Posted by BP Mom, a resident of Another Palo Alto neighborhood, on Sep 29, 2009 at 9:23 am
My child is in 4th grade and the EDM homework this week was to "write" about where you see numbers being used in daily life. He wrote sentences to describe how numbers are used on packaging and in thermometers etc.
This was a waste of time. I think 4th graders should be working on numbers, multiplications, divisions and figuring out calculations not writing in math class. Very disappointing. Please throw out this ridiculous program and get back to basics.
Posted by Some guy, a resident of the College Terrace neighborhood, on Sep 29, 2009 at 10:38 am
I didn't have the ability to *think* about math for a long time, it's not something you can really think about until you can do it! Why are kids in 4th grade writing about thermometers and not learning long division etc.?
This is Palo Alto, we don't need this 2nd rate education.
Posted by EDM Opponent, a member of the Gunn High School community, on Sep 29, 2009 at 11:24 am
I publicly opposed Everyday Math from the beginning because of years of experience with the program with my children. Now people are understanding why we didn't "trust the teachers" on the committee. Fortunately, our teachers will be able to use their judgement with the program and fill in the gaps. If they were required to stick with the program to a tee, we'd be in real trouble (bye-bye 900 API scores).
Posted by An Engineer, a resident of the Downtown North neighborhood, on Sep 29, 2009 at 11:29 am
"I didn't have the ability to *think* about math for a long time, it's not something you can really think about until you can do it! Why are kids in 4th grade writing about thermometers and not learning long division etc.?" - Some guy
"The purpose of computing is not numbers, but insight." - Richard W. Hamming, Numerical Methods for Scientists and Engineers
Try Googling Hamming.
I cause up trillions of number crunching calculations every working day. I cannot remember the last time I did long division, and I may have forgotten how to do it. It's an obsolete skill. However, those trillions of crunched numbers would be for nothing if I didn't understand how to set them up and apply their results.
Why does anybody in this Silicon Valley still want to torture kids with numerical drudgery to make them into very poor substitutes for five-buck calculators and turn them off of math in the process?
"It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could be relegated to anyone else if machines were used." - Gottfried Wilhelm Leibniz, co-discoveror of the calculus.
Posted by rukidding, a resident of Another Palo Alto neighborhood, on Sep 29, 2009 at 12:19 pm
An engineer -- despite your assertion that we don't need long division, children do need it to understand how math works. It is a mistake to see traditional math as turning our kids into cheap calculators. Not at all, they need the basics to build understanding. Sure, it's fine to have fun with numbers and do some projects. But don't gut the core of math learning. It doesn't work and wastes time and money hiring tutors to fix this.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Sep 29, 2009 at 1:48 pm
Surely you're joking. Long division teaches math only in the context of algebra, to illustrate the polynomial basis of our numbers and the deep genius that conceived it. Try long division with Roman numerals and you'll see what I mean.
By contrast, making kids divide 538091744865735 by 974509282524778 (be a sport -- get a pencil and do it) teaches them those "I Hate Math" T-shirts got it right.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Sep 29, 2009 at 2:26 pm
"Since when do the schools ask students to do long division as in your example? Schools want students to know HOW to divide but don't ask them to divide such huge numbers."
Well, why don't they? If long division teaches math, then longer division must teach math even better.
Enlightened schools for the 21-st century would show students how to use Excel, which handles such numbers with ease and elan, and which is in fact what I copied those numbers from. Dump the drudgery and teach the utility.
Posted by Jarred, a resident of the Midtown neighborhood, on Sep 29, 2009 at 9:56 pm
I don't think long division should be entirely eliminated from elementary school mathematics. It should be taught as an example algorithm, but not one that deserves extensive training for peak manual performance.
An Engineer is surely right that the quickest way to quench any nascent enthusiasm for mathematics is with pages of long division problems.
Given computers and calculators, the ability to do approximate calculations mentally is much more important than the ability to do exact arithmetic with a pencil and paper.
Posted by Jim H., a resident of the Duveneck/St. Francis neighborhood, on Sep 29, 2009 at 10:18 pm
It would be a shame if those attending turn this in to a public flogging of Everyday Math. Those people should stay home. Hopefully, those attending are there to learn more about the program and not complain about something that has already happened.
The work my 5th grader has brought home has been fine. I have no problems with it. In fact, it has made me think about how I do my own calculations and has helped me explain it better.
There's more to school and life than 900 API scores. If that's all you want from your child's education, that's a sad statement.
Posted by ggg, a resident of the Barron Park neighborhood, on Sep 30, 2009 at 8:34 am
"Why does anybody in this Silicon Valley still want to torture kids with numerical drudgery"
No one wants to torture anyone, so you can put your strawman back into the storage chest.
The goal is mastery of a subject area, and here mastery requires that you have done a bunch of long division. Only in this way do you get a good number sense. Neato idea to teach them to use excel, but that would be silly in the absence of master--without having done a bunch of long division, the kids would never know what to divide by what or whether there was some massive error in the output.
Posted by EDM Opponent, a member of the Gunn High School community, on Sep 30, 2009 at 8:43 am
Yes, Jim H., I did stay home. I already wasted my time trying to oppose the adoption. Didn't want to torture myself again.
Most Palo Altans move here for the API scores. Can't be admitted to a decent university with mediocre SAT scores and low GPAs.
Palo Alto will be OK with EDM because teachers will supplement and parents will frustratingly help their children or find programs to keep their heads above water. Still, those who do not receive help at home will sink and slow down the rest of the class.
Posted by rukidding, a resident of Another Palo Alto neighborhood, on Sep 30, 2009 at 9:08 am
EDM opponent you are right. Palo Alto parents won't let their kids sink and will either tutor themselves or hire tutors. So the real problems with everyday math will not show up. This has been going on for years. Really sad and it adds stress to students.
Posted by edmconvert, a resident of the Duveneck/St. Francis neighborhood, on Sep 30, 2009 at 9:43 am
Gotta admit, I was skeptical when it looked like the first thing 4th graders were doing was line segments and rays. It seemed odd for a way to kick off the year. But my son ate it up and has enjoyed everything since. We had a great discussion over what the mean and median really meant last week - he actually thinks math is fun this year.
Why on earth does it matter how many children or how old Engineer is? Is there a "wrong" answer that will make his arguments less effective? Or a "right" one that will make you suddenly agree with him?
Posted by Al, a resident of the Downtown North neighborhood, on Sep 30, 2009 at 9:51 am
> "It is unworthy of excellent men
> to lose hours like slaves
Children are not "excellent men" .. they are "blank slates" that need guidance, which hopefully includes a strong basis in the fundamentals of arithmetic, so that they can eventually engage mathematics.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Sep 30, 2009 at 10:14 am
"You overestimate Excel and underestimate students. How old are you, and how many kids do you have?"
Excel is a common engineering tool out here in the real world of working mathematics, along with MatLab and various higher-level language compilers. My alleged "underestimate" of students makes no logical sense in your context (perhaps you meant "overestimate," but I'd disagree with that assessment). Ditto for my age and fecundity. Suffice it to say I have decades of professional experience putting numbers together to achieve practical objectives, and I'm very good at it.
"The goal is mastery of a subject area, and here mastery requires that you have done a bunch of long division."
Uh-uh. I am an applied mathematician by trade, but I've not done a manual long division since I left high school. It doesn't come up in the real world; rote calculation is done by computers these days. People supply the smarts, which is what our schools need to prepare them to do, rather than how to be poor competitors to computers.
Long division teaches nothing about mathematics. To illustrate: assess your present state of mathematical mastery, then work the long division problem I posed above (no Excel now) and tell us how much you gained.
The only working arithmetical knowledge one needs is facility with the sums and products of single digit integers, which are also the basis of subtraction and division. Then you're ready for algebra, which is the actual introduction to true mathematics. Master it, then you'll understand the meaning of carry, borrow, shift, and the rest of what mathematically challenged adults mistake for mathematical mastery.
Posted by Jim H., a resident of the Duveneck/St. Francis neighborhood, on Sep 30, 2009 at 10:29 am
EDM Opponent: Actually the discussion is tonight. But, feel free to stay home tonight, as well.
If you moved to Palo Alto for API test score, you're wasting your money. Also, you link API scores with SAT's and GPA's and getting in to a good college. I'd like to see the data showing the correlation. API's reflect the entire school, where the others are achieved by the individual. Coming from a school with a high API guarantees nothing with regards to college acceptance.
To go further, college acceptance doesn't guarantee anything either. But, I'm sure your child appreciates the pressure you are putting on them to get in to a "decent university". Good luck with that.
Posted by EDM Opponent, a member of the Gunn High School community, on Sep 30, 2009 at 11:15 am
There are no guarantees in life.
I moved back to Palo Alto because I graduated from Paly and enjoy the people and convenience of living here. I appreciate that people have opinions here. Since I have children, yes, I do appreciate the API scores of PAUSD.
I speculate that there is data out there correlating students attending college and API scores, but let me offer this simplistic viewpoint about your thought on SATs & GPAs being an individual achievement: how likely is it that EPA or East LA students achieve high SAT scores? They are not learning what other children are learning. They are only skimming surface material because there is so much disinterest and behavioral problems. Our children are learning from school, their parents and perhaps whatever extra programs or tutors. They have a better chance of scoring well on SATs than other school districts. They are learning much more than I learned through PAUSD.
