# I May Have Found The Problem With the Climate Models

Via Carpe Diem:

Last quarter I taught Atmospheric Sciences 101 at the University of Washington, a large lecture class with a mix of students, and gave them a math diagnostic test as I have done in the past. The results were stunning, in a very depressing way. This was an easy test, including elementary and middle school math problems. And these are students attending a science class at the State’s flagship university–these should be the creme of the crop of our high school graduates with high GPAs. And yet most of them can’t do essential basic math–operations needed for even the most essential problem solving.

Here’s a link to a PDF version of the full test and results, and here’s a blank version to give your kids and friends.

Consider these embarrassing statistics from the exam:

43% did not know the formula for the area of a circle

86% could not do a simple algebra problem (problem 4b)

75% could not do a simple scientific notation problem (1e)

52% could not deal with a negative exponent (2 to the -2)

43% could not do simple long division problem with no remainder (see above)!

Actually, I am just having fun with this.  My guess is that this is a general college problem and not one limited to the atmospheric sciences, though I will say that my experience in engineering is that the “trendy sciences”  (whatever the trend might be at the moment, when I was in school it was a new energy program) tend to attract students less prepared for mathematical rigor.  Perhaps this is true of climate today?

• I’m embarrassed to say I missed one (the cosine). But then I barely graduated from high school.

• Metro Gnome

But boy, they can sure put a condom on a cucumber in a hurry.

Assuming the Atmospheric Sciences class did not attract a disproportionate number of dummies, how could 43% of high school graduates, never mind 43% of students in a *science* class, not know the formula for the area of a circle? I wonder how many of their *teachers* in high school knew that basic fact?

It sounds like you’ll be reduced to teaching in “grunt-and-point”.

• NancyL

Those who can’t, use a model to approximate it.

• RodG

I knew there was grade inflation in high school, but when did they stop teaching math altogether?? One note is that this is a 101 course and might have had some English majors that needed a science elective. However even an English major should get all of these in 5 minutes with the possible exception of one or two of the following 3: the negative exponent and the cosine (trig) and for sure the second algebra one, while not tough was the trickiest in the bunch.

• Its the same here in England. I left what is presumably the equivalent of you High School, having passed my higher exams in Maths, Chemistry and Physics and went into engineering. I studied “further maths” during of my part-time engineering studies to get membership of my professional institution. I certainly wouldn’t regard myself as being a mathematician, just the essential required for electrical engineering.
I was talking to my son-in-law who is a professor of mathematics regretting the fact that I’d never attended University, and he suggested that I should join his course as a mature student, as I would probably only need to do a little revision and he would be glad to have someone with a knowledge of the subject!
And what about statistics and probability? I would have thought these to be essential for any form of climate studies.
PS. Its “Maths” in the UK, not “Math”. Why we insist on the plural I just don’t know!

• Wow, that is quite striking, although I’m not very familiar with the US education system.

I remember doing really quite hard maths problems for UK A level Advanced maths in the 1970s.

Here is a comparison

http://www.mathsnet.net/articles/article_alevel.html

This one seems non-trivial ( from 1971 )

If a + b + c=a^2+b^2+c^2=a^3+b^3+c^3=2, find by considering values of (a+b+c)^2 and (a+b+c)^3, or otherwise, the values of (i) ab+bc+ca, (ii) abc.
Hence find the equation whose roots are a, b and c.

• Nacho

Yeah, 4b is actually kinda tricky. Not getting that could simply mean you forgot how to separate y-yx-x=0 into its x and y parts, or doing that simply didn’t occur to you. Not much shame in that, nor the negative exponent with the base of 2. You really don’t see that very much, and it may not occur to you to compare what you do with negative exponents base 10. So I understand those. Not knowing the area of circle or not being able to do long division though?

Of course I’m currently training a soon to be college grad and I have to repeatedly explain to him how to make say 100ug/mL solution of X in 10 mL Y when you have a 20 ug/uL solution of X to start with. I know he had the opportunity to learn this along the way, its likely just that his teachers didn’t set high enough standards. And this guy is going to be taking the MCAT in a few months….

• Doug W

I’m with Evil Red; I got them all except for the cosine. Oddly enough, I remembered the definition for tangent; not bad, since my algebra days are about 30 years in the past. But these days, I just push the “cos” button on my calculator; I’m sure that’s what all the college students are used to doing.

FWIW, my dad used to give me grief about not being able to use a slide rule. He was also disappointed I never memorized the log tables like he did.

• Doug W

Also, for English Pensioner: I’ve never been able to figure out why you call it “Sport” instead of “Sports”, either.

