Joel Stein Throws Numbers Around

I read several blogs written by mothers of children who have food allergies.
The food allergies are incidental to the purpose of their blogs for all of them.
Nevertheless, I have seen each one need to defend their concerns for their allergic children several times. Most recently, my blog-friend Rational Jenn wrote about the juxtaposition of a (thankfully) false alarm with her son, and a mocking diatribe by LA Times columnist Joel Stein suggesting that allergies to nuts are a figment of the Yuppie-Parent-Who-Wants-Attention's imagination. (You can read Rational Jenn's blog entry I'm Not An Attention-Seeking Psycho by clicking the linked title).

I followed the link Jenn provided to the Joel Stein piece, entitled Nut Allergies--A Yuppie Invention, and I read the column and the comments. According to some of the comments, the Stein column is supposed be witty and humorous. I failed to see either characteristic, but then I believe that humor and wit require more skill than was demonstrated in the writing I found. In fact, the Stein piece did a lot to help me understand why newspapers around the country are crying for a government bail-out. Stein cannot write well enough to clearly explain the facts he was throwing around, and the so-called humor was on the level of the TV sit-com that combines a continuous stream of put-downs and foul language with a laugh track and calls it funny. (This is why I have helped the Feds and the press go into crisis mode because I have not yet modified my TV for HD reception . . . but that's another blog entry).

Since I fail to even begin to see what is funny about Stein's column, I will instead put on my scientist hat and discuss his uncritical and uncomprehending way of throwing scientific language and statistics at the reader. Being an Educational Anarchist, I also discussed how to read and critique this kind of nonsense with my 15 year-old budding scientist, because even really bad writing can be an educational experience. So here we go . . .

NOTE: I will use quite a few biological terms below that are second-nature to me. Since they might not be for you, I will provide definitions at the bottom of the post.

Stein says: "genes don't mutate fast enough to have caused an 18% increase in childhood food allergies between 1997 and 2007 . . ."

There are two problems with this statement.

First, Stein is attributing an increase in childhood food allergies to mutations only, and he is thereby assuming that all food allergies are caused by one gene. In so doing, he is also applying the unstated assumption that no food allergies are polygenic (in which the phenotype expressed is created by a number of genes) or that there are epigenetic factors (the phenotype is created by gene-by-environment interactions). He is also assuming that all food allergy traits found in the population are attributable to genes alone (the heritability is 1), meaning that there is no environmental influence on the gene expression whatsoever. Given what we know about allergic reactions, and the number of proteins involved, as well as the variety of food allergies diagnosed each year, he is almost certainly wrong about every one of these assumptions. Finally, the statement indicates that Stein also assumes that there is no difference in gene frequencies among different populations, an assumption he states again, as we shall see. This statement, as Stein makes it indicates that Stein is ignorant of genetics and of evolutionary theory.

Secondly, Stein not only betrays his ignorance of genetics and evolution here, but he also demonstrates that he does not think critically about the numbers he throws around. Statistics do represent something real, and in bandying them about, it makes sense to think about what they mean. Let's look at the numbers he uses and how he uses them. I will repeat the statement he made to refresh our memories:
". . .genes don't mutate fast enough to have caused an 18% increase in childhood food allergies . . ."

First off, Stein does not provide the mutation rate for the genes in question. This may be because he does not know what genes are mutating, and if there is more than one gene that is mutating, and if so, how many genes he is talking about, and which genes are responsible for each food allergy, and if each gene is solely responsible for that particular food allergy (see above). But even if we give him all of this, his statement implies that an 18% increase in 10 years is a large number. However, to understand whether or not this is true, Stein should have asked himself this simple question: "What is the original number that has been increased by 18% ?" If the number of childhood food allergies is a small to begin with, and if we multiple that number by 18/100 (18%), we would get a very small number that represents the increase.

For example, although I do not know the number of total food allergies in the population, I do know that the number of peanut allergies diagnosed is about 1% of the population in the United States. That's a very small number. 18% of 1% (here you are multiplying two fractions) is smaller still. It is 0.018. This means that the actual increase is 0.118 per 100 individuals. That number is quite small, and since you can expect variance in the number of peanut allergies diagnosed from year to year, such an increase is not even statistically significant.

