A pity that the article does not include any excerpts from the books or detailed critiques of what's wrong with them.
Examining a Discovering Algebra book at http://www.amazon.com/Discovering-Algebra-Investigative-Appr... suggests that the book is not so bad (though obviously this only allows previewing a few pages)...however, I'm unsure whether this is even the same book, since the OP doesn't mention the name of the publisher.
It's hard to judge whether the books themselves are poor or whether the failure stems from teachers unwilling to adapt to a knowledge-building rather than a purely didactic approach. Education is important and worth spending money on but (as a European) I'm frequently horrified by American teachers, whose union seems defensive even of members who exhibit basic deficiencies in literacy or numeracy. It's still strange to me, for example, to consider that there are teacher's editions of textbooks that include answer keys for scoring homework - I ask myself what possible need a competent teacher could have for such a thing, and why school districts are wasting money on buying them.
I'm strongly against dumbing down school curricula; on the other hand, I think discovery of knowledge by experiment imprints knowledge far better than mere receptive learning (cf. recent HN posts about college physics students who learn the material well but are hopelessly incapable of applying it to a novel context). So I'm inclined to favor the approach of these textbooks (without endorsing their actual content). This article http://www.oregonlive.com/news/index.ssf/2009/01/the_constan... suggests that at least some of the problem stems from parental or school unfamiliarity with the methods, such as complaints about an 'overemphasis on...problem solving'.
Hmmm. I think we need to take a closer look before jumping onto the 'blame the book' bandwagon. The books discussed may well be inadequate, but it's hard to judge that without a more reasoned critique. If anything, this lends further support to opinion of many HN readers that we should be moving towards open-source textbooks instead of the current cosy arrangement between school districts and publishers.
Gotta side with the OP on this one, thanks for the link. It's not the math that's at fault so much as the total orientation towards grinding out the answer with a calculator, vs writing it. Oh dear :-/
It's funny, I do those "cluster problems" in my head to solve most multiplication and division problems...I presume that I invented the method myself at some point during basic education, as these books are encouraging kids to do. The standard algorithms are great on paper but suck to do in your head for anything very complex (at least for me...)
I can see the point though about disadvantaged kids having trouble with this. If someone is struggling and does not have good parental support, it would be hard to learn basic math skills reliably this way. Rote memorization of methods and figures is useful at pretty much all levels of math, and if you just want kids to be able to multiply two numbers, drilling them on one method makes a lot more sense than trying to create young mathematicians.
Yeah the lattice method was pretty cool, I don't recall seeing that before. I can't see any value teaching this to a 3rd grader unless they're absolutely sailing along in math and curious to learn more. Even then, I'm not really sure of the point, how does it reveal anything about multiplication?
I am made uneasy about someone that contrasts 'low income' and 'white' in their graphs.
I do however, still holding a low opinion of the discovery math pedagogical model in general, as it requires more math sophistication than is likely to be found in an elementary/middle/high school's teacher.
I was disturbed by the "low income" vs. "white" separation. Does the white group also include low income white students? Or, to further their point, did they decide low income whites aren't really white?
Nobody should have to "rediscover" the Pythagorean Theorem. I'll go out on a limb and say Newton, Leibniz, Einstein, Descartes, etc. just went ahead and read Euclid, and they did pretty well for themselves.
Learning to prove mathematical theorems is an important skill in mathematics. If you only learn to use what comes served on a silver platter, where will you learn to handle situations where you haven't had the theorem taught to you in advance? My impression of UC undergraduate students is that "find the correct formula and plug in the numbers" is the only type of math they know how to do, and encouraging that doesn't seem like a way forward.
It is important to know how to prove theorems. However, I don't think the correct way to do it is to say "Here's some vague hints, now try to guess what we're talking about by playing with these blocks". The way I was taught, which I found pretty effective, was that we'd be given an theorem, then in some cases (not all, or we'd never get anywhere) prove that statement. When you hand over the theorem and then make the student prove it, he applies and synthesizes previous theorems to explain the new one.
> My impression of UC undergraduate students is that "find the correct formula and plug in the numbers" is the only type of math they know how to do, ...
