A couple of weeks ago I read an article that almost made my head explode. Quickest summary possible: Kids are failing Algebra II. This math and math above it are completely useless in real life, so we should quit trying to teach it to kids and replace it with something that has a more practical application to real life.
My answer to this article would have been something like, “Stop dumbing down our kids! You want a more ignorant America because ignorance creates dependence. You use math every day in nearly everything you do. From how much time you need to drive to work based on a mathematical equation of distance and speed, to grocery shopping. Math is the universal language. Whether you’re in Billings, Montana, or Beijing, China, 2 + 2 = 4.”
I would have kept going with other practical applications people use daily without even realizing they are “doing math.”
But I was hoping for a more complete picture how important math is and why getting rid of math is never the answer simply because kids are failing. So naturally I forwarded the article to Stephen L. Hall, a mathematician. It’s a bit long, but I believe this is an important topic that should be discussed, so I hope you take the time to read it.
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Being asked to share my thoughts on an article forwarded to my, the premise of which was that some rather pedestrian and simplistic mathematics courses were too difficult for the modern high school and college students and facing such difficulties without the promise of participation trophies to encourage their fragile egos. To quote that most learned modern philosopher who seems to exemplify this post-modern perspective, one Barbie, by Mattel, “Math is hard.”
This enlightened criticism of the theoretical contribution of mathematics to the intellectual prowess of the elites of our society, the most educated, and the most erudite comes to us courtesy of “a longtime education reporter” discussing a book by a political scientist, with additional advice from a cognitive psychologist, about the imparting to students by education majors. What do I know about mathematics compared to such luminaries; after all, I’m only a mathematician?
As these people feel compelled to discuss the importance of mathematics, ‘tis only proper and just that a mathematician discuss the merits of their respective fields of endeavor.
Andrew Hacker is a political scientist. Interestingly political science, is not actually a science, there are no laws of politics, no objective scientific method which can be employed, no test of universal truth. Politics is the “use of intrigue or strategy in obtaining any position of power or control.” Random House Dictionary (1967). Political science is not about governing but about the race to govern.
Why would a political scientist care about mathematics in the first place, much less care so much that they would write a book dissuading people from learning mathematics? Because political science seeks to persuade people through rhetoric, sound-bytes, and emotional appeals. Mathematics is objective, calculating, discerning, rational, and logical. Those who understand mathematics can see right through the smokescreens of rhetoric and the distortions of emotional appeals.
When studying in a graduate level business course one of my professors told us about a person he knew whose main job was to make charts and graphs look the way that his bosses wanted, typically by changing what and how things were measured. Finance people do this all the time with stock charts by focusing on a small range of values that make an otherwise stable stock look highly variable.
But, a mathematician first looks at the axis of any graph to see exactly what it is measuring. The deceptive practices of political advocates of selectively cherry picking statistics, or economic measures or any other political issue fails in the face of a mathematically literate electorate. For example, the article presents that Republican seats required fewer actual votes than Democrat seats in Pennsylvania congressional districts as evidence of gerrymandering. Forfend that a political process should be political.
The article refers to his “numeracy seminar” which was reclassified as a “special studies” course because of “the math establishment.” The poor subjugated political scientist being abused by the math guys. So I looked up the one word in this article of which I had never actually heard or read. In The Random House Dictionary of the English Language, the unabridged edition (1967), I was unable to locate any reference to a word “numeracy”. Perhaps this political scientist should be being oppressed by the English department rather than the Mathematics department of his university.
The journalist laments that she might have found math more enjoyable if her teachers had been able to explain it better. So what about those teachers? Teaching has been taken over by education majors. Education majors have built their union on the idea that it is more important to know how to convey information about a subject than to have actual knowledge about that subject.
Hacker notes that studying mathematics does not lead to jobs in mathematics, that 38% of computer science and math majors were unable to find a job in their field. But the author notes that we hire 100,000 to 200,000 new teachers each year when less than 20,000 people were majoring in math annually. Having a degree in mathematics, it becomes rather difficult for me to get a job actually teaching mathematics because most state require an education degree, not a mathematics degree.
George Bush was at one time busily telling America that we needed more math and science majors. Working on a degree in mathematics this sounded like good news. Also working on a degree in economics, I noticed that economics graduates made significantly more starting salary than math graduates. My economics degree told me that President Bush was lying about needing more mathematicians.
At the same time, a newspaper insert listed the 25 best jobs and 25 worst jobs in America. Teaching was in both lists. There was a surplus of social studies, history, and English teachers making the likelihood of landing such a job very low. There was a high demand for math and science teachers, making the job security in that field very good. Odd that there should be both a surplus in teachers and a shortage of teachers.