The statement quoted above also discusses all food allergies and the title of the article refers to nut allergies alone, but in the text Stein switches between these two and allergies to peanuts as if these three terms were interchangable. This verbal sleight of hand reduces the clarity of the writing further, and obfuscates the real meaning of the numbers Stein throws on the page.

Although much of the article is, in Stein's own words, "saying something outrageous to get attention," he does throw another sentence at the page that shows his abyssmal ignorance of population genetics:

"A study of Jews of similar demographics and genetics in Britain and Israel found that British kids were 10 times more likely to have peanut allergies than Israelis."

First, the clarity of the writing suffers in that the reader must assume that he means "British Jews" rather than the more general "British kids." But more importantly, although he states that these two populations have "similar genetics" (by which he likely means that both are Ashkenazi), they are still separate breeding populations. This means that the founding gene pool of each was not identical, and that changes in the gene pool since the divergence between them have taken different trajectories due to natural selection, migration into and out of the gene pool, mutation, and genetic drift. The two populations are therefore diverging genetically with each generation. Joel Stein clearly does not have even an introductory-level understanding of genetics, population genetics and evolution.

And of course, my arguments above are made assuming that the phenotypes for food allergies are the result of genes alone. It is much more certain that they are not, which means that many other factors can account for changes in the frequency of the phenotype in question. Genetic expression in the somatic cell can be influenced by a whole host of environmental conditions that themselves change at the cell level, the organismal level and the population level. And on top of that, the frequency of diagnosis can change dramatically due to better analysis of symptoms, more efficient testing, and more widespread public understanding of a condition. With respect to this last, it is very likely that disparities in access to diagnosis (health insurance coverage, regular physician visits) could account for the class differences seen in the numbers of diagnosed food allergies.

Overall, Stein's column shows his ignorance of science, his woeful innumeracy, and his inability to critically think about what his sources are telling him. He also demonstrates a remarkably mean ill-will towards upper-middle class parents. It could be spite or envy, but whatever it is, the meanness obscures the feeble attempts at humor.

I am glad my local, independent newspaper, The Albuquerque Journal, buys syndicated columnists across the political spectrum that reflect much higher writing standards and much more sophisticated senses of humor. I would certainly not pay to read Stein's drivel.

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Definitions:

genotype--the actual genes the individual carries on their DNA

phenotype--how those genes are expressed, or more commonly, what traits the individual displays due to the combination of genes inherited

gene expression--the transcription and translation of the genetic code in the cell, which results in the making of proteins; gene expression is influenced by environmental factors and ultimately results in the phenotype

polygenic--a trait influenced by more than one gene

epigenetics--the combination of genetic and environmental influences on the expression of genes

heritability--the proportion of phenotype in a population that is due to genetics. A heritability of 0 would mean that the trait is question is entirely environmentally determined, and a heritability of 1 means that the trait is entirely determined by genes. Most traits of interest in a population are somewhere in between these two extremes.

allele--an alternative form of a gene that is located at a specific position on a specific chromosome

gene frequency (a.k.a. allelic frequency)--the number of alternative forms of the same gene in a population. If the allelic frequency of a gene is changing in a population, we can say that the population is evolving with respect to that trait.

mutation--a change in a gene (alleles are the result of mutation)

genetic flow--the movement of genes into and out of a breeding population (this occurs by migration of individuals into and out of the population)

genetic drift--the accumulation of random genetic changes that change the gene pool of a population

natural selection--the process whereby heritable traits become more or less common in a population due to their influence on survival and reproduction (some traits may be undergoing selection in an environment whereas others are not); also natural selection acts on the traits--that is the phenotype NOTE: the level of at which natural selection occurs is the population, individuals do not evolve

biological evolution--a change in gene frequencies in a population over time

divergence (divergent evolution)--when one gene pool becomes two due to some physical separation, the combination of natural selection due to different environmental conditions and gene flow, genetic drift, and mutation, changes the gene frequencies in each population independent of the other

Scientific Notation: You'd Think It Grows on Trees

Today's number is:

3.1 x 10ee12 in scientific notation.

Three-point-one-times-ten-to-the-twelvth-power

In England, they'd call that 3.1 million million.

In US terms, it is 3.1 trillion.

