Ten Plus One:
Strategies for Enhancing the Depth and Complexity of Math Tasks
In the U.S., students spend most of their time in math class memorizing and practicing procedures. They often do not understand why the procedures work or even what they mean. There is very little time spent learning concepts deeply.
So what does deep learning in math even mean? I often think of it by looking at the questions that students and teachers ask:
Traditional Math Learning
What do I do?
What is the next step?
How can I remember?
Deep Math Learning
What do I think?
What does this mean?
How does this connect to what I know?
You may notice that helping students learn to think deeply in math is going to require much more than simply tinkering around the edges of the way we teach. It is a whole new mindset about mathematics! It means asking our students to think much more independently and creatively about math. In a very basic sense:
Deep math is creative math!
When teachers ask me how to create deep tasks for their students, I often suggest this set of Ten Plus One strategies. It helps "open up" math tasks in a way that gets students thinking about patterns and relationships instead of answers and steps. Mathematicians and those who use math to understand the world will tell you that this is a much more realistic view of mathematics. Seeing math this way also makes it much more interesting, exciting, and beautiful!
When you use these strategies, be sure not to worry about "doing it correctIy." The strategies are simply meant to free you and your students to think more flexibly and creatively about math. If they accomplish this, then they have done their work. I hope you enjoy playing with the strategies and that you find them helpful. Please contact me with your experiences ideas, and suggestions. The more we talk about mathematical ideas, the more we grow and learn!