Comments

Great post!

I think we know the answer to the question of whether anyone was ever fired for poor teaching.

A simple no.

And btw, I probably have the same take on this that I assume you do; I wouldn't want a good researcher to be fired for poor teaching.

However, that doesn't relieve professors, who in fact are paid to teach (how many pure research positions do we have in life) from figuring it out.

I think the problem with T.A.s is simply that they don't have many years of experience. As we've all said a number of times, good domain knowledge is just the beginning.

Knowing how to communicate good domain knowledge is a Whole Different Thing.

I actually have a decent example of a variant on this in my brother-in-law, I think.

He's so good (he's the architectural engineer, and he's probably some kind of Engineering Savant) that when he's trying to teach his daughter, he can instantly see how it is she's understanding a concept, and shift his approach to the subject.

My sister can't do that. Her daughter is still at a level of math (algebra 1, I think) where my sister can help.

But my sister can't quickly hop from one approach or point of view to another (neither can I, that's for sure).

So....with T.A.s there are a couple of problems: they are rookie teachers, and even though their domain knowledge is good, they are rookie mathematicians, too.

Think about that fantastic article by the Israeli mathematician who taught grade school kids! (We have to 'blooki' that SOON.)

As he went along, teaching little kids, his understanding of elementary mathematics deepened.

-- CatherineJohnson - 27 Sep 2005

It's true, though, that T.A.s are more motivated & accessible as a rule. That's true with aides for autistic kids & adults, too.

Young people are so sweet, fresh, and good-hearted. (OK, not always, but you know what I mean.)

-- CatherineJohnson - 27 Sep 2005

Life is full of vain hopes and groundless fears

I love it!

Though I don't think this is a groundless fear!

-- CatherineJohnson - 27 Sep 2005

Your description of engineering schools sounds to me as if engineering professors need to think about coherent curriculum.

It's incredibly hard to be coherent, and to winnow things down.

That's why writers always say it's harder to write short than to write long.

It's incredibly hard to write short.

-- CatherineJohnson - 27 Sep 2005

I have a question (I'll probably pull this up front later):

Dan says:

The idea thread about math being easy for some people and hard for others is interesting. Throughout school, there are always kids who are “good at math.” I have no idea why. Perhaps their brains accommodate better “spatial reasoning” or something. Or, perhaps they just pay better attention, or they just enjoy solving problems (as distinct from telling stories or discovering foreign cultures or whatever). I think, though, that at some point, math becomes hard work (or confusing) for everybody. If, for you, that point is about the time you’re learning algebra, then I guess you’ve got a couple of choices: you can become a mathphobe or you start working hard at math. For all I know, you may become a mathematician through all that hard work. Others can get well into college before math seems confusing or hard.

Is that true?

Interesting.

(This is the kind of thing non-mathematicians have never heard.)

btw, it's not that non-mathematicians assume all math at all levels is easy for the gifted......but it's close.

-- CatherineJohnson - 27 Sep 2005

Engineering school is a rude awakening for most college freshmen. Take it from someone who persevered through engineering school and didn’t washout, like 2/3rds of my classmates by sophomore year. Here’s what you learned by the end of freshman year:

1. You had been coddled the past 13 years by your well meaning K-12 teachers. You were mostly spoon fed the material, at a slow pace, and then tested on how well you could regurgitate the exact same material back to the teacher in the exam. Rarely, if ever, were you required to apply your knowledge to solving new problems. As a result, you could, and probably did get by, with merely inflexible knowledge. You probably never mastered the material to the point of automaticity and you had little time to re-learn it now. This would be most apparent in ...