". . .college acceptance does not guarantee anything either". I completely agree, there may that charming salesman who becomes a multimillionaire, but that's an exception. The beauty of living in America is that it is full of opportunity and second chances.
You don't know my definition of what a "decent university" is, nor do you know my parenting, so that was a leap of assumption on your part. A college is fine too. I believe that children should have some balance rather than being academic robots.
Regarding the original topic, this forum has plenty-o-links about Everyday Math being unsuccessful in other school districts. Again, our town will do fine because parents are engaged. And remember, Everyday Math is for the elementary schools, which is basic math, not middle or high schools.
You can go ahead and pick apart my thoughts but you'd be better off surfing for information on EDM before you hit that meeting tonight so you can ask why they want elementary school children to learn 5 different ways to multiply when there is only one really fast and easy way to multiply in the head - the way we learned. I suppose they will answer with "Kohl's has signs which have the percentage off calculations for the customers, so why do people need to do it in their heads? Or just carry a calculator for those moments." Let me stop there before my blood begins boiling.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Sep 30, 2009 at 11:47 am
"Children are not "excellent men" .. they are "blank slates" that need guidance, which hopefully includes a strong basis in the fundamentals of arithmetic, so that they can eventually engage mathematics."
I think children should be raised to become "excellent men." And excellent women, to update Liebniz. Introduce them early to the beauty and utility of real mathematics. Don't sour them on the subject with needless, useless drill-and-kill slavery.
I know we've always done it that way in our schools, but that was before Silicon Valley and computers obsoleted the old rote "learning" paradigms. We are not living in the 1890s or even 1970s anymore. The world has changed. Get used to it and get on the train.
Posted by respect, a resident of Another Palo Alto neighborhood, on Sep 30, 2009 at 12:06 pm
the reason I asked if you had children in Elementary school, or how old you were is because no Elementary school child is asked to do the calculations you posted.
A national panel looking at Math education did not conclude that long division is out thanks to Excel, or calculators.
I don't think Excel or calculators are any more useful for teaching Math than Wii is to teach a sport. At the end of the day, it's about doing things yourself, and being developmentally ready for the next step. It's likely that long division is part of a body of skills that help children master certain levels of Math,
Can you be absolutely sure that you never did long division as a child, and it's how you became an applied mathematician?
Posted by An Engineer, a resident of the Downtown North neighborhood, on Sep 30, 2009 at 4:44 pm
"no Elementary school child is asked to do the calculations you posted."
Somebody pointed that out earlier. My response was to ask why they weren't. If long division teaches math, then it stands to reason that longer division teaches more math, right?
Significantly, no long division proponent, child or adult, has accepted my challenge to manually long divide those numbers. Their convictions seem to be more of the spectator variety.
"Can you be absolutely sure that you never did long division as a child, and it's how you became an applied mathematician?"
Try rephrasing the second part of your question to continue the context of the first. To answer the first part, I did long division as a child. As is common with math illiterates, my elementary school teachers knew only rote arithmetic, so I had to do reams of long division problems from workbooks. My classmates and I hated it, and to my knowledge none of them went into science or engineering careers. Fortunately, junior high algebra introduced me to real mathematics, and I simultaneously discovered the slide rule, then calculators and computers. I chose a math-oriented career, delegating the mindless drudge arithmetic to dumb machines that were far more capable of it and much more temperamentally suited for it.
Posted by WilliamR, a resident of the Fairmeadow neighborhood, on Sep 30, 2009 at 6:19 pm
I don't have any experience or opinions regarding Everyday Math, but an interesting scenario seems to be playing out here: If most people think EDM is a bad product and arrange outside tutoring for their children who are taking EDM, those students are likely to score higher on standardized tests as a result of the tutoring (not the EDM) than students who take 'regular' math and don't get outside tutoring. So the EDM proponents are able to say "Students taking EDM score higher, therefore it's a good product" whereas the reality may be that the higher test scores are in spite of EDM, not because of it.
Posted by CM - Army, Engineer, a resident of another community, on Sep 30, 2009 at 8:15 pm
To EDM Opponent,
You posted "you can ask why they want elementary school children to learn 5 different ways to multiply when there is only one really fast and easy way to multiply in the head - the way we learned." You are correct about the most expedient method, and we learned it with drill-and-kill. The procedure was droned into our heads. So what do you do in the classroom where 3 kids get it quickly, 10 may get it with a little extra time and another 8 are totally lost. Do you continue with the drill-and-kill or do you offer variety in hopes it clicks?
I view it as eating pizza...a majority of people just fold the slice over and bite. Those who don't want the juices dripping actually fold in the tip as well. And yet there are some who cut it into pieces and use utensils. Some start at the crust (honestly haven't found anyone yet - but saw it on a commercial). Is any one way the only correct way if the result is to consume the slice? AS such there isn't just one way for studnets to learn multiplication...they are offer a variety in hopes one will help them learn and possibly even peek their interests in learning mathmatics.
Posted by CM - Army, Engineer, a resident of another community, on Sep 30, 2009 at 8:22 pm
To BP Mom,
"My child is in 4th grade and the EDM homework this week was to "write" about where you see numbers being used in daily life. He wrote sentences to describe how numbers are used on packaging and in thermometers etc.
This was a waste of time. I think 4th graders should be working on numbers, multiplications, divisions and figuring out calculations not writing in math class. Very disappointing. Please throw out this ridiculous program and get back to basics."
Too often children just see numbers as numbers and feel there is no application of them. The exercise of having children find the numbers in their world around them is to connect them with the fact that numbers are all around us and a significant part of our lives. Additionally, there is a wide gap between students who are good with numbers and those who have the ability to explain their understanding in words to others. Usually if you are good with numbers, you do not perform as well with words. By having your child write it shows the importance of each curricular aspect being connected and that vocabulary only matters in English class...no it matters in math class as well. That is the reality of being able to communicate.
Posted by ggg, a resident of the Barron Park neighborhood, on Sep 30, 2009 at 9:40 pm
"I am an applied mathematician by trade, but I've not done a manual long division since I left high school. It doesn't come up in the real world; rote calculation is done by computers these days." Entirely irrelevant.
"People supply the smarts," Not if they haven't worked with numbers (in this case done plenty of long division). That's the point--they don't get smart. They don't get math.
"Long division teaches nothing about mathematics." Wrong, scroll up and reread.
You miss the point entirely. You may work with numbers every day, but you clearly have no idea how children learn. Your abilities in your field give you exactly zero insight into the pedagogical issues involved.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Sep 30, 2009 at 11:40 pm
Interesting thing going on in my kid's class. The kid loves EDM. The teacher is worried so is still using the old textbooks along with EDM. So the kid's getting drilled, but the EDM has resulted in a new excitement about math--but I have a kid who loves a new idea.
A private school administrator told me recently EDM was his favorite of the systems--volunteered it. A Kinder teacher (not here) on the other hand, told me she hated it, though she wasn't directly teaching it. There really seems to be a lot of range of opinion on
Frankly, with all the math focus on the kid's class, what I'm wondering about is whether there's enough time spent on other subjects . . . ah well.
Posted by EDM Opponent, a member of the Gunn High School community, on Oct 1, 2009 at 12:01 am
Re your statement, "So what do you do in the classroom where 3 kids get it quickly, 10 may get it with a little extra time and another 8 are totally lost."
Do you really think that the Palo Alto children of parents with college degrees and graduate degrees will really have difficulty understanding multiplication? We aren't an inner-city school. For children to multiply, they first need to memorize - no way around it. And it only takes about 2-3 weeks for their minds to memorize the table. And once they memorize, the traditional method of multiplying really is the easiest way, and the method they need to understand to progress onto middle school math. Teaching more methods is purely a waste of time. Plus, the frustration of the parents who have never learned the wacky five EDM methods of multiplying (thus cannot explain it to their children) isn't going to help the child's attitude towards math. They'll witness their parents finding math difficult which will affect their attitudes ("If dad, with a graduate degree in science cannot understand this, how can I?").
Posted by rukidding, a resident of Another Palo Alto neighborhood, on Oct 1, 2009 at 9:16 am
Proponents of the new math typically oppose memorization, drills, and structured learning. This debate has been going on for years. Integrating both traditional methods with project learning is very beneficial, and too much "drill and kill" -- as the proponents of the new math like to say -- is not what I want either. But to gut the core of math is just as wrong. New math looks good for awhile but when it gets really tough in the upper grades, the basic foundation is needed. Smart kids start to have a lot of trouble in high school and don't know why. The students who get the tutoring do fine.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Oct 1, 2009 at 9:57 am
"You miss the point entirely. You may work with numbers every day, but you clearly have no idea how children learn. Your abilities in your field give you exactly zero insight into the pedagogical issues involved."
It is all too common to conflate process with outcome, particularly when the arbiter has no concept of what the proper outcome is.
It's all about what unlearned people are programmed to mistake for learning. It is very easy to pronounce a child laboring over long division literate in mathematics, check the box on the list, and move on.
Long division is a rote chain of dreary mindless actions that produces no mathematical insight. Anyone who has forgotten that is invited to work the problem I posed above. Pedagogues have loved it because it fills classroom time, gives the gullible the illusion of accomplishment, and requires no pedagogical creativity. Before calculators and computers came along it could be justified as a sometimes useful skill. But that time has passed.
