Dangers in Teaching Key Words

Defining Problem Solving

Educators say we need our students to be better problem solvers, so we need to determine what problem solving truly entails.   According to BusinessDictionary.com it is:

"The process of working through details of a problem to reach a solution. Problem solving may include mathematical or systematic operations and can be a gauge of an individual'scritical thinking skills."

As I analyze this definition it is a much higher level of thinking that must go beyond teaching students to look for key words or determine the problem solving method (make a list, work backwards, draw a picture, etc.) approach that we have been using in schools since I was a student.  Problem solving  is about getting kids to think about the problem and what the problem is asking them to solve.  So how do we do this in schools?

 How To Encourage True Problem Solving

We need to give students a variety of real-world problems to solve.  As early as kindergarten students need to be exposed to math in their everyday life, we have 20 students in our class and 12 want chocolate milk, how many will drink white milk? Let students determine how this problem could be solved.  Instead we often try to proceduralize the problem solving, look for a keywords like "how many", etc.   Although many of us encountered problem solving in this manner, the philosophy is that we all will think the same way about how to solve the problem, and that we don't even need to really read and/or understand the problem, just look for keywords. 

Not only does teaching key words to all students make them rely on something that doesn't include critical thinking skills, it also does not always give the correct answer.  For example:

Ashton found the sum of 5 test scores to be 435.  What was his average score?

Molly had 58 cookies, if she shares 7 cookies with 8 friends, how many will she have left for herself?

If students only are coached to look for the key word(s) in the problem, students will get a wrong answer.

For more information on problems that by looking at keywords would give a wrong answer, watch Beware of Keywords a Math Snack  podcast designed for students.  Again we need to think about the goal of problem solving.  Is it supporting students with a process of working through all the details and encouraging the use of their critical thinking skills?  If not, we need to go back and think about our purpose.

The Fallacy in Math Education

Using key words as a strategy for teaching problem solving to all students is a fallacy we have been taught in U.S. education.  As more and more research in mathematics is being conducted and we are learning more and more about problem solving our beliefs about problem solving need to be expanded and challenged.  Problem solving can look so many different ways and problems can be solved in so many different ways.  I just read an article entitled Einstein's Secret to Amazing Problem Solving (and 10 Specific Ways You Can Use It)   I love his quote: 

Einstein is quoted as having said that if he had one hour to save the world he would spend fifty-five minutes defining the problem and only five minutes finding the solution.

In this article they look at 10 steps to help process problem solving.  It is probably one of the best articles I've read on this process, and looking for key words in not once mentioned. 

Finally, a good problem solver has and uses a variety of problem solving skills.  They understand the problem, make-sense of the problem, and have a variety of tools or techniques to solve the problem.  Cogntively Guided Instruction is a wonderful strategy for supporting true problem solving in our classrooms.  For more information contact me at michelleflaming143@gmail.com