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: 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!

Guest Blog: Transforming Math Instruction (Part 1)

We are blessed to have TWO guest bloggers this month! Kellie Lambert and Jessica Beeler, 4th grade teachers at Rutledge Elementary, have transformed their approach to math instruction to provide students the opportunity to explore, discover and uncover important mathematical topics. Both of these educators were willing to share their journey through a guest blog. First, we will hear Kellie Lambert's perspective on how she is teaching mathematics differently this year. I hope you will be inspired by her courage to try something new and different! Thank you, Kellie, for sharing your journey! 

This is my 9^th year teaching 4^th grade math and every year I feel like I pour my heart and soul into my math instruction every day and while some might be satisfied with the results I get, I have never been completely satisfied.  I have always known in my heart that there had to be a better way to approach math instruction where I’m able to reach more kids faster and take them further. 

I feel like I try to completely revamp my math instruction every year in order to find what works.  I’m constantly reflecting, researching, analyzing data, and attending numerous professional development sessions in hopes of finding new and better ways to improve math.

I have a tendency to try new big ideas and if I don’t see improvement, revert back to the mediocre approach that I’ve always known.  In fact, a coworker once asked me, “Have you ever wondered if the reason you feel like your students aren’t successful is because you completely change everything every year, and you never really give any of your ideas a chance to see if they actually work or not?” 

Hmm…well, that was an interesting thought that made me really start reflecting on whether or not my NEXT new big idea for math instruction would be the one that works.  I ultimately decided that if I was going to try a whole new approach (again), that I should seek advice from the experts.  I decided to get in touch with Beth Chinderle, one of our district’s elementary math facilitators. 

Beth Chinderle met with me before school started this year and we discussed my next big idea.  While Beth never discouraged me from moving forward with my idea, it quickly became evident that there was a far better way to approach math instruction than the route that I was headed in.   Beth Chinderle basically blew my mind with her ideas for math instruction in the elementary classroom and her philosophies on problem solving.   I held on to every word and couldn’t wait to collaborate with my coworker, Jessica Beeler about how we could improve our own math instruction. 

Jessica and I shared ideas back and forth and she was the one who had a stroke of genius.  After discussing Beth’s Chinderle’s visit (along with all of her shared wisdom), our own philosophies on math instruction, and considering the research that’s out there, Jessica came to the conclusion that if we simply flip our problem solving approach that we could change everything we know about teaching math. 

We decided to take a risk and go for it.  As we started sharing our new approach with others, we quickly realized how much of a mind shift our idea truly was.

Flipping the Problem Solving Model:

When we introduce a new math skill, we introduce it to our students in a word problem and allow them to explore their own approaches.  We have eliminated front-loading the students with strategies, tricks, and methods to guide them towards the correct answers.  Instead, we allow them to explore, discover, and draw their own conclusions about new math concepts.  For instance, when we started our division unit, we started it off with a division word problem.  Most of our students had never been taught division, however, they were all able to solve the problem correctly.   How was this possible?  Our students had enough prior knowledge to be able to use a variety of strategies to help get the right answer.  We then had students copy their strategies on computer paper and we talked about them as a whole class.  The division learning came naturally through our classroom problem solving talks.  Students started noticing patterns and wanted to try the approaches their classmates had tried.

When we start with problem solving to introduce a new math skill, it serves as a pre-assessment for us.  We’re able to quickly determine how much prior knowledge our students have and how much they don’t know.  We use what we learn from the problem solving to help guide our instruction.  Once we’ve explored with problem solving, we’ll go back and do some small group or whole group instruction about our new math skill in order to help fill in the gaps.  Then, the students can’t wait to attack the original problem we gave them all over again or attack a new problem. 

It’s really been eye-opening to watch the transformation in our math classrooms.  Our students take more risks, they aren’t afraid of a challenge, and they value the ideas and opinions of the others around them.  We’ve noticed that our students are developing stronger math foundations and that they’re able to apply their math knowledge in numerous situations when it’s presented to them in a variety of ways (something we’ve always struggled with in the past).

We’ve also incorporated Number Talks into our math routine and the discussions are remarkable.  The first thing I realized about number talks was that I should’ve been doing these for the past 8 years.  It’s fascinating to watch the students gain confidence and share their strategies despite whether they get the right answer or not.  The greatest thing to watch is when a student is sharing a strategy that didn’t lead to the correct answer and the self-discovery that takes place as they figure it out on their own.

