Math is Messy!

Today I filled in for a teacher who had to be out suddenly. It was so exciting! I’ve been coaching now for several months and I was anxious to slip back into teacher mode.

These were fourth graders who had been introduced to the distributive property the day before. The teacher was looking for something to both review and solidify their knowledge. I decided to try to connect their past experiences with multiplication to their new thinking from the day before. I wanted it to be a little messy!

The learning target:

I can solve multiplication sentences in more than one way.

I had the students rate themselves based on this success criteria:

0: “What is multiplication?”
1: “I’ve heard the word multiplication before but I do not have any strategies to solve it without help.”
2: “I can memorize facts, but I still don’t know what multiplication really looks like.”
3:  “I have more than one strategy to solve a multiplication sentence like 6 x 8: number lines, equal groups, repeated addition, etc.”
4:  “I can apply what I know for strategies to harder problems, like 16 x 8.”

Then, I put them in groups to solve the following two facts as many ways as they could on giant paper…6×8 and 17×5. The results were remarkable, AND messy!

Math is messy!

One student wanted a new paper, but I explained that mistakes feel kind of awesome. We should expect to make mistakes and try again, it is all about perseverance.

This messiness reflected the thinking of the students. I had to suppress the urge to organize their thinking into my own pretty little anchor chart. I had to remind myself that this wasn’t about an anchor chart, it was about letting the students know that math is messy and that they could learn from each other’s thinking.

After giving them about 10 minutes, it was time to share. We rated ourselves against the success criteria to see where each group was. Then, I asked them to think about which strategy was most efficient on their poster.  They laughed pretty hard about the inefficiency of drawing 85 circles/tallies.

Here were some of the favorite efficient strategies that students shared:

A nice notation of the distributive property, where the student broke the 17 into 10 and 7.

Classic repeated addition (bottom), and another way to note the distributive property on the top.

This person used the distributive property, but broke the 17 into 8 and 9! Very cool. I also appreciated how they showed their thinking below the number sentence.

My personal favorite was this one:

He broke the 10 into two fives! That is someone who really understands what he is doing.

It was wonderful to get them talking and sharing.  The person doing the talking is the person doing the learning!

 

When Things Go Horribly Wrong

There is a silent stress inside teachers, no matter how long you’ve been teaching.  I know you’ve felt it, and I know you’ve even seen it.  There are many times you feel alone.  Things are starting to go wrong in your classroom, and you desperately try everything to fix it. You are looking at your math lesson for the day and you can’t even begin to understand the best way to teach it.  Things go so horribly wrong that it brings you to tears and you feel stupid, embarrassed and frustrated. I saw it today in a new teacher’s eyes and it broke my heart.

I wonder why it is this way.  Don’t get me wrong, it’s great to problem solve and figure out things on our own.  But so often I notice teachers struggle with things until it gets so bad that they finally reach out for help, and feel embarrassment and apologetic in the process.  Why is it so shameful to ask for help?

With the demands on us as professionals in this day and age, we can no longer do it alone. Collaboration among teachers, teammates and support staff needs to become embedded so deeply that it is okay for anyone to seek help.  We should go about our day more slowly, and a bit more kindly to ask others what they need. Instead of cutting out that last little laminated magnet star to put up on your locker to make it look cute, ask the new teacher next door if they are ready for their math workshop set up.

Let’s promote a culture of asking and receiving in our schools.  Our students deserve it.

 

A Math Book to Change Your Teaching

This is a funny title for a post because I have to say that this math book hasn’t “changed” my teaching exactly, but it has opened my eyes to how we can simplify our teaching.

I’m reading Building Mathematical Comprehension: Using Literacy Strategies to Make Meaning by Laney Sammons. I chose to read this book because with all the demands in our teaching profession, I was seeking a way to simplify things.  We cannot get everything done in a day, a week or even in a school year, so I keep thinking that there has to be a way to integrate things so that we aren’t going crazy every day.

Now literacy and math are not the same. But they have similarities, check this out:

 

The entire book focuses on ways to use literacy strategies in math.  And when you read it, you’ll be thinking “Oh my gosh! This just makes sense!”

One thing I’m going to try this year as a math coach, is to model some problem solving lessons in classrooms. In this book she talks about using comprehension strategies before, during and after solving a problem. Since math truly is all about problem solving, I’m envisioning an anchor chart adapted from my reading (pg. 35-38). I think as we work through problems, it may help students get “unstuck”.  It’ll look something like this:

I say that it’ll look “something” like this, because I want to come up with the anchor chart WITH the students. I think doing a problem as a whole class (and using a think-aloud strategy) would help them see the kind of thinking that should be going on in your mind while problem solving.

This book has even more literacy strategies that you can use in your math classroom.  Using some of the same vocabulary in your math and literacy blocks can help students make great connections!

