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A collection of helpful articles on teachers and teaching

Structured Solutions

Some call them problem solving boards, others problem solving mats.  Tomato, tomah-toe.  I call them structures for solutions.  Students tend to perform higher on assessments that measure computational skills than they do when the same math is hidden in a word problem.  What is missing?  A structure for finding the solution.

So how do we help our kids win the game of word problems?  We teach them the rules and the steps to take to win the game.

Search the web for problem solving mats or problem solving boards. They have the following in common:
•    Students identify a strategy;
•    Students identify the knowns;
•    Students identify unknowns;
•    Students create a non-linguistic representation of the problem (picture);
•    Students write out their solution;
•    Students come up with an answer and;
•    Students evaluate the reasonableness of their answer.

Problem solving is a state of mind.  The board or mat helps provide a visual structure that students can use until they have mastered the process of dissecting a problem.  

So how is this any different from providing students with a list of steps for solving the problem?  Why put this in the form of a mat?  It’s the power of the graphic organizer.

In Robert Marzano’s book Classroom Instruction that Works the use of non-linguistic representations is one of the top nine instructional strategies.  In the book, they explain that knowledge is stored in two forms: a linguistic form and an imagery form (though there are others).  We tend to use a great deal of linguistic (semantic, word – we talk or the students read) representations in teaching.  By using an imagery mode the brain is stimulated and activity increases by the addition of the visual representation.  More connections to the same information in the brain promote learning and retention.  

Who should use a problem solving mat?  I have used them with second graders, fifth graders, eighth graders, geometry students and teachers in workshops.  

It seems too that the structure of the graphic organizer helps students avoid little mistakes that might get lost when they try to rush through a problem.  As they map out the problem and its solution, students can catch their own mistakes.  Combine this with cooperative learning in which groups of students share and compare strategies and solutions for even more success.  We know that people learn most by teaching.  Working in small groups, students can teach each other different ways to solve the same problem.  The benefits are many.  

Last, but not at all least, you can easily create your own problem solving mats.  No need to purchase any product.  You can examine one we have used by clicking here.

Happy problem solving.


Anne Douglas is Dean of Instruction for Sam Houston Math, Science and Technology Center, a comprehensive high school in Houston, TX.

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