The Challenge of Change . . .

I recently had an "ah ha" moment in a meeting as we were debriefing a powerful TED Talk by Diana Laufenberg. There is no doubt that teaching is one of the most challenging professions.  Even over the last 15 years, teaching has become much more demanding of our classroom teachers.  It makes me wonder if we as educators are putting more stress on ourselves because it's easier to do things the way we have always done them verses embracing change!

Our society has changed drastically over the years due to technology and the way that we can readily access information. But . . .  when you think about it, "school" really has not changed much from when our own parents attended.   

Take a minute to watch this TED Talk and think about how can we allow students to fail and empower their voice.



We are fortunate that Diana Laufenberg will be part of this year's Leander ISD Continuous Improvement Conference.  I look forward to learning more from her and seeing you all at our 20th annual conference!  

Counting Collections and Giveaway!

Although counting is one of the best ways to help children develop number sense and other important mathematical ideas, we do not do enough of it in elementary schools.

Why should I do counting collections?
Children need many and varied experiences with counting to learn which numbers come next, how this number sequence is related to the objects in front of them, how to keep track of which ones have been counted and which still need to be counted (Fuson 1988).

How do I begin?
It is as easy as placing a large pile of items on the tables and without any further instruction ask the students to begin counting their items!

Once you decide to make counting collections a regular routine in your classroom you will need to start collecting baggies of "stuff." Beans, pom-poms, buttons, cotton balls, rocks.... the sky is the limit!  A walk through a craft store will spark lots of ideas. Parents can donate collections are well. Make sure you have collections of different sizes to meet the students' different needs. You will need a method for the students to record their thinking. Math journals work great!

What does the teacher do as the students are working?
As students work in partners, the teacher is observing, taking anecdotal notes, asking reflective questions, and selecting students to share with the whole group.

Why do the students record their counts?
Most students will begin counting one by one with no strategy for grouping the items. Once the some time has passed, interrupt their counting and ask them a question and then tell them to continue counting. Many students will forget where they were and have to start all over! This is a perfect time to discuss strategies for grouping items and how they will record their counting in their journals.

What does Counting Collections look like in Kindergarten?


Counting Collections: Kindergarten - a common core classroom friendly exercise from Luna Productions on Vimeo.

What does Counting Collections look like in the older grades?


Counting Collections: Third Grade - a common core classroom friendly exercise from Luna Productions on Vimeo.

Are Counting Collections part of your math instruction?
Try backwards Counting Collections; You give the number and they make the collection!

Counting is fundamental to so many things we do in mathematics.  
Build their COUNTING POWER!!

To learn more read this article:
Counting Collections by Julie Kern Schwerdtfeger and Angela Chan in Teaching Children Mathematics / March 2007

For Leander ISD employees: To be eligible to win this amazing Counting Collections Starter Kit, add a comment below on how you would use this in your classroom. We will put all entries into the randomizer on Tuesday, January 29, 2013 @ 4 p.m.

We have a winner!  Heather Moseley from Bagdad Elementary - Congratulations. We hope you enjoy this amazing Counting Collections Starter Kit.  The contest is now over, but we hope everyone keeps on "counting!" 

Birds On A "Number" Line

What do you see?  

Call me crazy or math nerdy but I see a number line!

The traditional number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point.

In contrast to a traditional number line, an "open" number line is just an empty line that can be used to record children's addition and subtraction strategies. Only the numbers children use are recorded and the addition or subtraction is recorded as leaps or jumps.

Here are some examples of open number lines:

This example shows a student using incremental strategies. This means adding up in "chunks" or increments. One benefit is the students decide the "chunks" depending on the number choices.

This example shows a student using compensation. This means they add or subtract to adjust a number to make it friendly, solve the problem, and then readjust to find the solution.

This example shows a student a counting up for a subtraction problem. Look at the place value the student uses to compose and decompose the numbers.

Aren't open number lines awesome?  What a great way to model thinking!

So how do the birds on a line remind me of a number line? The birds just alway seem to be evenly spaced on the line so it just got me thinking about number lines!

Here is a problem to ask your students:

Name points A, B, C and D on the number line.  Justify your solution.

The next time you see birds just hanging out on the lines, I dare you not to think of a number line!

Can you think of any other real-life objects that remind you of number lines?

Happy Holidays!

From the Elementary Math Team ~
Wishing you and your families a very "Mathy" Holiday! 

As we take the next couple of weeks off to spend time with our families, friends and loved ones, we hope you will continue to find the math in all your Holiday FUN!!

            Yummy 4x3 array of
ham and cheese holiday sandwiches!

Holiday cake balls and pretzels!
What array(s) do you see?
How many treats are on this tray?

We would love for you to tweet us your favorite holiday math photos @lisdelemmath

Best wishes for a fabulous NEW YEAR! 

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 Powerful Array

How many meatballs do you see?

How many do you see now?

See how arrays are so powerful?

An array is a systematic arrangement of objects. This model is as important to multiplication and division as the number line model is to addition and subtraction. The visual representation of rows and columns helps students as they develop their proportional reasoning. Like the part/whole box for addition and subtraction, the array identifies the parts (factors) and the whole (total area of product) and can be used to demonstrate and prove student strategies. (Number Talks, Helping Children Build Mental Math and Computation Strategies)

As student move on beyond the basic multiplication and division facts, the array can model and prove partial products which is also called the distributive property. Students build arrays with color tiles, base-ten materials, or on grid paper.

