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

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!

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?
I enjoyed reading your post. I was taught math the same way as you. I knew how to do the math, but didn't understand why. It took a few years of teaching for me to become comfortable with not only showing how to solve math problems, but also showing my kids how the different areas or concepts are connected.

ReplyDeleteIt is really hard to be a great, conceptual teacher when it isn't the way you learned it.

DeleteI did well in math but it wasn't because I necessarily understood what I was doing. I guess that means that I didn't do well in math. I sure do want better for my kids.

ReplyDelete❀ Tammy

Forever in FirstIsn't it interesting how you can look back and say "I did pretty good in math but didn't understand it." I never want one of my students to have that feeling.

DeleteSimilarly, I just 'got' math as a child (and adult) and it has been a challenge to work back the concepts, which has been made easier for me as I am in Montessori - so there are lots of concrete materials that help with specific concepts. Its fun for me and the children! :)

ReplyDeleteIt is amazing how many adults feel this way!

DeleteGreat post, Tara! I had a similar experience in school including two years in grade 11 and 12 with an amazing teacher. I took two years of university math but then switched majors. My dream is to go back and finish a math degree.

ReplyDeleteLove your blog!