We need to educate our children for today's world, or that world will pass them by before they even enter it.
Posted by Resident, a resident of Another Palo Alto neighborhood, on Oct 1, 2009 at 10:23 am
I have not entered this debate as yet, but as a parent who sometimes has to help my kids do maths homework, I find it particularly difficult to help when basic arithmetic ideals have not been taught.
I do remember having to do boring long division on squared paper, keeping the columns in line, putting in zillions of 00s and often getting the wrong answer because of a silly mistake. However, I used to take some pleasure in seeing the long computations all over my page and seeing the patterns produced. Of course I would not like to do the exercise mentioned above, but there was a time I would have sat down and enjoyed doing the exercise as "easy homework". I am not a maths genius and found high school maths particularly difficult. However, without some of the foundations I learned in basic arithmetic I am not sure how I would have done at that level at all.
My kids come home with loose sheets of homework and squeeze their calculations in tiny spaces on the page, no neat columns and often very little explanation as to what is required. The homework is then handed into the child and may or may not be returned in a reasonable amount of time, but is often not filed away for future reference by the child when they need it to study for a test.
I would like to see the kids transferring their computations to homework notebooks of squared paper and a system whereby the homework is used as a study resource. This needs to be started in elementary grades so that the students in higher grades see how it can help them and have formed the habit to do so. Starting this habit in high school is too late as it feels like drudgery.
My kids are all out of elementary school now, but some of the bad habits they picked up there is definitely hindering them now.
I hope that teachers realise that the curriculum is only a small part of what they are teaching the kids when it comes to maths. The bigger part is that they are learning the building blocks for what they need to do algebra, calculus, geometry, etc. and that if they don't teach the basic skills in an organized way when young, then it will not help them at all in high school.
Number efficiency is only a small part of maths, roman numerals does that. Teaching the denary system and making sense of it requires more.
Oh, and there is a great chapter in the book "Outliers" (can't remember the author, I'm afraid) that shows why Asians are so good at maths. Part of it is to do with the names of the numbers. While English speaking kids have to learn the numbers eleven, twelve, thirteen, etc. with strange names, Asian languages are using "ten-one, ten-two, ten-three" like the twentyone, twentytwo, twentythree, system that we use above the teens. Interesting philosophy.
Posted by BayArea_Mom, a resident of the Duveneck/St. Francis neighborhood, on Oct 1, 2009 at 11:18 am
After reading thread after thread of posting, I decided to attend the EDM presentation last night. I found that my understanding of EDM has not changed. The games and real life applications in EDM are no doubt excellent supplementary material to student who has already grasps the basics of arithmetic. However, the new method in EDM to teach the basics, especially multiplication and division, is too long and tedious for even an adult to follow. I am not sure how we can expect our children to master it.
A few parents in my kindergartener's class have already planned to supplement with home tutoring. Our kids will learn math but we may have to spend more time/resource at home tutoring.
Posted by another parent, a resident of Another Palo Alto neighborhood, on Oct 1, 2009 at 11:42 am
WilliamR what you describe is "teaching to the gene pool", a common name for what goes on when the performance of students is not really related to what happens in the elementary classrooms. Students are successful because they are naturally talented, in which case EDM is amusing to them, or they are successful because they are being supplemented in the drills and fundamentals, in which case EDM is another type of supplement. Many teachers in PAUSD count on the parental gene pool to provide them with these two types of students so that they do not have to "teach the boring stuff".
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 1, 2009 at 12:36 pm
Look, if teaching here were simply a matter of teaching to the gene pool, we wouldn't have the variation in test scores among the schools or within the schools.
Resident, I've read Malcolm Gladwell's Outliers--and while it's an entertaining read, I have issues with its intellectual rigor. Are Americans really worse at math or do we simply delay math instruction? There's a lot of comparing apples to oranges. Our kids spend less time in school per day and per year, but spend more years in school.
The United States continues to have the top universities worldwide and east Asia, despite its high average math scores, hasn't produced a large set of great mathematicians. (India has.)
The great mathematical innovations haven't come from Asia--they've come from North Africa, the Middle East and Europe. I don't think rice growing has anything to do with the number of gifted Russian mathematicians. (Gladwell attributes Asian proficiency in math to rice-growing. However, the educated classes in China haven't been rice growers in many, many generations.)
This isn't meant as a defense of EDM. I find it interesting that my kid likes it--but math scores are going to be meaningless here because the teacher is using two texts. EDM is a problem for the Ohlone "way" in that our classes are mixed and EDM doesn't lend itself to that--ironically.
Posted by Resident, a resident of Another Palo Alto neighborhood, on Oct 1, 2009 at 1:34 pm
I do agree with what you say about Asians and rice growing. But, on the other hand, I find it very interesting about what is said about the language aspect of why Asians are good at math.
As someone who struggled learning 3 languages other than English, I found that learning to count in a different language was really difficult because the names for all the teens made very little sense. Looking at the names of what we call our teens makes very little sense mathematically although the names of 21, 22, do make a little more sense. When considering a denary numbering system, calling eleven, twelve, thirteen, etc. is not really sensible although by the time we are adults we don't think about it. But, when we consider a child learning to count to twenty, we are teaching them a list of names not a repetition of the numbers they have already learned to ten.
I think the fact that Outliers' author, Gladwell, points this out as a contributing factor makes sense to me. I hadn't thought of it before, but it would make sense that if instead of saying eleven, we said ten-one, we would be explaining straight away a mathematical concept.
Posted by GGG, a resident of the Barron Park neighborhood, on Oct 1, 2009 at 1:48 pm
"It is all too common to conflate process with outcome, particularly when the arbiter has no concept of what the proper outcome is."
Typical engineer worldview. Those who disagree with you are unlearned, and your domain knowledge gives mastery of all skills and knowledge. Thanks for the laugh.
Actually, I probably have a better math education than you, but that is beside the point. Again, it has to be said that you have no insight into the process of learning generally and learning math in particular. You conflate your knowledge of your narrow domain with knowledge of how to teach a wider domain.
It is time to educate our children for tomorrow's world, and for that they will need specific knowledge of math facts and a strong grasp of mathematical skills. If you don't teach students skills, they're not going to know how to use excel or any of the tools of the future.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 1, 2009 at 2:24 pm
And I agree with you that what Gladwell says about numbers and languages makes certain concepts innately clear. I'd forgotten about it, but it's a good point.
The older I get, the more I think that the key isn't math facts--per se--after all, that's a pretty limited set of knowledge, but how to figure out what kind of math to use to solve various problems--so both practical and conceptual.
I think there is some truth, also, that an overemphasis on the drill-and-kill aspects of math misleads people as to what math is. You can be slow at drills, but a good conceptual thinker in math. You can be great at drills, but have a poor sense of how to use math outside the classroom.
Posted by VoxPop, a resident of the Old Palo Alto neighborhood, on Oct 1, 2009 at 2:54 pm
Be a good idea to look into the development of the brain when talking about what and when to teach what part of math. Drill and kill is appropriate for brains at a certain developmental stage, it also fits with Gladwell's "10,000 hours to master a subject," which means a student has to learn the basics so the math mind has the equivalent of muscle memory in athletes or artists -- you "do" instinctively, and don't need to think about it. Then you can move on.
I have heard that our brains are not ready for algebra and more advanced concepts until teenagehood, roughly, and several physicists and a theoretical mathematician of my acquaintance all have said repeatedly that our brains are not developed enough to understand the beauty of math (by which they mean "have the ability to really understand really advanced concepts") until college or even graduate school.
P.S. The theoretical mathematician just uses a pencil and a pad of paper to aid his thinking.
Posted by GGG, a resident of the Barron Park neighborhood, on Oct 1, 2009 at 3:09 pm
In fact, I think there are two components needed for proficiency in a subject, whether it's math or social studies. You need a knowledge of some fact field (e.g. multiplication tables; relative populations of North and South before the Civil War); and you need a mastery of some domain specific skills (e.g. decoding a word problem; unpacking the diverse causes of an event).
Neither knowledge nor skill is very useful on its own. You can't figure out what kind of math to use to solve various problems unless you can do basic operations and know what the number line feels like (how much farther out is the next cube? the next prime?) But you also won't get far if all you can do is multiplication and division.
So it's not really an either or situation. We don't need to choose between drill and kill on the one hand and a conceptual focus with no mastery of multiplication. We need kids who have attained automaticity in math skills and who are deep conceptual thinkers.
That is the problem with edm--it lies at one end of the spectrum. It would be better if we had a more centrist text that gives kids both conceptual understanding and a firm grasp on efficient algorithms.
Posted by Jim H., a resident of the Duveneck/St. Francis neighborhood, on Oct 1, 2009 at 9:42 pm
Have you listened to yourself? "Do you really think that the Palo Alto children of parents with college degrees and graduate degrees will really have difficulty understanding multiplication? We aren't an inner-city school. ... Teaching more methods is purely a waste of time. Plus, the frustration of the parents who have never learned the wacky five EDM methods of multiplying (thus cannot explain it to their children) isn't going to help the child's attitude towards math. They'll witness their parents finding math difficult which will affect their attitudes ("If dad, with a graduate degree in science cannot understand this, how can I?").