I believe that Mass has come to his position against Discovery Math precisely because his students at the University of Washington can't even do that.
Typically, this sort of pattern means that "low income" includes low income students across all races, that's the only selection criterion for that group. The "white" group will include all white students (including low-income), and the "black" group will include all black students (including high-income). Nothing nefarious.
That's what I was hoping, and that's how I'd structure it if I insisted on including a "low income" group when everything else was racially divided.
I hope that the authors did it as you described. Would I be flabbergasted if they pulled some shaky crap? No, probably not, but to quote Mulder's poster, I want to believe.
Well, they should have to discover something. There aren't a lot of undiscovered results that are accessible to an elementary school student studying math, so that discovery will usually be a rediscovery.
Is it foolish to write an interpreter as a pedagogical exercise because someone has written a better one?
I agree that kids should not have to discover the Pythagorean Theorem. But the way it is now isn't good either. Kids are just told to memorize lists of mathematical facts and taught how to apply these facts to solve math problems. This is supposedly more useful than learning why the facts are true.
I find it telling that the article breaks down scores by race, not by income. Note that it claims that the difficulties are for low income families who cannot afford tutors / other resources, not black children. What's the crossover? What's the pass ratio for poor white children?
Granted, a book can easily be harder to read / understand for less-classically-trained children. I'm not saying it's not possible, just that the article is definitely seeing what it was looking for.
The first table cites the pass ratios for all low-income students at 37.3%, 28.3%, and 26.4% for 4th, 7th, and 10th grade respectively -- the pass rates for black children are lower than that. So one can accurately infer that non-black low-income children perform better.
Granted, this isn't as informative as breaking things down by both race and income. But, as far as I can tell, this is a limitation of the state's reporting data and not a selective argument made by the blog.
You have to look at the WASL specifically and filter on other criteria from there. For example, a bar chart of 10th grade scores comparing low/non-low incomes:
It's interesting to use an ethnic achievement gap as a legal basis for opposing a particular math program. That most United States school districts don't simply use Singapore Math
This is probably because the program you repeatedly suggest as the solution to all of the math education woes in the US has a distinct lack of statistically valid studies to back up the claims being made. It is popular among the homeschooling crowd but that does not mean it is effective or applicable at a larger scale (e.g. the LA unified school district alone has three times as many students as Singapore but only twice the budget, etc.)
LA unified school district alone has three times as many students as Singapore but only twice the budget
That's an interesting factual claim, which depends crucially on currency conversions between the United States dollar and the Singapore dollar. Do you have a link to a source for the factual statement, preferably one that "shows the work" (as a math teacher would say) by giving the school-age population numbers for each place and the all-sources primary education budgets for each place?
It's mainly convenience. In the educational establishment and some courts, equality is more important than quality. Challenging curricula on the basis "this is bad for non-asian minorities more than others" is more likely to be successful than "this is bad for everyone".
It is considered better for 100% of every group to be a moron than for 70% of blacks and 30% of whites to be a moron.
[Edit: Added words "it is considered" to last sentence. Before it looked like I endorsed this view, which I don't.]
OK, so it worsens the achievement gap, but what about absolute achievement. I'm fine if the poor are even worse off than the rich if they are 5% better off absolutely (i.e. the rich are 10% better off).
Persuaded me that the way I learned math is pathologically soul crushing; the way it's taught from kindergarden through university. The first two pages set up a nice metaphor: mathematics is argument and creativity and our traditional math education by memorization and rote repetition are akin to teaching music by reading and writing sheet music without first hearing or playing an instrument.
"No society would ever reduce such a beautiful and
meaningful art form to something so mindless and trivial; no culture could be so cruel to its
children as to deprive them of such a natural, satisfying means of human expression."
The rest of the article digs into some specific examples.
Mathematics instruction needs an overhaul and back-to-basics isn't The Right Thing.
