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: 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.

Problem-Solving Sharing: Whole Group Area

This week we are excited to add another element to the Math Classroom Challenge on Problem-Solving Sharing. Thinking of classroom space, it is essential to designate a large area of the classroom where students can come together and become mathematicians in a real mathematical community. Take a look at these pictures of Sandy Handrick's 5th grade classroom:

Sandy has a large area for these young mathematicians to come share ideas and strategies that emerge as students do the math and teachers facilitate discussions. Notice that she even has ample space on her white board for student sharing.

What is problem solving?
Problem solving is a process of inquiry where students are investigating mathematical and real-word situations. This could be in the form of a specific problem type in which careful number choices are selected to bring out mathematical relationships, or it could be a problem in which students are applying their mathematical thinking to an authentic, real-life situation such as problem-based learning or performance tasks. Problem solving is NOT giving the students a problem and telling them a certain operation to use and how to solve it step by step. If that's happening, who's doing the problem solving?

How often should students be problem solving?
Every day! Students should have the opportunity to solve a variety of problem types and real-world problems in which they can explore and investigate mathematical relationships. Problem solving every day is critical for a successful math community. For example, if students only have the opportunity to problem solve once a week such as every Friday, that is less than 36 times a school year that they will problem solve. That's not enough! Think of mathematical thinking like a muscle that students must exercise. It takes time and practice for that muscle to get stronger. Making a connection with reading, do you only have your students read once a week and expect fluent readers?

I have so many TEKS to teach, how do I fit in problem solving every day?
One of the biggest misconceptions in mathematics is that skills must be taught in isolation. This is just not true! Our math standards (TEKS) are connected in so many ways. When we only focus on one TEKS or skill in a day or week, this creates a misunderstanding in our students that skills are not connected. One good problem can encompass many TEKS.

How should students share their thinking?
This can be done in many ways! Here are a few examples:

1. Select 2 or 3 students to share to the whole group: We've all had the whole group sharing time where students aren't paying attention. Usually, this is because we select students to randomly share, students don't understand the learning goals, and therefore, they do not make any connections between the student who just shared their strategy and their own ideas about math. Good whole group sharing should only take 5-10 minutes and be focused around a clear instructional goal. Ask yourself, "What is my purpose for these students sharing?" Do you want focus on a big idea, connections between different solutions and strategies, or moving students from less efficient to more efficient strategies?

2. Partner Share: Partner students based on their levels of understanding. Partner a low with a medium and a medium with a high. Be flexible! As students grow in their understanding toward different concepts, partners will need to be changed. The main point here, is if you want to get the most out of sharing time, students should not be partnered randomly.

3. Gallery Walk: Have about half of the students post their strategies so they are visible. This could be done by writing on a chart paper, simply leaving their journal open, or using technology such as the "Show Me" app on the iPad. These students stand by their strategy as the other students walk around and talk, ask questions, collaborate, prove and communicate their thinking to one another. The next day, students can switch roles.

Where do I get problems?
Luckily, LISD's math curriculum is rich with examples of problem types and performance tasks to support this area of instruction. We have several problems and a performance task for each Unit of Study. Please remember that these are problem suggestions and we encourage you to tailor them to fit your student's interest and appropriate number choice.

We would love to hear your questions about this topic! Please share with us your thoughts! Happy problem solving!

The Math Classroom Challenge

Close your eyes and try to picture the perfect math classroom. Walk in the room. What does it look like? What does it sound like? What does it feel like?

Now, take a look at these two classrooms. After a quick glance at the two, is there a classroom you would prefer to learn in?

Did you know that classroom environment does affect instruction?

This summer, I recently presented a mini-conference called, 'Rate My Space.' In this half day session, we explored many necessities that every math class should include. Over the next few weeks, I will be blogging about these different elements of the math classroom. Let's call it the 'Math Classroom Challenge!' I encourage you to take the "Challenge" and try to rev up your classroom environment for this new school year! On the right-hand side of this blog, I made a button that you could grab and post on your blog. :)

By thinking about how space is used in our classrooms, we have to think about instructional priorities. Ask yourself, "What type of teaching am I going to do this year and what kind of space am I going to need to meet my instructional priorities?"

Here are the beginning topics and classroom spaces that I will discuss because I believe they should be instructional priorities in the math classroom:
1. Math Vocabulary: Math Word Wall
2. Problem-Solving: Math Manipulative Storage
3. Problem-Solving Sharing: Whole Group Area
4. Small Group Instruction: Small Group Area
5. Math Work Stations: System for Work Stations
6. Transforming Math Homework
7. Number Talks

In following posts, I am going to elaborate on each item and give some helpful tips in how to implement them into your own classroom. Real classroom pictures and examples will be included. There is no reason to reinvent the wheel when so many teachers are doing amazing things!

My hope would be for you to consider these areas in your own classroom. Would they work? Why or why not? 

Let's change the space in our rooms to create a structure of teaching that can open up opportunities to involve students in the learning. As Debbie Diller says, "when we model for students on how to create organized spaces, we will help them as learners over the years, too!" Please join me in taking the math classroom challenge!

<a href="http://lisdelemmath.blogspot.com/" target="_blank"><img alt="LISD Elementary Math" src="http://i1066.photobucket.com/albums/u408/Beth_Chinderle/00d1ecfd.jpg"/></a>

Don't forget to grab a button for your blog!

Is It All About The Answer?

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SLOW DOWN and enjoy the math!  

The first goal in math should be the mathematics learned.  So let’s slow down, because it's NOT all about the answer.  

What can we do as educators to make it more about the process, the reasoning, the thinking, and the common sense of math? 

Your students will take your lead! 

Make it your mission to give your students the opportunity to talk, process with each other and share different strategies. 

There is much to be learned from the “wrong answer”.  Are we taking advantage of those “just in time” teaching moments? 

Here in Leander ISD, we believe in the fail forward philosophy.  Let’s live that philosophy in our math classrooms and let the children experience learning from analyzing their work and growing mathematically from the mistakes that occur.   

Take a look at how one teacher is capitalizing on this very idea . . .

This idea could also be used as an exit ticket . . . really the possibilities are endless!