Math Problem-Solving: Don't Protect Students from Frustration

As American high school and college graduates enter the workforce, they are quickly introduced to real world problem-solving. Many of these young adults are ill-equipped to handle the challenge. They have not been trained to think. Classroom teachers are aware that students learn through different modalities-visual, auditory, tactile-but are they truly addressing this fact? When an instructor is facing 35 students per math class, the logistics of individualization become overwhelming. However, any teacher can stimulate higher level critical thinking and encourage strategy choice in problem solving. These kids don't know what they're capable of until they're actually challenged. It doesn't matter where they land on the intelligence spectrum; all students need to practice 'thinking'. Let them struggle. Let them fail. Many profound discoveries have resulted after much initial failure. Place the students into groups. Provide a nurturing environment. Allow them to choose their own strategy styles. I use this problem-solving approach in my middle school math classes and love the end results.. students with a sense of self-satisfaction due to their accomplishments.

Research
Students in low-performing schools in Newark, New Jersey, increased their math scores by 34% over a six year period. Their teachers let them struggle. Researchers at Rutgers University had found that allowing a struggle was beneficial, so these New Jersey teachers followed their model. Their students, although reporting frustration, said they felt more satisfaction and pride in the end when being left to solve problems in their own ways and then explain their results to others.

Problem-Solving Process
The basics of problem solving never really change. Mathematician and researcher G. Polya laid it out in his book, "How to Solve It" in 1945:

1. Understand the problem.
2. Devise a plan.
3. Carry out the plan.
4. Look back.

The differences are in the ways students choose to execute this process. Some are comfortable with solving equations. Others prefer, for example, drawing pictures or making models. Teachers need to let students know that no one method is the 'right way'.

What Works for Me
I present my students with a problem to solve. First I require that they work individually on it. I want them to have time to use the methods that work best for them. Next, the students get into cooperative groups where they share their explanations on how to best solve the problem. Group members offer constructive criticism, pointing out the positives and negatives of the approach. A lot of 'teaching' occurs within the student groups. The group eventually comes to a consensus about which solution they will present to the class.

At first, the biggest stumbling block in this process was the students' reluctance to be independent thinkers. I was repeatedly asked-before they'd even had a chance to do much thinking-"Is this answer right?" My retort was always, "I don't know, is it? You'll have to prove that to me." That was a source of irritation for them at first. They were used to solving an equation and being quickly told that the answer was either right or wrong. Many of them were used to having no accountability at all. It took some time to break them away from this line of thinking. We celebrate failures, focusing instead on the critical thought process that they have entailed. My students are never more engaged than they are during problem-solving times.

Additional articles by this author:
Teaching Metric Measures to Elementary and Middle School Students
Have Fun Teaching Perfect Squares and Square Roots
An Interactive Approach to Adding Positive and Negative Numbers