I'm done! Now what?

This year, I find myself with a good deal more of autonomy in my classroom.  With this newfound freedom, I'm more motivated to use data to drive instruction (funny how that changes when it's not forced), and focus on greater differentiation for the huge range of understanding I see in each of my classes.  Some of my fifth graders are ready to move on quickly and need very little instruction and practice to really master a concept.  Others are struggling with automaticity with addition and subtraction, making fraction and decimal operations even more challenging.

Self reflection has led me to realize that I am doing a much better job of assisting struggling students and need to give more attention to those students who are excelling and quickly getting bored.   After talking with colleagues, parents, and students, I've arrived at the following possible ways to further engage and enrich these students:

• An independent research project on the Fibonacci numbers, the Golden Ratio, or something similar.
• Activities from the 6th grade text
• A connected project per unit or standard
• Purchasing a couple of copies of something like this: The Cartoon Guide to Algebra
• A student brought this to my attention.  She's been working out of it with her grandma and asked if she could work out of it when she has finished her work.

I have several things that need to be worked out.  We have limited technology, so an independent research project is somewhat tricky.  Also, while any student could potentially have the opportunity to work on an enrichment or challenge activity, the reality is that some students will likely never get there, and this could cause some resentment (or maybe motivation?).  How is this work assessed?  If it is not for a grade, will students want to do good quality work?  Should it connect directly to the standards or is this a good place for some "extras?"

I really want to avoid giving additional or different practice and would like for the work to be challenging, interesting, engaging, inspiring, and worth while.  It is also important that the work be largely independent or collaborative among students so that I can continue to provide remediation for other students.  It would be wonderful if this work could be ongoing and long term so that students pick up where they left off.  What do you think would be the best way to drive these students forward and facilitate a greater love for math?  What have you tried in you classroom that was effective (or not)?

Brain Breaks and Perspective

This fall, my district is offering the Studying Skillful Teaching course through Research for Better Teaching and I have been lucky enough to attend.  It has offered an opportunity to meet many pre-K through 12th grade teachers in my district, and "talk shop" with a group of math teachers on a fairly regular basis.  For the most part, the course has reemphasized many important ideas in sound professional practice, such as backwards planning, using wait time, and cultural sensitivity.  Although it took some time, it, like most courses of this nature, has left me feeling inadequate.  This post by Tom Rademacher sums up my experience pretty well.

"The struggle isn’t just inevitable, it’s important. It shows us where to get better, where to adapt, where to throw out the old answers and come up with some new ones. There’s no better sign that things are going poorly in a room than a teacher who always thinks everything is going just fine."

I refer to this post from time to time to remind myself that when things go wrong, reflection and adaptation are my course of action and it's all part of the struggle.  It's just that sometimes, it all feels like too much.

Jim, the instructor of the RBT course, has been wonderful about emphasizing the idea of matching, that is to say finding strategies that work for the particular students in front of us and for our respective styles as educators.  He rejects the notion of "best practices" as one-size-fits-all solutions for classroom success.  This is all helpful and reassuring, but I still cannot escape the nagging feeling that I should be doing more.  And it's not just RBT that makes me feel that way.

Twitter is home to a fantastic community of math educators (Math Twitterblogosphere), where I can turn to help process challenging situations in the classrooms, get answers to pedagogical questions, and just generally geek out about teaching math.  It is through this network that I learned about Notice and Wonder, 101qs, and engaged in an amazing discussion about whether 2 X 7 should have really been written as 7 X 2 when considering the number of lenses in 7 pairs of glasses.

But here's the thing: as much as I love engaging with this community (and learning new things in RBT, or in general), I sometimes need to take a break because it magnifies the feelings of inadequacy.  You see, I arrive to work early, stay a little late, bring a bunch home, and spend a great deal of time communicating with students and families, correcting, planning, and generally working to make my classroom an amazing, positive, and inspiring place for my students.  I engage with online learning communities, read math teaching books for fun, and absolutely love what I am doing.  And it leaves me wondering how any one teacher can employ all of the engaging strategies and improve learning outcomes so effectively and efficiently.

