The Most Important Thing I Know About Mathematics Right Now

I have learned so much this semester about mathematics.  I began the semester apprehensive about my own skills in math as well as my ability to teach it.  As of right now, I feel confident that I have the ability to hone my own skills as well as make mathematics a more positive and empowering experience for my future students.

Although I have learned so much about different manipulatives and strategies to teach through problem solving, the concept that has stuck with me the most is the fact that the teacher is NOT the one who decides whether the solution to a problem is right or wrong.

wait... what?

It makes sense when you think about it.  Mathematics, more than any other subject, determines on its own whether it is "right" or "wrong".  I think that in every school subject the teacher can sometimes be viewed as the person who knows the answer to everything.  This assumption often closes the door to others who might have a different answer or explanation, and perpetuates the belief in the one correct answer.  Teaching students to own their problems by creating their own pathways to the solution as well as being able to check their answer against the problem is incredibly important - not only for cognitive growth but for self-esteem. 

On the subject of self-esteem, math seems to be where most students feel the most uncomfortable and unable.  By letting students have control of their own problems we can build in them a growth mindset - that they are in charge of their own abilities.  By telling the students who are faster at math what the "correct" answer is we leave behind the students who can get the answer with more time, and we create in those students a fixed mindset - they don't believe that they have the "natural" ability to do mathematics, and stagnate in their achievement.  

As a future teacher I think that this is one area that I will need to work on for myself.  I can imagine myself being tempted to direct students more than I should, and even give them the answer to some questions that they might be struggling with (although Jo Boaler says that struggle is incredibly important in learning mathematics).  I think that this concept is incredibly difficult for others in the class as well from what I observed over the last semester.  Hopefully we can overcome the urge to let others tell us what is right and wrong in mathematics!

This has been a very eye-opening semester for me in many ways, and although I know that I have a long way to go before I am ready to teach truly empowering mathematics, I have been given a good head-start.  Thanks to Mary for all of the great experiences and wonderful times that she has shared with us over the past three months!!