Nearing completion of a degree in economics, the reason was rather obvious. Math and science are more difficult subjects than English and social studies. But the jobs paid the same, the salaries for the teachers were set by the states which employed them, not by the market forces of supply and demand. Shortages and surpluses can only be sustained for any length of time by government interference in the market place.
Why can an admitted “longtime education reporter” not see this obvious discrepancy in few people wanting to study math and not having jobs in the education industry when they graduate? Perhaps because, as she proudly proclaims, she is not very good at math.
So, she seeks advice about the value of math from a . . . cognitive psychologist . . . Daniel Willingham, who proclaims that there are three legs on which math rests: math fact, math algorithm, and conceptual understanding. Proving, beyond any reasonable doubt, that he has absolutely no conceptual understanding of mathematics. If you want to improve people’s understanding of mathematics, then they need to be taught by people who actually understand the mathematics that they are teaching.
Quit hiring people who hate and fear math to teach math. Quit trying to solve economic problems by completely ignoring the laws of economics.
“Hacker hypothesized that tech companies wand an over-supply of entry-level coders in order to drive wages down.” I guess a blatantly obvious economic hypothesis which has been a known established economic law for more than two centuries is a novel and unique revelation to a journalist and a political scientist.
The bias of the article’s author comes out clearly after she tries to justify the perspective of the book she is discussing, that requiring students to study Shakespeare is justified but requiring them to study Calculus is not, to her computer programming husband with the statement, “Reading fiction builds empathy.” Her perspective is that feelings matter.
Mathematics builds logic; it builds reason. Hacker’s book tells her that, “lots of smart people hate math.” It tells her what she wants to hear, makes her feel good about her ignorance and ineptitude. I once heard a very profound statement by a mathematician with a Ph.D. about the low-level of math ability and the acceptance of people of such. He stated, “People who would be absolutely mortified to admit that they were illiterate and can’t read, will stand up and proudly declare that they can’t do math.”
When I was in school, people were lamenting loudly and publicly on national media that the average SAT quantitative scores had declined an estimated of 50 points, in real terms not nominal. However, during that same period of time and being ignored by the media the verbal scores had decreased over 200 points, on a 600 point scale ranging from 200 to 800 points.
Having tutored people in math, I have often had to focus on the English and verbal skills of the student, not the math skills. They have problems reading and understanding the problems, not in understanding the math. It is not reading for empathy that students need but learning vocabulary and comprehension so that they can actually do the math.
What victims of the evils of mathematics education are these leftist trying to protect? “For low-income students, math is often an impenetrable barrier to academic success. Algebra II, which included polynomials and logarithms, . . . drives dropouts at both the high school and college levels. The situation is most dire at public colleges, which are most likely to require abstract algebra as a precondition for a degree in every field, including art and theater.”
Condescend much? Poor, low-income, public college students are simply too stupid to understand basic algebra, a 100 level freshman class, which causes them to drop out in fear and despair.
Odd, growing up the son of a truck driver and cosmetology instructor, we would technically have been classified as upper-lower class to lower-middle class, one of those low-income people. I went to public schools and attended a public, land grant college. I am the very epitome of the victim they want to protect; who not only aced all of the available high school math classes, competed in the national math field day, on a team which placed second in our division, but went on to get a B.S. in Mathematics.
For people like me, she declares math to be often an impenetrable barrier to academic success. I guess that I am forced to rely only upon my other three degrees as I obviously may not count on my mathematics.
Mr. Hacker, to support his idea asserts, “For example, . . . that students will probably learn little about concepts of proof that are relevant to their lives, such as legal proof, by studying abstract math proofs. . . .” If only he had asked someone who had both a degree in mathematics and a degree in law. Oh, wait, I have that. Funny thing, legal proofs follow directly the very same logic as abstract math proofs.
I could go on about how mathematics and philosophy are very closely related subjects, or many other examples of the practical applications of geometry, algebra, calculus, and more advanced mathematics, but I will end on a topic specifically mentioned in the article and of special significance to our blog hostess, the fields of art, in particular dance.
Dance is applied mathematics in virtually every aspect of the field. A pirouette plays upon the dancer’s angular momentum adjusting the angular velocity in relation to the distribution of mass from the center of rotation. Choreography combines not only geometry but is a continuously changing vector field tracking the distances, velocities, and accelerations which is an application of calculus with numerous variables.
There is not a field of human endeavor which does not employ mathematics, and advanced abstract mathematics, even if the participants in that endeavor fail to recognize the mathematics around them.