So, you're saying, inner city kids are the only ones having trouble with math. A college degree means your kids will be smart. And, despite the fact that you are a Palo Alto genius, you'll have a tough time figuring out elementary school math shown in a different way than you learned as a child.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 2, 2009 at 1:54 am
As it happens, I also have issues with Gladwell's 10,000 hours idea that's so popular right now. He uses Bill Gates early practice as a programmer as evidence. One big problem: Gates has never been known as a *programming* genius. Terrific businessman, but there are better programmers. There are also fields, such as opera singing, where the wear and tear on the voice makes 10,000 hours a no-go. It's another example of what I find weak about Gladwell--he looks for facts that support his idea and ignores the facts that don't. He doesn't really try to disprove his hypotheses.
As for math--there's a lot of individual variation. I've known the child-prodigy types who did algebra in grade school. So, yes, it may require grad school to truly appreciate the beauty of math--but some people hit grad school at a much earlier age than do the rest of us.
There is an age issue with high-level math though--but it's on the other end. Mathematical discoveries tend to be made by those under 35.
I'm not denying the need to know multiplication tables--but that's really pretty simple. To use your Civil War example--the relative populations of the North and South won't mean anything *or be retained* unless there's a context.
Is there enough repetition and drill in EDM? My kid's teacher clearly thinks not. At the same time, my kid's new enthusiasm for math because of EDM interests me. If it's relatively easy for teachers to supplement EDM with drills and problems for the math facts while the kids improve their conceptual thinking about math, I could live with that--but we'll see what happens.
I'd be interested in hearing from other parents whose kids are actually doing EDM as the year goes along. Ohlone's situation is a bit singular because of the mixed-grades.
Posted by Redux, a member of the Palo Alto High School community, on Oct 2, 2009 at 4:08 am
No need to wait. Ask schools that have used it and since dropped it. Reading some of the old posts posted above, the list of former EDM school district fans seems quite illustrious including private schools around here with great teachers and students as smart as PAUSD's like Keys, International School and St Josephs. Didn't Poway, the S. Ca. public school district Skelly came from, drop it too?
There is even a post from a New Jersey school board member who explained why her district, teachers and staff, unanimously voted to drop EDM. Web Link about 15 posts down.
EDM didn't work for students there even though teachers supplemented and parents privately tutored. Her district sounds like it is much like ours - math/science related employers attracting smart, well educated parents to a district not wanting for resources which supported EDM with lots of professional development.
Posted by Kathleen Jalalpour, a resident of the Midtown neighborhood, on Oct 2, 2009 at 7:07 am
Keys School in Palo Alto has been using Singapore Math for 4 years, and we are pleased with its approach. Kathleen Jalalpour and Corrinne Lieu, 2 teachers from Keys, will be giving a free informational talk about SPM on Oct 14th at 7 pm at Cubberley Center in Palo Alto. Email ThePiProject@gmail.com for info, or to reserve a spot.
Posted by GGG, a resident of the Barron Park neighborhood, on Oct 2, 2009 at 9:17 am
The multiplication tables may be simple, but edm does not call for mastering them. Neither does it teach efficient algorithms for other operations. By using these operations, students gain a mathematical context. In the Civil War example, the relative populations of North and South are PART of the context, not something students should retain for its own sake. The point is not to memorize numbers but rather to understand the roles those numbers played.
Yes, it is possible for teacher to assemble an acceptable curriculum by supplementing edm with appropriate material. The problem is that not every teacher will do it and they will all do it in their own ways, meaning some kids are not going to be adequately prepared. The district should have taken a middle path and picked a text that guides instruction with both elements, conceptual and fact-based.
The kids who will lose out are those who come from families who are poor or disengaged from the schools.
Ohlonepar is right about age and math. The real heavy conceptual lifting in mathematics and logic has been accomplished by 25 or so. After that, the discoveries tend to be more mundane.
Posted by pamom, a resident of the Fairmeadow neighborhood, on Oct 2, 2009 at 9:34 am
Given that others have tried EDM and dropped the program, why the push here in Palo Alto? Most likely because parents will make sure their kids' math is supplemented and it'll make EDM look good. One of the problems here that has not been mentioned is that these kinds of programs are designed for all levels of ability in the classroom, i.e., no ability grouping allowed. So these programs are pushed not because they are great, but because they serve the purpose in eliminating ability grouping/laning/or tracking, a real no-no. Educators see ability grouping as elitist. If kids get dumbed down, tough luck.
Posted by Ze'ev Wurman, a resident of the Palo Verde neighborhood, on Oct 2, 2009 at 1:12 pm
I attended the EM meeting and came out very disappointed. As the district brought in the supposed "brains" behind the series, I expected more than mostly a sales pitch and a dog-and-pony show from them.
Instead, they sung paeans to certain class activities, they made people stand shoulder to shoulder to display the number line that kids supposedly see every day in the classroom and use as modeling tool, they enthused about games with making up numbers that kids play in class, etc. All nice activities if they happen in moderation, but the perception given was that those were the "fun" activities that comprise much of the class time. As I said, the focus seemed clear to provide parents with good fuzzies about the program, rather than delve into its depths or the reasoning and the research base behind it.
But I would not be telling the whole truth if I were to say they completely ignored the research. Unfortunately, if the large dog-and-pony section was disappointing, the smaller research section was misleading and deceitful.
Andy Isaacs did bring up the relative longevity of the program, some 25 years, and the large number of studies (he mentioned around 35, if my memory serves) that have been done on it. He repeatedly recalled the exalted name of the National Research Council that found EM to have the most research studies. At the same time he was very careful not to mention that the Department of Education's What Works Clearinghouse found even more studies of EM, 61 to be precise, yet it also found only four (4) of them to be of acceptable quality with reservations, and none (0!) to be of acceptable quality without reservations. Web Link
More interesting, the word "spiral" or "spiraling" did not cross his (or anyone's) lips during the presentation, yet until very recently EM prided itself of its extensive spiraling. Spiraling was, in fact, until recently described by Andy Isaacs himself as a hallmark of Everyday Mathematics Web Link, yet it curiously disappeared from his vocabulary since then. Instead of "spiraling" we now have "distributed practice" becoming the buzzword for EM, and one wonders whether there is any connection between Isaacs' amnesia and last year's National Mathematics Panel report Web Link that clearly came out against spiraling as a damaging practice without research support and, on the other hand, recommended "distributed practice" as an effective and research-supported technique. This is where I found Andy Isaacs' to be most deceitful -- he repeatedly praised EM's distributed practice and quoted the extant research support for it, but he surely knows that the distributed practice that has research support consists of (a) focused teaching to mastery including appropriate practice, (b) additional practice (but not re-teaching!) preferably including quizzing after 1-2 months period, and (c) selective and sparse inclusion of practice items throughout additional period of few weeks or months Web Link . Everyday Mathematics' so-called "distributed -practice" is nothing like that -- it meanders through non-focused teaching and re-teaching of a given skill over period of two or three years(!), not teaching to mastery at any point in time, and all repetitions including re-teaching. Basically this is the infamous EM spiraling, now hiding behind a new "respectable" name. So much for Mr. Isaacs's scientific integrity. Small wonder that the University of Chicago, where EM originated, decided to close its School of Education some 12 years ago.
I know I shouldn't be surprised, but I still found the meeting disappointing in its commercial pitch and research obfuscation.
Posted by EDM Opponent, a member of the Gunn High School community, on Oct 2, 2009 at 1:31 pm
Thanks for the summary, Ze'ev. Sounds like they know parents wouldn't like the program if they told the truth! EDM is a marketing scam led by a PAUSD committee who was bullied by the committee leaders into accepting the program. And politics prevailed. Fortunately, this "only" affects our elementary schools. We can teach our children elementary school math on our own.
Posted by Revisionist History, a member of the Jordan Middle School community, on Oct 2, 2009 at 2:46 pm
Thanks for the report.
Funny isn't it that just a few months ago the word "spiral" was a proud part of the PAUSD-EDM vernacular.
“This program has a “spiral” design that informally introduces topics for 2 years before formal study. If your child doesn’t master the topic the first time, understanding will increase the next time.”
PAUSD Materials on EDM (Board Packet “What is Spiraling?"):
“Spiraling refers to having students be introduced to a topic, concept, or skill, practicing it, and then returning to practice the skill again after a period of time. Often when the topic, concept, or skill is revisited . . . mastery is developed. The spiral may happen during a school year or over a span of grade levels.”
PAUSD admitted even back then that "continuing research involving ‘spiraling’ needs to be conducted.”
Could this new silence be because Palo Alto parents were convincing about the folly of a district adopting a "research-based" program designed around the "spiral" concept for which there is no research basis?
Posted by bad process, a resident of Another Palo Alto neighborhood, on Oct 2, 2009 at 3:03 pm
don't forget Barbara Klausner personally and single-handedly fixed everything wrong with EDM, we must have the new and improved version, and the Elementary principals did their own dog and pony show at the board meeting, to guarantee this would work. That alone should have shut this process down.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 2, 2009 at 5:06 pm
I'm well aware of the many, many complaints about EDM. What I'm interested in is how it's working here and now. It interests me how the teachers here are using it and how the kids here are working with it.
I know where to go if I want to read the EDM debates again. I'm more interested in what's happening and how EDM is and isn't being implemented.
I was interested when the private-school administrator volunteered that it was a favorite system--I hadn't given my opinion of it one way or another. He also said you had to take it on faith the first couple of years, but the results really showed from middle school on. So, it will be interesting to see.