2. Algebra: You didn’t learn it well enough. Actually, you don’t realize this yet. You think your problem is calculus. It seems much more difficult than it did when you took it last year in high school. This is because the pace is twice as fast and the test problems require more than a regurgitation of what was taught (or rather wasn’t, see below). You see, calculus is 10% calculus and 90% algebra (which includes a healthy does of trigonometry and geometry); and the calculus step isn’t all that difficult usually. Part of the problem is either setting up the calculus step or finishing the problem after the calculus step. In high school, they allowed you through the algebra gate without paying the full toll and you’re paying the price now, especially if you hobbled through on your calculator (A wonderful tool that shouldn’t and doesn’t get pulled out until the last step anyway). (Of course, anyone who has read Laping Ma knows that your problems started well before the first day you set foot in algebra class.) Anyway, you’ll need to know calculus and algebra cold if you expect to pass Physics I next semester. But this is going to be impossible because ...

3. Your professors suck and you don’t understand your TA’s poor English. This really isn’t the real problem though, you only think it is the problem. The real problem is that you are expecting them to be spoon feeding you the material like they did for the past 13 years. In fact, what they expect you to be doing is to be teaching yourself. In high school, your teachers taught you the new material, then you did the associated problems, then you reviewed them the next day. Now, you read the new material yourself, then you do the problems, then your TA goes over a few answers to make sure you did them correctly. At best, you learn from your mistakes, assuming you did the problems beforehand. Which you didn’t because there just isn’t enough hours in the day to teach yourself and then do every problem assigned in every class. So you dutifully copy down the answers that the TA gives you all the while thinking “hey, that wasn’t so hard, now that someone’s showed me.” But, “understanding when explained by others” is not the same thing as the “ability to explain to others” which will become brutally apparent ...

4. When you fail your first test. The first test you’ve ever failed in 13 years. Goodbye unearned self-esteem; hello, reality. You crammed the whole night before, but the test was too hard and too long. If only you had more time. Say hello to the magic number seven (plus or minus two). You know him, he’s been hanging around in the background for the past 13 years. He was good friends with all the kids who didn’t go to college, but he never visited you. He has lots of free time now though, and he’s looking to be your best friend for the first time. You’ll become casual acquaintances this semester and good friends next semester in Physics I because ...

5. All those damn equations. Your brain is full. It feels like every time you learn something new it’s pushing something else out – like your name and your address. Spring semester brings with it Chemistry II (which requires you to remember everything you learned in Chem I), Calculus II (also brutally cumulative with Calc I), Computer Programming (learning new languages isn’t easy, especially when that language is C++); English Composition (your only easy class, too bad you have to do a term paper that’s twice as long as anything you’ve ever written before); and lastly Physics I which will be the course that ...

6. You’ll blame when you transfer to business school. Physics I – the rock upon which many engineering education ships have foundered. Two reasons – word problems from hell and the magic number seven. Physics is your first real test in your education career. It tests how well you are learning not only physics (under a withering course load of other difficult courses), but also how well you previously learned algebra and calculus. It is the latter two that will be your demise because you need every brain cell you can muster to learn physics today. If you’re expending too many brain cycles recalling how to do the necessary calculus (most likely because you don’t sufficiently know the underlying algebra) sooner or later you’re going to meet the magic number seven. Meeting the magic number seven is like meeting your computer’s swap file: everything slows down as your computer accesses the hard drive because it has run out of RAM (i.e., memory). This is what your brain does too when it runs out of active memory. You become overwhelmed and inefficient. Eventually, it all ends in tears (or an extra year of college after you’ve transferred to a nice soft major like human resources, communications, women studies, etc). So you lash out and look for someone to blame ...

7. Like your professors and TAs? Wrong. The train was sliding off the tracks well before they came into the picture, most likely sometime in elementary school. Don’t blame them because the train finally derailed at their station. Don’t be like the drunk who’s looking for his lost keys under the streetlights because that’s where the most light is. A career in engineering or one of the hard sciences was effectively foreclosed to you by the 8th grade. In the land of the gentleman A, how were you to know that only the A++ students were king? No one told you that just because they tested you on x , you should really have made sure you knew not only x but also x+25 if you expected to pass engineering school. Nevermind, that no one ever told you that x+1 through x+25 were so important, much less tested. Most likely, you would have been none the wiser had stayed in the soft land of almost every other undergraduate field of study. Everyone would have been happier because, well, you don’t know what you don’t know. Anyway, you can at least find solace in the words of Homer Simpson when he said to Lisa and Bart afer failing: “Kids, you tried something hard and failed miserably; the lesson is – never try.” But why blame yourself when you can blame the real culprit ...

