Quest Blogger: Ending with Inquiry

Our quest blogger today is 2nd grade teacher, Emily Jones.  She shared a little bit about herself and her love of math, "This is my sixth year teaching. I have taught grades 1-3 and I have a passion for math! My kiddos are 11 and 14. Prior to teaching and being a stay at home mom, I worked in banking. I found a love for math from my banking experience and in teaching. I have greatly improved my math thinking as an adult." Thank you, Emily, for sharing your passion for math!

Right now the end of year checklists are begging for attention and teachers are trying to figure out how to keep their students engaged.  Let’s be honest, teachers are just trying to keep kids safe.  Having engaged learners during the last week of school is a BONUS.  So, how can we send off our students longing for more math?  How can we continue to focus on rich learning even when summer and swimming pools are on the brain?

Recently, I became inspired to seek out answers to these questions and after reflecting I arrived at these three words: novelty, exploration, and structure.  After modifying a few Bridges in Mathematics marble roll lessons I came to realize the magic of the fab three—the triple threat.  Novelty, exploration, and structure, I decided were the key to any great end of year lessons.  The result?  Instead of ending my year with guilt and glazed over eyes as I desperately tried to fill in any learning gaps, I was witness to happy, enthusiastic learning.

Novelty tends to be the first item checked off on my teacher-shopping list. When I get excited about a lesson, it is typically because I have found something interesting or unusual to add to it.  In this case, my novelty came from extremely long tubing because I just bought two new rugs and cool tubes were included in the packaging.  As predicted, the cool tubes sparked a ton of interest and drama.  But I’ll save that story for another day.  So, instead of using regularly shaped paper towel tubes we had intriguing sizes and shapes!  In an instant a plain lesson can go bold with the slightest of tweaking.

My second best friend is exploration.  If anything got me sucked into education, it is the art of exploring.  I could watch kids explore all day.  My class’ curiosity about our materials for the lesson mixed with summer fever made it very hard to give instructions on the front end.  Sometimes my strategy is to give freedom and then reign in.  So instead of giving a lengthy set up, I allowed them to create first without a ton of explicit learning expectations.  While I lead one group by digging deep into the heart of the lesson and facilitated, I allowed other students to construct, build, and test.

Equally crucial to a successful lesson at the end of the year, is strong structure.  I saw immediately that I would need to orchestrate a careful plan to make sure that students were learning at high levels.  I used my time working with groups to ask questions, speculate, and clarify any misunderstandings.  I managed switching groups and moving from more structured environments to less based on observing various groups. Then, I reeled everyone back in when I felt like the freedom of discovery had reached its limit.

In the end, not all of my students filled in every box or answered every question for their written portion of the assignment.  Instead, they had meaningful learning.  They had a purpose.  We had rich conversations, involvement, and excitement.  What more can you ask for at the end of the year? 

 

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!

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!