Image by Roman Mager.
Aside from all the other challenges this country faces, we’re just been told a K-12 “math crisis” has erupted in U.S. public schools after the first two-year onslaught of the COVID pandemic. It’s left “average” students a half a year behind who have yet to catch up, according to a recent study by a coalition of eight major newsrooms (The Education Reporting Collaborative ).
Alarmed school officials around the country have already used millions in pandemic funds to put “math coaches” in their middle schools. Parents of the math gifted spent small fortunes either on math tutors or the rise of a significant cottage industry teaching math (“Group of 4-6, $40 per session; Private 1:1, $75” ), revealed on Google’s “math programs” website.
But you can bet such panic involves only math “smarties,” not most Americans who gave up generations ago on this subject when teachers blatantly wrote us off as “boneheads.” Most focused solely on the few whipsmart kids.
Americans have been warned almost every decade that when smarties’ scores drop, the nation’s future is at stake. When George Bush was president, the Math Now crash program was inaugurated to address poor teaching of K-to-college students. It was soon followed in 2006 by his Executive Order establishing a National Mathematics Advisory Panel (NMAP) to “strengthen” mathematics education. Two years later, they reported that “our national system for teaching math is broken and must be fixed if we are to maintain our [economic] competitive edge.”
Presumably, nothing much was done about their recommendations because a revised new bill in Congress (H.R. 1735) claims the nation will need at least a million math-smarties in the professions and trades able to:
“…use computational tools to do mathematical and statistical problem solving….Rapidly emerging fields, such as artificial intelligence, machine learning, quantum computing and quantum information, all rely on mathematical and statistical concepts, which are critical to prove under what circumstances an algorithm or experiment will work and when it will fail.”
Its key committee’s recent 36-0 OK for a floor vote will provide $10 million from 2024-28 to the National Science Foundation “to increase mathematics and statistical modeling education in elementary and secondary schools.” Meantime, Congress has hiked the STEM (science, technology, engineering, mathematics) budget to $1.38 billion.
All this financial aid comes just in time for school openings and the arrival of COVID’s second and more complex wave. It has already has closed schools in Kentucky and cancelled extra-curricular activities in Texas and Hawaii.
In other words, it’s the continuance of throwing millions of taxpayer dollars to the 1 percent of math elitists, somehow believing it will trickle down to the 99 percent of those considered boneheads.
At this point, the questions no one wants to ask is whether all that energy, attention, and taxpayer dollars is unfair to kids who are not math whizzes. Answer: You bet. Is it true that what is spent is never enough? Absolutely. Will the constantly changing of math teaching methods ever be spent on boneheads? Unfortunately, probably never unless boneheads begin teaching it in non-traditional ways. Interestingly, every new, mandated method devoted to struggling smarties arouses legions of traditionalist critics insisting math is being “dumbed down.”
As an Oregon State journalism professor I was continually shocked at the staggering flunk and “repeat” rates of liberal arts majors—including ours—required to take it for a degree. Wasn’t high school math sufficient? Too, if liberal- arts faculty had a 5 percent flunk rate, they could expect a communiqué from the dean to either improve teaching skills or else. The math faculty seemed exempt.
I had a spirited discussion with a young math instructor from another state university about those flunk rates and teaching skills. I asked about boneheads being a drag on any math teacher’s labors. “Yeah,” he conceded and sighed. When I pointed out that the speed factor from kindergarten to college seemed to kill interest and accuracy for most students, he looked at me as if I’d just arrived from planet Pluto. He’d never thought about that factor because math for him was easy, he admitted.
I said that I’d had math teachers whose teaching methods were like throwing kids in water and indifference to their struggle to survive. That too many taught at the speed of light. His gorge began to rise: “Look! I’m the lifeguard who pulls ‘em out of the water!” he grumbled.
“But why then do so many kids drown? Or come to hate and fear swimming?” I said.
His voice and exasperation rose. “Kids learn best out of frustration!”
“That’s not been their experience,” I said, remembering a Marine veteran I was advising who would have to take College Algebra for the fifth time. He burst into tears: “They say I’m not trying.”
The instructor snapped “But math is supposed to be hard!”
“Why?”
“Because something that’s easy isn’t worth much!”
