Creating a Problem Solving Environment

Recently I was asked about an article that I had shared awhile back so I am sharing it again.   The focus is around the things we can do in our classrooms to help our students be more successful in regards to mathematics.

BIG IDEA

The ultimate goal of mathematics is to produce students who can think mathematically and solve
problems.

If that is truly the ultimate goal, we have to teach as though we believe it.  We have to maximize every
opportunity for students to think deeply, to create their own solutions, to build/write/draw/talk about their thinking!  Students learn important mathematical concepts THROUGH problem solving. This is a mind shift away from the idea that we teach math concepts procedurally first and only then can they do problem solving.

RESEARCH 

Quotes from Principles to Action: Ensuring Mathematical Success for All, NCTM (2014)

(Boaler and Staples 2008; Hiebert and Wearne 1993; Stein and Lane 1996)

(Stein, Gorver, and Henningsen 1996; Stigler and Hiebert 2004)

(Michaels, O’Connar, and Resnick 2008)

APPLICATION   

Here are some different ways we can change our practices to be more effective.

“KEY WORDS”  

We think we are being helpful, but are we handicapping them for later?

We used to help students identify words like “altogether” and “in all” in story problems and we said these meant to do a particular operation. I clearly remember posting lists of these words under various operations.  My intentions were good and I had seen it done by others.  Now, I know there is strong evidence that this practice may actually hinder students’ comprehension of the story!  Why?

1. Now we know that when the emphasis is on the “key words” themselves, students tend to find the numbers and just do the operation without thinking about the overall story in the problem.  

2. These words can be present in a story problem but not necessarily indicate a particular operation. For example,consider what operation you would use to solve the following problems that contain the word “altogether”:

• Jack has 8 marbles. Jill has 4 marbles. How many marbles do they have altogether?

• Jack and Jill have marbles. Jack has 6 marbles. If they have 14 marbles altogether, how many marbles does Jill have?

• Jack has 6 sets of marbles. There are 7 marbles in a set. How many marbles does Jack have altogether?
• Jill wants to put her marbles into containers. Six marbles can fit into a container.  If Jill has 52 marbles​ altogether, how many sets can she make?

3. Standardized tests often make a point to avoid these key phrases. When students become dependent on finding the key words and doing that operation, they no longer have a strategy for solving problems when the words aren’t there.

Even at the earliest grades, our focus needs to be on comprehension of the story and true problem solving.  It is with good intention that we offer up tricks or shortcuts, but in the long run, these tend to expire and negatively impact student learning.
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At every grade level we want to be sure that we are presenting students with practices that create a problem solving environment because that is where true learning and enduring understandings are taking place.

This post brought to you by Carol Lucido, the K-8 District Math Coordinator