At the beginning of this year, several of the teachers at one of my buildings expressed frustration with the fact that their students did not seem to be getting any better at problem solving regardless of all the work they had been doing. This was not a problem specific to one grade level, but across the board K - 6. Soon after those conversations, I started noticing that something similar was happening at the other building I work at.
Both buildings were using Larry Bell's wonderful UNRAAVEL system.
Underline the question
Now predict
Read the word problem (I think this should be re-read)
Are the important words circled?
Apply the steps you choose to solve the problem
Verify
Eliminate wrong answers (for multiple choice).
Let the answer stay or rework the problem.
You can visit this PowerShow http://goo.gl/wTHFh7 to find out more about this tool. You can visit Larry Bell's sight here https://goo.gl/roV3Ah to purchase the poster.
Anyway, once I really started working in some of the classrooms and looking to see what the students were doing with problem solving, I noticed was that while they were doing the UNRAAVEL steps, the students were not really doing the thinking that each step required in order to help them solve the problem correctly. That is when I decided to take matters into my own hands and help the students find steps based on Larry Bell's system that would help them to do the thinking. The other goal I had was to make sure that the Practice Standards under Common Core were being utilized by students.
After much playing around and with student's help, I finally arrived at these steps!
1. Think about what is the problem asking for! In other words, what kind of label will the answer need? What kind of number does the answer require (whole number, fraction, decimal)? Do they know if the answer is going to be larger than or smaller than a certain number?
I find that most of the time students will read the problem, quickly make some assumptions that may or may not be correct, and use the numbers they see to plug them into whatever formula or equation they "think" it calls for without thinking what the end result should be. This step is meant to help students think about what the problem is asking them and slow them down.
2. Now reread the problem and circle any important information and cross out any information that is not needed.
This step needs to happen after they do step one so that they know where they are going and are able to more easily determine what matters. With word problems being more complex under Common Core, this step can keep students focused!
3. In this step the students determine how many steps they will need to do to solve the problem and what is required in each step.
Often times the students will try to acquire the solution in one step. Common Core standards require that students identify the equation that matches the action in the problem - not just a pathway to solve it. This step is meant to help lead them to this in the next step by acknowledging the action(s) taking place in the problem.
4. This step is where the actual calculating takes place. Student sets up the equation for each step(s) and solves.
5. The final step is to check their work, but not in the traditional way.
In the traditional way, the students would just look at their answer or redo the math they had already done and call it good. But under Common Core Practice Standards students must determine the reasonableness of their answer so this goes beyond checking to see if their math is correct. It requires students to think about if the answer they are getting "makes sense"! In this step the student looks back at the criteria for the answer they established on step 1 and determines if their answer makes sense or not. This tie between step 1 and 5 gives greater impact to that first step beyond just understanding the problem.
This picture shows a poster that I have created to help the students understand and remember what the steps are.
This picture shows a poster that I have created to help the students understand and remember what the steps are.
The examples are geared towards 2nd grade and up. But if you let me know in the comment box that you would like to see examples of problems for kindergarten and first grade, I'll get those posted. This poster is available in color and black and white from my Teachers Pay Teachers store. https://goo.gl/MFWqdi
Once the students I was working with at different grade levels got comfortable with this process, the teachers and I started to see a big difference in how well students were able to attack and solve word problems. In fact, after finishing a coaching cycle in a 6th grade classroom the teacher did not continue using these steps and she saw a decline in how well the students did when doing problem solving. This prompted her to reestablish these steps in her classroom to which the students reacted by doing just as well as they had before leaving us both convinced that these problem solving steps DO work!
Another item available at my store is this problem solving organizer that I use with students in grades 2 and up. In kindergarten and all the steps except 4 are done as a group. The organizer facilitates students work by helping organize their thinking and making sure they do the 5 steps of the process. Therefore, the steps become more internalized and a habit. With younger students, the work space is often too small and so they will use the back side of their paper as well.
This is available by itself https://goo.gl/LI6MbR or as part of a problem solving bundle at my Teacher Pay Teacher store.
As I continue on the journey of helping students be better problem solvers I look to seeing how these steps continue to impact student problem solving skills. I hope that if you choose to try them, you will leave a comment to let me know how it goes!