To win a copy of this book, you will have to enter by clicking the link below.

There are a bunch of us talking about great books that have changed our teaching, so don’t forget to check out Mr. Elementary Math’s book, he is next in this blog hop.

 

What Does Success Look Like?

Pretend with me for a moment, that you have never seen an apple before in your life. Now pretend that someone has asked you to peel it, but you’ve also never peeled anything before in your life.  How do you know what to do to be successful? How will you know when you have been successful?

That in a nutshell is what “success criteria” is.  It’s all about letting students know what success looks like, and how they will know that they have met the learning target.

In my mission to examine learning targets and communicate them, I learned that it wasn’t enough to simply display them for students. It STILL wasn’t enough for students to write them in their math journals.  My students needed to see the learning target, write it, and then have some sort of interaction with it.  This is where I combine this idea of success criteria (Hattie 2012) with Marzano’s Levels of Understanding.

Here is an example of what this can look like.  You begin your content lesson by reading the learning target out loud, allowing students time to write it down in a math journal (or some other place to take notes). Notice the learning target starts with “I can”.  (It would be just like saying, I can peel an apple.)

I can read and write numbers up to 1,000.

Now some students will have prior knowledge about the learning target, so allowing them a moment to interact and think about this learning target is essential.  You can show them (or you can do this orally) what the different levels of understanding look like. Here is what it could be for this particular learning target:

Using success criteria in the classroom can help students understand the outcome of their learning.

I use Marzano’s Levels of Understanding to anchor my thinking (which I blew up and posted on the wall-this is a free resource by the way!) because the students connect easily to the language.  After I show them what each level looks like, I have the students rate themselves on the current target. Their goal is always the same every day, get to the next level, get higher and get better.

After this mini intro, I teach the lesson. We practice with tiered examples so that everyone is challenged, we talk it through with each other, we help each other come to an understanding.  We break into independent practice work where I can catch the students who still feel like a 1 or 2.  Then we close the lesson with an exit slip or an assignment, rating ourselves once again to see where we fall on the scale.  I take a look at what they wrote for their final rating and catch those students during the review, intervention block or some recess time the next day.

This seems like a lot of work, and I won’t lie that at first it was for me. It was a different way of thinking.  But soon after I started to do this, I noticed that it was easier and easier to think about what a 0-4 looks like.  If I ever skipped the rating part, my students would actually shout at me “What does a 3 look like?!” They wanted to know what it would take to be successful! It was very powerful.  You may not have time to write it out like this for every lesson, but you can do it orally while referring to the levels on the wall.

This tweak to my instruction was a total game changer.  Thank you John Hattie and Robert Marzano for your inspiration!

 

Build A Strong Math Culture With The Standards For Math Practice

With all of the current criticism about the CCSS and “Common Core Math” (I put that in quotes because that phrase has been driving me crazy, now that is another blog post in my mind), I’ve been happy to see that the Standards for Mathematical Practice have been left alone.

I’m glad that they’ve been left alone in the criticism because the Math Practice Standards are all encompassing thinking habits, more than they are standards to be met.  They encourage us to teach mathematics more as a learning subject than a performance based subject. Math absolutely should require lots of messy critical thinking, deduction, discussion and reasoning.

Someone last year said/asked me, “I just don’t understand what these standards are for.  What are they?” I explained them the best way I could, since I had just spent a month researching them to know them better:

1. The math practice standards are a set of math habits, ways in which we should think about math. (That sounds so simple, but the way the standards are worded, it has driven many of us crazy while trying to understand them.  Reason abstractly and quantitatively? Huh?  It sounds like a completely different language!) The standards are all about developing positive habits and attitudes about math.
2. They allow students to explore math as a learning subject.  They begin to understand that math is not about the teaching asking a question, and the student must answer it correctly. Most importantly they begin to see the connection to their lives.  Math connects so beautifully to real life, but because the U.S. has such a worksheet culture, we’ve lost that connection.
3. Math from K-12 has the same underlying theme with these standards. As the years tick by the content standards become more complex, but the practice standards remain the same.  With the Standards for Mathematical Practice, we can develop a very positive culture surrounding mathematics.  A culture of persevering when encountering a problem, making sense of the world with math, using prior knowledge to solve new problems, being precise and reflective, patterning to find faster ways of working, explaining our thinking, understanding others thinking, knowing what tools will best help to solve problems, and connecting the world with abstract numbers and symbols. This all makes us excellent THINKERS.

We’ve had math coaches, administrators and other teachers pass out posters to put up in our classrooms. We’ve seen freebies and posters that we are meant to download and print. We’ve put them up on our walls with very few of us digging in to what they actually mean. I WAS one of those people. I had a poster of the kid friendly standards up for two years, and it wasn’t until last year that I realized one of the standards was completely inaccurate on the poster.  I had never bothered to check, and I assumed that the source knew the standards.  Can you blame me? I didn’t have the TIME to dissect what each one means.  It felt like another thing…another plate to spin…another added responsibility. I truly didn’t understand the importance of the standards to create a culture.

