Thursday, January 26, 2017

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.

Wednesday, January 25, 2017

"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.

Saturday, January 21, 2017

Reading & Sharing in the #MTBoSBlogsplosion

Round #3 of the #MTBoSBlogsplosion is all about reading & sharing, which really, is what the MTBoS is all about; collaborating with and ultimately learning from other math educators.  Since going public with my twitter account over a year ago and got introduced to the MTBoS, I have connected with so many other amazing math teachers all over the world, and have brought things into my own middle school math classroom, that I never would have thought of on my own.  So here are some of the specific blogs and posts that have helped me become a better math teacher:

Math = Love is one of my favorite go-to math blogs.  I even used this Broken Circles task that Sarah posted about last July for my first day of school activities for my 7th & 8th graders this past year!  I also was inspired to bring the game of Set into my math club after reading this post. I cannot wait!

Crazy Math Teacher Lady is another one of my favorites.  I was really inspired by this post from this past November on what is good teaching.  I find that I can relate to so much of what she says, especially about trying real hard to be awesome, just ask any of my students.

I was introduced to Vi Hart  just this year.  I shared her videos on doodling in math for my Fibonacci Day celebration with my 6th, 7th, and 8th graders this year.  I will also be sharing her videos on hexaflexagons with my 8th graders in our current unit on geometric transformations.

Math with Bad Drawings is a new blog that I started following because of this post earlier this month on Why Mathematicians Are So Bad at Math? which was a very interesting read.

I love Math Easy as Pi because she is a fellow middle school math teacher, with really great classroom ideas.  I am also really interested in her Books Worth the Read list.

Communicating Mathematically and I Speak Math are two other inspiring middle school math blogs that I love to check out.  Ironically both have referenced Desmos activities lately, which makes sense because Desmos is great and a tool I am using more and more in my classes this year (my 7th & 8th graders use it pretty regularly, and it is my goal to introduce it to my 6th graders before the end of the year).

Another great middle school math blog to check out is Middle School Math Rules especially when I need organizational tips.

Last but definitly not least is Roots of the Equation.  This is the blog of one of my friends, and current high school math teacher.  He is an amazing math teacher, who has helped tutor me in math in college, and this past Spring when I was studying for my Math Content Praxis.  I would have loved to have been a student in one of his classes.

Saturday, January 14, 2017

The Soft Skills of Teaching Middle School Mathematics

This week's theme in the MTBoS Blogsplosion blogging initiative challenges us to reflect on the soft skills of teaching math.  As a middle school teacher, this is something I think about often.  What makes a great math teacher?

#1 I think is content knowledge.  A great math teacher is first and foremost, a math learner themselves.  Now, I know, strong content knowledge doesn't really fall under "soft skills", but they have to be willing to put themselves in the (sometimes uncomfortable and messy role) of learning.  I think this is true of any good teacher really, but it is especially important for math teachers.  Being a life-long learner, not being afraid or ashamed to ask questions, and wanting to make sense of problems and persevere in solving them (as the first Common Core math practice states) are all soft skills.  A passion for learning is truly a beautiful thing.

A question I ask myself often is "how am I deepening my own content knowledge?"  I've been teaching middle school math for ten years now.  I have taken advanced math classes in high school, and college, and I have passed several math content teacher certification tests, including the Math Content Knowledge Praxis Exam last year in order to apply for a Master Teacher Fellowship at Math for America.  I know what I need my students to know, but, I am sad to admit that rarely do I make the time to explore mathematics outside my classroom.  Don't get me wrong, I love exploring things with my students.  Ask any one of my current or former students, and I truly believe that they would say that I enjoy exploring math with them (which is another essential soft skill of a great math teacher, I believe), but rarely do I venture outside exploring something mathematical not related to my job.  I'd like to say that this is because of lack of time and the demands of balancing work and life, but what it comes down to, is that sometimes it is just not a high enough priority of mine.  And that is something I want to consciously change over the course of the next few months.  I want to push my own mathematical thinking and learning.  Great math teachers are always learning, not only in their craft, but in their own depth of content knowledge.

Some of the other soft skills that I think are essential to great math teaching, especially in middle school, are the ability to balance that fine line between teaching children and teaching young adults.  My students are different people every single day, and that can be challenging.  Middle school teachers have one of the highest teacher turnover rates, and almost every time I tell someone new that I teach middle school math, the response is usually one of pity (or insanity), but I genuinely love what I do, and I know that what I do is important.  Teaching (and enjoying teaching) middle school math requires a very unique set of soft skills, including communication, again, balancing being able to talk about the (often) silly things that entertain teenagers that and then the beauty of linear or quadratic equations.  We need to be mentally strong, and stable, because being a teenager is not.  We need to be forgiving, but also not shy away from consequences.  We need to be genuine listeners, because a middle schooler will do almost anything for you, if they realize that you do indeed care about them as individuals.  And lastly, we need to be (appropriately) human in front of them, which means admitting when we don't know something, disappointed in them when they are not being their best selves, and their biggest cheerleader when they deserve it.

