Guest Blogger: Creating Math Thinkers

Our Guest Blogger this week is our Math Teacher Leader, Kevin Williams, a dedicated 5th grade teacher from Reed Elementary. Today, he writes about his experiences with learning and teaching math for understanding. Thank you, Kevin, for sharing your journey with us today as you create math thinkers in your classroom!

Hello, my name is Kevin Williams, and I'm a mathaholic. I wasn't always addicted to math. In fact, as a student I barely even liked it. I had many good teachers, but it was a different day and age. All students had to do back then was repeat procedures and algorithms. I was an expert at memorizing formulas, repeating steps, and passing tests. Passing tests was so easy back in the day. They were mostly computation problems with very few real-world applications. I didn't even realize how math ignorant I was. Not until I became a teacher.

At first things were great. State tests were ridiculously simple, requiring very little from teachers as they prepared their students. It wasn't long before new math standards and expectations came into play. Suddenly it wasn't enough for students to add, subtract, multiply, and divide in isolation. My students had to actually think. While I was great at teaching steps, procedures, and tricks, I was at a loss for teaching thinking.

It was at a Marilyn Burns training that I began to understand just how little I knew about teaching math, and really how little I understood math personally. As the leader worked with a group of students, she asked the simple question, "What is area?" Every hand reached for the sky. "It's length times width," they all shouted. I was so proud. "That is how you can find area. But what IS it?" It suddenly hit me. I was guilty of teaching methods to find answers when my students didn't even really understand the questions!

Much has changed for me since then. I began a personal journey to truly learn the reasons why all of the procedures, algorithms, and tricks I taught worked. I'm embarrassed to admit some of the concepts that I finally began to understand--like when I discovered arrays and for the first time understood square numbers! I became addicted to playing with numbers.

Why tell you all of this now? I guess it's because of the new Bridges materials that we have in Leander. The materials require kids to manipulate and play with numbers. It gives students opportunities to apply knowledge and skills. It enables kids to build number sense. It makes us communicate mathematical thinking. And we play games. Lots and lots of games. Games that make kids think. I can't wait to see how it will eventually transform our kids and their deep understanding of math. I have been around long enough to understand and expect an "implementation dip" in the short-term. I'm confident, though, that if we stay the course, we will see dramatic improvement in mathematical thinking in the near future.

Thank you, Leander ISD, for providing us with a resource that will prepare our students for a brighter future, with more options due to their better understanding of math. I see many more mathaholics in our future!

Guest Blog: Open Tasks from a 4th Grade Classroom

Our Guest Blogger this week is Jessica Beeler, 4th grade teacher from Rutledge Elementary. Jessica has had great success with using open tasks in her classroom and was willing to share an example of how she facilitates mathematical learning through this type of open-ended problem. Thank you, Jessica, for sharing your knowledge with us today!

         This year I have been a huge advocate for problem solving in the classroom as a primary way for the students to learn and investigate new concepts.  They have really blown me away with their level of learning. I have challenged myself to use a variety of different facilitation methods to aid their math discovery.

         So I decided to pull out some open-ended problems to get the students thinking more deeply about their work.  The different problems they created were so exciting.  One student, who is usually quite quiet and with-drawn ripped through the first answer (3 ½ brownies) with a great problem.

        She was able to tell me how she figured out they needed 14 brownies total.  She drew the 3 ½ brownies for each person then simply counted them up, combining halves as she went. 

         I was able to easily differentiate another problem for her (2 ¼ brownies) which she created equally as quickly. 

         Then she moved on to 1 2/3 brownies,

and finally 5/3 brownies.  By this point she was very confident in her strategy and really understood it well. She really got excited by the different problems and did not have a single drift-away moment.

         A few of the students gravitated toward subtraction problems instead of equal share problems.  This was fine, but not what I was anticipating when I created the answers.  To avoid this the next time we did the activity I included the word each in the answer, “5 2/4 brownies each.”

         I have done a few similar problems in homework before, but am definitely going to start doing more.  It is an easy thing for me to create, and incredibly beneficial for the students.

