Math Practice...What Should It Look Like?

Raise your hand if you have been traumatized by math in your life?  Do you have math anxiety?  I'm going to say that is a strong YES for me.  It was not until my adult life that I realized I was not taught math in a way that made sense to me; therefore, I just thought I was not good at it.  This is certainly not true.  But it took me way too long to figure that out.

Currently, I am reading Mathematical Mindsets.

I highly recommend this book.  It is helping me to confirm many things that I have been reading over the past few years about math and the way that it is taught.  This book has also helped me to realize that I was never given time to fully understand math.  Instead, procedures and rules were fed to me, which led me down a path of not having foundational number sense needed to play with numbers.
Boaler says...

Notable, the brain can only compress concepts; it cannot compress rules and methods.  Therefore students who do not engage in conceptual thinking and instead approach mathematics as a list of rules to remember are not engaging in the critical process of compression, so their brain is unable to organize and file away ideas; instead, it struggles to hold onto long lists of methods and rules.  This is why it is so important to help students approach mathematics conceptually at all times.

 What does this mean to me?  My students need to be playing with numbers.  Talking about problems.  And seeing a variety of problems and solutions.  Boaler goes on to explain that practicing a method over and over and over again is not helpful.  Students must see math concepts in a variety of different situations.  Isolating a method does not help students to apply those methods to actual problems.

So I need to continue to chew on this thought over the summer.  How can I continue to work with students on their number sense and application of understanding across a variety of problems?  As I read more of this book, I hope to gather some more ideas on this subject.

Em