I understand your concern, but I'm not convinced that the district and its teachers won't work to keep PAUSD's math scores up. I don't think the kids are going to be left hanging high and dry.
FWIW, there were already huge variations in how teachers taught and what they taught under the old system. If anything, the EDM controversy seems to have increased the focus on how teachers are teaching math in the district. I have a hunch, actually, that scores will go up not because EDM is a better system or because parents are using more tutoring services, but because the teachers and the district feel they have something to prove. In fact, I wouldn't be at all surprised to see math scores rise while reading scores drop.
Ze'ev, of course the EDM folks didn't talk about spirals in their presentation--why would they when it's become a loaded term around here?
Posted by An Engineer, a resident of the Downtown North neighborhood, on Oct 2, 2009 at 5:27 pm
"Typical engineer worldview. Those who disagree with you are unlearned, and your domain knowledge gives mastery of all skills and knowledge. Thanks for the laugh."
I seem to have pushed somebody's button, somebody who cannot tell the difference between class innuendoes and debate. He/she also claims a better mathematics education than mine, having no idea of my background. Data-free approaches like these can never lead to a correct result.
For the record, I make two points: (1) Long division of numbers is an obsolete skill in today's real world, and (2) long division of numbers is a purely rote exercise that conveys no real understanding of the mathematics involved.
Posted by respect, a resident of Another Palo Alto neighborhood, on Oct 2, 2009 at 6:46 pm
I think you conceptualize several things when you do long division, you also develop a practice of manipulating longer sequences of numbers, and it's also a little bit like a test.
This goes into this how many times? and this minus this is how much? And did I check my answer? oh look how long this is, I can do it!
I loved doing long division when I was a kid, and now I also use Excel.
However useless you want to make long division, it's not nearly as harmful as allowing a bad process to run amok, to adopt an expensive and slick new program that may be the last thing we need. The dog and pony show and deceit that Ze'ev pointed out is not about real Mathematics, this is Elementary school! it is about a very big $Sales job.
Posted by Cm - Army, Engineer, a resident of another community, on Oct 2, 2009 at 6:51 pm
To EDM Opponent,
It is not about where you live that impacts your knowledge base. Additionally, if ALL the students grasp multiplication using one method, then the instructor would not have to broach other methods of teaching. Not everyone learns the same, you have your visual, auditory, tactile, kinesthetic learners...to name a few.
Personally I can't stand the latice method. But if it helps some kids feel a sense of accomplishment before moving on to a more efficient method, then do it...so as to avoid frustration. It sounds as though it is the parents who are then frustrated because it is foreign to them. If you can do it better, then home school your child and stop griping about what the public schools are doing.
Posted by Ze'ev Wurman, a resident of the Palo Verde neighborhood, on Oct 2, 2009 at 7:15 pm
"of course the EDM folks didn't talk about spirals in their presentation--why would they when it's become a loaded term around here?"
Let me understand. Spiraling has been used in education to describe curriculum for easily over forty years and for twenty five years EM regularly -- and quite proudly -- described its approach as a spiraling one. Now, you believe that because it has became a "loaded term" around Palo Alto, it is OK for one of the leading researchers behind EM to casually substitute "spiraling" for another term, "distributed practice", even if distributed practice is already widely used in education research literature to describe a completely different concept from spiraling; all the while also claiming the research support for the original distributed practice, as a support for his ersatz term. Did I get it right?
Posted by GGG, a resident of the Barron Park neighborhood, on Oct 2, 2009 at 9:04 pm
"He/she also claims a better mathematics education than mine, having no idea of my background. "
You claim privileged knowledge in this debate because you're an engineer. I pointed out that your domain knowledge is irrelevant (and frankly your sense of your abilities seems inflated--after all, engineers tend to get through the math, not do well with it; no need to get touchy: you invoked your "expert status").
You certainly have strong opinions about what to teach children in terms of math, but your opinion is untethered to knowledge of pedagogy and curriculum.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 3, 2009 at 1:45 am
No, you shouldn't be surprised. You, like many other people, adapt your message so that it stands the best chance of being received well by a given audience. We both know that you're aware of that.
If a term becomes loaded, then it's not surprising that a different term would be used so that people don't put up an immediate negative reaction and tune out the argument.
For what it's worth, I did find several ed. cites that used both "spiraling" and "distributed practice" to describe EDM and date back more than five years. It's possible that the terms aren't as fixed as they were a couple of decades ago. "Distributed practice" was used in 2003 in a discussion of Everyday Math here:
There are earlier links as well--from its inception, according a 2000 EDM research link, EDM was developed in a way that attempted to incorporate "distributed practice". Does it do it successfully? Well, that, I think, is a legit argument. My personal hunch is yeah, but with some supplementing on math facts. (And, sorry, I consider it a plus that my kid likes it. When kids like something, they learn and they retain. That said, different kids enjoy different things, which is why I'm interested in how it's working for other kids in the district and how the teachers are handling it.)
So the use of "distributed practice" in context EDM predates last year--I think your insinuations go a bit far. I think you're better off arguing that EDM doesn't meet its goals instead of accusing Isaacs of deep deception here.
Oh, by the way,
Actually, there have been numerous famous musicians who never learned to read music and play by ear. Only a small percentage of people who make music ever learn the formal rules of theory and composition--and that only much, much after they've learned how to make music. You hear some three-year-olds sing--they don't know the rules, they just know how to repeat what they've heard.
People were making music long before they figured out rules for it.
Posted by First learn, then practice, a member of the Palo Alto High School community, on Oct 3, 2009 at 7:51 am
From what I know about EDM, it does incorporate distributed PRACTICE. Some call this spiral review (aka review of what has already been learned and mastered). There is ample research support for this post-learning/post-mastery reinforcement method. It's a good thing.
It's just that Andy Isaacs is calling EDM's PRE-mastery learning method "distributed practice" too. Calling the LEARNING part something that it isn't in order to piggy back on favorable research is the sales job Ze'ev is referring to.
EDM's pre-mastery LEARNING method is a spiral. Per EDM, it is no biggy if kids don't understand before teachers jump to a completely different topic. EDM says that students will see it plenty of times over the next few years and one day it should sink in if for no other reason than that they will have seen it so many times. In EDM-world, there is no focused working on something until you get it.
Why did Mr. Isaacs conflate the two concepts in his talk the other night? He cannot talk about spiral learning research and sell books because:
1) There is no valid meaningful research support for spiral LEARNING.
2) Everyone knows that, especially now that the National Math Panel's final report is public (1st recommendation to elementary schools -- run as far away as you can from programs based on spiral learning).
3) Distributed PRACTICE research shows that you need to learn, understand and master the concept before you start practicing it.
So if a student hasn't mastered the concept because of spiral LEARNING, EDM's distributed PRACTICE doesn't do him or her much good.
Don't get me wrong, students benefit from the conceptual that programs like EDM offer. Given that EDM says that students need to work on the conceptual in class 75-90 minutes a day though, the problem is that teachers don't have time to teach EDM AND teach concepts to mastery. Hence the reason for parent pleas last year calling for a text book in the middle (not the far left end) of the spectrum so kids could get it all during the day and just be kids when they got home. Now that we have EDM, many kids come home after a long school day to 30+ minutes of parent-driven tutoring so they can learn and master the concepts EDM touches and runs from.
To someone else's point above, there will be some PAUSD students who will master it the first run through. The problem is most won't, even in Palo Alto.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Oct 3, 2009 at 5:23 pm
[Portion removed by Palo Alto Online staff.]
I have made my points based on my professional experience using mathematics every working day for decades. You may find it easier to teach children as they have been taught for generations. I understand how you may find that much easier. However, that approach is obsolete; it does not prepare children to cope with today's real world professional environment.
Posted by EDM Opponent, a member of the Gunn High School community, on Oct 3, 2009 at 7:13 pm
CM: if a child can learn the lattice method or the other EDM approaches to multiplication, the same child can learn the traditional method. Those other methods are no easier than the traditional method. EDM tells teachers they have additional ways to teach multiplication so if children cannot understand the traditional method, they can be taught another method. So teachers think the additional methods are easier, when they are not.
An Engineer: Do you realize that EDM is for elementary school only? You are talking about preparing children for the real world - that's middle school and high school math, not elementary math.
Posted by GGG, a resident of the Barron Park neighborhood, on Oct 3, 2009 at 8:45 pm
Yes, you did indeed try to make points based on experience using math, but as I suggested to you, that experience is irrelevant. The question is not mathematical but pedagogical.
When you suggest that anything besides edm is teaching children "as they have been taught for decades," you make it very clear that you have not engaged with any of these issues in a serious manner or even informed yourself. Almost no one involved in this debate advocates returning to the dark ages. You would have a better chance of making a germane and coherent point if you read up before trying to comment.
You are overly invested in your own experience with long division and as an engineer, and you miss the larger debate about learning mathematics at a deeper level.
The best way to prepare children for the real world of tomorrow is to adopt a middle-ground textbook that expects children to learn to mastery and supports deep conceptual learning.
Posted by Try Really Listening, a resident of the College Terrace neighborhood, on Oct 3, 2009 at 9:17 pm
I went to the EDM talk and I walked away fairly impressed with the material. It's clear that there has been lots of thought put into the materials. I also appreciated the fact that there seems to be some division between EDM's marketers and its authors. The folks at University of Chicago appear to have veto rights over what is in the material. I hadn't heard of that and it sounds like a good idea.
