Challenge Them To Create
A study by Dr. Karlsson in 2015 looked at mathematical problem solving and its impact on the brain. He worked with two groups of students and used MRI to study brain activity. Martin Buschkuehl summarizes the study and the findings here. Essentially it was determined that the group of students who were taught an algorithm - a series of steps to solve a problem - were out-performed by peers (called the creative group) who were left to their own devices to solve the same problems. The creative group not only out-performed the algorithmic group, but they did so with less cognitive effort. This study underscores the critical importance of productive struggle.
All too often, students are faced with rules and procedures that are to be followed. They are shown exactly how to solve a problem, how to think, and how to proceed before they are then asked to practice what they were just shown. It is time that we embrace what the research has shown us repeatedly - "Students Learn Better When They Figure Things Out On Their Own."
Mahesh Sharma writes about explicitly working on these habits of mind and effectively improving working memory stating, "Developing the ability to observe, discern, expand, create, and apply patterns is an antidote to working memory failures and the means to enhance the working memory."
In addition to productive struggle and an awareness of the demands on working memory, we also can't underestimate the role of engagement. Rather than presenting contrived textbook problems that students can't relate to, we are more likely to engage students when we present them with real world problems. A favorite cartoon of mine says it well:
Engagement and productive struggle are high when we use tasks like those found at Yummy Math or Robert Kaplinsky or at Bedtime Math for our youngest of learners.
The search for the magic wand to solve all math troubles, for the perfect checklist, for the exact lesson or strategy to show our students can end here. The magic is within the students already - challenge them to create and they will achieve great things!