either. Saxon Math is a favorite 'traditional' curriculum of mine and Catherine's, sort of an 'anti-Connected Math' -- and it's served us very well in teaching our own boys -- but here is a roundup of what the (scarce) research says about it.

First, there is one study of Saxon Math that fully meets WWC's (the What Works Clearinghouse's evidence standards for a quality research study. Here is what WWC has to say about the study.

Peters, K. G. (1992). Skill performance comparability of two algebra programs on an eighth-grade population. Dissertation Abstracts International, 54 (1), 77A. (UMI No. 9314428).

WWC: Peters (1992) reports that students in the intervention and control groups showed gains on the Orleans-Hanna test during the course of the school year (that is, from pretest to posttest). However, the test score gains of the two groups did not differ significantly. There was no evidence that the Saxon Algebra curriculum (intervention) was more or less effective than the University of Chicago Mathematics Project curriculum (control).

The WWC warns that the number of kids involved in the study (only 36 kids total) was so small that it was very difficult to tell whether there had been a significant effect.

A second study of Saxon math met the WWC's evidence standards with reservations (meaning there was some not-quite-fatal flaw in the study's design).

Crawford, J., & Raia, F. (1986, February). Analyses of eighth grade math texts and achievement (evaluation report). Oklahoma City: Planning, Research, and Evaluation Department, Oklahoma City Public Schools.

WWC: Crawford and Raia (1986) found that students in the intervention group scored significantly higher than students in the comparison group on math computation, but not on total math or math concepts.

Here's what they did: they had one class working from Saxon Algebra, and one from Scott-Foresman Math (is this another non-fuzzy program? I wish someone would compare Saxon to a fuzzy curriculum!). They used a test (the California Achievement Test -- CAT) that breaks up the math scores into a math computation and a math concept subscore; they gave both a pretest and a posttest.

When they were ready to do their analysis, they matched students from each group one-for-one according to their total CAT score. That means that Fred may have been matched to Annie, because they both got X as a total score on their tests; but Fred may have far outscored Annie on the concepts subtest (with Annie stronger on computation).

They then looked at the mean posttest subscores of the matched children as a whole. They found that the mean scores were improved significantly in math computation, but not in math concepts.

The problem with this analysis is that, because the kids were matched by their total scores, one class may have had more conceptual skills to begin with as a whole. So interpret these results with care. However, here's a

Non-statistical side comment: I have read some parent reviews of Saxon that agree that it is great for developing computational skill, and not so great for developing problem-solving skills. These results are consistent with those comments.

To Summarize the Research: Of the two studies the WWC has reviewed on this topic, the second study has (to my mind) a flawed design, and the first shows an insignificant effect from the Saxon Math curriculum over the University of Chicago curriculum.

I'd love to be able to say that science proves Saxon is clearly superior; so far, it doesn't. However, Catherine and I have both said in the past that we would definitely recommend Saxon for kids who are struggling in math, and need to build their confidence by experiencing success; and I'll stand by that.

With Saxon, your kids won't miss out on any critical skill, either.

I received an email today from Joanne Cobasko of Save Our Children from Mediocre Math (SOCMM). She drew my attention to a couple of articles, describing the improvement in California test scores after the new California standards were adopted.

I looked at the attachment and skimmed the second article. It's not a research study (i.e., it would not meet the WWC's standards of evidence for a well-designed study); but it is definitely one situation where Saxon went head-to-head with fuzzy math, and won.

Here's the letter (thanks, Joanne!):

Hi Carolyn:

Both these studies show fantastic classroom results achieved in CA classrooms which are attributed to Saxon Math. I believe Bishop & Hook down play the Saxon Math connection in favor of the "CA Key standards" so as not to promote any particular curriculum over another, they choose to promote the math standards employed.

You will find references to the curriculum in their write ups though.

http://www.nychold.com/talk-hook-040404.pdf
http://www.nychold.com/report-wbwh-040619.pdf

There is also a great district comparison of standardized test results from Manhattan Beach, CA and Palos Verdes, both well to do communities (the comparison was provided to me by Martha Swartz from Mathematically Correct). [Note: Joanne points out that Manhattan Beach uses Saxon Math, and Palos Verdes uses Everyday Math. -- Carolyn]

Palos Verdes has the edge with a 26% Asian population, and one Kumon or other type tutoring facility for every 429 grade 2 - 6 elementary age student (the tutoring info was my informal review of the school population per the state testing info and a print out from the Kumon & other centers indicating their locations within a 5.22 mi radius).

Manhattan Beach, with a 7% Asian population and only 1 KUMON facility in town for 2,1113 grade 2-6 students, outscores Palos Verdes on the 2004 test scores.

Jo Anne Cobasko
Save Our Children from Mediocre Math (SOCMM).

We have used both curricula, and will continue to talk about both of them frequently in these pages.

However, different kids need different curricula, and we wanted to help parents make a choice that benefits their child best (and also matches best their own ability and willingness to support their kids' math learning; Saxon is probably a lighter-maintenance curriculum than Singapore).

Along those lines, I've been planning to post these links to Saxon and Singapore word problem comparisons at Paula's Archives for a while. Have a look. Although it's not really an accurate comparison to pull word problems out of each book and compare them at random, I think it's generally true that Singapore has exceptionally good word problems. Any kid reared on these problems is going to be mathematically in darn good shape.

Here, too, are Paula's Archives on Saxon Math and on Singapore Math individually.

When assessing your kids for their placement in Singapore Math, you'll almost certainly find that their placement level doesn't agree with their grade level. Somewhere on this site, though, someone posted that the Singapore math levels through 6B are actually completed when Singapore kids are in the 8th grade (or the age-equivalent grade in Singapore, whatever it is) -- something to tell your kids if they refuse to back up and do something they think is meant for younger kids (I sure wish I could find the post where that comment was).

Here's a post Catherine did on a price comparison between the Saxon and Singapore product lines.

And let me say, once again (repetition is key!), that if you have a kid who is getting lost or has gotten lost in math, and needs to make up lost ground and rebuild their confidence, I still don't believe anything beats Saxon math's approach.

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.