• Tony Hansen

Noticed that the average scores for each section are similar. Was this to be expected?

Were the average scores to be expected?

Would the scores have been much different 30 years ago?

Is there a higher percentage of kids going to college instead of getting trades/jobs than 30 years ago?

• I do not take well to numerical mathematics. I went into synthetic chemistry to avoid it, synthesis being purely intuitive. I can visualize things in my mind but find it very hard to think intuitively in terms of equations. It’s been nearly 20 years since I’ve used math much, since I’ve been making design products instead of doing science and most of the math involvedis handled deep in the guts of CAD programs. However, I did all of these problems in my head, quite quickly, except without pen and paper I was utterly stumped by 4b. For the others I could feel how my mind was using little rules of thumb and memory tricks as an aide since this was a total pop quiz I wasn’t prepared for. Bigger/smaller rules were being verbally invoked in 1a-e, such as knowing that division by 10^-5 made the result bigger, so the question was merely how much bigger. I had forgotten what a cosine was verbally defined as, but immediately reasoned that it must be a division by the “special” hypotenuse and that sine must be the “symmetric” one (straight across from the marked dihedral angle) since cosine has always sounded like its little brother.

All but 4b are a measure of training (unless perhaps you are a savant who sees numbers as polytopes that combine together to make a new 3D shape that make the answer obvious). Without that training they are just digits arranged in space on paper with no formal rules of relationship attached to them so there is little chance of using high intelligence to figure them out. If you know the rules of what various types of exponents mean, there is little skill needed.

To anyone with the proper training (maths education) only 4b is a measure of skill once you remember the rule of what the arrangement of symbols on the paper means.

That said, when I stare at these basic mathematical relationships, I start to think intuitively and get drawn into them and things start to indeed make sense in a disturbingly uncanny way. A negative or fractional exponent *does* have perfect symmetry with their positive or multiplicative partner. It’s like color symmetry (somewhat). Trigonometry becomes fun as I visually imagine the hypotenuse swinging around like a second hand on a clock, smashing the vertical side down to zero height and then dragging it deeper and deeper below the horizon.

I was upset that I had forgot the name of the PV=nRT equation, thinking it was named after an obscure scientist but it’s just called “The Ideal Gas Equation”. Having looked that up, I still forget what R is. Grrr! What must it *have* to be? Well, Pressure P x Volume V intuitively feels like a measure of accumulated energy, embodied in the entropic drive a gas experiences to expand. I think of a tank of gas and how violent of a rocket it would make if I used a sledge hammer to break the valve stem off. So I need an energy-like body on the right side as well or what use is an ‘=’ sign? I think n is the number of molecules or is a constant. It being non-capitalized is throwing me off, since that might indicated it being a constant. If it’s number of molecules (probably in moles…= 6*10^23 molecules?) then R would be the constant that handles the arbitrary units involved. So again, Number-of-Molecules n x Temperature T “sounds” like a measure of bad-ass-ness (energy) as well. If I heated the hell out of the tank before knocking the top off it would blow its cork more forcefully indeed. Let’s check…whew! R is called the “Gas Constant”. Now it’s “obvious” (except it wasn’t obvious before since I think I wondered if R was related to entropy).

This type of reasoning is exactly the sort of strategies I was forced to use in order in the first place to make up for a temperamentally poor memorization and paradoxical lack of ability to hold figures in my head despite their graphical nature and my fondness for visualization in three dimensions. It’s coming back to me now. I should stop thinking now or with some beer and loud music and playing with math I’ll start to rave like the character in the wonderful movie “Pi”.

I at one point passed senior level college calculus etc. with flying colors, including entire courses on mathematical proofs, quantum mechanics as well as statistics as a part of quantitative/analytical chemistry. In a philosophical sense this little test is not that much less difficult than advanced math. It’s just that the training required to understand this level of math at a gut level is indeed much less involved. Thank god for computers though, since trig tables were a drag. I could never figure out crystallographic symmetry groups in any intuitive way and this was profoundly disappointing. It’s not taught intuitively so it would have been up to me indeed to “crack” it. I did figure out Maxwell’s equations, intuitively. They are not so much “advanced” math as much as a very compact way to describe what magnetic lines of force are allowed or disallowed to do. That kind of blew my mind. They are utterly reliant on verbal rules about what the arrangement of symbols meant. They are a rather jury-rigged way to force geometrical ideas into the form of equations.

Its quite disturbing though that Pi never resolves itself to a final value, meaning any real-world circle can never be a perfect one. Bucky Fuller used to rail against the very idea of straight lines and circles for this very reason, and rejected the idea that nature itself “uses” Pi at all. Pondering such drama makes it a lot easier for me to remember the equation for a circle.

