Secrets of amazing teachers: What both sides of the education debate get wrong
salon.com
salon.com
Certainly some teachers say "we need more autonomy!" and some teacher critics say "we need more accountability!" but neither one is saying "...and if we had THAT, everything would be perfect and teachers would know what exactly they need to do to improve!" So it's not clear that the people who want autonomy and accountability are actually getting anything wrong.
The writer appears to think that good teaching can be taught, but doesn't (in this article) say how.
Doesn't it? The author asserts clearly that a great teacher is, first and foremost, defined by their ability to gleen "where the mind fired incorrectly", rather than it being some innate, unlearnable thing. A great teacher is more like a programmer debugging a problem in the kids head than a "born performer". And I found this insight, well, insightful.
So for this point to be useful, we'd need both (a) stronger evidence that it's actually true, (b) evidence that it's teachable. Absent those things, it's just somebody's random assertion. And wouldn't it be just as easy to tell a story of that sort claiming the key to great teaching is empathy, or flexibility, or knowing the material really well?
(Actually, the featured anecdote featured TWO attributes. (1) skill at debugging what's going on in the student's brain, (2) skill at figuring out how best to CORRECT the misconception without unduly harming the student's ego. And I'm sure these are both useful skills for a teacher, but I would need more convincing that they matter more than all the OTHER skills such as being organized, speaking clearly, presenting NEW material effectively, etcetera.)
Side note: in the back of my mind while I read the piece I was probably thinking about Direct Instruction. One provably superior teaching method is to have teachers follow an exact script that is carefully designed to minimize misconceptions in the first place. If teachers could get better at not introducing misconceptions to their students, it might be less important to be good at debugging those misconceptions.
You see this often, even in university students. The problem isn't solved with more accountability or more teacher autonomy. The only solution is better teacher training and a different syllabus.
Also this: http://www.inference.phy.cam.ac.uk/sanjoy/benezet/
I saw this sort of thing a lot when I tutored physics in college. My students would crank through the formulas and come up with an answer. I would point out that their answer says the roller coaster is seventeen light years tall, or the bowling ball weighs less than a grain of sand, and this couldn't possibly be right. I always tried to get them to look at the shape of the problem first, and then look at the details. Otherwise you're just pattern matching, and don't know when you've gone horribly wrong.
It's tricky, though, because you need to strike a balance. Seeing the big picture really well doesn't get the job done if you don't have the mechanics to back it up. If the goal is a precise answer, then knowing that 7/12 is around 0.5 and is definitely not greater than 1 doesn't get you there. But it seems that schools have gone way too far the other way, focusing on the mechanics almost exclusively. The "word problem" seems to be the one concession to the big picture, but even those are taught as pure pattern-matching exercises.
Not really, no.
1. Students have to have a good concept of division, as you suggest.
2. Students have to know a method of division that accurately gets a precise answer. (whether this is via an algorithmic method or via a calculator)
3. Students have to know that their answer to (2) should correspond to their concept in (1)
4. Students have to recognise that they can check their answer using (3), and then remember to actually check this.
A good teacher will teach all four parts of this process. However, it's not possible to teach part 4 without first teaching parts 1 and 2. Every single child makes this same mistake at some point in their learning. This is not really a "problem" and it doesn't indicate a failure of teaching - in fact, the opposite here: the important thing is that the teacher has identified it and can advise the child on how to improve their understanding.
That's what teaching is. As you say, many adults have not consistently achieved part 4 - in fact, it's not immediate at all: it has to be learned.
Most of us are well served by the physicist approach to estimation, because even in the rare case we do need the precise answer our estimate will prevent obvious errors. And having a "feel" for OOM estimates is handy almost everywhere.
And, actually, the approach even gives you a short cut to the precise answer. It's about 1/2, because it's so close to 6/12. In fact, it's only 1/12 away from half. Which means the answer is 1/2 + 1/12 (which is actually a better answer for, say, a carpenter). Note also that this problem is really crappy to do in decimal, as 1/12 yields a repeating decimal (.08333...), which is natures way of saying "use fractions".
This doesn't seem right. What algorithm did you learn in school that would produce 1.5 from 7/12?
When you see "7/12 is 1.5", is your first thought "one sec, let me calculate that and see if the answer is correct"? Or do you just know, without any computation, that the statement must be false?
If you understand division, it's far easier to explain why this answer is wrong without appealing to an algorithm than by appealing to an algorithm.
And besides, the very example we're discussing proves this isn't the case!
The student was able to use the algorithm correctly; his error was at the boundaries of the standard algorithm -- correct input and interpreting output properly.
Simply practicing arithmetic will not prevent you from ever making a silly (or not-so-silly) mistake. Rote practice of the algorithm without also acquiring an intuition for the meaning of division won't help.
With correct guidance, practicing the algorithm can help students form this intuition, but that requires an a priori realization that we need to teach something other than just the rote algorithm, even if we teach it by discussing executions of the algorithm on specific inputs and outputs.
That's a profound lack of knowledge, he does not understand decimal notation. If you do not know what these number symbols mean, how can you communicate using those symbols? It all degenerates into futile pattern matching.
I understand what you're getting at but some kids don't get all of this all at once in a blinding flash - they become more and more familiar with it over time.
which, again, is a symbol misunderstanding. it's extremely presumptuous of you to say that two chained symbol misunderstandings by a fifth grader new to a subject are "the problem [of] rote learning of algorithms [by someone who] does not connect classroom learning with the real world [or] understand what the answer means"
when you're a hammer, everything looks like a nail
That's just absolute nonsense or he was pandering to a constituency. Their parents and their family income and where they live are absolutely the most important factors. You take a school where the average kid lives in a single-parent home, with an uneducated, unemployed parent on welfare, who moves three or four times a year, or whose parents are in and out of jail, meth users, or otherwise completely irresponsible and negligent, and you can put the best teachers in the the world in that school and it will still be a failing school on every standardized measure.
An alternative hypothesis is that Obama's intention was to shift the Overton Window. The budget for public education is huge, and it's not unreasonable to assume that some of his campaign donors are associated with charter schools or testing services.
http://opinionator.blogs.nytimes.com/2013/10/09/turning-educ...
Think of it as an overall problem with code - how do you teach someone how to get good at debugging? A more generic version of that question may be simpler, but maybe even harder to answer: how do you teach general problem solving skills?
The teacher in the article was doing nothing less than debugging erroneous logic as applied by her students. Not just for the procedural errors, but for the underlying faults which allowed the logical errors to manifest.
That's pretty hard core.
Compare teacher salaries to average salaries in countries with the highest academic performance on standardized tests. The ratio in such countries (e.g. Canada) is almost always significantly higher than in the U.S.. Educational requirements to hold teaching positions are also typically higher. That's the secret to improving teaching quality on a demographic scale. Pay more, but expect more.
Why does autonomy work in Finland, as mentioned in the article? First, we have invested in the teacher training. Second, we have provided more resources to the schools with a more troubled student body. No need for the blame game that is the recent Global Education Reform Movement. Could you implement this in a US state similar to Finland such as Massachusetts, if not staight away in all of the US?
The thing that teachers and schools need is more responsibility, more power to plan and decide how they teach, but still keeping an eye on the results.
The mentality of punishing schools with low scores will however not help. Beating the weak rarely makes them stronger. Give more resources and guidance for schools that are lacking behind, and award more autonomy for schools that work properly.
10 things you've been doing wrong for years.
etc.