In plain numeric notation, it is $3,100,000,000,000.00

I have to express it in scientific notation just to get a handle on it. Very large numbers are hard to read, so scientists developed a way to deal with them called scientific notation. You count up the number of zeros to the left of the decimal point, and any number but the largest. This makes the exponent. There are twelve places to the left of the decimal point and to the right of the three, so we place the decimal point just to right of the three and then express all those places as an exponent.

Scientific notation is good for very small numbers, too. You just count the places to the right of the decimal point and express those places as a negative decimal.

I wish this number were very small.

It is the proposed amount for the US Federal Budget. With substantial cuts to programming.

Wars are expensive indeed.

Thanks to Judy Aron over at Consent of the Governed for providing the number.

Even politics can be used in the service of teaching math.

Politics is also good for teaching math concepts.

Math: Taming the Speed Demon

Last year a You-Tube video done by a west-coast weather forcaster made the rounds of the homeschooling virtual world.

The weather forcaster started with the complaint that when she went back to school to study meteorology, she noticed that the math skills of her young colleagues was lacking and that this limited their ability to be successful in their studies. Thus far her argument holds up. It would be difficult to be successful in any scientific field if math skills are lacking.

But then the argument took an interesting turn. She said she went home and took a look at the methodologies that were being used to teach her children math. And she zeroed in (no pun intended) on three different methods used for multiplication. All three methods worked. That is a student could use any of the methods to calculate a correct answer. The argument came down to speed. She concluded that the problem her fellow students at the university level had with math was that they had been taught inefficient methodologies for problem solving, and so getting to the correct answer was taking more time. Another You-Tube video was made by a man who calculated exactly how much more time the alternative methodologies took and there was a difference of at least several seconds. The man did not calculate whether that difference was significant or not.

As I watched this You-Tube and the minor sensation it made in the homeschooling virtual world, I had a nagging sense that there was a real problem with the framing of the argument but I did not take the time to follow it through. Instead, I had flashbacks to third grade math with Mrs. C. With all the best intentions, Mrs. C. gave timed tests of multiplication and division. These were not timed tests of knowing the multiplication tables only. Instead, the people who did multi-step problems the fastest were considered math whizzes who would go on to be scientists and techno-geeks. Alas, I was not to be one of them. I was one of those kids who had poor motor skills and held my pencil too hard--which I still do when I am nervous--and so I never had the "whiz-kid" speed. And so I developed the idea that whereas I was good at reading, science, and history, I was no good at math. I continued to think so all the way through Algebra, Geometry and Algebra II and Trigonometry , Math Analysis and Pre-Calculus in high school.

I thought that I was no good in math, even though I got A's in my classes. I thought that I was no good in math even though I understood numbers and got very excited by ideas like negative numbers and scientific notation. I thought that I was no good in math right up to the point where I too the PSAT. Then I realized that there was something wrong with my assessment of my math ability. And when I found that I enjoyed calculus and what it could do for me in physics and chemistry and biology, I concluded that there was probably nothing wrong with my math abilities. (Yes--I am a Geek, first class. I also really enjoy statistics).

I don't know how many people in Mrs. C.'s third grade math class became scientists. I do know that I did. And I now understand that when it comes to math, accuracy is far more important than speed. I don't know about you, but when I cross a highway bridge, my confidence in the engineering is based on a sense that the engineer can make accurate calculations. I really don't care if he did the problem seven seconds faster than someone else. Seven seconds is not really a very long time compared to the years that would be taken off my life if the bridge collapsed with me on it.

These are the thoughts that guide me as I go about re-teaching math to my son, N.

N. had a much more traumatic experience with math in third grade than I did. His fine-motor skills and hand-eye coordination were so compromised that he used to have great difficulty even lining up words or numbers corrrectly on a page. And mental math requires strong auditory working memory, another issue for N., who has Central Auditory Processing Disorder--a specific learning disability--on top of his AS diagnosis. You can imagine what happened when his teacher gave him timed math problems. We were told that N. did not know his math facts and that he was "slowing the class down." The third grade teacher added insult to injury by labeling N. publically as "lazy." It does not take a rocket scientist to conclude that N. was not motivated to actually learn math.

