Unable to find skilled workers, Kentucky manufacturers are training their own technicians with help from a community college. Advanced Manufacturing Technician (AMT) trainees work part-time on the factory floor, earn an associate degree and qualify for jobs that start at close to $65,000 a year. Many applicants don’t have the math skills to qualify.
I don’t agree with everything this author says, but let’s look at her credentials and see if she merits at least a listen:
My degree is in engineering. I spent five and a half years refurbishing nuclear submarines, and then I quit work to bear, rear, and eventually homeschool our three children.
As a homeschool mom, I participated in co-ops, taking turns teaching groups of homeschooled children subjects such as nature study and geography. As our children entered their teen years, I began teach to teach algebra, trig, and calculus to small classes of homeschoolers at my kitchen table. And as our children left home for their four-year universities, two to major in engineering and one in art, I began teaching in small private schools known as classical academies.
This last year, I have also been tutoring public-school students in Common Core math, and this summer I taught a full year of Common Core Algebra 2 compressed into six weeks at an expensive, ambitious private school…
OK, she has some qualifications and some practical knowledge. Let’s see what she has to say:
Fifty years ago, transformations were not taught, although math-bright students would figure them out for themselves in analytic geometry (second-semester pre-calculus). Today, they are taught systematically beginning in elementary school.
The treatment of transformations reminds me of the New Math debacle of the 1960s. The reform mathematicians of the day decided that they were going to improve mathematical education by teaching all students what the math-bright children figured out for themselves.
In exactly the same way, the current crop of reform math educators has decided that transformations are an essential underlying principle, and are teaching them: laboriously, painfully, and unnecessarily. They are tormenting and confusing the average student, and depriving the math-bright student of the delight of discovering underlying principles for herself.
One aspect of Common Core that did not surprise me was a heavy reliance on calculators.
Huh? What’s that? Reliance on calculators? She definitely has my attention there. I’ve written plenty on that topic (here and here, among many others); the links are there if anyone wants to go read them, there’s no need to rehash the arguments here. Let’s get back to the Common Core piece:
Common Core advocates claim that they are avoiding that boring, rote drill in favor of higher-order thinking skills. Nowhere is this more demonstrably false than in their treatment of formulas. An old-style text would have the student memorize a few formulas and be able to derive the rest. Common Core loads the student down with more formulas than can possibly be memorized. There is no instruction on derivation; the formulas are handed down as though an archangel brought them down from heaven. Since it is impossible to memorize all the various formulas, students are permitted – nay, encouraged – to develop cheat sheets to use on the tests…
The oft-repeated goal of Common Core is that every child will be “college or career ready.” Couple that slogan with the oft-expressed admiration for the European system of education – in European countries, students are slotted for university or a dead-end job at age fourteen, based ostensibly on their performance on high-stakes tests, but that performance almost inevitably matches the student’s socioeconomic class. Do we really want to destroy upward mobility and implement a rigid class structure in the United States of America?
That doesn’t sound like an admirable goal, but the author is correct. She follows that explosive comment up with her denouement:
I predict that if we continue implementing Common Core, average students will drop out of math as early as they are allowed. Even math-bright students will hate math. Tutoring companies will proliferate to serve wealthy families. The educational gap between rich and poor will widen. If we want to destroy math and science education in this country, keep Common Core.
How many kids will have been harmed before we admit that this was a political mistake?
From the Onion: A teacher is fired for “gross incompetence” after declaring, “I just love being around the students—I honestly think I get more out of these classes than the kids do.” She adds, “I learn something new from them each and every day. They teach me so much—far more than I could ever teach them.”
This brings to mind a (real) quote from Michael John Demiashkevich’s Introduction to the Philosophy of Education (1935):
An old schoolmaster dedicated his book to all his old pupils, at whose expense, he said, he had learned everything he knew about education. This is either a case of exaggerated modesty or it is a belated confession of incompetence. It is necessary to distinguish strictly between broadmindedness and ignorance.
I suspect, though, that the Onion teacher was really fired for her use of fluffy phrases like “so much,” “honestly think,” and “each and every day.” If she had said, simply, “I enjoy learning from the students as well as teaching them,” she might still have her imaginary job, and she could still learn “something,” or even “a lot.”
Some adjunct professors make less than minimum wage — with no benefits or job security. These days, the majority of college instructors are part-timers.
After Joanne’s introduction and Diana’s open cheerfulness at being a co-guest blogger here, you might think I’d offer up more intellectually stimulating fare than funny pictures of Starbucks references. For those of you who were disappointed, I’ll endeavor to make it up to you in this post.
In a recent Wall Street Journal piece, Barbara Oakley posits that the Common Core standards, and the pedagogy that is often pushed with those standards, prioritizes “conceptual understanding” at the expense of slighting repeated and varied practice that leads to computational mastery:
Conceptual understanding has become the mother lode of today’s [Common Core] approach to education in science, technology, engineering and mathematics—known as the STEM disciplines. However, an “understanding-centric approach” by educators can create problems….
True experts have a profound conceptual understanding of their field. But the expertise built the profound conceptual understanding, not the other way around. There’s a big difference between the “ah-ha” light bulb, as understanding begins to glimmer, and real mastery.
As research by Alessandro Guida, Fernand Gobet, K. Anders Ericsson and others has also shown, the development of true expertise involves extensive practice so that the fundamental neural architectures that underpin true expertise have time to grow and deepen. This involves plenty of repetition in a flexible variety of circumstances. In the hands of poor teachers, this repetition becomes rote—droning reiteration of easy material. With gifted teachers, however, this subtly shifting and expanding repetition mixed with new material becomes a form of deliberate practice and mastery learning….