When I decided to figure out what they really mean, introduce them to my students from the start of the school year, work through the problems with them, and embed the language in the classroom, the culture really changed. We became mathematicians who could work through anything. It was remarkable. We put our work on the walls to help remind us that these were to be a part of our classroom daily.  We truly became vicious problem solvers, we worked together and math was about learning.  Math became FUN.

After a month of research I created posters, problems and activities to help myself understand them, but also to help teachers understand them, too.  (Feel free to check out the preview which walks you through the first standard.)

Build a culture by introducing, working with and revisiting the Standards for Math Practice.

Even if the Common Core goes away (which it most certainly will, and already is in many states), I will always keep the Standards for Mathematical Practice.  It is a foundation in which we can all build upon, year after year!

 

You are NOT Bad at Math

Did you know that there is not a “math gene” that makes us good at math? If you haven’t read this yet: Why Do Americans Stink at Math? I would highly suggest taking the time to read.  The long and short of it, is that during the industrial revolution, we took the fast track and tried to teach math the fastest way possible.  We taught shortcuts instead of conceptual understanding.  This method of teaching allowed our students to go directly from their education into a factory job, but it did a great disservice to a generation.  This is why people believe that they are “bad at math”.

The world has changed and we can no longer do this to our students, but according to the article above we still are.  Despite many attempts at changing our math practices, we still find the majority of U.S. teachers using traditional methods. Of students attending 2 year colleges, 60% of them are placed in remedial math classes, and only 25% of those students pass those classes! (Silva & White, 2013)

I would strongly recommend that you watch this video by Jo Boaler, of Stanford University. It is 20 minutes long, so if you can’t watch it all, try the first 8 minutes.  In it she talks about how we need to make math a learning subject (exploratory, messy, open ended and challenging), not a performance based subject (math is only about answering questions correctly).

To return math to being a learning subject, we can use rich open ended tasks, inquiry activities, real world projects and problems that encourage math talk and discourse!  Please check out my free Reasoning Puzzle Set to try out an activity that will really get your students thinking and talking and most importantly, learning at high levels.

Reasoning Puzzles to promote student to student math talk.

These are most appropriate for 3 and 4th graders, but even could be beneficial for fifth graders that are not used to thinking this way!  If you end up using them, I’d love to hear how it goes.

Writing Clear Learning Targets in Elementary Math

If you missed it, I’ve already lamented about my lack of organization with learning targets. When I started to rethink this whole learning target thing, I knew that teaching in isolation was no longer going to work. This happened to be the same year that we had a new teacher join our six person team. Her joining this team started a transformation, we realized that we should be planning together, and even though our learning targets might be the same, we’d still have our own spin on how we taught it.

So we started with math, because math learning targets seemed manageable. We also started with our text as a resource.  We already had a curriculum/pacing guide set up, but it happened to align with the textbook, and it had been written almost a decade ago.  So we looked at both learning targets, and the pacing of our content at the same time.  It was not easy, but it was some of the best math conversation I’ve ever had with other staff members.

We transformed our learning targets little by little. We did the first unit together, then we split up and trusted one another to do future units.  It was amazing. Our learning targets went from complicated and confusing, to clear and concise.  Most importantly, they became student friendly.

Here is an example:

We took the long and wordy objective from the book, and converted it to what the student must absolutely be able to do.

What was listed in the book was wordy, long and full of teacher noise.  In this case, this is a HUGE objective, writing and reading numbers that are both 3 and 4 digits, especially when written in various ways (standard form, word form and expanded form). We asked ourselves 2 questions to narrow it down.

1. What is it that the student must absolutely learn? (What is essential for the next grade level?)
2. What does the student need to be able to DO as the END goal?

This original learning target:

Students will read and write 3-digit and 4-digit numbers using place value understanding.  Students will use expanded, standard, and word form when working with numbers.

Became the following two targets for two days of instruction:

I can read and write numbers up to 1,000.

I can read and write numbers up to 10,000.

We used this common assessment at the start, middle, and end to find out what they already knew: Number of the Day Quick Check (FREE!)

I will not lie, the process was a little hairy to start. Many of us struggled with the rest of the objective…why aren’t the various forms of numbers included in the target? Why don’t we use the words place value in the new targets? We came to the realization that all of THAT comes into play during your instruction.  Students find out those words as you play with and explore the numbers.  In addition, teachers give them success criteria so that they know what it means to read and write numbers up to 1,000. Once we had that understanding, it became easier and easier to write clear learning targets.

Stay tuned for more on success criteria in my next post.