The parents with whom I talk seem fairly happy.
What was not impressive was Ze'ev's activities during the meeting. I have always found him to be a nice person, but at the meeting he, another older man, and an older woman spent the whole time talking among each other, despite the fact that they were sitting right in front of the presenters. I have rarely seen people act so rude. I am surprised that Ze'ev could recount what happened. He seemed too busy with distracting side conversations and rolling his eyes. It did not reflect well on him or the community.
Posted by bad process, a resident of Another Palo Alto neighborhood, on Oct 3, 2009 at 11:42 pm
try really listening,
"also appreciated the fact that there seems to be some division between EDM's marketers and its authors. The folks at University of Chicago appear to have veto rights over what is in the material."
I don't think anyone expected for the marketers to have written the materials.
Actually what works well with EDM is the marketing. And the materials have been impressive all along. That doesn't mean it was reason to adopt an expensive program, costing not just a lot more money, but time (for Elementary Math!), and to have accepted the shabby process. Ze'ev and the other "older" people talking amongst themselves is no big deal compared to that.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 4, 2009 at 12:04 am
It's early in the process, but so far EDM doesn't seem to be difficult for the kids I see. I'll be interested to see how that goes as the year progresses and, I assume, more advanced concepts are introduced. The textbook I've seen doesn't seem too off-kilter to me, but it's not an area of expertise for me.
But it seems to me that what you're talking about is two sides of the same coin--i.e. going back and reviewing reinforces learning. However, doesn't that indicate that there wasn't complete mastery of the subject in the first place. I mean, I'm at a place where reviewing my multiplication tables won't do anything for me--they're solid.
As to who learns what when--I keep thinking back to some study or another that shows that homework in excess of mastery becomes counterproductive. It's one of the issues with teaching gifted kids--too much repetition, not enough new, makes them tune out. EDM seems to cut both ways here--it's stimulating and has less repetition, at the same time it limits differentiated instruction among individual students--at least so far.
Thanks for giving your view of the meeting. It seems to me that good old-fashioned note-passing or up-to-date texting would have been better than talking through a meeting. Clearly, the math wars are a cause near and dear to Mr. Wurman, but it would be a courtesy to those of us who actually have children using the program to let us hear about it without disruption. (And then blog and post about it online).
Posted by Ze'ev Wurman, a resident of the Palo Verde neighborhood, on Oct 4, 2009 at 11:53 am
"[G]oing back and reviewing reinforces learning. However, doesn't that indicate that there wasn't complete mastery of the subject in the first place. I mean, I'm at a place where reviewing my multiplication tables won't do anything for me--they're solid."
As you say, this is not an area of expertise to you. Why don't you spend some time on the Dept. of Ed web site I provided before: Web Link and listen to cognition experts speak on this topic? You are simply wrong that the benefits of distributed practice have to do with mastery of concepts, or that they "reinforce learning". The focus of distributed practice is on long term memory storage and retrieval -- concept mastery is assumed. In fact, an actual *damage* may happen if one does distributed practice with a topic that is not well understood, as one codifies misconceptions in one's long term memory, and uprooting them later is much more difficult. That, in fact, might be the essential mechanism underlying the ineffectiveness of spiral teaching, in addition to its enormous time waste.
As to your specific example of multiplication table, there is no concept to understand in it, after understanding once what multiplication table is. There is no additional "depth" in knowing that 6x8 is 48 than there is in knowing that 2x4 is 8. All that is left is effective storage in long term memory and fast retrieval, and distributed practice will probably be helpful in that.
Posted by Ze'ev Wurman, a resident of the Palo Verde neighborhood, on Oct 4, 2009 at 12:54 pm
A slight correction to my previous post. I interpreted and used learning in "reinforce learning" in the sense of learning & understanding of concepts. It is also reasonable to use learning in its narrower sense of memorization. In that case distributed practice does "reinforce learning."
Posted by An Engineer, a resident of the Downtown North neighborhood, on Oct 4, 2009 at 6:03 pm
"When you suggest that anything besides edm is teaching children "as they have been taught for decades," you make it very clear that you have not engaged with any of these issues in a serious manner or even informed yourself."
G3: Had you not been so totally fixated on bashing my profession and had instead actually read my postings to inform yourself, you would know that I have said nothing about EDM per se. I am merely stating an informed position, based on long professional experience, contrary to the drill-and-kill pedagogy advocated early in this thread.
However, I have made my points, and thoughtful participants (like my fave OhlonePar) have joined in a debate, so if you don't mind I'll ignore your further japes and follow that discussion.
Posted by GGG, a resident of the Barron Park neighborhood, on Oct 4, 2009 at 9:06 pm
Be my guest: backpedal all you want. It's not really possible to engage when you first deride alternatives to edm as ineffective, then say you have no opinion, and finally change tack in the same post to say that everything besides edm is drill and kill.
You keep invoking your engineering background as giving you an informed position in a totally unrelated field, education. On that basis, I'm sure you wouldn't object if pastry chefs piped up with an "informed position" in engineering--I'll just send them down to your workplace, shall I?
As far as informed positions go, there is fairly widespread consensus that EDM is a fringe program with tremendous problems. It is a shame that the district decision was hijacked in picking it. It's a shame they did not choose a middle-of-the-road program. However, given that approach, the district will not be surprised if parents come out swinging the next time a controversial matter arises. Parents are now aware that the district listens only to threats.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 4, 2009 at 9:27 pm
I'm more a visual than an auditory learner, so I'd always rather read than listen to experts on my erratic connection. It's a large site--which research would you like me and other people to read?
I said going back and reviewing reinforces learning--you're not really disputing that, are you? I think we're having a confusion with terminology here. We all look at our notes and in reviewing can see connections we didn't see before.
Yes, multiplication is simple in concept. So is most elementary-school math--the beauty of math, in my opinion, is the clarity of its basic concepts. It's not ambiguous in the way of history, say.
Your objection, as I understand it, is that children won't learn something correctly and short reviews of that subject will reinforce erroneous thinking--i.e. if you learn a piece of music incorrectly, practicing it reinforces the error.
My own experience with both math and music is that this is more of an issue on the practical level, not the conceptual. Indeed, it *is* one of memorization--physical memory in the case of playing an instrument.
So what is the "actual damage" that may ensue? I ask this because I find it's the norm that a fair number of people will be "unclear on the concept" at any given point. I always figure that if you discuss it enough, find the right words, give people time to mull things over or experience things that eventually or at least occasionally a light bulb goes off. That, indeed, this is known as life.
You would argue, then, that math instruction is different than this because later concepts build on earlier concepts? My counter would be is that historically we haven't taught conceptual math well in the early years. Instead, historically, the heavy focus has been on practical math with a somewhat abrupt introduction of conceptual math in middle school. The first round of the "new math" was meant as a corrective to this.
I'm hearing slightly different things here, though. Your concern seems to be that too little,too early results in long-term misunderstanding of concepts. But most of the anti-EDM stuff I've read (and that means the links people posted in the earlier debates)focuses on kids not knowing practical math--i.e. multiplying fractions.
If the former is the issue, then I'd like some links to specific research on it. If it's the latter, then I think the supplementing that's occurring should create a workable system.
Speaking of bad process, two wrongs don't make a right. When I attend a meeting where I know the speakers are going to annoy me, I tend to sit in back and scribble derogatory notes--but there is a fundamental courtesy that I think is a good thing.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Oct 5, 2009 at 12:10 pm
"Engineer -- who advocates "drill and kill" as you put it? I don't know any parent who wants that. You are saying it's EDM or there's no alternative? For an engineer, you really limit your options."
If you read this thread from the beginning you'd find the answer to your question. Specifically, I've been responding to the sentiments expressed by BP mom (poster #1): "I think 4th graders should be working on numbers, multiplications, divisions and figuring out calculations not writing in math class...throw out this ridiculous program and get back to basics." and by Some guy (poster #3):"Why are kids in 4th grade writing about thermometers and not learning long division etc.?"
For the record, I have neither supported nor condemned EDM, unfounded accusations by certain individuals notwithstanding. But I do vehemently condemn the drill and kill approach espoused by many of its critics, which turns off children to the wonder of real math, and that inculcates a mindless rote methodology which they then have to unlearn before they can discover anything new in math.
Long division is a pet peeve of mine. It not only exemplifies my points in spades, but it is an obsolete, useless skill in a world of ubiquitous computers and calculators.
Posted by respect, a resident of Another Palo Alto neighborhood, on Oct 5, 2009 at 2:06 pm
Learning styles don't exist,
Add to the myth alerts you posted, the pet theories like Engineer's on long division, and Ohlone Par's incessant analysis and argument for everything that can bolster trendy mythological ideas about education. Parents that will try anything. Plenty of experiments to still be had in schools with support like that, not always for the benefit of students. Are there any wacky learning theories that have transformed education so far?
