Sunday, December 15, 2013

"I Don't Know Where/How To Start!"

I get that type of plea often on physics forums and when students used to come and see me for help with homework-type problems. Often, the person asking the question simply typed in the problem, and showed nothing else other than the claim that he/she just simply didn't know how to tackle the problem. This was despite my explicit requirement that required students to show their attempts.

Not only that, this policy of forcing the person asking the question to actually show attempts, or at least, what they know, has also been criticized. Somehow, this requirement was deemed to be unusually harsh by some people

There are three separate issues here that will require a bit of explanation on why this policy is in place. And this policy is especially applicable homework problem in physics/engineering/chemistry/biology, etc.

1. In order to assist, help, and teach you how to solve a problem, we must know (i) what you know and (ii) what you don't know. We need to know what you have already understood, and then build from that. It is useless to simply tell you something that has no connection to what you've already understood, because if we do that, you will end up MEMORIZING it without understanding it, which is a recipe for disaster and failure in physics. When we can connect it to something you already know, then you can see a connection and a logical progression of your knowledge. The information isn't just hanging there in mid air. It has some logical connection with what you've learned and already know.

This is why we always need to know what you have attempted. It is not because we want to force you to do it, but a good teacher will be able to figure out what you already know and where you got stuck! We can point it out to you where you made the wrong turn. You, in turn, should also find this highly useful, because you learn more from your errors than from what you did right. You can do your own self-diagnosis on why you did something wrong, and why such-and-such is correct. This is the essence of learning!

If you simply say "I don't know where to start!", it tells us absolutely nothing. You simply must know SOMETHING in order to be given homework problems. Did you sleep through the class? Did you not even read the chapter in the book? You must know something! Can you even make a sketch of the problem? If it is a simple kinematic problem, can't you even show us a free-body diagram? At the very least, we can tell if you know what the relevant forces are! You must know something!

2. There is a misunderstanding of what a "starting" point is. When we ask you to show what you have attempted, we don't just mean "equations" or "calculations". In fact, in my personal approach, when you tell me that you don't know where to start, I will quiz you if you even know the relevant physics concepts that are applicable in the problem. Let me give you an example.

Say that I give you this problem: After a completely inelastic collision between two objects of equal mass, each having initial speed v, the two move off together with speed v/3.  What was the angle between their initial directions?

If you come to me and tell me you don't know where or how to start, I will ask you what is the relevant concept here.

If you tell me that it is the conservation of momentum, then I will at least know that you are aware of the physics being tested here. That is a big plus! And that, by itself, IS THE STARTING POINT! If I'm grading this problem, if the student simply did nothing else but indicated that this a conservation of momentum problem, he/she would have already received partial credit from me.

So now that I've already determined that the student is aware of the relevant concept, I want to see if the student can actually APPLY the concept. I will then ask "So if this is the conservation of momentum problem, what can you tell me about the momentum before and after the collision?"

If the student says that the momentum before the collision from both objects must be the same as the momentum of the two objects sticking together after the collision, then there is another indication that the student simply just didn't memorize the concept, but has some understanding of how that concept works.

Next, I will ask the student to sketch out the problem. Often, for this question, this is where the student gets stuck. The question doesn't say how they collided. Did they hit each other head on? At an angle? Via simple physics, we can rule out the former, because head on collision of identical objects with equal and opposite velocity will not result in a net velocity of a final object AFTER the collision. Furthermore, making them collide at an angle is a more "general" problem that we can solve. So if this is where the student got stuck, then we have found the source of the problem. As an instructor, I can make a mental note to make sure I emphasize on this aspect of problem solving. As a student, you learn where you got stuck, and how to get unstuck.

Note that the ability to make this sketch is crucial! By making use of the symmetry of the problem, the student will simplify this problem because the final velocity will only occur along the x-direction. This means that the momentum before and after along the y-direction will be zero! This ability requires insight, understanding, and repeated practice.