         They also love checking each other’s problems to make sure that they truly do work out correctly.  I have had some great conversations with individual students as well as they have been designing their problems. I love seeing the excitement in their eyes as they see they can not only understand the math, but also create the math!

Integrating ELA With the New Math TEKS “Like a Pirate”

The new Math TEKs have proven to be a challenge for both students and teachers this year. Students have struggled to learn new strategies to help them become successful and teachers have been forced to think outside the box to keep students engaged and learning.

By integrating content areas to create a learning “experience” for students, the 2nd grade teachers at Block House Creek Elementary seem to be having just as much fun teaching as students are at learning.

In March, teachers combined the skill of comparing and contrasting works by the same author with organizing data in a bar graph using intervals. Along with the exciting NCAA basketball tournament hype, March Madness - Book Edition began. Using the diverse and often humorous books of Mo Willems, the entire 2nd grade set off on a two-week journey to find their favorite Mo Willems’ book.

Each day the 2nd grade teachers would read the same book to their classes and then each class voted on their favorite. Each math class got the opportunity to count up the votes and decide how they would like to graph the results. There was a large bracket in the hallway during this process so the students could see who won each round as the narrowing down process continued.

On the last day, all the classes read the two finalists at the same time and teachers tallied the votes. At the end of the day the big reveal was held in the gym. The students were so excited to find out if their favorite book won. It all came down to “City Dog, Country Frog” and “Pigeon Finds a Hotdog,” two very different books. The children cheered as the winner, “Pigeon Finds a Hotdog” was revealed. They were then surprised by a five-minute dance party in the gym. Teachers and students danced together for a brief moment of fun and silliness that seems to rarely occur in our daily treadmill of demanding curriculum and many tiny needs.

Although change can be uncomfortable and overwhelming at times, with the help of innovative ideas and collaboration, everyone wins in the end. Everyone gets to share in the joy of learning.

Argh!!!

2nd Grade Team

BHCreek

#tlap

Celebrating a Lifelong Learner!

Last week at our math teacher leader meeting, we honored and celebrated Kathy Boling, as she will be retiring at the end of this year. Of course, we are thrilled for her, but we also want to share with you today why we will continued to be inspired by her passion and dedication for learning.

Kathy has served on the math teacher leader team for almost as long as we have had math teacher leaders in LISD. However, we consider Kathy one of our "extraordinaire" math teacher leaders because she is continually learning and always trying new things, even after 36 years in the profession. For example, when we asked her to try out math interviews on her 2nd graders, not only did she commit to administering every interview, but she gave specific feedback on the advantages and disadvantages of each interview. As if that wasn't enough, she also attended every single after school meeting willing to collaborate and ask questions of others. When Kathy makes a commitment, she perseveres in accomplishing it.

This year, we encouraged math teacher leaders to spread their mathematical expertise by presenting at this year's February Conference. Kathy was one of those teachers who accepted the challenge to present, and she went above and beyond the call of duty. During the presentation, she engaged the participants in a number talk that she actually used with her students. Kathy understands that we learn best by doing and she wasn't afraid to step out of her comfort zone to try something different.

These are just a few examples to illustrate how Kathy is a lifelong learner. In fact, it is her ongoing, voluntary, and self-motivated pursuit of knowledge that has enhanced the culture of our math teacher leader team and will continue to inspire us all. Let me say this in another way. From the words of Dana Nathanson, "She has been an educator for over 30 years, and she is STILL learning as we all are!"

Thank you, Kathy, for your growth mindset, dedication and passion for learning, and your years of service in LISD.

We wish her a wonderful journey as she starts a new chapter in her life! Please help us congratulate her by leaving her note in the comments!

The Mystery of My Walks

This week I downloaded the APP called "MapMyWalk" onto my iPhone and was excited to try it out. This APP records my walk by putting it into a map. It also records my total time and my pace per mile. What wonderful math!  But boy was I surprised! 

