U.S. Adults & Students Bomb Out In Math, Science ....Again!

Conducting a workshop in August, 1978 to help Caribbean teachers with the CXC Astronomy syllabus

One of the amusing comments of Caribbean teachers attending a CXC (Caribbean Examinations Council)  astronomy workshop in August, 1978 in Castries, St. Lucia was:

"Why is there so much physics and math in this syllabus content? Are we expected to be able to integrate both these subjects?"

Well, uh, yes .....that's why this subject is called Integrated Science and why astronomy is taught for one trimester as part of it. After doing some basic background review, however, most of the teachers grew a bit more comfortable.  Though astronomy ultimately became defunct after five years - because fewer and fewer teachers were prepared to handle it - the seeds sown in the inaugural year allowed a vast number of science teachers to enhance their physics and math skills.

Could a deficit in physics and math background, skill also explain why U.S. students continue to not do so well compared to other advanced nations? According to recent results of a world wide test - administered to over 156,000 people in 20 nations, between the ages of 16 and 65 - the conclusions are not sanguine, for the students or the adults. In the case of the high school students they placed 31st in math, and 24th in science, not having changed position in the last decade.

Meanwhile, the students of Shanghai, China (the nation that's just dispatched a space craft to the Moon) scored highest, with their results equivalent to at least one additional year of school - over U.S. competitors. Nor was this simply a matter of regurgitating material, but instead the students demonstrated they "were very good at higher order skills reflecting what you can do with what you already know."

One example of this type of problem would be:

"A group of 4 astronauts lands on Mars with solar radiation collection material of total area 2000 m^2. If the efficiency of the material is 30%, and the ambient night time temperature on Mars for their base location (Isidis Planitia) is -40 C (10 C day time high), will they have adequate collecting material if the solar constant on Mars is 620 W/m^2? (Assume insulating material with a thermal conductivity of 0.08 W/mC, and a need to keep the inside area of their domecile at least at 10 C, requiring solar radiant energy collected of at least 1,200 W per minute for an area of 10 m x 10 m.)

Estimate the thickness of insulating material they're likely to need in order to make it work. Comment on whether this expedition is even feasible given the limits of their materials, and that no more than 100 m^3 of insulating material can be taken."

That Chinese students are proficient at doing this type of critical thinking application problem and U.S. students mainly are not, ought to be severe cause for worry. In addition, this divergence can also explain why so many in the U.S. still fail to grasp the basics of climate change, including why spates of frigid weather and snow do not contradict it.  This take is also reinforced by the fact that American adults scored below the international average on a global test in math, reading and problem-solving using technology — all skills considered critical for global competitiveness and economic strength.

Meanwhile, adults in Japan, Canada, Australia, Finland and multiple other countries scored significantly higher than the United States in all three areas on the test, according to results released Tuesday by the Organization for Economic Cooperation and Development, which is made up of mostly industrialized member countries.  Are we a nation in profound decline? I submit to you that given the results on multiple levels, we are, and there's no gainsaying it.

How complex were the problems? Maybe you are thinking they were similar to the sample one shown above. Not so! Beyond basic reading and math, respondents were tested on activities such as calculating mileage reimbursement owed to a salesman, sorting email and comparing food expiration dates on grocery store tags.  None of which require profound insight or genius level skills, or shouldn't. But recall that a similar test given in the 1980s disclosed adults who: didn't know the Sun was a star, and believed the Sun moved round the Earth, not vice versa.

Not only did Americans score poorly compared to many international competitors, the findings highlighted the gap between American high- and low-skilled workers, and how hard it is to move ahead when your parents have not. To fix ideas,  in both reading and math, for example, those with college-educated parents did better than those whose parents did not complete high school.

Most worrisome, the U.S. tested below average on literacy. Coupled with the nation's "large social disparities, the test's findings reveal that for Americans, social background has a major impact on literary skills," the study said.

As we confront an era with ever more advanced technological issues, not only climate change but (very soon) the advent of quantum computing and bio-engineering, one wonders just how prepared Americans are. While too many still remain mesmerized by the bubbling DOW, they'd do much better to ensure they attain essential critical thinking skills - for themselves and progeny.

A set of sample math and science questions to see how you fare:

1)  In a given week a salesman travels 134 miles, during which he pays an average of $3.29 per gallon for gas. If his Buick Enclave gets 12 miles to the gallon, how much should he be reimbursed?

2) You're given a straight rule, a doughnut and a circular disc. Draw a sketch of each and mark the center of gravity in each sketch. What is meant by the center of gravity?

3) A girl is given 100 cubic centimeters of boiling water in a beaker, to which 50 grams of  ice is added. Using a thermometer, how will she know when the mixture has reached thermal equilibrium?

4) One Big Mac and Cheese with condiments has 3,800 calories. You want to burn them off with exercise, and choose jogging. This allows 150 calories to be burned off per half hour,. How long will you need to jog to burn off the Big Mac?

5) An air conditioner consists of a fan coil unit and a compressor unit.  When switched on, the fan coil unit rated at 250 watts, operates continuously. The compressor unit - rated at 1.6 kilowatt- operates only 40% of the time. If the air conditioner is switched on for 12 hours a day, find the total electrical energy in kwh (kilowatt-hours) consumed in a 30-day month.

6) Find the value of x, if:

6x - 24 =   12 - 3x


7) If seven  pencils and 5 erasers cost $11.60, but 5 pencils and 3 erasers cost $7.60. Find the cost of 8 erasers.

