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  Weekly Feature: (September 8, 2001)


Answering Problems in Math
Carey's Weekly Feature

Many a mark has been lost on math tests when the wrong answer was written. Deductions, not because students misunderstood the given information, or came up with procedures that do not work, or did the math incorrectly, but because in the final stages of the solution students did not really answer the question. 

For example, would a student writing "x = 240" acceptably answer the following question?

"A train leaves a station and travels at 40 kilometres per hour. Two hours later a second train leaves the station and travels at the rate 60 kilometres per hour. Where will the second train overtake the first?"

A problem with the written answer is x, what does it represent? Even if x was defined as the distance from the station where the second train overtakes the first, should you answer a "where" question with "x equals ". Then is it 240 kilometres, or could it be metres or miles or even minutes? 

Clearly 240 metres is nowhere close to the correct answer and it could not possibly be 240 minutes, although that is the amount of time it would take the second train to overtake the first. 

240 miles is close to the correct answer, but a good answer should not be in any way ambiguous. 240 would be a barely adequate answer only if the problem asked, "how many kilometres from the station would the second train overtake the first?"

Even though the student must have done a lot of good things, "x = 240" does not answer the question "where will the second train overtake the first?" 

Every answer should be given a second look. Is it reasonable? Is it sufficient? Is there only one way to interpret what is written? Taking the extra second to look at your final answer can never be considered a waste of time.

Links discussing problem solving. 

The cure for the "I can't do word problems" syndrome
Mathematical Problem Solving
Learning to Think Mathematically

Links that could help your problem solving skills.

Request_ Response_ Result
Problem Solving Strategies 
Dr. Math: Word Problems


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