How come a handful of my 87 students are failing, despite many attempts at differentiation and remediation?  How can I better include more strategies from my RETELL course to reach my English Language Learners?  Why are some students still not finding a common denominator to add or subtract fractions?  Why are some students using the handy foldable to help them add and subtract decimals (for the love of all that is holy, line up those decimal points!)?  Where is the balance between conceptual understanding and skill development?  How do I move on when some students are exceeding the standards, and other are not working at grade level?  Now that we've noticed and wondered, when will we have the time to do more with our "wonders"?

Sometimes, I need to step away from Twitter, put down the math book, and remind myself that I'm doing the very best that I can in this moment for the learners I have been given the opportunity to educate this year.  The day I stop learning from my mistakes, adjusting my practice, and growing professionally, is the day I should hang it up.  Thankfully, that day is no where on the horizon.  Hopefully, I will learn to be more inspired by those educators who are able to answer most of the questions posed above and remember that none of us really feels like we have it all together.

Fractions Rally

I've noticed something in observing students subtract mixed numbers, especially when the second fraction is larger than the first and regrouping could be used.  If the problem is set up vertically, students will subtract the whole numbers down, then subtract the fractions up.  There are a couple of issues here that need to be addressed with students.

In an effort to emphasize the importance of looking at fractions first when subtracting mixed numbers, I began chanting "fractions first!" to my 5th graders.  As expected, they quickly joined in.  It wasn't long before a small stick figure rally was drawn on the board and I pointed to it as students chanted while we subtracted together.  Students were quite enthused by our new mantra and wanted to know if we could make posters and march outside the school chanting "fractions first!"  With a giggle and an "I'll think about it," we trudged on.

After a lengthy school day and hosting a math class for parents, I came home in a state of delirium and began further entertaining the student's desire to loudly proclaim their fraction knowledge.  The kiddos also need reminders to find a common denominator, but it doesn't yield itself to a chant quite as well.  Then it came to me.  I need a bullhorn.  Think...

Me: "What do we want?" 
Students: "Common denominators!"
Me: "When do we want them?"
Students: "Now!"

This all simultaneously seems absolutely absurd and genius.  Why not have a fraction rally?

So now, I turn to you.  These kiddos want to make posters and make this happen.  I want to maximize the educational benefit (and the fun).

• What other concepts do you think we could easily incorporate to our fraction rally?  
• What am I not considering that could make this amazing or a disaster?  
• Have you launched a successful fraction rally?  Let me know how it went!  

Rainbow Pooping Unicorns

Two years ago, I began a journey that turned out to be far less positive than I had imagined.  This year, I find myself if a position that could not be more opposite.  The job is the same, but the location, grade, and experience are totally different.  There are still plenty of times I've found myself questioning my effectiveness and career choice, but already, in just two short week, I've had multiple experiences where I've thought "this is it!  This is what teaching is and it's glorious!"  I commented to my colleague that sometimes it seems as though unicorns are prancing through my classroom.  She replied "and they're pooping rainbows."

With the freedom to make my own professional decisions, a little inspiration from Tracy Zager's Becoming the Math Teacher Teacher You Wish You'd Had, and the Math Twitter Blog-O-Sphere (#mtbos) community, things are moving right along in room 125.  We start our year learning about equivalent fractions, comparing fractions, and fractions greater than one.  I was blown away by all of the fabulous ideas and thoughts students have shared along the way.  Just take a look at a couple of the interpretations of building fractions equivalent to one half.

After a morning of standardized testing and a somewhat ineffective class involving note taking and practice problems, I decided it was time to reboot.  For my last class of the day, I handed out index cards cut in half.  Under the white board, I had a clothes line number line with 0, 1/2, and 1 marked.  Students were asked to write a fraction between 0 and 1 on their index card and then order them from least to greatest in their groups. Some students weren't sure what "a fraction between 0 and 1" meant, so they were asked to just consider the types of fractions we'd been working with to write their own. When the finished, they came to the front and had a seat on the rug with their index cards.    The objective for this lesson was to look at ordering fractions, but it turned into much more when students had enthusiastic discussions about where each fraction should be placed.  We used benchmark fractions to start, but the more fractions added to the line, the more debate there was about placement.  Discussion organically evolved into finding ways to know for sure we had the fraction in the right place (common denominators) and whether using the number of unit fractions from a whole was a reliable method for comparison.