True mastery doesn’t mean you use crutches like laying out 25 beans in 5-by-5 rows to demonstrate that 5 × 5 = 25. It means that when you see 5 × 5, in a flash, you know it’s 25—it’s a single neural chunk that’s as easy to pull up as a ribbon. Having students stop to continually check and prove their understanding can actually impede their understanding, in the same way that continually focusing on every aspect of a golf swing can impede the development of the swing.
Understanding is key. But not superficial, light-bulb moment of understanding. In STEM, true and deep understanding comes with the mastery gained through practice.
I recently wrote on a similar theme, quoting from a newspaper article about a Stanford paper that demonstrated, among other things, that children should memorize multiplication tables and addition tables. Quoting:
Next, Menon’s team put 20 adolescents and 20 adults into the MRI machines and gave them the same simple addition problems. It turns out that adults don’t use their memory-crunching hippocampus in the same way. Instead of using a lot of effort, retrieving six plus four equals 10 from long-term storage was almost automatic, Menon said.
In other words, over time the brain became increasingly efficient at retrieving facts. Think of it like a bumpy, grassy field, NIH’s Mann Koepke explained.
Walk over the same spot enough and a smooth, grass-free path forms, making it easier to get from start to end.
If your brain doesn’t have to work as hard on simple maths, it has more working memory free to process the teacher’s brand-new lesson on more complex math.
‘The study provides new evidence that this experience with math actually changes the hippocampal patterns, or the connections. They become more stable with skill development,’ she said.
‘So learning your addition and multiplication tables and having them in rote memory helps.’
As a math teacher I explain it this way: to truly understand algebra a student must already have mastered operations with fractions, decimals, and negative numbers. The simple calculation of calculating the slope of a line between two given points could include all three of those, and if one expends all his/her brain power on that simple calculation, there won’t be as much brain power “left over” to understand what the answer, the slope, actually means or represents.
Some things must be memorized–not for their own sakes, but because they are useful tools, they are means to an end.
In professional development sessions I’m often told, as if it’s an obvious fact that cannot possibly be doubted, that if you cannot explain how something works, then you truly don’t have a “deep” enough understanding of it. You have rote memorization, nothing more, and rote memorization is useless. Sometimes I’m even told this by math teachers, who will at lease concede that memorizing the multiplication tables is a valuable exercise. I put up a division problem, usually something simple like 515/3, and ask “Who can perform this calculation?” Everyone can and all hands are raised. Then I ask, “Who can explain why the standard algorithm (which everyone our age knows and uses) works, and why?” Even most math teachers cannot, but everyone recognizes why that standard algorithm is important, useful, and efficient–everyone, that is, except for those who think that some Indian lattice method leads to “deeper understanding”. Beyond knowing that division is akin to finding out how many “groupings” of a certain size can be made from a certain number, how “deep” does one need to understand division? It’s useful only as a tool to get to bigger and better things, IMNSHO.
So repeat and repeat and repeat until the repetition begets memorization. That’s what Mrs. Barton did until every one of her students knew the multiplication tables. Don’t allow a pet pedagogical theory to harm students’ ability to calculate. Teach them what works. Give them the most efficient tools out there.
In Legally Blonde, Ellie Woods submitted a video essay to get into Harvard Law School.
Goucher College is piloting a new admissions policy that allows students to submit two pieces of work and a two-minute video instead of a high school transcript. The decision has already drawn criticism–for instance, from Brian C. Rosenberg, president of Macalester College, who wrote in The Chronicle of Higher Education, ““This move sends an awful message to high school students and to a broader public that is already fed a steady diet of nonsense about the nature and value of education.” On the whole, thought, criticism has been fairly guarded, according to The New York Times. Proponents and critics alike seem to be taking a “wait and see” attitude.
Dr. José Antonio Bowen, who became Goucher’s eleventh president this summer, believes that the new policy will be more equitable than the old.
“People have learning differences, they mature at different speeds; a lot of great people might have blemishes on the transcript, and think they can’t get in,” he said. “We get mail from teachers thanking us for this, because they have students who want to hang themselves because they got a C in algebra.”
There are at least two distinct issues here. There are students who are not academically prepared for college—or whose preparation is highly inconsistent. Then there are others who are well prepared but who, for one reason or another, don’t have stellar grades.
Will the video option help the first group of students? It may do no more than mask their lack of preparation. The only exception is if they are applying for a trade school, art school, or other program that does not rely primarily on academic work. Even there, a video may or may not represent their abilities or accomplishments.
In the second case–of students with superb academic qualifications but imperfect grades—why not simply make allowances for them? Allow them to supplement their transcript, but don’t replace it. Stop expecting students to be all-star students and athletes and leaders, and instead allow for intellect (which is rarely evenly spread) and character. What does a video accomplish here, unless it supplements the overall picture?
A video could allow a student to demonstrate specific abilities and accomplishments, such as acting, language proficiency, rhetorical skills, or musical performance. It could allow a student to comment on a course or project. It is not a viable replacement for Algebra 2 or American Literature.
Fifteen California community colleges will be allowed to offer bachelor’s degrees in vocational fields. That makes California the 22nd state to let students earn four-year vocational degrees at two-year colleges.
If you haven’t been to the Math With Bad Drawings site, set aside a little time and be prepared to laugh.
For the sake of your monitor I would not recommend doing this while drinking coffee. And on that note, here’s a recent post about The Starbucks Experience, In Graphs.
Raise your hand if you can relate