A Lesson In Teaching Physics: You Can’t Give It Away

[kuruman]

A central principle of Physics Forums regarding homework help is not to provide solutions on demand but to guide students along a path to the answer.  The rationale behind this principle is articulated in the familiar saying, “If you give a hungry man a fish, you feed him for a day; if you teach him how to fish, you feed him for a lifetime.”  That said, I will quote another familiar saying, “You can lead a horse to water, but you can’t make him drink.”  Then I will blend the two into “You can teach a hungry man how to fish and lead him to the water, but you can’t make him fish.”
This mélange epitomizes a conclusion I reached after decades of teaching minds, some hungry some not, how to think. How I reached this conclusion and how I eventually came to terms with it are the subject of this article.
The seeds
When I began graduate school, my duties included helping with grading hourly exams in large classes (150-200 students).  Here is the exam question that started it all.
An...

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[Swamp Thing]

An electron of charge −e enters a region of uniform magnetic field B with velocity v directed into the page.

Isn't this a bit confusing, given that the figure shows the electron moving "within the page" ? Or is it a deliberate trap?

 

[kuruman]

Good catch! It should read "An electron of charge $−e$ enters with velocity $v$ a region of uniform magnetic field $B$ directed into the page." I cut and pasted in the wrong place. The typo has been fixed.

 

[vela]

I couldn't help but notice the irony in that you ignored what your mentor David told you just as your students ignored what you told them.

 

[gmax137]

I found this to be a very interesting read. Thinking back to my school days, I don't think I had the maturity and good sense to have worked through all of the booklet. My main strategy was to carefully read the textbook, and pay close attention in my classes. I don't think I appreciated how important it is to do the problems. I didn't figure that out until my third year.

I will say that I did note whenever the professor would say "this will be on the exam." Sometimes they didn't say it explicitly but "I could tell."

 

[kuruman]

I couldn't help but notice the irony in that you ignored what your mentor David told you just as your students ignored what you told them.

Yes, I didn't realize it immediately. At first I thought that David wanted to spare my feelings by not saying "I told you so." His smirk was more devastating. It made me see the similarity between him "telling" me and me "telling" my students. Disregarding good advice is a common trait among humans.

 

[hutchphd]

Are you aware of similar attempts by others? I think it is very good strategy and particulary like the "leave it in Algebraic form on test day" part. Also cuts down on my least favorite question: "will that be on the test?" My personally favorite ploy was allowing a single-sided 8.5x11 inch cheat sheet (this was pre-printer/computer days and microfiche was not allowed)
Did you publish the list of problems for public consumption? Might be interesting to have generic lists for the intro courses

 

[kuruman]

Are you aware of similar attempts by others?

I am not aware of similar attempts by others.

Also cuts down on my least favorite question: "will that be on the test?"

And it cut down on my least favorite question: "do I have to know this?" I made sure that the booklet covered all the aspects of understanding and skills that I expected students to acquire in the course. However, I never said "If its not in the booklet, you don't have to know it."

Did you publish the list of problems for public consumption?

They were available to students through the Blackboard platform that my institution had adopted. A password was needed for access so no, they were not available for public consumption. However, the very first three or four booklets came into being before course websites were commonly available. They were literally booklets consisting of paper sheets stapled together and made available to students at a nominal fee to defray the photocopying costs.

 

[berkeman]

Are you aware of similar attempts by others?

I am not aware of similar attempts by others.

In my last physics course as a sophomore many years ago, the professor did use the notebook technique to frame the homework and exam questions. It had about 100-120 problems in it, similar to yours, and he had the same policy that exam questions would be from the booklet.

It was a very large class (around 500 students), and I was really enjoying Physics at the time (but would later choose EE for my specialty starting in my junior year). I worked through every problem in the booklet during the course, and was left with only 2-3 that I could not solve going into the last couple weeks and preparing for the final exam. I went to a large study session in the lecture hall the week before the final, where the professor and TAs were available to help with questions. I was first to raise my hand and asked about one of the last problems in the booklet that I was having trouble with. The professor smiled (he knew me) and asked the rest of the large group if there were any problems near the beginning of the booklet that they wanted help with. About 30 hands shot up, so I realized that the session wasn't for me, and headed off to study more on my own.

During the final, I was able to work through all of the problems pretty quickly, except one that was one of the problems that I had not been able to figure out in the booklet. Fortunately I had about 10+ minutes left in the exam to keep working on it, and thanks to all of the time I'd already put into working on it during the semester, I was able to figure out the key concept that I needed to apply and was able to solve the problem. I was so happy as I was finishing up the solution that I started quietly laughing to myself and looked up to see one of my favorite TAs from the course who was sitting in the front of the lecture hall proctoring the exam. He saw the expression on my face and just smiled at me.

So I agree that the handbook approach can work well, especially in larger lower-division classes. But I also agree with what you wrote, that it works best for students who are highly motivated to learn and to do well.