When I undertook to teach him math last year, I found that there were big holes in his understanding of basic operations. It was clear that he had missed important steps and concepts in his elementary school math training. This probably springs from two sources. One is that he had so much difficulty following verbal instructions that he simply missed much of what was being "taught." (My very wise professor in Special Education Assessment says that if a student hasn't learned something, the first hypothesis ought to be that he was not taught it. Covering material for a student is not the same thing as teaching that student). The second problem with math instruction in public schools is that, in their frantic urgency to improve standardized test scores, districts tend to change curricular programs very often. Program changes in the middle of someone's education tend to create gaps in learning because each program builds on previous instruction in different ways.

The other problem we face in order to re-teach math to N., is the issue of motivation. When N. sits down to do math, his anxiety climbs quickly to the red zone. He has learned that he is "no good at math." A large part of that problem has to do with speed. He has been inadvertently taught that if he cannot come up with the right answer in 15 seconds, then he is hopelessly stupid and there is no point in continuing.

Aside: In my opinion, this problem extends far beyond N. and far beyond math. I believe that one reason our schools are failing is that we have taught our kids that filling in the blank or the bubble for the "right" answer in all areas is far more important than actually thinking something through.

But enough! Back to the main story.

We have developed the following principles for re-teaching N. math.

1. Teach basic math from the beginning.

When N. expressed the desire to learn algebra, I took him out for coffee and we had a conversation about math instruction. I explained to him what I had observed about how poorly math is taught in elementary school in general, and what was lacking in his math instruction in particular. I listened while he told me about the feelings of fear and anxiety he has whenever he sits down to a math problem. Then I told him that it was my hypothesis that if he started math from the beginning operations and systematically studied them, we could certainly be doing algebra by next year.

We made an agreement about how we would help N. reach his goal. So that N. could learn from the beginning of the operations, we ordered Basic Math from the Teaching Company's Great Courses. We also agreed that we would not be concerned about time. N. would proceed through the material systematically, taking all of the time he needs to learn each operation and concept well. And we agreed that would work on auditory working memory outside of math i.e. there would be no verbal drills. And this all leads to:

2) Speed is not important, accuracy is.

Our goal at present is that N. should use a variety of methods in order to learn algorithms and to understand the number theory underlying them. Just as we are not worried about how long it takes for N. to learn the math, so we are also not concerned about how long it takes to do a problem set.

We have taught N. a new mantra: "This is why pencils have erasers." Since accuracy is more important than speed to us at this point, it would be easy to fall into the trap of thinking that errors are fatal. But at this point, we are far from designing bridges and airplanes, the important point here is that N. learn to check his answers and learn to find and correct his mistakes. To do that, N. must understand the concepts that underlie the algorithms he is learning. When he comes to apply math to things like bridge design, it will be very important that he can check his answers for himself and be able to know that they are accurate.

I know, I know! What about standardized testing? That is the big question that the Math Speed Demons out there will definitely be asking. Isn't speed important to those?

Answer: Yes, in a way. Actually, what those tests require is familiarity with the basic operations to the point of automaticity. That means that the student is able to add, subtract, multiply, and divide without needing to develop the algorithm each time. This allows the real problem-solving power to be applied to more complex math using algebra and calculus. And here is the take-home message to this idea:

When a student is learning to understand math operations and develop algorithms, he will be slower at working problems. As the algorithms become automatic, the speed will increase.

Think about it. When you take it upon yourself to learn a complex skill, it goes slowly at first. As your brain builds the needed neural connections, your speed and accuracy improve. Eventually, you have made certain skills automatic and now they can be applied to more complex problems. For example, when I first started to embroider, I did not know any of the stitches. So my first project took what seemed like forever, as I learned the basic stitches needed on each part of the project. The more projects I did, the faster I completed them, until I was able to do large and ambitiously complex projects with enough speed to actually enjoy them.

By going back to fill in the gaps for both knowledge and skills without concern about speed, we hope that N. will "automate" the basic math operations. As his skill and accuracy improves, so will his timing.

But the ultimate goal is not to be fast! It is to appreciate numbers and enjoy applying math to real-world problems in order to get good results and satisfying answers to the big questions.

Back to Normal-- Sort Of: Floors, Chores, Math, and SET!