I think the real problem is that intuitive understanding is not encouraged at all and so pure memorization must be relied upon and memory is simply not up to the task of surviving long periods without practice. Maths make sense in a delightfully trippy way if you force yourself to really wrap your mind around the idea that the symbols on the piece of paper are merely the surface of things and that toy-like “entities” are being described as they move about, expand, contract and change shape. Careerism trumps the idea of a calling or the idea that maths really mean something other than mere calculation.

• Mesa Econoguy

Government education promoted by government largesse and further academic laziness.

Mike Mann is a moron. Fire him now.

• WillR

I want to believe that this is a joke.

I expected something terrible when I downloaded the PDF — I expected to be embarrassed by what I forgot…

Words fail me…

• RobTzu

I missed 4.b, but looking at the answer, I feel silly for it. I have an Associates Degree, stopped about 20 hours short of my B.S. in biology to work as a operator/chemist in a powerplant for pretty good money. Never had Calculus, if I did I would have went for a B.S. in chemistry instead of biology ^^
It is not cool to be smart. Being smart does not get you laid. The incentive is to be too cool for school. So here we are. Privatize schools, and let them be single sex schools.

• Mark

Dang I could do all the problems in my head. The only one I was hazy on was the cos one, (was it opposite over hyp, or adjacent over hyp) but then I remembered the great Native American SOHCAHTOA.

It is pretty sad – if you are in a science class in college you should be able to get at least 85% on that test, especially if you have paper and pencil.

• Waldo

The most pointless post yet on this blog.

• dearieme

“Yeah, 4b is actually kinda tricky.” On the contrary, it’s “do it in your head” stuff. Look on the LHS as y/1. On both sides of the equation add the numerator to the denominator. Then you have
y/(y+1) = x/1. QED.

Do they teach anything much in school these days?

• hunter

Waldo,
Then leave.

• I spent the first ~20 years of my career working in remote sensing. I worked with countless atmospheric scientists (remote sensing requires the removal/correction for atmospheric effects). I can tell you that atmospheric science is a very rigorous and challenging discipline, not a “trendy” or fluff degree. These were some very bright people.

Regarding global warming/climate change, what I’ve seen is that the atmospheric scientists working in academia tend to be very AGW-centric, and those who are working in industry, etc. (whose grants don’t depend on AGW) tend to be far more skeptical of AGW.

• English Patient

The key point is this:Todays students attend courses which are generally useless at preparing them for the real world.

Education is meant to be a choice:Do you sacrifice time and effort inorder to aquire skills and knowledge such that you become more valuable or do you work with your current knowledge and contribute to maintaining your lifestyle as it is now?

Too many students attend courses dreampt up by Institutions perpetuating the myth that education is an end in itself:it isnt .

We have too many courses and too many institutions

lets get people back to work and allow them to study through application of skills relevant to their field rather than wasting time on theory
in the belief that their educated mind will pave the way to a better life.

• Bob Sykes

Many years ago, I team-taught a class in environmental science and engineering to a mixed group of graduate students in biology. The course was intended to introduce biologists to environment problems in air, water and soil, plus some public health stuff.

One day, I put up the Streeter-Phelps equation, which describes the variation of oxygen along a river. This equation contains several terms that involve e (the base of the natural logarithms) raised to an exponent. After discussing the formula for a while, a student asked, “What is e?”

• Mike

4b almost got me too, mainly because I got sloppy and went from “y-xy=x” to “y=x-xy” instead of “y=x+xy”. But the answer just looked wrong, so I rechecked and found the problem. Even with that, the whole thing took less than 60 seconds to get done (with no errors).

Of course, I had an advantage in that my math teacher my junior and senior years of HS was a bit of a fanatic. No calculators, of course, but by the time she was done with us, we could also calculate square and cube roots and estimate common logarithms longhand; had memorized the conversion factor to natural logs and the sine, cosine and tangent of all multiples of 15 degrees; and memorized an absolute horde of trig formulas. That all saved my grade in college when I had consecutive calculus, physics, and mechanical engineering finals, and my calculator’s battery pack failed five minutes into the first final.

Bob – that reminds me of the time I was teaching a business calculus class, and in the middle of working out an example problem on the board, one student asked “how did you get X over X to be one?”