 

[Nik_2213]

My last Math teacher pre-Uni had the most unfortunate reputation of asking 'trick' questions. As, that year, none of us were noticeably 'gifted', we soon learned that 'obvious' replies were probably superficial, wrong. This led to paranoid mind-set where no-one dared reply without a 's_l_o_w count' to study what we'd now call an 'IED'...

"Red wire ? Green ? Blue ?? The grey 'Coax' ???"

This led to trap where 'simple' schol-paper problems, meant to shake out the 'rote-learners', were more time-consuming than the 'hard' ones intended to make you think...

Shades of Sherlock's "When you have eliminated the impossible, whatever remains, however improbable, must be the truth..."

By cruel irony, I ran into the guy about a decade later at local 'all-formats' computer club: He was so proud of his Commodore PET, but he'd seen my Apple ][+ 3D Astronomy program, published as cover-article in small-press. I'd only used basic Trig plus compound Sin/Cos formulae for the stellar coordinates' tri-axial rotations, but I'd done them right...

I caught my breath, apologised that I'd not been one of his better students. He replied to effect that no bad students had attended his course.
Let's put it this way: a life-time along, I still cannot figure if that was insult, neutral or compliment...

 

[symbolipoint]

Continue reading...

I just took a brief look at that article. I read the "Germination of an Idea" part. That section reminds me of what someone said, "We are like our students."

 

[malawi_glenn]

In the booklet, are there "hints", "answers"?

Regardless of ability, all motivated students realized I did not design exams to expose their ignorance but to consolidate their learning. That was a big win for them and me.

As I wrote elsewhere recently, I have national final exams to consider and prepare the pupils for. Questions like your "seed" question will be on such tests.

I liked problem 6.5 I have a similar one in my "booklet". The dotted circle is in the same plane as the wires I guess.

 

[bland]

Then I will blend the two into “You can teach a hungry man how to fish and lead him to the water, but you can’t make him fish.”

Or even better, "you can build a man a fire and he's warm for the night; but if you set a man on fire he is warm for life".

 

[kuruman]

In the booklet, are there "hints", "answers"?
$\dots$
I liked problem 6.5 I have a similar one in my "booklet". The dotted circle is in the same plane as the wires I guess.

No hints. There are numerical answers highlighted in blue. All numbers are removed before a problem is placed on an exam. See comparison below. Yes, the plane of the circle is in the plane defined by the two wires.

In booklet

On test

 

[malawi_glenn]

And for that problem on a test, how would you expect and accept students to answer? In other words, how would a "full credit" solution look like in this case?

 

[kuruman]

And for that problem on a test, how would you expect and accept students to answer? In other words, how would a "full credit" solution look like in this case?

First I put down the step by step solution as I would write for a solutions manual. Then I would assign points for items that I would expect to be present. The exam would be accompanied with a formula sheet, so I did not give any points for copying formulas from the sheet onto the exam. In this case, putting down $B=\frac{\mu_0}{2\pi r}$ gets no points as would $B=\frac{\mu_0}{2\pi r^2}.$ I award points for what is there and correct. I do not subtract points for incorrect nonsense.

Solution (What I expect to see and how I would score it)

Strategy and justification
Let $\varphi$ be the unknown angle. The point of interest must be in the region $0 < \varphi<\alpha$ because that is where the field contributions are in opposite directions. For the field to be zero the contributions from each wire must have equal magnitudes and opposite directions. (1 point)

Diagram
Diagram showing the distances from the point of interest to each wire and angle $\varphi$ and identifying all symbols used in the solution. (2 points)

Implementation of strategy
$$\dfrac{\mu_0i_1}{2\pi r_1}=\dfrac{\mu_0i_2}{2\pi r_2}\tag{1 point}$$ $$r_1=R\sin\varphi\tag{1 point}$$ $$r_2=R\sin(\alpha-\varphi)\tag{2 points}$$ $$\sin(\alpha-\varphi)=\sin\alpha \cos\varphi-\cos\alpha \sin\varphi \tag{1 point}$$ $$\mathrm{Consistent~algebra}\tag {1 point}$$

Answer $$\varphi = \arctan\left[\frac{i_2\sin\alpha}{i_1+i_2\cos\alpha}\right]\tag{1 point}$$
Total: 10 points.

Notes

• The trig identity is awarded 1 point because it is not on the accompanying formula sheet. Students who studied the booklet would know that they should memorize it.
• The two points for $r_2=R\sin(\alpha-\varphi)$ are further split (1 point) for using the sine function and (1 point) for using the correct difference between angles.
• Consistent algebra means that if the student made an early mistake but the algebra is consistent with the mistake, the point is awarded. For example, if the student used cosines instead of sines for the expressions for $r_1$ and $r_2$, the point will be awarded as will be the point for the final answer if it is consistent with the mistake.

 

[malawi_glenn]

If this was a problem on one of my tests (remember, I work in Swedish high school) this would be an A-level problem with 3 points awarderd. Basically 1 point for that picture you draw with motivation, 1 point for the $r_2 = R\sin(\alpha - \varphi)$ and 1 point for correct answer.