Day 1:

Okay, I know I am slow but at least I was off the couch!

Day 2:

Was my APP not working?  How could the same walk give me two different distances? 

If my APP is working correctly how could this be? 

Share this problem with your students and help me solve the mystery. 

Please add comments, questions, answers below.  Thanks for your help!

Guest Blog: Ponderings from the Treadmill

I am very excited to introduce our new Guest Blogger!  April Chauvette is our secondary counterpart in the world of LISD mathematics.  April is a Secondary Math Facilitator and mostly works with grades 6, 7 and 8.  She is also our "go to girl" for everything middle school.  We love collaborating with April and appreciate her educational and mathematical insights.  Please join us in welcoming her and thank you April for your pondering . . .   

So, I’ve decided start running more frequently.  It all started with a twitter post from Principal Salome Thomas-EL urging faculty and followers to live a healthier life and challenging them to be a part of #500in2014 (as in running 500 miles in 2014). 

Let me be clear, I am no marathoner.  I’m in decent enough shape, but don’t consistently go out running, its rather sporadic.  And while I don’t mind running and actually kind of enjoy it (if only my HS coaches could hear that!) I seldom do it.  For whatever crazy reason though, I decided to accept this twitter challenge and am working to stay on pace to be able complete the 500 miles this year (it’s only about 10 miles per week right?!?).

I really am going somewhere with this, so bear with me…Like I said, I’m in decent enough shape.  When I did actually run before, my natural pace was around a 10-minute mile over my general 2 to 3 mile path.  Not bad, in my estimation. Not going to blow anyone out of the water, but solid enough. 

But as the crazy Texas winter of 2014 has unfolded, I’ve found myself at the gym on the treadmill more than normal.  My MO had been to hop on the treadmill, adjust my tunes, and crank it up to 5.8 mph to get started.   (While I know you can do the math, 6 mph is a 10-minute mile.)  So I’d start at 5.8 (just below my typical pace) for a ½ mile or so and then eek it up 0.1 mph every so often (to keep challenging myself over the run) then a little more than half way through the run, I’d start tapering back down.  I’d get up to maybe 6.5 mph for a little bit but that was usually a max.  6.5 mph is not bad. That’s peaking at a 9:13 minute/mile pace.  I’ve been pretty content with that, having really just started running consistently in January.

On Friday, I must have been particularly distracted as I got started on the treadmill.  Perhaps it was because I hadn’t run in over a week and was feeling behind, maybe it was the fact that I was actually out in the middle of the day on school day due to our cancellation, maybe it was because I had just dropped my two kids off in the gym daycare and who knew how that would go.  Regardless, I fiddled w/ my iPhone, started my Nike+ app, fixed my headphones and started cranking up the treadmill.  I’d been going for quite a little bit when I looked down at the display and saw that I had started myself off at a 6.5 mph pace.  And was doing fine.  I reactively reached out to slow it down, but then realized that I was doing fine.  Intrigued, I left my setting as it was and proceeded with my normal routine of cranking up the challenge little by little over the course of my run, eventually peaking at 7.2 mph (a 8:20 min/mile pace), without much trouble at all. 

My mind raced far more than my legs that day.  How often do we operate in this manner in our classrooms?  We have what we think is our pace, our zone, where our kids perform best.  We have a bar of expectations for our kiddos. Our MO is to start right under that bar and work up to it and maybe little beyond it and then ease back down.  It makes me wonder, how accurate are we with our initial bar setting? Are we selling ourselves and our students short?  What if we started the day with the bar set a little higher and still worked to stretch students more, little by little, what would we achieve?   Incrementally increasing my speed felt just as challenging when I was running the slower pace as I did at the surprisingly faster start pace.  Would I have known the difference if I hadn’t looked down?  Would our students?

It doesn’t mean that there won’t be stumbling blocks.  I had to pause my run on the treadmill, to deal with a nagging sock that was bunching up between my toes.  But was able to resume the run feeling much better having straightened that out. Extend the metaphor in your mind.  What does the pause in the run look like in your classroom?  What is the cause? What’s your bunched up sock?  Stop and take the time to deal with it.  Then get going again, the rest will go smoother having done so. 