8. Your rotten K-12 education. Oh sure, they meant well. But look what happened. You see, you’re not part of the lower half of the bell curve who probably shouldn’t be pursuing a career in engineering or the hard sciences anyway. Nor, are you part of the 2 standard deviations and above gang that have the ability to succeed and compensate for a rotten education. You’re part of the curve that needed a good education to succeed and you didn’t get it. And, it wasn’t a single chop that lopped your head off, rather it was death by a thousand tiny paper cuts. The accumulation of 13 years of inefficiencies and unsound practices that prevented you from mastering and overlearning the material you needed to succeed. Constructivism, discovery learning, and child centered education, social promotion are a few of the culprits, but certainly not the only ones.

That’s the advice from someone who’s been through it twice. Once through the mathematics side and engineering school and once through the verbal side and law school.

-- KDeRosa - 27 Sep 2005

Hi K!

I think this the first time I've seen you here!

And I think you've been reading Dan Willingham, am I right?

(Looking forward to reading your Comment thoroughly--thank you!)

-- CatherineJohnson - 27 Sep 2005

Algebra: You didn’t learn it well enough. Actually, you don’t realize this yet. You think your problem is calculus. It seems much more difficult than it did when you took it last year in high school. This is because the pace is twice as fast and the test problems require more than a regurgitation of what was taught (or rather wasn’t, see below). You see, calculus is 10% calculus and 90% algebra (which includes a healthy does of trigonometry and geometry); and the calculus step isn’t all that difficult usually.

I love it!

This is GREAT.

This backs up Bernie's post of a couple of weeks ago--yes?

I think he, too, was saying you need SERIOUS algebra skills to take calculus.

-- CatherineJohnson - 27 Sep 2005

OK, I have now Read The Whole Thing.

whoa

-- CatherineJohnson - 27 Sep 2005

Whoa, indeed.

Excellent post!

-- CarolynJohnston - 27 Sep 2005

Yes, I have been reading Willingham, who I discovered only after reading KTM. I had first learned that cognitive psychology was fertile ground for education research by reading E.D. Hirsch, but Hirsch didn't give much detail. Willingham is great, I just wish more of his stuff were available and/or more people like him wrote about this research that is not so widely known. The real education "research," such that it is, is appalling and the guys at the whatworks clearinghouse are moving much too slowly debunking all the pseudo-research bandied about by the educrats.

-- KDeRosa - 27 Sep 2005

I've got his textbook now, which I think is terrific, and will try to get as much of it 'blookied' as I can.

I've also got his book of cog-sci greatest hits. The first (and so far only) article I read turned out to be children's 'eureka' moments learning arithmetic.

Great, great stuff.

-- CatherineJohnson - 28 Sep 2005

"The real education "research," such that it is, is appalling and the guys at the whatworks clearinghouse are moving much too slowly debunking all the pseudo-research bandied about by the educrats."

Hear, hear! WWC is a great idea, but it's just not moving fast enough. I also was led to cognitive psychology by reading Hirsch (check this post out -- it's a short summary that I took from a Hirsch article).

Catherine, is Willingham's cog-sci textbook actually a collected set of articles by him and/or by others?

-- CarolynJohnston - 28 Sep 2005

He has two books. One is a traditional textbook (but great) and one is a collection of articles from ... I've forgotten which journal they're from. The collection is also intended as a supplementary textbook in a cog psych class.

Both are terrific.

-- CatherineJohnson - 28 Sep 2005