Productive Struggle

 

I think productive struggle is one of the hardest things to let students experience.  Most of the elementary teachers I know are not really into math so they instruct, following the method given by the textbook.  I have observed that many students would rather just have the teacher help them through the problem, rather than trying to work it out for themselves and many of us teachers were taught to be "helpful". 

Productive struggle is a necessary part of learning mathematics because it allows them to work through any problem, making it less likely they give up.  Productive struggle helps students look at making new connections while trying to find different ways of solving the problem.  It allows them to try new types of problems they've never seen before.

In real life, most mathematical problems do not have neat answers nor can they easily be solved.  These problems are messy.  They have answers with decimals or fractions.  The problems often have fractions in them.  Students have to persevere in the face of these types of problem.

It cannot be assumed that all students who arrive in high school are able to work their way productively through problems. We have to help our students learn to productively struggle through problems.  There are things teachers can do to help them.  First of all, call on students who may not have the right answer.  Many times, those who get the correct answer are rewarded, rather than celebrating the attempt.  If a student gives the wrong answer, ask them questions designed to help them question their thinking.  

Instead of praising students for being smart, praise them for sticking with it and trying to solve the problem.  When you praise the effort, students are more likely to face challenging  problems. To reinforce this, display problems that show creative solutions rather than the papers with the highest scores because it showcases productive struggle. 

Give problems that cannot be solved by following memorized processes. Using problems such as these require them to make sense of the problem itself, before deciding how to solve it and what math is actually needed.  It is important to provide students with feed back that is informative.  This means providing context to help them head towards the answer. 

It is important to refrain from giving easier problems to struggling students because it gives them the message that they are unable to do challenging problems which can reinforce their perception they can't do math.  It reinforces the closed mindset.  Provide students with time to ask questions and play with ideas to help with retention.  Allowing students more time can improve retention. Take time to encourage students to adopt a growth mindset as a way of reminding students that everyone is capable of doing math.  

By allowing students to productively struggle when solving non-standard problems, it helps them develop creative thinking and apply concepts to non-standard situations while experiencing rigorous problem solving.  This all leads to deeper learning of the material. 

On Friday, we'll talk about ways to develop rigor since many textbook problems do not contribute that much to rigorous problem solving. Let me know what you think, I'd love to hear.  Have a great day.