Some students created fractions greater than one which led to conversations about how to recognize when a fraction is greater than one and how to convert it to a mixed number (is this a term we're not using any more?) by recognizing how many pieces make a whole and what is left over.  The number line grew, but here are a few shots from early on in the process.

 

It was refreshing to facilitate respectful discussions about math that were well informed and showed what students really knew, as well as what they were just starting to form an understanding about.  Students also learned that I was not going to confirm their answer, but that their peers were going to share why they agreed or why they disagreed.  Students who were comfortable with the lesson created much more challenging fractions to place.  Those who were less confident created and placed more common fractions with the aid of their classmates. The activity was repeated with all 4 of my classes and equally as successful in each.

My experience is not all unicorns pooping rainbows, but the success and authenticity of this lesson has encouraged me to work hard to create more like it as often as possible.  And it has made my weekend a whole lot more enjoyable!

A Magnificently Extraordinary Beginning

Thursday marked the start of a new school year.  Both my son and I entered 5th grade.  If the first two days are any indication of how this year will go, it's going to be great!  It's a long weekend and both of us are itching to get back to school.

Some quick observations: 5th graders are much smaller than 7th graders.  They are also much less mature, interrupt more, want to please and LOVE having lockers (even if learning and entering the combination is extremely stressful for some).  Thus far, I am quite enjoying these little people.

Our first week activities included

• passing a hula hoop through the class as we held hands in a circle
• answering the question "What is math?" 
• writing questions for a given image (a la 100qs) 
• See, Run, Do.  

Some classes had more time than others, so when all of the activities are complete I'll share a bit more.  In the mean time, the hula hoop activity was such a success that students begged to do it again.  When writing questions to go with a given image, aome students were so excited, they asked if they could write more than one.

In one particular class, we completed the hula hoop activity (twice) and then answered the question "What is math?"  I was blown away by their responses.  The only prompting I suggested was that they be honest, as if their math teacher were not in the room.  When they got a bit stuck, I asked them to finish the statement "When I know math is next I feel..."  Here's their list.


Prior to this year, I was lacking a great deal of confidence in my skills as a teacher.  The position I held was not a good fit for my personality or skill set and really took a toll.  While the students were sharing words like extraordinary, lovable, and magnificent, I was overwhelmed with the notion that things are going to be much different.  These students have no idea what I gift this was.  Some of these students are frustrated and bored by math.  They find it tricky and complicated.  In the same room, other students find math magnificent and extraordinary.  I have the very important job of teaching each and every one of these learners, regardless of their feelings.  The task of changing some perspectives and maintaining those extremely positive ones are equally as daunting, but I can't wait to really dive in!

Parent's Academy

After a handful of years staying home with my children, I returned to the classroom and was met by the dreaded Common Core.  Most of my friends have children younger than my own and I hadn't heard much opinion, either positive or negative.  It didn't take long before those opposed to the new standards voiced their opinions.  Thankfully, I had the opportunity to form my own educated opinion first.   Here's the thing: the standards are not bad and the math is not different.  I promise.  The standards are designed to more deliberately develop student number sense.  A good amount of time is spent really laying the foundation for thinking about numbers and how they come together.  Math is much more than this, of course.  While the Common Core State Standards, CCSS for short, are not bad, sometimes the way we (or texts) go about delivering them to students is not so great.  Case and point:

This problem was on my 2nd grader's homework.  All I could think over and over again was "WHO CARES ABOUT THE PAPER CLIPS?"  If I'm thinking this as a math teacher, what are non-math teacher parents thinking?!

Several years ago, I implemented a Parent's Academy where I host adult homework helpers in the classroom where their students learn.  Humor is mixed with content knowledge to acknowledge their struggle and concern, teach them WHY things are different, and how to effectively help their students on their own (more positive) math journeys.  The program was relaxed and well attended.  Parents asked great questions and made connections about their own math experiences.  They quickly realized that it was low stress and informative.  Not only were parents exposed to this "new math" first hand, they were able to form an ongoing relationship with me as the classroom teacher.  Parents knew that their students could have their questions answered (guidance, facilitation) via email or other online resources after school and encouraged self-advocacy on the part of their learners.  The home-school connection was powerful.