Worse, though, was the HS junior I once tutored in basic math. When she got to the part in a problem where she had to multiply 6 x 6, she pulled out her calculator. The “6” key stuck once and she actually punched in 66 x 6, getting 396, which she wrote down and kept going. I suggested she might want to recheck that, so she grudgingly punched it in again, got 36, looked at both answers, then tried it a third time on the theory that the answer that came up twice was probably the right one. After that session, I told her father that she needed WAY more remedial help than I was capable of giving.

• You are absolutely correct. The quality of public education sinks lower and lower. In my opinion a major factor is the insistence that the only qualified teachers are those who have jumped through the hoops set up by “teachers colleges,” excuse me, the “colleges of education and human sciences” that waste space at our universities.

• ruralcounsel

Teachers unions dislike teaching quantitiative material like mathematics and science, because problems have distinctly correct and incorrect answers. Why would this be a problem?

Because it means that it is simple to ascertain whether the instructor is doing their job or not. It becomes too easy to distinguish the good teacher from the ineffective one, and that is anathema to teachers unions. God help them if it comes to pay for performance!

It’s much easier for everything to be subjective, for everyone to be right, to celebrate their mediocrity, and to enhance every little ego’s self-esteem. Then everyone is happy with the teacher.

When these kids reach college, they’re incompetent at basic math and science. Given the outrageous tuition bills they pay, universities are reluctant to flunk anyone out. So we get people with mediocre skills going into the trendy areas. Does anyone seriously doubt that climate science type classes aren’t trendy these days? Particularly given the degree of research funding heading that direction.

Kind of goes to the peer reviewer (Ed Cook at Lamont-Doherty) who wanted to reject the “ugly paper to review because it is rather mathematical”. I wonder what Cook’s age and background is? Ahh, just looked it up…wildlife biology, geoscience, watershed management. About the same age as me. All his degrees from the same school. I’d have thought someone in watershed management would have to know math…groundwater hydrologists certainly do. But now he works in a “tree ring laboratory”…and has never held a position outside of LDEO since 1975. Hmmm. I don’t know the guy, and maybe I’m jumping to conclusions, but maybe this explains a lot.

Yeah, Waldo, pointless for someone in psychological denial.

• Fred from Canuckistan

As bad as their math skills are, students today also have very low spelling abilities.

• maxwell

I don’t know what this class has to do with climate models. If you went and read Cliff’s whole post on this topic, you’d see that less than a quarter of the class were physical science majors. That means there were likely not even all of these students will end up majoring in atmospheric sciences. Nothing from Cliff’s post has anything to do with climate models.

• mahtso

I do not doubt that math skills are lacking, but considering that (1) there was no negative consequence to getting these questions wrong; and (2) low scores on this test would (presumably) result in easier problems on tests that do count, I question whether any relevant conclusions can be drawn from the test results.

• the other coyote

Warren, I clicked on the links but got a “forbidden” message. Any way you could email me a copy of the test? I’d like to try it. coyote_ridge_ranch@yahoo.com

• the other coyote

I could get to the test from carpe diem.

• Waldo

Glad to see so many geniuses here – you are all so self aggrandizing, it’s hilarious. Put that MIT PhD to work there, Ruralcouncel?

However, I will concede that perhaps poor math skills may account for part of the reason that so many people are willing to be bamboozled by denier pseudoscience.

• hunter

Waldo,
You are not even fooling yourself anymore about not being a troll.

• DaveK

ruralcouncel:

Be careful for what you ask for when you invoke “pay for performance!” In theory, it’s a system that should reward excellence… For PFP to work as advertised, you must have very motivated and well-trained supervisors who are devoted to performance of the organization as a whole. If the supervisors don’t really buy in to the entire program, it becomes a system that is extremely easy to game. Anybody who is even slightly clever can figure out how to set what appear to be difficult goals that are, in reality, slam-dunks, and probably do not contribute to the overall goals of the greater organization. Already, you find that when students are meet “competency requirements” in order to advance or graduate, far too many of the teachers are training students to just pass the tests, rather than to actually learn something that will help them to survive in the real world. [an aside: When was the last time that you saw someone actually “counting change” instead of looking at the register and just dipping out the amount it said they should return to you?]

“Pay for performance” has been the downfall of a lot more organizations than it has actually saved.

Been there, done that, got the crappy T-Shirt!

DaveK

• DaveK

oops!

that should be “…when students are required to meet “competency requirements”…”

• Waldo

Now, now, little hunter – get it right. I’m a troll for truth, justice, and the American way.

• hunter

Waldo,
Trolls are never for truth, justice, and the American way. As you demonstrate so well.
BTW in your fan dance about your educational achievements, I lost track: Are you a PhD in science, or did was that just more trollish costume?

• Doc_Navy

Why do I have the feeling that Waldo falls into the “I can’t do the basic math” section of this article?

