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
I look forward to guest-blogging with Darren! I have many obligations over the next week–so my blogging won’t be prolific. I will try to post a few pieces, though.
Nearly two months ago, Steven Conn’s opinion piece “The Rise of the Helicopter Teacher” appeared in The Chronicle of Higher Education. (Conn is a professor and director of the public-history program at Ohio State University.) He described a classroom exchange where a student asked for the “rubric” and he had to ask what it was. He then replied that there would be no rubric. In the piece itself, he attributed the demand for rubrics to a general trend toward “helicopter teaching” and “spoon-feeding.” (Note: I agree; I would add that rubrics can even penalize outstanding writing.)
The student who asked me for a rubric did so because she gets them in all her other classes, and has gotten them during her entire school career. Without such road maps, so I have learned, students feel the free-floating anxiety that they will have to do all the work of writing a paper on their own, that they might not do it well, and thus might wind up with a B on the paper. Which as we all know is the same as a C. Hey, I’m sure I’m just as guilty of inflating grades as anyone.
The piece received a range of comments, including not-so-subtle suggestions that Conn should not be teaching. In the minds of some, the refusal to provide a rubric was a sign of laziness or unwillingness to meet the students where they were.
But rubrics and guidelines are not the same, nor (presumably) is college the same as high school.
Rubrics, in my experience, risk being reductive rather than instructive. What makes a good paper? In general, it has a clear and well-supported idea. The structure suits the purpose. It addresses counterarguments and complications. It is free of errors and distractions. It cites its sources properly. At higher levels, it shows original thinking as well as a command of style, cadence, and rhetoric. Now, one could spell this out in a rubric, but to what good end? [Read more...]
I’m going to Andalucia for two weeks — and I just used two-thirds of my Spanish for the headline.
Darren Miller, who blogs at Right on the Left Coast, and Diana Senechal, who blogs here, will be guest-blogging. Darren is a high school math teacher in Sacramento. Diana teaches philosophy at a New York City high school.
Since school started this month, my 15-year-old son, Zak, has been having trouble sleeping. He’s been waking up in the middle of the night, worrying if he’s finished everything on his to-do list.
Compared to many students in our San Francisco neighborhood, Zak has a “light” schedule. He goes to school, participates in jazz band and does his homework. By design, he’s not the classically overscheduled child.
And yet, Zak’s daily routine of school-band-homework still manages to eat up most of his day. When Saturday finally rolls around, he’s not the carefree teen I wish he could be. Instead, he’s anxious, calculating whether he has enough time to get together with friends in between weekend assignments.
Some high school students work very hard to get into selective colleges, which now require lots of AP courses and extracurriculars. What percentage of teens are on the high-stress track?