Look at the array below. How many different ways can you find the answer to 8 x 25?

Here are just a few different ways that can be proved by cutting or folding the array.

Halving and Doubling:
(4 x 25) x 2
Four 25s equals 100 (think money) and double it you get 200.

Partial Products:
(8 x 20) + (8 x 5)
Eight times 20 is 160 and 8 times 5 is 40. 160 + 40 = 200

Using Multiples of 10:
(8 x 10) + (8 x 10) + (8 x 5)
80 + 80 + 40 equals 200

Here is an example of how base-ten materials can be used to build a 24 x 36 array. How would you count this?

Click here for a GREAT lesson:
So Many Ways to Separate Arrays

Now, share how you use arrays!

Guest Blog: Transforming Math Homework

About a week or so ago, Rayla Rucker, a fourth grade teacher at Pleasant Hill Elementary, asked me what I thought about some math homework she created for her class. As I opened the Google Doc, my eyes got huge and my heart jumped out of my chest. It was the best homework I have ever seen in math! So, I asked and Rayla agreed that she would share her thoughts on homework as our guest blogger this week! Thank you, Rayla, for inspiring us all as you do what's best for your students.

Homework.
There isn’t another word in the English language that elicits more dread.  Kids don’t want it, parents either want more or less of it, and teachers (myself at least) don’t have time to grade it…so, usually it is a meaningless endeavor that no one is happy about.  I mean, sure, there will always be student’s that have it in your hand before it’s due, but there will also be kids that never, EVER turn it in no matter how many times you call or email.  

So, how did I get all my kids and a lot of my parents (I can only speak for the ones that have tweeted or emailed about it) excited about math homework???

It all started with a tweet.

If you talk to Mark Koller, my principal, about me,  he’ll probably joke and say...”Be careful, she’ll tweet about you!”  because he knows I have gone a little twitter crazy.  The above tweet was one of my first with a real life problem solving idea.  I thought, how can I make kids and parents see that math isn’t just something you do for 75 minutes a day 5 days a week?

And then this happened,

and I thought, “Well that’s pretty awesome! Maybe I’m on the right track.”

This was just the beginning of a shift in thinking about what math is, or can be, or maybe should be.

I have a student that just can’t stand math.  He rushes through worksheet assignments and turns them in without a second glance with an abysmal degree of success. One day he was done, and I was meeting with a group and I just could not get him to settle.  I was irritated.  So, I called him up, handed him one of those catalogues we all get, full of junk to buy for our  classrooms. I said, “Hey, Johnny (names changed to protect the innocent),  I have $50 to spend on the classroom store.  Can you take this catalogue and see how much we can get?  I want the most and best for the money. Write down the items, how many we’ll receive, and the total spent and give it back to me.”  Well imagine my shock when he spent a couple of days quietly studying,  adding, subtracting, multiplying, and dividing whole numbers and decimals.  He was doing a whole lot of math without even realizing it.   A reluctant student was all over it, AND the math was correct.  The difference in real life, she’s going to order these things for our classroom, let me help...and ugh, another boring worksheet, was definitely apparent.  

Obviously, that made me realize that maybe, just maybe math worksheets weren’t the way to go.  Honestly, I have never been a fan of worksheets, but in math especially, I saw the benefit of extra practice.  It’s weird because in Language Arts I have always been a stickler about keeping everything authentic, so why the disconnect in math.  Can math be authentic?  What would that look like? That’s when I met Beth Chinderle.  

Beth sat down with my team, answered our questions, and helped me understand what authentic math could look like.  The best part was she gave me permission to cut out the worksheets for homework.  I don’t know why I needed that permission, but I did.  From there, my brain was really on fire with the possibilities.  One night, I was sitting at the computer and it came to me.  I created a choice board revolving around what families and kids actually do in their everyday lives that will allow them to practice the specific skills we are exploring and learning in class.  They can see from these choices that math is a skill, like reading that they will do all of their lives, and can be enjoyable.  

So, I tweeted about it, sent an email about the change, and nervously brought it to my students.  I guess the nervousness came from my excitement, I mean, what if they hated it?  They gave me that familiar, what are you up to now glance and looked it over.  I went through the choices with them and they were totally digging it.  

Now, I have been teaching long enough to know that the initial excitement can dwindle when the task has to actually be accomplished, but to my surprise the next day when I asked how many of them had done their homework, over half raised their hands.  On Friday, homework was due, and every single kiddo was excited to share what they had done.  Many of them had completed 2, 3, or 4 of the tasks.  They were only asked to do one for the week.  Several even asked if they could submit ideas for the next time!  

This change in homework is part of an even bigger, and much scarier transformation of my math class.  Scarier because it’s not what I am used to, but maybe it’s just what I, and more importantly my students need.  So, I am happy, proud of my kiddos, and a little proud of myself, too.  To me, students are like play dough, they roll and bend with the changes easily.  Most teachers, though, are more like that really hard modeling clay.  We can and will change, but it takes a lot more work to get us warmed up enough to shift in a new direction.

Check out the homework here: Rayla's Real Life Math Homework

Thank you again, Rayla, for sharing your journey! :) I've also added this post to the Math Classroom Series as an important element of the math classroom.