LearnBop Community Blog

Two Types of Struggle in Problem Solving

Posted by Cindy Bryant

Mar 22, 2016 6:00:00 AM

 
Have you ever encountered a problem you couldn’t solve?
 
Needless to say it often leaves me feeling frustrated and confused, and plays havoc with my self-esteem. None of us like to struggle or to see anyone else struggle, least of all our students.
 
But mathematics educators and researchers both agree that in order for students to solve problems and learn and make sense of math they must experience some struggle.
 

However, there are differences in the struggles that both we and our students experience when solving a problem.  Hiebert and Grouws (2007), use the term productive struggle to refer to the “effort to make sense of mathematics, to figure something out that is not immediately apparent.” 

A different kind of struggle that Jackson and Lambert (2010) refer to is destructive struggle. As you would expect, the two are quite different as can be seen in the comparison below. Destructive struggle is harmful and can be debilitating, whereas productive struggle is considered fruitful, useful and helpful in solving a problem.

 

Two_Types_of_Struggle_2.jpg

 

Adapted from Jackson and Lambert

Struggle can be manifested in different ways and may or may not be visible (Warshauer, 2007). I’ve found that you will not observe struggle if the problem is easy enough that the student can do it without difficulty. And I’ve also found, that students simply do not choose to tackle a task that is too difficult so it goes without saying that there’s no struggle in this instance as well.

Teachers like you and me continue to struggle with the when and the how of the help we offer students to support them in productive struggle.  There’s a fine line between supporting productive struggle and doing the problem with or for the student.  If we don’t let students grapple they certainly won’t experience productive struggle. But if we don’t provide them the right assistance at the right time then their experience can become that of destructive struggle. 

 

 

So what do you do to support productive struggle when you see your students struggling with getting started, carrying out a process, giving a mathematical explanation, or expressing misconceptions and errors?  Do you offer too much assistance or do you simply provide them information and/or steps they must follow, give direct guidance, offer probing guidance, or provide a visual clue that will assist them in their work?

Please feel free to share your questions, comments, and suggestions about productive struggle below.  Thanks!


About the Author
 
Cindy_Bryant.pngCindy Bryant is LearnBop's Director of Learning.
 
Cindy is the former head of K-12 mathematics for the state of Missouri, a former member of the NCTM Board of Directors, and a former Presidential Awardee.
 
 
 

Topics: Teachers Using LearnBop, Differentiating Instruction, Implementing the Common Core, Resources, Teaching & Learning, Algebra & Algebra Readiness

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