8) The floor of a room is in the shape of a rectangle. The floor is c meters long. The width of the floor is 2 meters less than its length. State, in terms of the unknown c:

i) the width of the floor

ii) the area of the floor

If the area of the floor turns out to be 15 m²    then find the width of the floor in meters.

Why E.O. Wilson is Wrong on His Anti-Math WSJ Op-Ed

Let me preface this by saying I have immense respect for E.O. Wilson, the eminent evolutionary biologist and author of the excellent book, Consilience. However, I believe he is totally wrong in the opinions expressed in a recent op ed in The Wall Street Journal, "Great Scientist Doesn't Equal Good At Math' (April 9).

He claims in the piece that for many young people who "aspire to be scientists" the "great bugbear is mathematics". He then poses the rhetorical question: "Without advanced math how can you do serious work in the sciences?"

Whereupon he proceeds to address the question by saying you don't need advanced math, and also fessing up to his own lack of advanced math background. This perceived inadequacy led him to finally sit in (as a tenured professor) on Harvard calculus classes with undergraduates. He concedes he was "only a C student" and "advanced only a small amount".

This experience clearly reinforced his pre-existing perceptions and led him to conclude that "pioneers in science only rarely make discoveries by extracting ideas from pure mathematics." We are asked to accept instead that "real progress" comes by way of "being in the field, writing notes". He does concede, however, that "exceptional mathematical fluency" is required in disciplines such as particle physics, astrophysics and information theory. Indeed! And these were grand discoveries! From the neutron to quarks, to black holes and gravitational deformation of space-time (in general relativity).

And indeed, no one can dispute that Albert Einstein was a great scientist, or Richard Feynman, or Paul Dirac (whose advanced mathematics exposed the positron.)  So basically where Wilson takes exception is the biological sciences. He argues:

"The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail. Possibly no more than 10 percent have any lasting value. Only those solidly linked to knowledge of real living systems, have much chance of being used."

He does say that "if your level of mathematical competence is low plan to raise it" - but "meanwhile know that you can do outstanding scientific work with what you have."

Maybe, but it's interesting that evidently Wilson's own math exposed the deficiencies of one of his biological models  allegedly showing support for group selection. Some of the critics, as recently pointed out by Edward Frenkel (Notices of the American Mathematical Society, Vol. 60, No. 7, p. 838) :

"pointed out that one source of error was in Wilson's math."

And of course, evolutionary biology is replete with math that is crucial - but doesn't even rise to calculus level. For example, the success of natural selection is measured by the fitness (w) and the selection value (s): E.g. w = 1 – s.  This is generally applied to a species and population after some defined time, say via three genotypes be exhibited in the population: DD, Dd and dd (say the German cockroach species with dominant allele D, denoting resistance to the pesticide dieldrin, and disadvantaged allele d that denotes non-resistance.)  Then it can be shown that over successive generations of these roaches the gene frequency (of d) will decrease by:

delta q = -s p q^2 / (1 - sq^2)

where p denotes the frequency of the favored allele, and q the frequency of the  "deleterious" allele. A simple table can be constructed (via successive iterations of the previous formula) showing the declining gene frequency of d relative to D.

Needless to say, this sort of math ought to be in EVERY would-be biologist's "wheel house".  I mean it doesn't even rise to the level of calculus.  The critical insight revealed is that each new (delta q) feeds back to reduce q in the next iteration. Thereby the loss of 'd' genes through selection is balanced by the gain of the 'D' genes that confer reproductive advantage.

Wilson, however, appears to depict any kind of math above basic algebra as some kind of airy-fairy "art form" that really isn't needed as an essential tool. Let's also bear in mind here the critical role of mathematics in the ordering or information, as well as the capacity to represent objective truths clear to everyone. As Frenkel observes (ibid.):

"While our perception of the physical world can be distorted, our perception of the mathematical truths can't be. They are objective, persistent, necessary truths. A mathematical formula means the same thing to anyone, anywhere- no matter what gender, religion or skin color."

  For example, the way in which we are able to describe mathematically the twistedness of solar magnetic fields in the vicinity of sunspots, e.g. via the Helmholtz equation, viz.

1/ r  [¶/ ¶r  ( r  ¶/ ¶r)] B  +  (a)² B = 0

where r is the radial coordinate, B  the magnetic field intensity, and a  the "force free parameter". Then the axially symmetric (i.e.- in cylindrical coordinates r, z, q) Bessel function solutions are

B _z (r)    =   B_o J_o(a r)  

B _q (r)  =  B_o J₁(ar)

The biologists, like Wilson, may not need to know this specific illustration, but they ought to be facile with every mathematical tool that can support their own models, or theories! Obviously, they'll never use the advanced mathematics used by those of us who do astrophysics, say the analysis of the evolution of the Sun's largest magnetic fields, but they do need to know enough to, say,  amply show any claimed support for group selection.

This gets us to the real issue, which is admirably articulated by Prof. Frenkel (ibid.), i.e. how to improve our math education and to eradicate the fear of mathematics that is rampant (even among science disciplines) and which Wilson gives voice to. Readers already know my stand on this, which is that we need to get more top math specialists into the role of math subject teachers. What we don't want to see is majors in Phys. Ed. or Social Studies teaching subjects like algebra, advanced algebra or god forbid, AP Calculus.

GRE scores show the validity for this view, with education majors typically scoring 1000 total or less while subject specialists score significantly higher. If we are ever to enhance and improve Math Ed in this country we have to change the system!