This is the first year that I have ever been really excited about math because I finally feel like we’re on the right track.  In the past, I’ve felt like there were pockets of greatness here and there, but overall, I still felt like there was so much more that still needed to be done. 

This year has been an incredible ride and I wouldn’t have wanted to take it with anyone other than Jessica.  It’s amazing to work alongside someone who has so much passion for teaching math and who truly understands what works for kids.  After what I’ve seen this year in math, I can’t fathom teaching math in any other way.  I think we’ve finally discovered the next big idea that actually works and I can’t wait to see where this journey takes us!

Please feel free to leave a comment or question below for Kellie. Next Monday, we will post Jessica Beeler's perspective and hear her thoughts. Stay tuned!

Guest Blog: Transforming Math Instruction

Rayla Rucker, a dedicated 4th grade teacher at Pleasant Hill Elementary, recently wrote a guest blog on Transforming Math Homework. Parents, educators and students throughout our district were positively impacted by this post. Rayla has agreed to write another post about her journey as she continues to transform her math instruction. Thank you, Rayla, for offering us your insights and expertise as you commit to problem solving every day!

"Mrs. Rucker, can you give us that in a word problem so we know how to solve it?” EL, 4th grader

Sometimes you never know when or if you’ll have a breakthrough, and sometimes the evidence comes in a simple question from one of your students.

This year I decided to make a change in math.  Problem solving every single day. I was skeptical. I didn’t know how I would “fit that in”.  All I could see was the hundreds of millions of skills I am supposed to teach my class of twenty-four 4th graders in a period of 9 months, more or less.  Oh, and also throw in those awesome Number Talks every day!  And Estimation! And Vocabulary! And on and on and on...

It is quite daunting when you look at every single thing you want to do for your kiddos.

The first valuable A-Ha moment for me was realizing that the skills and the problem solving weren’t two separate things in most cases.  Duh?  Right?  A little slow on the uptake sometimes...So, I thought, at the very least, I could tailor my student’s learning around those skills contextualized into word problems, the more real world the better.

And that’s what I have done.  Every single day we do problem solving...Every. Single. Day.

Believe it or not, my kids actually look forward to it.  I find that they are becoming very adept at knowing which operations and in what order they should use them.  I don’t use HIDE or any form of problem solving Must Do’s.  We start on Monday with a brand new skill.  We unpack the problem and show/share our strategies.  Every day during the week, we use a similar, but increasingly higher level, multi-step(ier) problem.  And on Friday, we have an assessment on that problem type.

Not saying this structure will work for everyone, but it works well for us.  

More recently, I have been tailoring the problems around the Number Talk strategies.  So, those two aspects of my math workshop have melded together quite nicely.  I also use problem samples from the units of study.

Here are some things I have learned from this grand experiment.

1.  Change is super hard.  

We know what has worked for us in the past, but sometimes what works for us is not what works for our students.  Deciding to change is easy for me, that’s the type of person I am, but that doesn’t mean it has been a piece of cake.  In the beginning, I felt as though these changes were not working and wanted to give it up, but I stuck with it.  


2.  It gets easier.  

My class is in a groove with problem solving.  It has become second nature, and they actually smile and get all giddy when they know that’s what we are about to do. If I’m being honest 95% are giddy....I still have about 5% that can’t stand it...but we’re working on it!

3.  You will see success.

First and foremost, I have students who are excelling that never thought they were good at math.  It makes them feel so good about themselves, and that makes me very happy!  Secondly, and not nearly as important, I spoke with some other teachers that are problem solving every day.  Everyone I spoke with had more success on the problem solving on their 18 week benchmark than ever before!  Oh, and don’t forget... When I give a naked number problem, they ask for it in a real life situation!  That is the greatest success, isn’t it?

4. Our students will have to be problem solvers for the rest of their lives.  

We really do owe it to them to give them as much experience in this area as we can.  It really isn’t just about math, it’s about thinking, and creating thinkers is what this business of teaching is all about.

So, if you aren’t problem solving every day, I challenge you to give it a try.  I committed to it, and it has made all the difference.