Thanks for the pointer, Delbows. That was a truly depressing article. The one bright spot is that the teacher, Walstein, seems like he is really something special. I wish there were more like him around.

For those who don't have time to read the whole thing, here's the executive summary:

Walstein, "arguably the most highly regarded high school math teacher in the county", teaches in the math and science magnet program at Montgomery Blair H.S. in Silver Spring, MD. He claims that, in their zeal to reduce the achievement gap (one of the directives of NCLB, no?) administrators have ruined the math curriculum in MD. The problem, he claims, is that their strategy has been to dumb down middle school math so that more kids can do well in it. The result is that more kids are taking advanced math earlier, but they leave these classes less prepared than they used to be. This doesn't show up on the test results because the MD state exams are so rudimentary. More kids do well on the exams and the state gets to congratulate itself, but nobody gets a solid foundation in the fundamentals. At least that's what Walstein claims. The administrators, of course, claim that Walstein and his colleagues are just curmudgeons. If it's true that he's such a star teacher though (and the article gives some pretty good evidence) then I'm inclined to believe the boots on the ground.

In this end this all seems like one of those depressing stories about how bureaucracy screws up education. Even NCLB - which I'm no fan of, by the way - has a potentially reasonable motivation. Namely, it wants more kids to learn more. All else being equal, that sounds like a good idea. The problem is in the accounting. If you can make it look like more kids are learning more by dumbing down the tests and then teaching to them, then there's lots of bureaucratic pressure to solve the problem that way. Certainly much easier than actually teaching the kids! So that's what happens. And the resulting curriculum effects the brighter kids too, since the teachers aren't given time to teach the subjects in any depth, even to them.

One more reason why in an ideal world I would home school my kid. Unfortunately, for all the usual reasons, it's not an ideal world.

BB

sigh...I read a similar report some time ago.

So you raise the broom stick so all kids can limbo under it.

Very nice way of putting it.

Sigh...

BB

"While he says some teachers apparently manage to provide the necessary background, increasingly students coming into the magnet have not been taught certain math concepts in enough depth for the concepts to become ingrained."

That seems to sum up how we feel. It is our biggest concern for our daughters who show both an aptitude and interest in math. DD8 could be much further ahead, but we've tried to introduce different formats for the same concepts to alleviate boredom. Also, when she does move ahead we spiral it back and do a little re-emphasis of what she learned.

I'd love to hear what the really math savvy parents think about this issue.
In addition to BB and Dazey, of course!

This is exactly what I was talking about on another recent thread, with my fears about "algebra for all" in 8th grade, .

I read a similar article in the Washington Post a while back that attempted to compare Algebra 1 classes across the different MD districts. They found wide variability among individual schools with some learning to use calculators as the main part of the curriculum while others were doing real Algebra. As you might guess, it was the schools with the lower achievement rates that had the "easier" classes. I followed the reaction to the article and there was some discussion about standardizing the curriculum and a lot of opposition on the argument that you need to meet children where they are.
My guess is there will always be some who want Algebra to be a weed out type of course, and others who want to gently encourage kids to not be afraid of abstract concepts. The people that set the curriculum standards have a difficult challenge. Did these discussions take place pre NCLB?

You all know my stand on this

If forgot, read The Calculus Trap.

It takes knowledge on the parents site to relize that getting A in class and having no problems with assigned exercises does not mean that your child is actually learning anything. Last year, when DS was in Algebra 2 I spoke at lenght with other parents that had kids in that class. None saw the problem ! They all looked at me like I was from Mars or something - after all my son is a math genuis at this school, so why am I complaining???
What I am finding ironic and really sad in this article, is that it is the teacher from a well known science/math magnet school that is raising an alarm. The teacher who gets the brightest in the district. How are other kids doing, the ones that did not get to M.Blair but also took Alg 2??? A huge disservise to not so bright math students too, ha?

It took me a while but I did learn. And DD is not taking Algebra this school year as a 6th grader. She will do pre-Alg,even though the rest of her class from last year will be in Algebra. Funny thing is , she was the best math student in that class

Is this what you referred to?

http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php

I wish I knew how to figure out if my child is learning in enough depth. Can my son just work through Aleks and get what he needs? He certainly doesn't learn the way I did. Is there some test that can tell me when he really has all those pre-algebra concepts down well enough to move on to algebra?

My husband's 37-year-old boss was never grade skipped and she learned math concepts well enough in public school that she was able to test out of college level calculus right after high school. I think she could probably figure this out, but the highest level math I took was college algebra and that was years ago. I never took calculus. How am I supposed to know if my son is learning concepts in enough depth? I don't think I understood math concepts as well as some people who were more interested in math, but I did well enough on tests that I studied for and then forgot it because I never used it.

