My Failures as a Math Student

So of course after I posted my week 4 post for the MTBoS Blogsplosion blogging initiative, I thought of some more failures of mine, only this time not as a math teacher, but as a math student.

Failing One of My HS Math Regents Exams
Growing up, I was a fairly good student.  My parents always emphasized the importance of getting a good education and I got good grades pretty easily.  It was right around 8th grade, when all of a sudden, these good grades I was getting started to slip, particularly in math.  That was also the year that I wasn't just taking 8th grade math, but also 9th grade (Sequential 1) math after school.  For the first time in my life, math wasn't coming easily to me anymore.  But I get through it, and did well on the Sequential 1 Regents that June, which meant that in high school, I would be taking all freshman classes, except for math, where I would be a year ahead.

My failure came in my second year of high school, when I was taking Sequential 3 (again a sophomore taking a Junior year math class) and I got lazy.  I wouldn't say my behavior wasn't typical.  I was a sophomore in high school whose priorities wasn't really school.  Also, by now, I had gotten used to math just not really making sense, so why put in the extra effort for something I just wasn't going to ever understand (or need)?  And that June, I failed the only Regents I would ever fail... Sequential 3.  And it broke my heart.  That was definitely a wake up call.  All my friends would more on to pre-calculus the following year, but I might not.  Luckily, I was able to get into pre-calc with the expectation that I would take the Sequential 3 Regents the following January.  And boy did I put in work for it.  I don't remember what I got on it, but I passed and I had learned my lesson.

Failing the Math Content Praxis
I continued to struggle with math in high school and college, which just always meant that I had to put more work into it than other subjects.  Even in college, being a psychology and sociology major, I ended up taking math and science classes all four years in college because I wanted a Bachelor of Science, not a Bachelor of Arts.  I even took classes that were part of the math major sequence.  But I got through it.  The irony of all of this is that at the end of college I would be accepted into the NYC Teaching Fellows, as... you guessed it, a math teacher.  I was able to pass all my certification exams (including math) easily and I became a certified 7th - 12th grade math teacher.

Last year, I was introduced and fell in love with Math for America.  From the moment I went to their first open house, I knew I wanted to be a part of their organization.  So, I applied.  Being a middle school math teacher and being certified 7th - 12th grade, that meant I had to take the Math Content Praxis Exam, which I hadn't ever taken, since NYC uses another exam for teacher certification.  Every free moment last Spring was spent studying number and quantity, algebra, functions, calculus, geometry, probability, statistics, and discrete mathematics.  I even got in touch with my old math tutor from college to work with me for a few sessions.  And I failed.  My heart was once again broken because I wanted to get in so badly, and wasn't going to be able to because of a math test.  I was a failure.  Luckily, I still had a small window to take he test again before the application was due.  So, again I went back to immersing myself in all of it, and went in, still feeling shaky, but knowing that I was giving it my best shot.

The day of the test, I felt more confident with my answers.  I paced myself better, and when I didn't get a preliminary score at the end (it's a computerized test) felt good that at least I hadn't already failed.  Sure enough, a few weeks later I got my score, and I had passed.  And damn, it felt good.

Both of these experiences stay with me because they are both living proof that I am a tough cookie when it comes to mathematics.  They also make me sensitive to the students who may be sitting in my classroom who feel like failures themselves sometimes, or simply have a hard time passing a test.  I wanted to share these experiences because the best math teachers are also math learners, and sometimes that comes with failure.  But that's OK.  I am always mindful that if I had let my early failures in math shut me down, I would, quite literally, not be where I am today.

"Take Chances. Make Mistakes. Get Messy."

This week's MTBoS Blogsplosion theme is all about reflecting on and proudly sharing a mistake/error/failure we made.  I'm not going to lie, I was not super thrilled when I first read about it.  It's not easy to admit when we are wrong.  But the more I thought about it, I tell my students every day to "be brave" and "give it a try" and that "it's OK to not know something... yet," so here I am.  Now, I could very well blog about my whole first year teaching ten years ago because I am pretty sure that most of that year,  I felt like a failure.  But I survived.  It wasn't easy or pretty, but here I am ten years later, still teaching middle school mathematics, and still enjoying it (most of the time).

I=prt
When I think back to a specific time I felt like a failure as a math teacher, a couple different things come up.  Once, in what had to be my fourth or fifth year teaching, I was going over interest with my 7th (?) graders, and of course, was being observed by my Bank Street advisor at the time, and I confidently taught my students that interest = principle times rate times time (I even had it written on my slide) and even emphasized to them that it's principle not principal, which, of course, is wrong, and was the first thing my advisor pointed out in our debrief.  I felt mortified.

Integer Chips
Another time, also around the same time, is when I was trying to move from direct teaching of integer operations to conceptual teaching, using red and black integer chips to model addition and subtraction number sentences.  Growing up, I was taught the algorithms for these, and knew that when subtracting integers, you simply just "keep, change, change" or keep the sign of the first integer, change the subtraction operation to addition, and change the sign sign of the second integer.  All of a sudden I was supposed to use these red and black chips, to model subtraction.  Not wanting to introduce them to the tool before fully understanding it myself, I spent many a lunch period trying to make sense of the chips until one day, it all came together.  Zero pairs!  Yes, I can put in as many zero pairs as I need without changing the value of the number sentence, and then, once I have enough chips to subtract, I can then follow through with the subtraction.  It was so clear!  And it was kind of nice to see the algorithm in a whole new way.  I think what stuck with me the most however, was an important reminder that sometimes, understanding something in math just takes time, and that is OK.

This Year
Although there are many more examples of mistakes/errors/failures I could mention throughout my teaching career, I would be lying if I said that they are all a thing of the past.  I still make them, and will still make new ones in the future.  Luckily, I can say will fair confidence that I solidly have middle school math down, and so not much surprises me in terms of content, but every once in a while, I will come across something I said, that mathematically turns out to be untrue.  The nice part about that is then, I can proudly admit to my 6th, 7th, and 8th graders that I was wrong (if they haven't already caught me) and that mistakes happen and they are OK.

As for feeling like a failure, I can't think of one great teacher, who, doesn't think of themselves as a failure sometimes.  How can we not?  Even the best of us (I'm talking way better than me) still have bad lessons and bad days.  I feel like a failure when I have tried everything I know to help a student make sense of something, and they still don't.  I feel like a failure when it takes me more than a week to grade an assignment, because teaching five classes across three grades is a lot of prep and grading work.  I feel like a failure when I know I wasn't able to give a lesson 100% because I didn't have the time to plan better.

But mistakes don't mean the end of something.  Mistakes give us the opportunity to change our thinking.  After all, if we all thought the same way and always got everything right, we might not be creative.  We might not see different perspectives.  We might not be afraid to try new things, out of fear of failure.  To borrow a phrase from my favorite cartoon teacher & hero, Ms. Frizzle, mistakes give us the freedom to "take chances... and get messy" ;)

Mistakes are messy.  Math is messy sometimes.  And that's OK.