Now, I will tell you that it did cross my mind that this run was a fluke.  Maybe I had extra energy having taken week off.  Maybe it because I was on a treadmill and not outside.  Maybe it was because I was playing mindgames with myself over those 4 miles.  Interestingly enough, having had two opportunities to run since and test this hypothesis, it’s holding, once outdoors and then back on the treadmill (thanks Texas weather).  I’ve continued to outperform my typical self (not just for a moment but over the course of a whole 4 or 5 miles) when I’ve started at a more challenging pace. 

Where have you set your bar?  What surprising successes are you keeping yourself from?

Guest Blog: Transforming Math Instruction (Part 2)

Last week, you might have read: Guest Blog: Transforming Math Instruction (Part 1) written by Kellie Lambert. This week, we are proud to share Jessica Beeler's perspective on how she has transformed her approach to math instruction. Be on the lookout for these two educators during February Conference this year. They will be offering a session on this topic if you are interested in learning more about their success in teaching math differently!

What's that saying? An insane person does the same thing over and over again expecting different results.  Every year that was me.  “I will start fractions earlier, harder.  I will talk louder to make them understand.  If I say the same words just a few more times than I have for the past 13 years of teaching fourth grade the students WILL get it this time.  Yes, of course, I am just not being emphatic enough with my standing at the front of the room and telling them what fractions are.”  Eureka!!

Um, no.  Not even close.  So when Beth Chinderle was visiting Kellie Lambert I heard the discussion afterward. She was showing Kellie student work and going over the different levels of student understanding.  I saw what she was talking about all the time in my classroom.  It all makes sense,  so many kids understand more than I am giving them credit for.  So many still need time to practice and grow.

Actually it was a two-part moment of discovery for me.  Months before at February Conference I went to a class about fractions and they put a dividing fractions problem on the board.  My old learning kicked in and I quickly whipped out my algorithm that I had stored in the back of my brain, applied it to the problem, got my answer, and then...THERE IS NO WAY THAT IS RIGHT!  This is a dividing problem, how did I get a bigger answer? I proceeded to rework the problem and forced it to get an answer that made sense.  Ah, much better.  Then the ladies presenting the class used the same numbers in a word problem.  I swear someone started playing background "Hallelujah" music.  It all suddenly made sense.  My original answer was correct.  Why did no one show me this sooner? I would have been saved a lot of grief as a child/teenager. Just seeing the same information in a real world context made all the difference.

So Kellie and I talked.  And talked.  And talked.  Why not try a different approach? It was not as if I had been using the perfect way. If we did not like it we could always go back to our normal routine.  Let's try it together.  It is nice to have someone to jump with you.

Ok, where to begin? In years past I have stood at the front of the room, taught a skill, had the students take notes, done practice problems, then set them off on their own to apply their newfound knowledge to the worksheet or activity I gave them.  Then I collected all the students that did not "get it" and retaught the skill so they could get a better grade on the assignment.  I can still hear the student groans.  

Today.  A paradigm shift. A new concept? Let's start with some sort of problem solving.  At first the students were very hesitant, "but I don't know how to do this." My reply, "just try something." It was slow.  They were unsure.  They were unwilling to take the risk of getting a wrong answer.  It took some coaxing.  Ok, a lot of coaxing.  THIS IS NOT FOR A GRADE.  Not everyone tried that first time.  Some did not try very hard.  That was okay.  I walked around, asked questions, gave some reassuring back scratches, and let them get it wrong.  I learned SO much.  I quickly saw which kids had no conceptual understanding, which kids had only a little, and which kids understood what the problem was about.  I also saw where there were misconceptions.  A wealth of information, and I had yet to teach a thing!!!! That very first day I was hooked.  Fail or succeed I knew I was going to see this through.

Thank you, Jessica, for sharing your journey. Please leave her a comment or question below!