As I embark on a new professional journey this year, I hope to bring back the Parent's Academy to help enhance a positive math experience for my students.  It takes courage for parents to set aside their own math anxiety and frustrations and attend a math class at night, but hopefully they will see it's worth and have a little fun along the way!

Are our students really thinking?

For the past three days, I have been setting up my new classroom.  There is quite a bit of bulletin board space and so many options for their use.  As of right now, there are two small boards for students to display work that they are proud of and one larger board that is split in half.  One half is dedicated to fraction related vocabulary and I couldn't quite decide on what should go on the other half.

Inspiration came in the form of the book Becoming the Math Teacher You Wish You'd Had by Tracy Zager.  This is a wonderful resource for K-8 teachers, whether they love math (like me) or are just beginning to cultivate their "like" for math.  Zager was talking about Dan Meyer's 101qs, a website dedicated to his 3 act tasks, and focused on question posing.  Question posing is an important skill for our students.  It really requires a great deal of thought, and too often our students do not exercise their ability to think.

I settled on an image of soda bottles and began planning the bulletin board, but was still unsure if this is the direction I wanted to take it and if it was the best use of space.  My resident 5th and 3rd graders passed by, so I asked them to tell my the first question that came into their head when they saw the image.

It took the 5th grader four tries to be able to ask a question!  I was shocked.  His initial response was "I think it's addition."  From that instant, it was clear that this bulletin board was a great idea.  Many of our students are so interested in getting an answer, or better, a correct answer, than hearing (or reading) what they're being asked to do.  I've seen it over an over again.  They just don't think, and I suspect that is because enough of us are not asking them to.  We lead students directly to the solution with lots of scaffolding and remove the need for thoughtful mathematical decision making.  What fun is that?  Incidentally, I suspect that my 5th grader perceives a "correct" answer as the answer that I want to hear, which is a problem unto itself.

This image was chosen specifically because it could easily be physically created in the classroom for students to answer some of the questions they've generated.  I cannot wait to see what they come up with, and even more, to foster their development as thinkers!

Labels are Important

And so it begins.  My excitement is difficult to contain.  This year, I have been granted the opportunity to change grade levels and districts.  After many years of teaching primarily 7th grade math, I'll be getting to know some 5th grade mathematicians.  Using what I know about the math that 7th and 8th graders need to know, I hope to inspire a love of math and learning in this new group of humans I have been entrusted to educate.

This week, Building Math Minds is hosting a Virtual Math Summit, where Pre K - 5 educators are engaging in cyberspace about many ideas that impact student learning and classroom practices.  After viewing just 15 minutes of the first presentation I chose to view, I came upon this.  Graham Fletcher of gfletchy.com presented a situation involving 5 oranges cut into quarters.  Here's a screen shot:

In my experience and teaching, I would have expected an answer of 20.  I asked family members to answer as well.  All of us said 20.  One person said they multiplied by 4, another said they flipped the fraction and multiplied.  I was immediately struck by the denominator of 4, not just because of the image, but because Graham said that the answer was twenty, one-fourths.  In later communication with Graham, he would reveal that the solution should say 20/1, which made a whole lot more sense to me, but I am left thinking about two things:

If 5 is a whole number, and you're dividing into 1/4 size pieces, does it make sense that you have 20 whole pieces?

Labels are so important in understanding context and solutions.  

That first question was initially raised because of the solution on the slide, but even with the corrected solution of 20/1, I'm still thinking about how both 5 and 20 are whole numbers, but 20 is used to represent  a quantity of parts.  This could be tricky for students for sure.

In 5th grade, fractions are abundant.  Teaching 7th grade, I had taken for granted that students had already formed the necessary foundation to understand these sorts of answers.  Looking back, most clearly had not.  This image will be embedded in my brain as I take on the new challenge of educating 5th graders.  It will be an important task to ensure that students develop a solid understanding of what unit fractions are (1/2, 1/3, 1/4, ...  fractions with a numerator of 1) and how they relate to our solutions.  In this scenario, each piece is 1/4 and there are 20 of them.

As I look at the image above, I'm also struck by how many questions students could pose if the equation were removed, and how many patterns could be observed.  I'm excited and inspired to work with 5th graders and cannot wait to facilitate their mathematical journey's this year!