Furthermore, he declared, math’s difficulties and complexities gave students a dose of reality. Kids needed to learn that survival is hard. Competitive. His eyes narrowed. The jaw tightened. Only the fittest deserved to survive in the rarified air he’d all but killed himself to breathe over the years.
I then sprung my key public-university question: vested interest and moneymaking courses. Weren’t repeaters financial “rainmakers” for the university (at $800 per term ) and state payments ($5,580 per 15 students = one full-time equivalent) for departments? That five sections of 30 students earned departments $44,800 each quarter term? We both knew some public universities had sections of 250 students, but not that departments were earning today’s national average FTE of $8,859 .
End of conversation. He strode away.
At an OSU faculty luncheon not long after, a professor of teaching grade-school arithmetic listened to my woeful tales of flunkouts. She smirked: “Well!! If they can’t pass College Algebra, they don’t belong in college.” I said most math and science majors in my classes could barely write, so they probably didn’t belong in college either.
“It’s not the same thing!” she snapped, reinforcing the intellectual elitism of math.
All the evidence does lead to the inescapable conclusion of a sacrosanct intellectual class system, supported through the ages by outspoken, militant, and biased math faculties and practitioners. Why else would they privately label those who insist they “can’t do math” with pejoratives such as “boneheads,” “turkeys,” “deadwood,” and “dummies.”
Worse, too many “boneheads” have willingly accepted that verdict for the rest of their lives without ever challenging how the subject is taught. Or that most math teachers excelled in the subject and still cannot abide “the slow.” We “boneheads” may even buy into the popular idea that we’re part of the right-brain demography of the creative and intuitive instead of possessing the left-brainer’s skills in analysis, verbal expression, and methodical thinking.
Yet we now know that all brains have those two halves, and that neither dominates, thanks to the 1970s research of the Nobel prize winner psychobiologist Roger W. Sperry . A 2013 test of his conclusions by a neuroscientist team proved him right. They used magnetic resonance imaging on 1,000 people and found that the two halves of the brain work together. As Healthline’s Ann Pietrangelo explained the phenomenon:
“Bundles of nerve fibers tie the two hemispheres together, creating an information highway. Although the two sides function differently, they work together and complement each other. You don’t use only one side of your brain at a time.” Consequently, for a “right-brainer” to cross into the left-brain takes a few minutes and vice-versa for “left-brainers” forced to use the right.
Meantime, Sperry’s research was followed by experiments at Massachusetts Institute of Technology. Neuroscientist Earl Miller’s team expanded the left/right-brain phenomenon in attention-deficit disorders into front-brain, back-brain differences. Most important for most of us boneheads, he found survival reflexes (e.g., distractions)—were primary. They’re located in the back of the brain (the parietal cortex). Concentration comes from the front (prefrontal cortex). His tests on primates found:
“The electrical activity in these two areas began vibrating in synchrony as they signaled each other. But it was at different frequencies, almost like being at different spots on the radio dial. Sustaining concentration involved lower-frequency neuron activity. Distraction occurred at higher frequencies….Reflexive attention is a more primitive survival tool, while concentration is more advanced.”
So the more threatened we feel, the higher the electrical frequency waves of “fear-or-flight” sent by the parietal cortex. The frontal cortex shorts out from overload. That explains why kids born into surroundings and situations they perceived as threatening—dysfunctional home, dangerous neighborhood, hostile schoolmates and teachers, etc.— constantly protect themselves. How can they possibly concentrate on mathematics? And the more they fail, the more they continue to fail.
I can now personally attest that little has changed in most teachers’ attitudes toward boneheads.
Sensing a book defending them and waiving College Algebra for liberal arts majors to get degrees, I decided to audit that killer course at a community college (CC) to see what was going on. I soon learned CCs were the route taken by thousands to fulfill that college requirement (“It’s easier.” “It has better teachers.”). Some high schoolers take it before entering a four-year college or university. They’ve been advised not to “waste time, energy, and money” “cluttering up” their degree programs.
So off I went to register for Fall-quarter College Algebra at nearby River City Community College (the name has been changed).
I didn’t expect a placement test for College Algebra. It had four prerequisite courses—(none for graduation credit): Math 20, Math 30, Math 50, and Math 95. It was the same at state public universities, the clerk consoled me. Obviously, not only were these extra classes moneymakers, but designed to weed out the first-timer “deadwood” from College Algebra. Moreover, if students failed any of these four prereqs, they would have to repeat them.