Posted by Ze'ev Wurman, a resident of the Palo Verde neighborhood, on Oct 5, 2009 at 3:37 pm
As you already heard from others, your "learning style" is probably more a matter of your personal likes and dislikes than a matter of "style." Be it as it may, the "spacing learning over time" is the specific topic, and "psychology of learning" is the overarching subject on that web site that I pointed to Web Link . On that site, the "Learn What Works" section has the highest fidelity of explanation, and its expert interviews are its highlights. The "See What Works" section has examples of practices that are reasonably close to the intended ones, but they should not be taken as perfect. In other words, if you have limited time stick to the expert interviews.
You write that surely "going back and reviewing reinforces learning." In a sense you are right, but that's akin to saying "learning is good." It is so general as to be meaningless.
Distributed practice is a rather specific approach to the pattern of 'learn-practice-delay-reinforce through practice' sequence. It has been studied and found effective. Spiral teaching does not fit this specific pattern, and anyone who is reasonably steeped in education research understands the difference. While it may not be obvious to you, it is supposed to be obvious to Andy Isaacs -- after all, he came to us as a "representative of the 25 years of UCSMP scholarship behind Everyday Math", to paraphrase his own words at the last week PAUSD talk. If he behaves as if the two are the same, either he is a terrible researcher or he is being disingenuous. Neither one should be acceptable to us.
Finally, you misinterpret my concerns. You believe that my objection "is that children won't learn something correctly and short reviews of that subject will reinforce erroneous thinking--i.e. if you learn a piece of music incorrectly, practicing it reinforces the error." I suggested that reinforcing erroneous understanding *may* be a contributor to the ineffectiveness of spiral teaching. I have no evidence to support that suggestion, and I simply made that comment as something that may be worth considering. My real objection was to the fact that spiral teaching has found no serious support in empirical research yet Andy Isaacs, who is brought in by PAUSD as a *scholarly* authority, cavalierly conflates two distinct educational practices to prop his own program. My educational argument is not with you, particularly since you acknowledge your limited knowledge of the subject--it is with the false cloak of academic authority that PAUSD found itself behind.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 5, 2009 at 10:57 pm
Learning Styles and respect,
Please look at what I wrote before you leap--i.e. I never used the word "style" and I would never use it in such a jargon-y fashion.
However, since you would jump, I wouldn't say that that clip demonstrates that learning styles don't exist, simply that not all types of knowledge lend themselves to multiple modalities of learning. The professor, in fact, admits that there are people with stronger visualization skills than others.
What he demonstrates is that a rather limited test of different learning styles (remembering a list of words) doesn't lend itself to multiple styles of learning--because of the nature of the task. It would have been interesting if he'd taken the task a bit further--spelling the words, for example. How much does it or does it not help to write the words out v. look at them?
This is one reason why I prefer to look at things in print--it's easier to see the parameters of the experiment.
Basically, the prof. is claiming that his test disproves more than it does. Not an uncommon gambit in academia. You see it on the other side of the debate as well.
However, will someone with strong visualization skills have an easier time recalling the shapes of countries--a visual task? Sounds like, yes, indeed, they will. And, I suspect, they are likely to be drawn to pursuits that take advantage of these aptitudes. Can one use the word "style" to describe this? Why not? It's not a scientifically precise term, after all.
In my case, I read much faster than people speak and much, much faster than my computer puts through little YouTube clips. And, yes, my visualization skills are strong.
As for "whacky learning theories" transforming education--history is full of them. Public education and literacy for all are two big ones I can think of. Then there were those very odd theories about women actually being capable of learning anything. Current education is very, very different from education 150 years ago.
Really, respect, you set your self up with a comment like that. When you snipe at someone for "incessant analysis", it pays to think for three seconds before posting. But, hey, maybe masochism's your bag.
The word "style" has everything to do with personal likes and dislikes. I'm sorry to see such a solid old word subverted into jargon. You might also ponder what causes those likes and dislikes.
Though I was not attempting to start a debate on *that subject* I have a preference, never said it was otherwise. In part, because I have my own set of critiques of Howard Gardiner's work on multiple intelligences--I find them more useful on a practical level (why not try it this way if that way didn't work?) than theoretically sound--doesn't hang together at all.
Back to the topic, from that sounds of it, there's a dispute about definitions here--and how far research can be stretched to support a particular system. You feel, as I understand it, that some research is being ignored and that some is being unduly appropriated.
As for "misinterpret"--not precisely. I was extending the logic to get a clearer idea of what you meant--hadn't gotten to the point of interpretation. We do not know each other and do not share a common frame of reference on this issue. As much as anything, I'm trying to cut through the jargon.
Nor, I think, do we share the same concerns. I don't have a "side" on this argument. (Which has constituted a side in itself.) My concern is will my kid learn math? So, far, I think yes.
This is why I was interested in your speculation about why kids didn't learn with spirals. That was a little different that what I'd been reading (And, honestly, was not my experience with math as a child. It was not an issue of misunderstanding, but of not-understanding. If I didn't understand something, I didn't misuse it; I didn't use it.) The main issue I've heard is that the kids aren't as solid on fundamentals as they could be. That strikes me as something that can be dealt with with supplemental materials.
Is it ideal? No--but I don't think there's an ideal system because children differ in their likes, dislikes and aptitudes.
Posted by paloaltomom, a resident of the Fairmeadow neighborhood, on Oct 6, 2009 at 9:33 am
Engineer, here are your examples of "drill and kill": Specifically, I've been responding to the sentiments expressed by BP mom (poster #1): "I think 4th graders should be working on numbers, multiplications, divisions and figuring out calculations not writing in math class...throw out this ridiculous program and get back to basics." and by Some guy (poster #3):"Why are kids in 4th grade writing about thermometers and not learning long division etc.?"
My response to your examples above, is that is not proof of "drill and kill" to me. How else are students going to learn basic math if there is no practice? Or no drills at all? People practice all kinds of skills in order to master them in just about any field you can think of.
You go on with "For the record, I have neither supported nor condemned EDM, unfounded accusations by certain individuals notwithstanding. But I do vehemently condemn the drill and kill approach espoused by many of its critics, which turns off children to the wonder of real math, and that inculcates a mindless rote methodology which they then have to unlearn before they can discover anything new in math." My response: But I doubt that traditional math has turned kids off to math en masse. What does turn them off is when they get to high school and find they don't have the necessary skills to take the higher level math courses.
Other countries have not gutted their math programs and their students do much better in math. These new math programs that focus too much on project learning do a disservice to our kids.
Posted by An Engineer, a resident of the Downtown North neighborhood, on Oct 6, 2009 at 9:56 am
"What does turn them [kids] off is when they get to high school and find they don't have the necessary skills to take the higher level math courses."
Bingo! What students need is a solid understanding of fundamental MDAS (multiply, divide, add, subtract) concepts, what they mean and how to apply them.
To quote the great applied mathematician Richard Hamming once more: "The purpose of computing is not numbers, but insight." It is those insights that will enable the students to quickly and firmly grasp the higher math concepts. A rote based, memorize-and-regurgitate approach will not work. Students will lose time and opportunity unlearning it -- provided they have the personal insight or coaching to try and the dedication to succeed. Many just give up in bewilderment.
Posted by Ze'ev Wurman, a resident of the Palo Verde neighborhood, on Oct 6, 2009 at 10:55 am
"Back to the topic, from that sounds of it, there's a dispute about definitions here--and how far research can be stretched to support a particular system. You feel, as I understand it, that some research is being ignored and that some is being unduly appropriated."
I think Bill Clinton should have had you as his lawyer, when he claimed that he "had no sexual relations with that woman." After all, as you say it so artfully here, wasn't that simply just a case of a "dispute about definitions" there? Or, as Bill Clinton put it less artfully, didn't that simply depend "on what the meaning of the word is is"?
But no, you are wrong. This is not a dispute about definitions. This is about scholars and integrity. And about the defenders of scholars who behave like politicians.
Posted by EDM Opponent, a member of the Gunn High School community, on Oct 6, 2009 at 11:12 am
Re your statement: "Bingo! What students need is a solid understanding of fundamental MDAS (multiply, divide, add, subtract) concepts, what they mean and how to apply them."
Everyday Math tries to teach math before the students even have the concept of numbers, before they even know how to add, subtract, multiply. That's why it is so confusing to children!!! They try to jump ahead and have children estimate numbers before they even know what 300 or 60 is. Those children who already have an understanding of numbers or already know how to multiply, divide, add, subtract can understand EDM easier than others. This is where the teachers will have to supplement EDM.
Posted by EDM Opponent, a member of the Gunn High School community, on Oct 6, 2009 at 7:28 pm
Think... I have the same questions for you. My family experienced EDM for 5 years. Yes, longer than a simple drop-in-to-see-EDM-being taught-in-a-classroom as you have (or have not). The teachers at the school were frustrated and so were the children. Mine, however, were not, because I supplemented them with drill worksheets which they did not mind at all. They said if they hadn't learned their addition/subtraction, etc. through the worksheets, EDM would have been confusing.
Posted by bad process, a resident of Another Palo Alto neighborhood, on Oct 6, 2009 at 9:02 pm
I think we may now be spiraling here.
in the end, the only measure of success will be if the achievement gap kids do better in Math or that more kids go into the advanced Math in Middle School . Already math scores are very high for most Elementary schools and a large percentage of kids do well in math after 5th grade, I've heard there are like 6 math lanes in High School, and probably 2-3 are fairly advanced.
the story here is the bad process and EXPENSE. How shiny did this program need to be, we just had to go for the excess. We have good teachers, good kids, good parents, just kind of stupid to become a data point to help EDM's sales. PA better be getting deep discounts for all the ongoing bells and whistles.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 7, 2009 at 12:54 am
You don't want me to get started on Clinton and the GOP.