Next, I will ask the student to proceed to actually write down the mathematical form of the conservation of momentum. This will tell me if the student has the ability to translate "word concepts" into "mathematical equation", which is necessary to solve this problem. If the student gets stuck here, then I know where the problem is. This is also another common issue with many students, trying to translate conceptual ideas into mathematics. If the student realizes that this is where he/she often gets stuck, he/she can make a conscious effort to pay closer attention to when the instructor makes such a connection. I, on the other hand, as the instructor, will try to make a clearer emphasis during lecture, or when helping a student, that this is where we formulate our understanding into mathematics.

For this problem, we can write the momentum before and the momentum after, based on the sketch that we had drawn:

p1_x + p2_x = pf_x = pf
p1_y + p2_y = 0.

Notice the simple form for the y-component of the momentum as mentioned before.

From now on, it is just a matter of solving the math by substituting what we know and given from the problem. There is no more physics involved here.

2mv*cosθ = 2mv/3
cosθ = 1/3
θ = 70.5 deg.

So the angle between their initial directions is

2θ = 141 deg.

This demonstration and example is an illustration where there is a step-by-step progression in solving the problem. Every step is distinct, and as someone who wants to help the student trying to solve this problem, it must be clear if the student either understands, or is able to make each of the step. When he/she can't, then we have diagnosed the problem, and that is extremely important. One has to figure out where the source of the problem is, where the student got stuck. This is because it is a symptom of a bigger problem where there is a lack of understanding or knowledge in that particular area. Knowing where the problem is is beneficial not just to the instructor, but also to the student! He/she at least will know where to pay closer attention to and try to overcome that hurdle.

I've lost count how many times I hear students complaining that they find physics very difficult, and they can't solve physics problems. Upon undergoing a similar diagnosis such as this, more often than not, the most common problem that the students have was their lack of mathematical skills! In other words, I could have set up the problem for them and ask them to write down the vector components of the momenta, and they can't because of their lack of ability to do algebra and trigonometry. So here, we have also diagnosed the problem, and hopefully, the students realize that they have issues, not with physics, but rather with mathematics. Again, knowing this, the student has the ability to take the necessary actions to correct this.

The important thing here is that when a student is stuck, one has to figure out WHERE the sticking point is. Simply saying that "I can't do a problem" or "I don't know how to start" provides ZERO information to diagnose this.

3. If you look at the above example that I've given, you'll notice that the physics part actually comes in at the beginning. Being aware that (i) this is a conservation of momentum issue and (ii) being able to write down the mathematical form of the conservation of momentum that is relevant to this problem ARE THE PHYSICS PART! Once those are known and written down, the rest is mathematics. To put it bluntly, any monkey that knows math can, from that point on, solve this problem without knowing any physics!

This is important to realize for those who complain that we must help the student who don't know where to start. By telling them how to start, we are doing the physics for them! This is the most important part of the problem and it is why they are in the class studying it! As an instructor, I am keenly more interested in seeing how the student start and approach the problem. I have very little interest in seeing if they can deal with grinding out the math and spitting out the final answer. The physics here occurs at the very beginning!

So giving a student the starting point is not helping. It is depriving him/her of using the physics to set up the problem. The start IS the physics. You might as well tell the readers who did it at the beginning of a mystery novel. If I tell you how to start, I've practically done the physics part of the problem for you. I then have no clue if you didn't know what physics concepts were applicable, or if you've never heard of the concept, or if you didn't understand how to use it, etc. This deprive both of us in diagnosing the source of your problems, and because of that, there's a good chance that your lack of understanding will continue to perpetuate beyond this problem.

It is why I have such a policy.


Note: The example I took here came from a terrific set of example problems from Prof. Marianne Breinig at U. of Tennessee.

Her examples of worked problems in that link are exactly how I would teach and approach problem solving in physics, where there is a systematic identification of each step. It clearly shows where the "starting point" or how to start tackling a problem is the identification of the relevant physics concepts involved in that problem. This is what I want to see from a student.

1 comment:

SFG said...

I tell students that telling me "I don't know how to start!" is like telling a mechanic "My car doesn't work!"
Okay... Does the starter turn over? Is it out of gas? Have you lost the keys? If I don't know what you know or what you've tried, I really don't know how I should be helping you.