Tuesday, February 24, 2009

Word Problems

Today I take issue with word problems. What idiot decided that some math problems should be classified as word problems, and given special treatment? Somehow the notion was created in elementary schools, that word problems are not pure math and must be translated into pure math before then can be solved. Many years later some of these students enter physics and engineering and follow the same habits they always have. They see a problem, and immediately attempt to translate it into the right equations and then solve those equations.

These students need to see that, instead, they should be solving the original problem as stated. I’m approaching this both as a grader and someone who knows that sometimes, in the real world, you want to solve a problem, write it up, and then keep the solution around as reference for future engineers, or just to remind yourself later of why (or how) a certain design decision was made. Being able to follow the thought process and look for logical missteps is key to this. Instead of this word problem translation step, problem solving procedure should be closer to this:

Given a problem, pull out what information is available from the words and figures. Indicate what is known, and what is being sought. Guide the reader through the process of your solution. What are you doing? What are you assuming? Then state an equation that represents what you are doing. Tell your reader how you are manipulating the equation (if necessary). Do the manipulation, and repeat these last few steps each time a new step occurs. Reach a solution and indicate it. If this problem is for any real-world application, at this point another bit is needed to explain what the solution means.

As with nearly any form of successful communication, the work must tell a story. Most of that write up is in words. I don’t expect the story to make sense without the equations, but rarely do the equations by themselves provide all the information needed to understand it.

I will admit that I, as an undergrad, did not do this. I reached for the equations I thought solved the problem, and threw them down. Massaged them slightly, converted the variables to numbers and found an answer. A lot of my understanding of how a problem should be worked and presented, didn’t come until a) I started working in the real world and b) I started having to grade 40+ homeworks on a regular basis. Not everyone gets the chance to do this, and see the shortcomings of the translate the word problem approach. I think a lot of fear and apprehension about physics and engineering assignments could be alleviated if word problems, or real problems, weren’t ever held out in such a special light, made to seem hard, different, or incomprehensible. They should be easier, because they have some physical meaning, something 2x + 6 = 10 will never directly have.

• Posted by jfs at 02:16:57 in Life As A TA
• 3 comments