Clearly you have strong feelings about the matter--honestly, I see evidence going in both directions. A couple of your claims--i.e. that using "distributed practice" in reference to EDM is recent, when it's several years old. Your most striking allegation as to why spiraling fails is an untested hypothesis.
The "proof" that learning styles don't exist--not from you, I know--turns out to be a narrative of an experiment that doesn't disprove what it claims. It's poorly structured
So, I remain on the fence as far as EDM goes. And I mean on the fence--I'll keep your objections in mind as I assess my child's learning.
I'm sorry, but your claims are simply wrong as far as EDM and PAUSD are concerned. Children here learn to add and subtract in the K/1 years. EDM is introduced in the second grade. And the district wants it implemented through direct instruction--so the teachers are very involved. As I mentioned much earlier, teachers supplement.
All these opinions and you can't be bothered to know how many math lanes we have in the high schools or how advanced they are?
I think what Engineer is getting at is that overemphasizing math facts means that kids may know how to do long division, but may not know how to think mathematically. By this I mean, knowing how to look at a problem and then know how to set up the right equation to solve it--to understand what mathematical techniques should be used and the logic behind a given mathematical technique. A lot of it is the ability to perceive and define patterns--and a certain chunk of EDM is focused upon that. There's an attempt to foster creative thinking in math--to learn how to try things out.
Creative thinking in math is highly valuable later on, but it's not something that's well measured by standardized tests. Is EDM the way to foster this creativity and understanding? I don't know--but I do know why educators and mathematicians would like to find a way to encourage this kind of thinking. I can also see how the EDM texts are geared toward this--that's why there's that sort of odd array of tasks.
Posted by EDM Opponent, a member of the Gunn High School community, on Oct 7, 2009 at 9:42 am
OK, OhlonePar, now you've completely lost all credibility. A kinder in our neighborhood came home with Home Links worksheets, which is EDM (the parent complained they cannot learn from it). What makes you think EDM starts in second grade? It's a K-5 program. Perhaps your Ohlone teachers aren't starting it until second grade and you ASSUME all of PAUSD is doing the same?
Plus, if teachers have to supplement, we are back to the usual system of our students having inconsistent learning where the quality of learning depends upon the teacher.
With the huge assumption of yours, OhlonePar, I speculate that if your teacher impresses you with this year of EDM plus, you will be convinced that the program is wonderful for the entire district, without realizing that not all students in PAUSD had exactly the same experience with EDM.
Basically, the GOAL of elementary schools is to properly teach addition, subtraction, multiplication, division so the students can excel in middle school and beyond. Beyond elementary school, students need to know those calculations backwards/forwards, and with SPEED. Everyday Math is more conversational/analytical math and does not emphasize the importance quick calculations. If students cannot quickly calculate in their heads, they will simply run out of time on math tests.
Posted by Anonymous, a resident of Another Palo Alto neighborhood, on Oct 7, 2009 at 10:49 am
Yes, EDM has definitely been rolled out in PAUSD from kindergarten through grade fourth grade this year. I don't know where OhlonePar is getting the idea that it starts with second grade.
It's a little unclear to me what's going on in fifth grade. I had been under the impression that this year's fifth graders were escaping the EDM implementation. I thought that the fifth grade teachers had objections to EDM and wanted an extra year to evaluate it and be comfortable that EDM was hitting all the required standards. I had understood that EDM would not be implemented for fifth graders until the 2010-2011 school year and had breathed a sigh of relief for my own fifth grade child.
But no such luck...my child traipsed home with the fifth grade Home Links during the first week of school.
My advice to PAUSD K-5 parents is to begin afterschooling your child in math now (or find a tutor or learning center if you can't afterschool). Do not trust the EDM spiral. You may think that you should keep an open mind and give EDM a chance to work. But by the time you realize your child is thoroughly confused, you will be playing a catch up game.
I do feel badly for the achievement gap kids who may or may not have access to outside tutoring in the community or by family members. I fear that the math achievement gap will only widen under EDM. When it does, perhaps the school board will come to its senses and reverse the EDM adoption. It's unfortunate, however, that many children without tutoring will be years behind in math by the time this happens.
As for OhlonePar, you go ahead and sit on the fence as long as you like. Check back with us in a few years and let us know how your child does on the 6th grade math placement test.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 7, 2009 at 3:29 pm
Okay, wrong information on my part on the implementation. Should have doublechecked before trusting my memory.
Anonymous, since my kid gets supplementation in the class, placement on the sixth-grade math test isn't going to mean much. Though, interestingly, the private-school educator who liked EDM liked it because the kids did better in middle school.
Honestly, I'm always a bit puzzled by the whole caught-by-surprise issue. I'm at the no-assigned-homework school and know where my kid is at and what the benchmarks are for every grade on a steady basis. I also work in the classroom and have a good idea of relative performance.
I haven't jumped to any conclusion--you have. My current take on EDM is that it's an interesting approach to a particular issue--how do you teach mathematical thinking? I also think that there's quite a bit of information that indicates that the program does not stand on its own. Where I tend to differ from the EDM-is-evil crowd is that I'm not convinced that that supplementation is onerous or can only occur outside the classroom. I think some drill sheets might do it.
I don't view this in black and white--the idea that our kids will start failing math tests in aggregate over this strikes me as melodramatic.
I don't know how to break it to you guys, but elementary-school math just isn't that hard.
Posted by bad process, a resident of Another Palo Alto neighborhood, on Oct 7, 2009 at 4:17 pm
"I don't know how to break it to you guys, but elementary-school math just isn't that hard."
that's the point, it's not that hard, it does not require the latest model or most expensive program, or the one that sucks up more time from teachers. This was supposed to be a text book adoption process but turned into a much bigger buy in.
it will probably not result in much harm thanks to the great teachers we have, but the bad process should leave at least pause for the next adoption.
you sound so smug Ohlone Par, I usually gloss over your long comments but I think I will now gloss over all your comments.
Posted by bad process, a resident of Another Palo Alto neighborhood, on Oct 7, 2009 at 6:36 pm
Ms Wu seems to be suggesting that Elementary Math is sophisticated enough that specialized Math teachers are needed, quite a different ball game from the EDM subject. It's a wonder we put a man on the moon without all this stuff we seem to "need." If anyone dissected the reading process, as marvelous as it is, we'd probably need some other expert to teach it.
I hear some of the higher achieving kids getting into college these days are home schooled. I think those parents need to write an article and help keep this all in perspective.
Posted by Stop talking out of your..., a resident of Another Palo Alto neighborhood, on Oct 7, 2009 at 8:43 pm
The link to the article was directed at OhlonePar who has repeatedly made comments about elementary math not being hard. Elementary math is more sophisticated than many people realize.
To quote Wu, "It is unrealistic to expect our generalist elementary teachers to possess this kind of mathematical knowledge - especially considering the advanced knowledge they must acquire to teach reading."
Plenty of people have dissected the reading process. What is needed there is explicit phonics based direct instruction.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 8, 2009 at 5:23 pm
What I meant by supplementation is what I said earlier--the teacher's supplementing EDM with older materials. The sixth-grade scores will indicate something about how PAUSD teaches math, but not about EDM because there's more than EDM being used.
Why is it you want my attention, anyway?
Give them the help they need. Education's not one size fits all.
Posted by Anonymous, a resident of Another Palo Alto neighborhood, on Oct 8, 2009 at 6:44 pm
The mistake that OhlonePar is making is assuming that whatever "supplementation" with "older materials" that the teacher is providing now will be adequate to prepare her child for sixth grade math, and, ultimately, the end of sixth grade math placement test. That test will determine whether her child will take "Pre-Algebra" or "Pre-Algebra Advanced" in seventh grade, and therefore whether her child will take "Intro to Algebra" or "Algebra I" in the eighth grade.
However, OhlonePar won't be sweating this issue. She has made it clear in the past that she thinks that mathematics is overvalued in Palo Alto, with respect to other core subjects. Also, elementary mathematics "just ain't that hard" and her child doesn't have "learning issues".
For the rest of the K-5 parents who are not so optimistic, it's time to start afterschooling.
Posted by OhlonePar, a resident of the Duveneck/St. Francis neighborhood, on Oct 9, 2009 at 2:18 pm
The mistake you're making is to assume that I don't know what's going on with my kid's education.
And, yes, I do think the panic some parents here have about their kids progress both sort of sad and funny. Basically, you're saying your kid's not good enough to acquire elementary math skills unless exactly the right methods are used.
What a wonderful message you're giving your child.
Posted by Anonymous, a resident of Another Palo Alto neighborhood, on Oct 9, 2009 at 10:11 pm
No, OhlonePar, I am saying that I do not have faith that the mathematics curriculum that PAUSD has put into place for K-5 will adequately prepare children for sixth grade math and beyond. I do not trust that improvised "supplementation in the class" (varying from teacher to teacher) will make up for the shortcomings of the adopted curriculum. I am saying that I will personally ensure that my child learns elementary mathematics to mastery, and I advise other K-5 parents to do the same.
The wonderful message you are giving your child is: "Math ain't hard. If you don't get it, you must have learning issues. Or, maybe you're just not smart."