If you want an example of math education that does a lot right, take a look at what's been done in Chicago [1,2]. Unfortunately, substandard K-12 curriculum is all too common. I don't even want to think about the billions of dollars society would save by implementing effective programs across the board. Makes me sad. :-/
As a university level instructor, I find so many things high school teachers have to put up with appalling. I choose my text book for one. My lesson plans are not approved by anyone except me (yes, in fact my sister-in-law had to use recycled old lesson plans because they were "AP approved") The decision rights should be located as close to the in-the-trenches information unless the coordination benefits outweigh the costs. I doubt the benefits come anywhere close here.
Why not offer both types of instruction and let the teachers recommend which students should learn by which method. It seems like having an option would make it more likely more students would do better. Why limit the students to only one option.
The categorisation of children's test scores into different racial types I think says a lot about how far America has yet to go in dealing with issues of segregation and unequal opportunities - despite Obama's election as president.
From the article >>In this approach math is substantially dumbed down for "equity" reasons and students are asked to discover age-old principles on their own.
Charlotte Iserbyt, former Senior Policy Advisor in the Office of Educational Research and Improvement (OERI), U.S. Department of Education, wrote the free eBook (pdf) "The Deliberate Dumbing Down of America" http://www.deliberatedumbingdown.com/
I looked at that link. I admit that I only read the preface, but when I got to this passage:
America’s transition from a sovereign constitutional republic to a socialist democracy would not come about through warfare (bullets and tanks) but through the implementation and installation of the system” in all areas of government—federal, state and local. The brainwashing for acceptance of the “system’s” control would take place in the school—through indoctrination and the use of behavior modification...",
I gave up.
American schools may be many things, but only the delusional can claim that they are a plot to socialism. They do have a certain totalitarian bent compared to the schools I remember, for sure, but I'm not sure what that has to do with social democracy...
There is also a certain irony in the fact that the schools in "socialist democracies", by which I assume they mean countries like Sweden, consistently show better results than their American counterparts. I'm not sure how the "system" would think that dumbing down the school system will help them achieve that.
"Dumbing down" and "discovering age-old principles on their own" are not necessarily the same. There is definitely value in learning to do creative work in math and science, beyond just rote memorization and learning to regurgitate what the teacher tells you. It pretty clear that many people with high grades in school are poorly prepared for situations where you actually have to do original work, like grad school. Of course, there has to be a balance between base skills and that.
> "Dumbing down" and "discovering age-old principles on their own" are not necessarily the same.
Indeed not. I'm writing an interpreter for a Lisp-like language right now (does Lisp count as "age-old"? I guess in computer terms it does), but I don't consider that a dumb thing to do.
The problem with rote memorization is that it gets results. You cannot do algebra until you know your times tables by heart, and how did kids learn their times tables in ages past, when men were men and went to the moon without the aid of calculators? Drill, drill, drill.
Going on and on about the beauty of math is all well and good if your brain is wired that way, but when 90% of America's high school grads are stymied by making simple change, you fall back on what works.
The point is that if all you do is drill, by the time you get to the beauty, your students have already made up their mind that math is the most useless crap in the Universe. Motivation is a powerful force and unless people see that there's any point to what they are being ordered to do, they will comply with the smallest amount of effort they can get away with.
And to say that they want to fall back on "what works" sounds a little funny given how dismally American students in general are doing. If people are so afraid to make the mediocre worse, they'll never discover what works better.
Besides, I'm not even sure I agree that you need to be able to multiply numbers before doing algebra.
Saxon Math is getting kids numerate to a high school level where constructivist horseshit is not.
Saxon Math is largely drill and repetition based, with some practical applications like counting money and so forth.
Therefore, you're wrong. QED.
As for what American students in general are doing, drill and repetition were how it was taught in the mid 20th century, when America led the world in science and technology. (My father was given a pencil with no eraser in the second grade; the teacher told the class "You're second graders now. You shouldn't be making mistakes.") We abandoned that sometime in the sixties and it's been downhill since.
Ms Iserbyt, according to her bio at that same website, is also 'best known for her 1985 booklet Back to Basics Reform or OBE: Skinnerian International Curriculum and her 1989 pamphlet Soviets in the Classroom: America's Latest Education Fad which covered the details of the U.S.-Soviet and Carnegie-Soviet Education Agreements which remain in effect to this day.'
