Solving Physics Problems: Manipulate Equations or Plug in Values?

[Jimmy Snyder]

Homework Statement

In solving an elementary physics problem, do you advise students to manipulate the formula first to isolate the unknown, then plug in the values, or plug in the values first, then manipulate the equation to isolate the unknown?

Homework Equations

(1) F = ma
(2) a = F / m

The Attempt at a Solution

I am a tutor at the local community college and I find that the students have two issues. 1. They don't know which formula to use. 2. They have trouble manipulating the equations algebraicly. For obvious reasons, they are not looking to become physicists, they just want to survive the course. I always manipulate formulae algebraically before plugging in values. I believe I can give objective reasons why this is the better way to go if you are handy at these things. However, one of my students told me that the professor told them to do the plugin first, then manipulate.

Suppose that of the two formulae above, only formula (1), F = ma, was presented in the book. Suppose I gave you F and m. Would you plug them into formula (1) and manipulate, or would you manipulate formula (1) into formula (2) and plug in?

I believe there are obvious objective reasons for doing it the second way, but I have a lot of experience at solving such problems and can do them almost effortlessly. Is there someone here with pedagological experience that can tell me the advantages of doing it the professor's way. Is it easier for the less experienced, less talented students to do it that way?

 

[rock.freak667]

Not sure if this belongs in this forum per se, but I will give you my take on it.

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Suppose that of the two formulae above, only formula (1), F = ma, was presented in the book. Suppose I gave you F and m. Would you plug them into formula (1) and manipulate, or would you manipulate formula (1) into formula (2) and plug in?

I believe there are obvious objective reasons for doing it the second way, but I have a lot of experience at solving such problems and can do them almost effortlessly. Is there someone here with pedagological experience that can tell me the advantages of doing it the professor's way. Is it easier for the less experienced, less talented students to do it that way?

Usually I would manipulate first and then plug in the numbers mostly because of the accuracy required and it takes less time on the calculator.

On the other hand, if you plug in and then manipulate it becomes easier to calculate when you have a long formula. (So you're less likely to make an error in calculation).

If they feel comfortable with the plug in and manipulate way and you want the answers to say 2 decimal places, make them write down their answers to two decimal places but they the answer to 3 dp in their calculations. [I am assuming they can easily use their calculators to do simple things like 3(0.25)³+0.13²+9 or similar).

 

[Jimmy Snyder]

Not sure if this belongs in this forum per se, but I will give you my take on it.



Usually I would manipulate first and then plug in the numbers mostly because of the accuracy required and it takes less time on the calculator.

On the other hand, if you plug in and then manipulate it becomes easier to calculate when you have a long formula. (So you're less likely to make an error in calculation).

If they feel comfortable with the plug in and manipulate way and you want the answers to say 2 decimal places, make them write down their answers to two decimal places but they the answer to 3 dp in their calculations. [I am assuming they can easily use their calculators to do simple things like 3(0.25)³+0.13²+9 or similar).

Thanks for your insight rock.freak667. You raise a good point about the significant digits. You addressed my question as I meant it.

But, unfortunately, not as I worded it. To avoid misunderstanding, let me clarify. I don't much care how the homework helpers solve these problems. I'm pretty sure you all manipulate first and plug in afterwards. My question was meant to be: What is the best way to teach the inexperienced.

 

[rock.freak667]

I'd teach the manipulate and then plug in until they get some more experience with it, then they can easily switch to plug and then manipulate when they see fit.

 

[Borek]

IMHO manipulating first is a better approach - that forces them to get some algebra skills. Way too often I see students unable to solve for m, and no matter what they think - if they want to pursue their education (not necessarily in physics or math, say in medicine or biology) sooner or later it will hit back.

 

[eczeno]

i agree with borek, getting them to do the algebra sort of kills two birds with one stone. and it is usually the more efficient way to go (but not always).

cheers

 

[ideasrule]

Not only is it more efficient to isolate the unknown first, it helps you gain insight into the question. It's very revealing to see what variables the answer depends on, what it doesn't depend on, whether it increases or decreases when a certain variable changes, what its behavior is at boundary conditions, etc. Certainly helps catch a lot of errors.