All of my son's gifted friends all have parents who are teachers or were teachers at one time and I know they are curious about what we do at home. His friends ask us a lot of questions about what we do for different subjects, and what grade levels he is working at, and I feel good about everything he is learning except for the math. I really do need a math mentor.

Yes, that's the article, Austin. Not to answer for Ania, but I didn't want to leave you hanging.

Good question. Let's go even further - how do non mathy parents assess their kids knowledge in math? Clearly getting straight A's and being the best in the class does not prove anything.
Competition? Most math competitions, especially the elementary ones involve speed - not all kids will do well just because of this factor.
So what to do, how to make sure that they are on the right path?

Going back to the OP article, look at how accelerated the kids at M.Blair are. They are expected to do pre-calc in 9th grade, so it puts them as starting Algebra 1 in 6th grade. No matter how right the article is, I still envy those living in MD. My state does not have an option like M.Blair - there is no HS here that takes cream of the crop. How unfair to my kids, I think. How can we even talk about standard education?

Oops, sorry..
Yes, the linked article is the one I was referring to

Hi Lori,

My dd8 is schedule to start honors pre-algebra this fall. She had to take the placement test from JHU CTY for grades 5-7 before being allowed to sign up for the class. She will also be tested for placement the first week of school for math placement there. The JHU CTY placement test is pretty comprehensive and difficult (they actually had some trig and advance algebra questions thrown in there). Maybe you could have your son take a placement test or do an out of level test?

I think it really depends on what "depth" you consider enough? I think a lot of kids (here) could easily go through the standard math curricula at a quicker pace than normal. But all that means is that they end up at the same place a more average learner would end up, albeit at a younger age. If your child has great talent, and the passion to go with that talent, then that probably isn't good enough. I'm generalizing here, which I don't like to do, but I don't think that any regular math curricula is enough to foster the kind of math talent and knowledge that many of us are looking for here for our children. Like Ania mentioned in her post, my son has always been at the top of his math class (and he's been whole grade skipped twice with a further year in math). By all appearances he is a strong math student. It wasn't until we enrolled him in a math course specifically geared to high ability math kids (AoPS) that we realized how far he has to go. And he's not enrolled in calculus or anything like that. This is just an Algebra I class geared to middle schoolers. But it is taught at a whole new level than that which he's been exposed to in school. If I had to guess, based on student participation in the class, he's probably right in the middle of this class as far as ability goes. I know he will come out of this class with an "indepth" understanding of Algebra that he would never had obtained in school.

I'm not pushing AoPS here. It's a good course, but online format doesn't work for everyone. There are other resources geared to high ability kids. I just think that if you want your child to have a knowledge of math that goes beyond the regular student, you can't expect them to get that knowledge simply taking regular math classes at a faster pace. I'm all for acceleration, but without the depth to go with it, it's just a quicker road to the same end.

CFK ^^AoPS classes are an eye opener, aren't they

YES! The class just had their first "turn-in" howework assignment due. This was the first time in his life he could not answer all of the questions in his math homework!

My son "did" a serious math camp this summer. It was an eye opener for him (AoPS was more of the same for me), a true eye opener.
I will write more about his experience when he gets back home from a boy scout camp.

Also, my dd likes working on the CML problems. They are very challenging and really tests their problem solving ability and higher reasoning. I believe Mathcounts also publishes books that have all the problems they used in competition.

Bianca, does your DD do it^^ by herself, in a clasroom or with you?

I recommend including some enrichment like Ed Zaccarro books along with ALEKS or regular elementary classroom math. Once you get to algebra AoPS and math contests are good forms of enrichment. Elementary and secondary math education is lacking in this country. I went through Calculus in high school and made all A's. When I got to college I realized that I learned a great deal of "how to do math" in K-12 but not much about "the whys behind the math." I figured much of that out in my college level engineering classes. It was not that the concepts were difficult; it had more to do with the way the concepts were presented.

Oh, sing it, sister! That's how I felt about my math education, too, and it's one of the things I'm really trying to avoid with DS7. I want him to be a thinker in math, not just a doer, like I was/am.

Kriston, et al, you might find this interesting; right now in our elementary school system there is a struggle between folks who have instituted a new system of math based on the whys and what fors behind math (pattern recognition, estimation, etc.), and parents who feel their kids are not getting enough ROTE math work to reinforce concepts. Really, I think we are lucky they are at least trying to go broad, and when Dh and I feel ds8 needs more rote work on an area, we cover that at home. - The repetitive work is the easiest part to work on at home, imo.
I mean literally I see ds8 coming home with work dealing with concepts applicable to computer science, science in general, pure math, (math for funs sake!) etc. In 1st grade he was inspired to make up a game involving tallying up various truck types as we drive. We still enjoy playing this one on the road together, and the accompanying discussion of why in this area or city there might be more of one type... Maybe the whole system will be a bust, but I see my son still enjoying math, so I think that is ok.