Now, while I'm no lover of teacher's unions or abandonment o tried and tested instructional methods, her suggestion that american pedagogy is a communist plot is itself an example of 'dumbing down'. I'm reading her e-book, and it's little more than bad polemic, absolutely riddled with logical fallacies and cheap rhetorical gimmicks. Sophistry is unfortunately not confined to one end of the political spectrum.
I dispute this assertion. When I was growing up, Ireland was ethnically homogenous with poor economic security and hostility to welfare cases like those of single mothers (for religious reasons), but there was still a distribution of ability and academic application. there were poor kids that studied hard and rich kids that didn't give a fuck, though more of the former than the latter, since high schools there employ streaming. You need more evidence for this assertion that the existence of welfare automatically results in poor academic outcomes.
I suggest that the disparity of result may have always existed, but in the past there were fewer women in the workforce and more jobs in manual labor such as manufacturing etc., so that a lack of academic achievement didn't necessarily result in economic insecurity.
Yes - and yet there is still a range of educational outcomes, from excellent to abysmal. The country has a more generous welfare regime than when I was growing up, but AFAIK this hasn't substantially altered the educational landscape.
So your argument that poor educational outcomes can be attributed to inverted racism doesn't stand up. It may well be a factor, but you appear to be arguing that poor non-white kids with a bad attitude are primarily responsible for dragging down overall results, and I don't agree.
If we're being hard-headed, we should also consider the possibility that intelligence is just not evenly distributed, and while schools should seek to improve as many students by as much as possible, we need an economic infrastructure that can make productive and self-sustaining use of less intelligent people as well as smart ones.
In short, dumb people are not going away, so there needs to be a means for them to earn a legal living.
Well, they way system is set up right now, it obviously doesn't work, wouldn't you agree? Basically, the government is throwing money at poor/minorities, and they end up having more kids.
Same exact thing happens in African countries. Every time somebody donates money/food, it goes towards procreation, not improvement of the quality of life or education.
I remember one successful African story. This group of volunteers instead of building a water well decided to involve the residents in the process. So they served as architects, while locals were doing all the hard labor. The results were really good - locals knew how to support the well. They became self-sufficient.
That, in my opinion, is the solution. It's a slow process, but I don't see many alternatives.
Minnesota has better school achievement than the USA. There must be something to Northern latitude icy winters producing improved academic achievement. Canada is also better than USA in math. Maybe not using the $100 million NSF grant created math books and a few other publisher clones of same has a positive effect.
Examining a Discovering Algebra book at http://www.amazon.com/Discovering-Algebra-Investigative-Appr... suggests that the book is not so bad (though obviously this only allows previewing a few pages)...however, I'm unsure whether this is even the same book, since the OP doesn't mention the name of the publisher.
It's hard to judge whether the books themselves are poor or whether the failure stems from teachers unwilling to adapt to a knowledge-building rather than a purely didactic approach. Education is important and worth spending money on but (as a European) I'm frequently horrified by American teachers, whose union seems defensive even of members who exhibit basic deficiencies in literacy or numeracy. It's still strange to me, for example, to consider that there are teacher's editions of textbooks that include answer keys for scoring homework - I ask myself what possible need a competent teacher could have for such a thing, and why school districts are wasting money on buying them.
I'm strongly against dumbing down school curricula; on the other hand, I think discovery of knowledge by experiment imprints knowledge far better than mere receptive learning (cf. recent HN posts about college physics students who learn the material well but are hopelessly incapable of applying it to a novel context). So I'm inclined to favor the approach of these textbooks (without endorsing their actual content). This article http://www.oregonlive.com/news/index.ssf/2009/01/the_constan... suggests that at least some of the problem stems from parental or school unfamiliarity with the methods, such as complaints about an 'overemphasis on...problem solving'.
Hmmm. I think we need to take a closer look before jumping onto the 'blame the book' bandwagon. The books discussed may well be inadequate, but it's hard to judge that without a more reasoned critique. If anything, this lends further support to opinion of many HN readers that we should be moving towards open-source textbooks instead of the current cosy arrangement between school districts and publishers.