Math is About More Than Number Crunching and Formula Writing

I have been participating in a book study over at the Math Coach's Corner on this book.  

Teaching Numeracy

It describes 9 habits kids (and adults!) need to support mathematical thinking.  I was reading about habit 3 which is identifying similarities and differences and recognizing patterns and I saw this quote:

“If identifying similarities and differences is basic to human thought and boosts student achievement, why, then, are we still content to settle for number crunching and formula writing as the dominant form of instruction?”

This got me really fired up and as I was leaving a comment over on the book study, it turned into the story of my own mathematical education and why I think there needs to be a shift in teachers' focus from teaching kids how to do math to helping kids think about math.

Here it is!

I was taught arithmetic in elementary school and didn't find it particularly interesting but was always quite good at it.  When I think about my own instruction in math, it is amazing that I didn't completely hate it.  We used Addison Wesley style textbooks and everything was taught as a procedure.  Nothing was ever connected for us at all.  In fifth grade I remember we had a wide range of ability levels in our classroom.  The teacher allowed another student and I to start from the back of the fifth grade text book and work our way forward.  I don’t think we ever got any teacher time, we just did page after page of rote practice.  We even checked our own work and graded our own tests with the teacher’s edition.  I thought it was a great adventure then but now it seems like a recipe for disaster!

In middle school and for algebra 1 and geometry, I was able to follow the procedures that had been taught and relied on my great memory to “plug and chug” my way through these classes with excellent grades.  Looking back, I see that I didn’t really understand the math but I could do it.  I was never taught to think about the numbers I just operated on them.  It wasn’t until tenth grade when I stepped into an Algebra 2 class that I ever started getting the connections between things.  I had a fantastic teacher who helped me to see connections and challenged me to live up to my mathematical potential.  Luckily I had the same teacher twice more before graduating from high school and he really helped foster my love of mathematics.

As an undergraduate, I had a dual major in elementary education and mathematics and took some very challenging math classes.  I had the widest range of professors you can possibly imagine ranging from the very good to the completely inept.  I had a dynamic, inspiring teacher for my combinatorial theory class and to this day I get so excited about combination problems and I love doing them with my students.  I also had some of the worst professors imaginable and I think now looking back it is because they couldn't or didn't connect what they were trying to teach me with what I already knew.  I don’t know if they actually understood the connections themselves.  I remember one professor who taught a class on groups and rings would have the entire class show up at his office during office hours because none of us could figure it out.  Finally he told us all that if we showed up for class and tried our best, he would give us all a B. 

It wasn’t until I began teaching and started working on my master’s degree in K-8 math instruction that I finally really understood the connections in math.  Being introduced to things like the area model for multiplication and finally getting that multi digit multiplication, fraction multiplication and polynomial multiplication are all connected by this model changed the way I view math.  Instead of a list of disconnected procedures, I had a visual model that could help me solve ANY multiplication problem.  Through my master’s program, I also finally got the connection between algebra and geometry.  When I was in high school they were taught as two different subjects but through the problems I worked on in this program, I got to see that you can solve many problems with algebra or geometry.  I also learned that I tend to favor solving problems with algebra and really had to open my mind up to see how the same problem could be solved with geometry.  It made me a better mathematician and a better teacher. 

When I think about my own math education, I can see why I teach the way I do and why I am always annoying my students with my sayings like “think about the math, don’t just do it!”  I spent many, many years just doing the math and was quite successful at it.  However, I was missing the passion, understanding and beauty of mathematics.  I could not solve novel problems.  I could only plug numbers into formulas.  If I forgot a formula or a procedure, I had no way to go back and re-create it for myself.  I have a great memory so I did well in general because I tended to not forget.  As my deeper understanding of mathematics developed, it helped shape me into the teacher I am today.  I get the connections now.  I know if my answer makes sense.  If I forget a formula or a procedure, I can rely on other things that I know that are connected to it to help me out.  I love nothing more than jumping into solving a novel problem.  I thrive on trying new math and applying my new knowledge to what I have learned in the past.  I love math. 

I want my students to feel about math the way I do now.  I want them to have the connections and be passionate about using what they know to solve new problems.  I don’t want them to settle for being taught how to do it!  I want them to construct their own knowledge and learn to think instead of just applying procedures.  I am not willing to let my students learn math the way I did.  I want more for them.  It is time to stop teaching kids how to do math and start helping them learn to think about math!

How do you make math about more than number crunching and formula writing?