For instance
On a place where the geomagnetic flux density is 53 μT and has angle of inclanation 72° the following experiment is conducted. Two straight wires are placed vertically against the ground. In these, an equally large 2,1 A current flows in directions as indicated in the figure. In a point P an horisontal compass-needle is placed. The figure depicts the experiment as viewed from above. At what angle and in what direction will the compass-needle point?

Answer: 37° as measured from the north to the western direction.
1 C-level point: determines the horisontal component of the geomagnetic flux density.
1 A-level point: correct setup for determining how the magnetic field from one of the two wiers will interact with the compass-needle in point P for instance by splittning it into one North-South component and one West-East component.
1 A-level point: correct determination of the total magnetic flux density at point P due to the two wires.
1 A-level point: correct answer with a clear written and structured solution.

 

[kuruman]

If this was a problem on one of my tests (remember, I work in Swedish high school) this would be an A-level problem with 3 points awarderd. Basically 1 point for that picture you draw with motivation, 1 point for the r2=Rsin⁡(α−φ) and 1 point for correct answer.

OK, let me ask this. Of these 3 points that this problem is worth in your system, how many will you give to a student who instead of sines uses cosines for $r_1$ and $r_2$ and comes up with the consistent answer $\varphi=\arctan\left[\frac{i_2-i_1\cos\alpha}{i_1\sin\alpha}\right]$?

In my scheme this student gets 80% of the total which seems about right because the answer shows good understanding of the physics and a lapse of judgment in the trigonometry. In your scheme, this student will get 1 point for the picture with justification, 0 points for $r_2=R\cos(a-\varphi)$ and 0 points for the final answer which amounts to 33.3% of the total. In my opinion, a score of 33.3% for this problem does not accurately reflect how well the student can deal with this question.

Part of the problem with your scheme is that the third point is awarded for the correct answer, not for the consistent answer. Having lost a point for the wrong trig function, the student is automatically doomed to lose the third point since the final answer will certainly be incorrect. This problem is exacerbated when numerical answers are required in which case trying to trace consistency is a Sisyphean task.

 

[malawi_glenn]

how many will you give to a student who instead of sines uses cosines for r1 and r2 and comes up with the consistent answer φ=arctan⁡[i2−i1cos⁡αi1sin⁡α]?

If that is the only mistake, and everything else is perfect - 2 points.
There is almost always a leeway for small mistakes made early on, even in the score card for the course exams (which are not made my my), but not on all problems.

But yeah, life is hard in Sweden for high school physics students. Physics 2 is the most failed course on the natural science program. The students I fail are failing not because of lack of math skills, but lack in knowledge of physical concepts.

A course criteria for highest grade (A) is that the student is able to solve complex problems with a very good result - thus a high percentage of the points given for a problem is for a correct solution.

 

[vcsharp2003]

Continue reading...

How can a student feel thirsty while being taught Physics? I mean how can a student start feeling interested in a Physics course.

 

[kuruman]

How can a student feel thirsty while being taught Physics? I mean how can a student start feeling interested in a Physics course.

If a student is not interested in learning Physics, or anything else as a matter of fact, a student will not learn. Motivation to learn has to come from within. That's the point of the article.

 

[symbolipoint]

How can a student feel thirsty while being taught Physics? I mean how can a student start feeling interested in a Physics course.

The analogy would say, if student is thirsty but feels no/not enough thirst, student will die of dehydration.
More practically, some courses of Physics are either necessary for some degree objective or they are not. If they are necessary, then interested or not the student must study them. If the lack of interest in such courses is strong enough that student has insufficient motivation, then he needs to choose a different major field.

 

[brotherbobby]

Excellent article, and I haven't completed it yet. But I have a small correction to make.

“Even if you tell them, there will always be some who won’t believe you.”

I think it's worse than that. Many students simply don't care. I suspect most of them believe a teacher. But it's motivation they lack.

 

[kuruman]

Excellent article, and I haven't completed it yet. But I have a small correction to make.

“Even if you tell them, there will always be some who won’t believe you.”

I think it's worse than that. Many students simply don't care. I suspect most of them believe a teacher. But it's motivation they lack.

Yes, I agree that there are many students who simply don't care about their classes and enroll in order to leave their homes and be part of the overrated "university experience", a synonym for "socializing", also known as "partying." They are not on my radar screen.

The statement that you quoted above is followed by "Flashback to the student who rejected my holiday gift." It refers to the student who cared so much about doing well that she chose not to believe me when I said "Choose any two of the three questions."

 

[DeBangis21]

That's a nice article.

 

[Muu9]

I'd like to see this sheet, personally

 

[kuruman]

I'd like to see this sheet, personally

Which sheet?

 

[Muu9]

Which sheet?

I meant the booklet with the numerical problems

 

[kuruman]

Here are some more problems. It's not everything, but it's all I have.