Do you even understand the terms “Blackbody radiation” and “Watts per square inch” and what their mathematical expressions have to do with Climate?

Doc

• ouch

MBA of Finance and I scored under 50% –

Back to 6th grade with me. 🙂

• Al

To Climate Skeptic: I hope you’ll think hard about whether you leave the comments section open on any of your posts for all and sundry, because it becomes a forum for those of least intellect, and yet clearly also the least understanding of their own limitations, to come out in force, and spray around their favorite epithets, such as “moron” and “troll”. Waldo’s comment that they are self-aggrandizing is certainly correct, but, more to the point, how do they add any value to your blog? Surely it would be better if comments were moderated to only include the insightful and germane. Otherwise the comments section is surely just a waste of time and deters the average reader from revisiting your blog.

• IT Guy

Another MBA of Finance and Information Systems. Scored 100%. Maybe the math major and physics minor undergrad helped.

• Matt

I think it is “maths” in the UK because it is short for mathematics.

Is the subject of numbers called mathematic in the US?

English belongs to the English. It is only on loan to everyone else.

• Stephen J.

Counting a couple of answers as half-points, because they were the correct value but simply not correctly expressed in the final answer, I got 75%. (Forgot the calculation of a cosine and how to deal with negative exponents that aren’t factors of 10.)

Now for me it’s been, oh, cripes, nearly 22 years since I did any significant math beyond arithmetic. But that could just mean that I have an exceptionally good memory, or it could mean that the frosh coming in are *seriously* underskilled.

• Keith W.

Well, my only mistake was due to misunderstanding the problem. I thought 1F asked for the decimal equivalent of 23 and 1/7, not 231 divided by 7. I guess I over thought, but the instruction to give to the tenths position threw me off, and I was looking for something harder. Decimal listing of sevenths was always one of my favorite memorizations since it developed from the multiplication of seven, 0.142857 and back to the beginning. Technically, the correct answer, based upon the stipulation of the question, is 33.0

• Darren P

I am ashamed that I never did better but then again, I always find it easier to do math problems if there is context to it and not just a bunch of letters and numbers spewed out. Call me crazy.

• Waldo

Hunter, never said what my degrees were in. Your response to “truth and justice” cracked me up. You do take this quite seriously, don’t you?

Doc, a black body refers to a mass or an object which absorbs radiation. And may I assume that the “watts per square inch” you are referring to has to do with California’s purposed ban on certain energy inefficient devices? Or perhaps you were referring to the use of big screen TVs in general? Is this an infringement on the American way of life?

But, since you are apparently new to my relationship with CS, I have always claimed to be a layperson worried about the disinformation and often outright deception that blogs such as this one purvey. And I worry about the people who have some small science background but who – most likely for political reasons – prefer the deniosphere to the actual highly trained scientists and complex science that makes up the GW community.

• Richard Saumarez

This is horrifying. Can one really teach any branch of physics without elementary calculus? I have had the experience of teaching a third year class in biomedical engineering at a major UK University, having been out of academia for a while and I was struck by the difficulty the students had with some mathematical concepts, although they were well taught. When I discussed this, the reason emerged that maths has been so dumbed down in high school that the students have to have remedial mathematics in their first year.

I suppose that this simply reflects trendy post-modern teaching in that you don’t have to learn anything but just absorb political attitudes

• hunter

Al,
Good idea. I pledge to drop my troll feeding.

Climate Skeptic, you obviously don’t know anything about climate science.

The students should have ‘peer-reviewed’ the other students’ test results and built a scientific consensus. Then you would obtain proper answers to your questions. For example: What is the equation of a circle? Pi radius squared is the skeptic view and as far as I know has not appear in the climate science literature. The consensus view is that circles are causing catastrophic and irreversible changes to our climate, and it is recommended that government take action by immediately imposing heavy taxation on eyeballs, nipples, and double taxation on testicles.

Besides, what’s with all this focus on ‘answering questions’. The science is settled. It would have been far more useful if you assessed their ability to properly wipe a hard-drive.

• Thanks for the info. My daughter (13) is in 2nd Year of High School, Special Science Class, here in the Philippines, which concentrates on math and science subjects. The trig she has not done at this time until next year but she is OK with the rest.
Interesting results from your sample – sad, really, and confirms the generally reported feeling of the dumbing down of the US education system.
Anyway,she achieved 70% in a 10 minute workout on the paper, leaving out the coursework not yet done. I think she would have achieved her passmark of 85% doing the complete paper.
Thanks for the test.
Clive G. Smale – Philippines

• Richard Saumarez