Because it was years since I’d passed Algebra I in high school, I tested into Math 30. If I passed, it would be Math 50. If I passed that, I’d take Math 95, and College Algebra in subsequent quarters at Enormous State University.
In retrospect, the five courses indicated nothing had basically changed in math teaching or the prevalent indifference toward boneheads. The main failings to me of their instruction were: 1) speed in lectures and tests; 2) impatience, contempt, and ridicule of us plodders; 3) group work; 4) retention of material, and 5) textbooks largely written by math smarties for math smarties, never for boneheads—or women.
Speed still seems to be the chief obstacle for most from first-grade arithmetic to College Algebra. The teachers’ excuse was always having to stay on schedule with the units (“We have to move on”) even if many students fell by the wayside.
I’m convinced both “numbers alienation” and speed begin when a first-grade teacher like our Miss Johnson (not her real name) put the numbers “2 and 2” on the board, attached an addition sign at the left, and asked us to find the total with our “thinking caps” (our minds). Six-year-old Martin instantly announced the answer was “4.” If Miss Johnson had given the rest of us time, of course, we would have calculated the same number.
Quiet jealously followed when she rewarded him with a dazzling smile and compliment (“Wonderful, Martin!”). From then on, her principal focus was on Martin and two other speed demons always first with the answers and at the blackboard. Instead of a teacher going slowly and thoroughly so all students could build solid foundations on processes, the swift seemed preferred over us slowpokes. So a lot of us gave up through the grades.
Speed
Breakneck speed was the teaching pace in all five classes I took. In College Algebra, “Speed-Queen Kate” informed us in the first lecture that: “We’re going to go very fast. If you can’t keep up, consider retaking Math 50 or 95.” That attitude prevailed by too many tutors in math labs. Most plodders could do just as well if the meter wasn’t running. I recently learned that college officials have advised faculty to give Iraq/Afghanistan veterans extra time on exams. I doubt it will ever be granted to boneheads.
In professions where math is essential, speed is rarely a priority—unless it’s a medical emergency. Who would dare say: “Two-minute warning!” to a surgeon doing a delicate operation or pharmacists compounding prescriptions? Or a navigator calculating coordinates for a bomb run? An Internal Revenue Service clerk examining our taxes?
Ridicule
The second obstacle to math mastery is teacher ridicule, that soul-scaring, cruel weapon too often liberally wielded against those regarded as total and unreachable ignoramuses at every level of public education. Even kindergartners recognize the body language: A sigh of impatience. The smirk. The rolling or narrowing of eyes. Throwing up both arms in exasperation. Ignoring raised hands from those regarded as dumbbells.
I first encountered ridicule when Miss Johnson caught me using my fingers to count. Never mind that other cultures use an abacus, stones or twigs. My soul froze as she raised my offending pinkies and loudly announced that “some little girl isn’t using her thinking cap to solve the problem.” As Miller’s team deduced, my thinking cap was full of joys, woes, a dysfunctional family, and, from then on, Miss Johnson.
Public humiliation in our formative years usually shuts down learning to thousands, including those at neighboring desks. Many victims cry, slam a desk, or refuse to calculate anything. However, rebels like me soon recognized that though Teacher holds the power of the grade and passing, it’s only a temporary arrangement.
In Math 30, the no-nonsense, 30-40somethings working two jobs were not averse to issuing loud responses (“Didn’t you say there was no such thing as a dumb question?”). Or marching into administrative offices to voice them. They knew at CCs, the cash customers were almost always right.
Perhaps the worst instance of mass ridicule and contempt for student effort was our Math 50 instructor. One day he breezed in late, heaved four weeks of corrected homework on a side table under the blackboard. Then chalked a note above it saying “the school doesn’t pay me enough” to return our work on time. The five percent grade for homework—I and other boneheads often used six hours daily— indicated his disdain was universal for many teaching the prereqs.
Few other departments would permit such a deed, perhaps because of possible legal repercussions from appalled and litigious students. But by term’s end, nobody cared enough to confront him. Or spend energy and time complaining to the Dean about his cavalier attitude toward hardworking, cash customers.