Ah, yes, these are the Math Wars.

FWIW (not much!), I do think that there's a need for practice of arithmetic skills. I just don't think that arithmetic = math, and I don't think drill-and-kill is the way to teach math.

Rote Drill has its place. Its a great tool. I highly recommend it.

By rote drill, I mean being able to solve a problem or recite a theorem on demand with no hesitation and at the fastest speed possible.

To survive Very Hard tests in college, I had to have some things down cold. I took advanced thermo and stats classes that required us to derive methods to solve general classes of problems then solve specific cases. All the math had to be second-nature. And we ended up using ALL our math skills - from calculus, diff-eq, Linear Algebra, theorems from RA, Stats, etc. Those kids who did could not slam out the math or reach for a theorem, were left behind.

The first week, the instructor told us we had to take this "easy" week to get up to speed. He told us how to do it.

I had already been doing rote drill for calculus and Linear Algebra prior to the semester to get warmed up. But he upped our game. Every night I spent 12 hours outlining all my other texts, categorizing problems, setting up flash cards, then just started going through it. I had over 200 flash cards with theorems and problems - both pure and applied - on them. Once I had all the subjects down, I shuffled the cards, then took 50 with me on the bus each morning. As the class progressed, I added cards from that class.

After I started this method, I usually finished the finals in one hour vs four most of the other students needed. It all came down to that rote drill. A friend of mine started using it when he was in the math program and from then on he got A+ in classes.

To this day, I can look at most applied math problems and do them in my head. And I can usually look at something that is not right and be able to grasp the theorem being used and which of its givens are being violated.

When you look at other human pursuits - such as sports or marksmanship or cqb - rote drill is a key part of the training method. Sure, there are unstructured problems - but the solution to them often involves pieces taken from actions which are down cold. Academics - and problem solving - are no different.

A mathy kid should start his or her set of flash cards by putting the hardest problems from the week on them. Its like baseball cards for math! On the front should be the problem statement. On the back should be the elements for the solution.

Another set of cards should have definitions and theorems on them. Name of the item on the front, the explication on the back.

This method can be explanded to other subjects as well.

Sorry, Austin, but rote drill would destroy my 7yo's interest in math. Like with a sledgehammer.

I'm not saying practice and even memorization don't have their place. I just don't think the place for the sort of drill you're describing is necessarily elementary school math...which is where most of it is currently located! Flash cards are about the worst way to teach my son. I know--we tried them!

Different kids have different needs, so different approaches suit them better. A lot of GT kids are concept kids, and drill-and-kill simply isn't the right approach for them. Especially for visual-spatial kids, they need to see the big picture first and then the details come more naturally to them.

One-size-fits-all just doesn't work.

I understand Kriston. Good point. I am a spatial learner, too. There were times I would take the whole deck and organize it in one big jigsaw puzzle just for fun.

The way I used the cards was to organize the information and then ensure the retainment of information once the knowledge was obtained. Once I had the stuff down, it got a few cards, then they went into the deck.

I did not use it to learn new stuff.

Yes, that makes sense. As a review tool or to build speed where speed is desirable, I think strategies like that can work wonders.

DS7 is not fast at anything except learning! And he probably never will be. I always say that there are (at least) 2 kinds of GT kids: the fast and the deep. DS7 is deep. He prefers time to mull things over.

I think that style difference affects learning strategies, too. Things like flash cards or even educational video games that require quick retrieval of info stress him out. We're working on it, but I'm pretty well convinced that we have to come at things that are typically memorized--like his times tables--from another direction or it will not be good for his love of math. He needs lots of concept, very little drill at this point.

Maybe that will evolve as he gets older. I guess we'll see...

Kriston - your post rang a bell for me. In "Re-forming Gifted Education" the author wrote about two different types of gifted kids. Those that need to learn fast and furious, more, more, more and those that need time to ponder, need to go deep, deep, deep.... those two types should not be in the same gifted program as they will frustrate each other.

Makes sense to me!

I am late to this post. Going back to TexasSummer comment about engineering math tgught him the "whys", engineering requires applied math. I started in premed and took calculus, but then switched to enginnering and had to take applied calcullus in the spring to make up.

I think teaching physics is a good way to teach applied math. My opinion. I think of physics as applied math, chemistry as applied physics etc. And there are many simple experiments to do in physics that help with math.

Ren