Yesterday, after a full lunar month of fitting life in around the holidays, we felt we had finally got back to normal.

Since Bruce is working on the living room floor now--or is that again?--anyway, my living room is partially in our bedroom sitting room. So I set up in there, sitting in the recliner, working on my presentation for NAGC, reading a paper for Psychology, and another for Neurophysiology.

Aren't the roses pretty?
Bruce splurged on them for Shabbat.

But of course, the whole day I had planned of normality--that is enjoying getting some needed work done was not to be. The phone rang. Seems that Bruce had promised to pick up beds for the Interfaith Hospitality Network--Congregation Albert is hosting this week--and then we had completely forgotten it.


So it was grab the keys, run the brush through my hair, and we were off to the synagogue, in Henry, of course. It was not us they wanted--it was Henry, the Big Red Truck. We were just along to drive.

Two trips from Montgomery Church of Christ to Congregation Albert, and we had delivered all the beds but one. Seems a new family was starting the IHN program that day, and we needed one more bed. So another trip was in order--this time to the network office, to get the extra bed. It was pleasant--a cool but sunny fall day, nice conversation with the volunteers at Montgomery Church and at CA and at IHN office down at the First Congregational Church. N. came along, too, and he was a big help loading and unloading with Bruce. All I had to do was drive.



After a stop at the store, where Bruce ran into an old colleague, it was home again, home again, jiggety jig!

On the way into the house, we saw this amazing Orb Web Spider on the porch. She moved as I snapped this picture. I'll post another shot later. N. moved her off into the bushes so that no one would step on her.





Three hours had passed from the time we left, so I went to the kitchen to start dinner. Bruce finished closing up the cooler for our side of the house, and then did a little floor work in the living room.

He's got a bit laid out--almost half--but he did not get to gluing this weekend. It may be next weekend before that gets done!

Here he is, deciding on how to lay out the boards. He has a spread sheet to make sure that he doesn't end up with too many boards of one size at the end of the room. The Geek!




While I made a salad, N. relaxed on the couch--that part of the living room is currently in the dining room. He is reading Peterson's Guide to Western Reptiles and Amphibians. He has become quite a reader in the past year--it is no longer a scheduled chore, but something to do at every opportunity. I consider it part of our homeschooling time--even on Sunday.

This morning, I got up just before sunrise, and was out with the dogs as the first light turned south mountain a wonderful pink. We had our first freeze last night--it was 31.7 F when I left the house. I enjoyed my breakfast with the newspaper and got some housework done before it was time to wake and feed N.


N. has arranged with me to work on Math on Monday and Wednesday mornings--and now that the holidays are passed, we finally got back to our regular schedule. I am afraid math has taken a back seat to other learning during most of the past month!

N. is up to Introductory Fractions with his Teaching Company Course--Basic Math. The DVD segment goes over several concepts for fractions very quickly, and N. felt he wasn't getting it. He was frustrated with himself. When asked, I suggested that we go over each concept separately, watching only that part of the video, and then work on the problems for that concept in the workbook. So today, we worked on finding the unknown in equivalent proportions. (That's where you have something like 7/8 = X/24 and you have to figure out that X=21). I showed him the quick and dirty way to cross-multiply--the DVD does not teach that, but it is so much easier! He liked that. Then, at his request, we went on to work on resolving improper fractions to mixed numbers.


After the math, we had agreed that we would work on some reasoning together, which we did by hauling out my old SET! game. I last used it two years ago when I taught an elementary school gifted program. In SET! there are cards that are combinations of three different shapes, three different numbers of the shape on a card, three different shading patterns and three different colors. The object is to pick out a set of three cards in which three of the four parameters are either the same or different. N. beat me hands down, of course! But the cool thing about this game is that he has to hold all of the parameters in his working memory while he decides whether a particular combination is a set or not.


Here he is with a set: same shape, same color, same number, different shading.

Warning: This game is addictive! We kept saying to each other; "Just a few more rounds and then we'll stop!" We played for over an hour. N. has a much greater tolerance for this kind of learning than he does for slogging through math problems.

However, I was proud of him. He chose the math course because he set a goal for himself. When he got frustrated, he sought out help. And today he worked on two different math concepts before he was ready to call it a day and play SET!

Back to normal. Yeah!