Group Learning
Group work goes back to the nation’s founding with the Little Red Schoolhouse technique of older kids ordered to help younger ones. For at least 200 years, that system has been used successfully in dozens of other fields: political science, history, literature, the sciences, music, theater, and the like. It deepens and retains subject mastery, teaches teamwork and respect, and cultivates fellowship. One of my journalism teams had a group photo made after the class ended. Many made longtime friendships beyond graduation.
I was to learn there are good reason why groups don’t work in math. It’s a highly competitive, individualized, specialized subject unsuited for the Little Red Schoolhouse dynamic. Nevertheless, the current push for groups in math started in the late 1980s. Math educators and textbook publishers are now promoting it heavily.
My suspicion is that college and university department heads only decided to try group learning was to retain and relieve overwhelmed faculty and graduate assistants. They are forced to teach the proliferating sections of College Algebra and its prereqs because of that 100-level math graduation requirement. It permits an instructor of, say, 30 students to divide them into five-person groups. Instead of having to grade 30 assignments, it’s only six.
As expected, the system is getting mixed reviews. One study found the system doesn’t work unless the instructor matches skills by group. That breeds intellectual classism, of course. Boneheads get less respect, interest and attention from teachers lavishing it once again on the smarties. Moreover, what student wants the shame of being revealed to classmates as a bonehead by being grouped with other boneheads?
Most of those group researchers and supporters obviously have never been in a math group pulled together randomly.
Our Math 95 teacher grouped us in fives by “chair proximity.” A-students to recidivists. Forget the Little Red School communal spirit. We were not to move from one question to the next in our collective assignment until everyone “understood” each process. We were also admonished to be “respectful” of classmates’ collective contributions to those dozen questions.
Our group’s nemesis was Clarissa, a straight-A isolate furious at having to share her prowess with dimmer lights. We would lower her grade—especially any loafer riding her coat-tails—by sharing her A’s. It was unfair! We did have Jack the Loafer, but the rest of us kept up with her until Al and Mary disagreed with her calculations on one question—and were right. She was affronted enough to rework it twice—and seethe.
On the toughest question, Clarissa sped through it. We asked for a repeat (“slower, please”). She lost it. We got the deep sigh. The eye roll. The fists poised to pound the desk. “I’m NOT repeating it! If you guys didn’t get it the first time, tough toenails!” she barked. That brought the instructor running and my warning shot to him: “You stay out of this!” Clarissa jammed her things into a bookbag and stormed out. We four quietly finished the assignment (our loafer recording the results) and handed it in. We got a B on it, but no fellowship. No more group work was assigned afterward. I’m still convinced our experience is nationwide.
Retention
As for math retention, those who will never use the equation’s “slopes” or other processes again, usually relegate it to the brain’s black hole immediately after tests. Math has to be relevant or in regular use for mastery. True, those with natural photographic memories do have an edge. But several online lessons teach how to develop one. Sadly, retention lasts only until aging or trauma shrivels memory from white-matter disease or brain atrophy.
Too, much time spent away from math—summer vacation, term breaks, or a pandemic—needs resurrection by us non-math types when classes resume. It’s why hours of daily homework are vital.
Biased Textbooks
Some students in my classes were aided by textbook authors and illustrators seemingly catering to smarties chiefly because math reviewers govern publishers’ decisions. The plethora of colorful photos, cartoons, and sidebar “helps” were a sop to the “math challenged” to convince most of us that math was fun and exciting. That’s probably why the online CliffNotes presentations of processes must have millions of hits (including mine). Also, because clothing, hairstyles, and cars quickly date those images, it enables publishers to regularly issue new editions, yet another major expense ($34-$227 ) for repeaters.
Perhaps because men have always outnumbered women in math classes, authors still seem to assume neither boys nor men want to solve word problems involving girls and women. Our textbooks were still male-oriented: soccer-field dimensions, racecar rates, chemical mixtures, rockets, airlines, etc. One problem estimated weights and heights—of men. They never used cooking, wallpaper estimates, children’s needs, yard-good measurements, vacation costs, or mortality rates of men.
These unending “math crises”—especially in higher education—will be insoluble (and insufferable) until its officials waive the 100-level degree requirement for math by those unlikely to ever use its contents. But considering that course’s earning power and intellectual prestige, not even a mass demonstration at Homecoming against it—by thousands of math boneheads, parents, and bitter alumni—is liable to succeed. Perhaps only when pigs begin to fly.