One of the greatest gifts we can give our students is the opportunity to struggle and persevere and, in the end, feel the joy of success that comes from a job well done.

It used to be that struggling students were looked upon with pity because they found school to be challenging.  Each year that I taught, however, I found that it was my struggling students who ended up being the most successful in the long run.  These students did not shy away from challenge.  They dug in and could sit with a problem until they figured it out.  They were not afraid to ask for help and were able to listen thoughtfully to the help offered.  

Healthy Struggle

I think we should turn our perception of appropriate classroom tasks upside down.  Rather than creating tasks where every student will be successful within a class period, we should consider how we can create times where each student can engage in healthy struggle.  For an adult a satisfying work experience is one in which they have to struggle to figure something out.  They work on it, they talk to others, they read some about the topic, they work on it some more and eventually they come to a clearer understanding about the topic and often create a creative product to go with it.  We do our highly capable students a disservice when we deny them this struggle and feeling of success.  

So often gifted students are able to do their work quickly.  They see answers easily and think there is something wrong if they have to really try hard to figure something out.  They do not learn skills for what to do when they don’t know what to do. They don’t have the satisfaction of meeting a challenge and succeeding. When I taught gifted students I would often recommend to the students that they take music lessons.  No one sits down and plays an instrument well on their first try.  Learning to play an instrument takes practice and perseverance.  These are life skills all students need.  Struggling students develop these skills often because they need to figure out how to tackle problems and how to sit with problems when the answer does not come easily.  We need to create this experience for highly capable students as well. 

Practice and Perseverance

Interestingly the skills of practice and perseverance are also woven into the Standards of Mathematical Practice.  Students are required to “Use appropriate tools strategically. (MP5)” It is only through repeated practice with different physical tools and thinking tools that students come to realize which tool is the best for different types of problems.  Standard algorithm is not always the best approach.  Under Common Core, students are required to use strategies based in place value as well as standard algorithm.  They also need to be able to use one strategy to solve a problem and another strategy to check their results. They need to practice in order to be fluent with different strategies and be able to choose among them.

“Make sense of problems and persevere in solving them. (MP1)”  In order for students to work on this math practice, they need problems that are complex.  Low floor, high ceiling problems, such as problem solving, can fill this need.  These problems have multiple entry points so that students can look at them from different angles and chose the best approach. Many highly capable students look at complex problems and say they are impossible because these students do not yet know how to break the problem down, try different solutions, and stick with a problem even when the answer is not readily apparent.

When discussing problems, a learner needs to think deeply about the reasoning of others and work to make sense of it.  They are working to “Construct viable arguments and critique the reasoning of others. (MP 3)” As they process this reasoning they ask questions and decide to either accept or reject what the other person is offering.  By doing so, they become more confident in their own thinking about the problem.  They become stronger by incorporating new methods and often they are sparked to develop new solutions of their own through the conversation.  Writing about their thinking further solidifies the ideas in their mind.  

Incorporating complex problem solving into our classrooms gives students lots of experience with the Mathematical Practices but also follows one of the Mathematical Teaching Practices.  These practices, outlined in Principles to Actions from NCTM, outline a vision of excellent teaching in mathematics classrooms.  One of these practices is: “Implement tasks that promote reasoning and problem solving.”  This is one avenue for developing math students who understand mathematics as opposed to students who just memorize formulas. If we use problem solving in our classrooms, we can not only teach students to be strong mathematicians, but we can also teach them life skills that they can apply to any endeavor.