Teaching middle school math is hard.  But man is it worth it ;)

Saturday, January 7, 2017

MTBoS 2017 Blogging Initiative: My Favorites

As a math teacher, and fellow member of the MTBoS, this week they posted about the MTBoS 2017 Blogging Initiative.  This week's theme is "My Favorites," so here are some of my favorite go-to resources that I have used so far this year:
  • Mathalicious - Great real-world, engaging middle & high school math lessons.  My $10/month subscription is totally worth it.  I have used it in all three grades that I teach this year.  A great resource!
  • Illuminations - How could anything by the NCTM not be great?  Great tasks and lessons I have, again, used in my 6th, 7th, and 8th grade Algebra 1 classes!
  • Illustrative Mathematics - Great tasks, broken down by Common Core Standard.
  • NRICH - I have used the tasks on here both with math club and just yesterday, with my 8th grade Algebra 1 class and with one of my 6th grade classes.  Very engaging, especially for differentiating up.
  • Mathematics Assessment Project - I have used some of these as homework problems this year.  Tasks are broken down by standard and come with rubrics.
  • Inside Mathematics - Great grade-level performance tasks, also with rubrics.
  • TED-Ed Mathematics -   Interesting videos on a variety of topics.  I mostly use the math or science ones, usually as a launch for lessons or to make connections.
  • Desmos Classroom Activities - I've used Desmos with both my 7th and 8th grade Algebra 1 students so far this year, and hope to introduce my 6th graders to it by the end of the year. Perfect for graphing linear and non-linear functions!
  • My favorite project so far this year, besides the Stock Market Game, has been the Road Trip Project that came from Carl's Teaching Blog.  My 7th graders definitely have had the best projects this year - this one was perfect for out linear relationships unit.  So much fun! My 6th graders also made their own Fraction Cookbooks, which they really enjoyed.
  • Lastly, a resource that I haven't used yet, but am very much looking forward to using this year are Dan Meyer's Three Act Tasks (hopefully to blog about in the very near future).  

Wednesday, January 4, 2017

December/January Projects & Tasks

So, in keeping with my goal to get back into blogging on here, here I am.  I want to first reflect on December, which is usually a crazy month for us teachers, but I must say, this was probably my smoothest (and most fun) December yet.

6th Grade
My 6th graders finished up Let's Be Rational and I modified this Operations with Fractions Cookbook Project for their unit project and they came out awesome.  They really went above and beyond, which was adorable.  This week we started Covering & Surrounding, which will end with their biggest project of the year, The Coke Package Design Project.  I switched this unit with Decimal Ops, to follow CMP3s suggested pacing order this year, so we'll see how that goes.  The Coke Project will take us right up to Mid-Winter Recess next month.

7th Grade
My 7th graders finished up Moving Straight Ahead and and then I extended the Desmos Marbleslides to include all the Desmos Linear activities, which both they & I loved.  Last year, I didn't introduce my 7th graders to Desmos until the end of the year, and I am glad I moved it up and fit it into this unit this year.  I also modified this amazing Road Trip Project as their unit project.  One of my classes finished it before Winter Break, and my other class is working on it this week.  I wish I knew about this project last year because it is super fun and a great real-world connection to linear relationships.  Our next unit is What Do You Expect? on probability and expected value, which has so many fun experiments, and I found this unfinished 3 Act Task on bottle flipping (it's big in 7th grade right now) from Dan Meyer and want to look into how I can bring it into my classroom (more to come).

8th grade Algebra 1
Last but not least, my 8th graders finished up Looking for Pythagoras last month and we learned how crazy the Pythagoreans and their cult of numbers really were.  Two of my favorite tasks included having them create their own Wheel's of Theodorus (which became by December bulletin board) and this awesome task from NASA (yes, the NASA) where they had to analyze different routes for the Lunar Rover and create a proposal with their recommendations.  This week we started Butterflies, Pinwheels, and Wallpaper.

All three grades had some really great Mathalicious tasks, that fit nicely into our December units.  Next week all three grades will be taking their second interim assessment of the year, so I will get some testing data to look at.  I also got picked to score the Algebra 1 Regents at the end of the month, which I am grateful for, since this is my first year teaching algebra 1 in a while.  Last month myself and the Living Environment teacher attended one day of NY Ed Tech Week and in two weeks I signed up for the Google Teacher's Lounge, which I am curious about, and of course, I have been keeping up with the MTBoS on Twitter.

In a few weeks, we will be at the halfway point of another school year.  Even though teaching five classes across three grades is a lot (I am forever behind on grading) I really do enjoy what I do, and I am very lucky about that.  Hopefully I can keep this up an continue to grow and get better at what I do.  Here's to an inspiring start to the new year!

Monday, January 2, 2017

New Year, New Blogging Inspiration

After more than a month of not having the time to blog on here (or rather, not making it a priority) here we are in the new year and, after ten beautiful, work-free days (including my birthday), I want to get back into it.  December went really smoothly at work.  All of my classes ended their current units, and will be starting new units tomorrow, and I really enjoyed the projects and investigations my students did (which I hope to reflect more fully about in a later post).

I came across this post by Dan Meyer on his winter break in recreational mathematics and then by AJ Juliani on his 30 Day Blogging Challenge, so I wan inspired to write on here.  Coming off last year's MfA experiences, like Dan Meyer, on of my professional goals includes doing more math, which means doing more recreational mathematics, which I must admit, I have slacked on since last summer.  Hopefully I can use this space to change that.  As for the 30 Day Blogging Challenge, my goal is to write 100 words a day for 30 days (yes, I know it's small, but I want to stay realistic), and to publish one post per week.  So here we go, day 1.  As we enter into the cold, dark school month of January, it may be rough, but it also the half-way point of the school year, which reminds me that even though there's work to do, it goes by really fast, and I want to make my time with my students count.

Here's to an inspiring, reflective, thoughtful 2017!