I think I’ve discovered the number one problem in just about every math classroom. It’s a problem that I see over and over in every math classroom. Students that struggle and students that excel have this problem. They tend to look only at numbers, not thinking about what they represent. They try to memorize vocabulary without connecting those words to anything in their life. We race through math curriculum teaching quickly because we have to get through SO MUCH CONTENT. With standards and interventions and assessments to give, we don’t have time to think about what the numbers and vocabulary mean.
So we have to sneak it in.
We need to make math real all day. Not in some silly contrived way, but to make our thinking known as we notice math throughout the day. Take this example of real life geometry:
When we connect these terms to their real life, they begin to sink in, and you don’t have to write some fancy lesson for it. When they open their pencil box, their desk, their books we can mention these words and bring the vocabulary into the front of their minds.
When we have two packs of gum, let’s connect it to numbers. Do we have enough for the whole class? Is there another way I can write that number sentence?
If you think about it, we read all day long, we write all day long…let’s make an effort to bring mathematics forward all day long!
So this is my WORST habit. When a child doesn’t understand something, I pick up their pencil and start explaining. Bah! It’s my immediate go to strategy because the solution path is clear in MY mind.
Why is picking up a child’s pencil a terrible idea?
- Some parts of the thinking may be clear in their mind, and I’ve just muddled it now with my own strategy.
- After several times of picking up their pencil they may believe they need to wait for me for the next time they struggle, can you say learned helplessness?
- I do think that from the moment you pick up their pencil, they check out and stop thinking…some students even feel like they’ve given up.
3 ways to combat this and develop perseverance:
- Model the struggle. Over and over and over and over. Every day model the struggle yourself. Screw up, get stuck and talk out loud about how you get unstuck.Kids who struggle have no idea how to work through that inner dialogue that comes with digging yourself out of struggle. Have other students share their struggles in front of the rest of the class if they are brave enough. Make struggle and mistakes a normal and wonderful part of your math culture. I mean really…if you make a mistake when you read a word, you can still read. When you make a mistake in math, you can still do math!
- Promote positive self talk. We need this in all parts of our day, but the recent studies on Mindset really truly are RIGHT ON. When you hear a student say something really positive, capture it and repeat it.
- Give kids as many opportunities as possible to see each others work. Right after they solve for a minute, ask them to slide their papers together to compare each other and look for similarities and connections. When they start to see more thinking, they start to make more connections, giving them ideas for how to get “unstuck”. We have the luxury of walking around to see all of their thinking, so let them have that same experience.
In what ways are you putting down the pencil?
A third grade teacher I was working with was feeling anxious about differentiation, as we all do. It’s a constant worry for teachers, and I’ve been on a mission the last few years to find small ways to differentiate in the classroom.
I’ve come to realize that rigor comes hand in hand with differentiation. That often times even my own daughter, who has been identified as a gifted and talented student, has not learned mathematics deeply. She can do some amazing calculations, but when asked to go deeper she isn’t always thinking deeper. And neither were these 3rd graders, or most students that I meet on a daily basis.
Enter our math challenge. We decided that rigor can mean understanding the complexity of something…not harder, more and not even always something different. Differentiation can simply mean deeper. So we chose ONE problem from the assignment that the students were working on and asked them to do this on the back of their paper:
We were pretty surprised with what happened. They could build it with tools, they could make visual models, but not ONE student could do either a real life story or tell us how it works. Their stories were muddled, didn’t make sense or were missing information.
So, for the next few weeks, we put an emphasis on the story. Every day we picked one problem and had them all write a story about it. This story was shared then to the rest of the class to help the rest of the students become better. And it worked, more and more students were able to match the equation with a real life situation (hello math practice standard #2!).
This is a great small step for differentiation because of the open ended nature of the two prompts on the right side of the poster. After a few days, students started asking very cool questions. They were talking about why we regroup when there is 10 of something. Why not 7? Why not 9? It led to much deeper conversations with our gifted students as well as elevating others.
EVERYONE had access to this rigor. EVERYONE is learning. EVERYONE is going deeper, not just your gifted students.
Don’t tell my principal, but at the last staff meeting I wasn’t perfectly focused on everything he said. For a few minutes I was thinking about all the stuff I had to do at work, about how I needed to mow my lawn REAL bad since it was looking like a jungle out there, and how I couldn’t wait to see my daughter.
Imagine if I was 30 years younger and had an even smaller attention span, a need to move in my seat more and unclear expectations of what I was supposed to be doing. Maybe this doesn’t happen in your classroom with your students, but it happens in mine. And basically to every teacher I ever talk to. So let’s all just assume that this is a common problem, right?
So while we won’t eliminate this problem, we can certainly reign it in a bit. With crystal clear expectations laid out for our students, and an added bonus of posting their photos we start to see some changes. When you’ve been on video or see yourself in a photo, do you find yourself immediately analyzing every bit of it? You’re looking at your messed up hair, you’re thinking about what you are wearing, thinking about what you are doing in the video or the photo. So…we can do that with kids, but instead of making them look for what they AREN’T doing, we can catch them for what they SHOULD be doing.
I tried this first in a second grade classroom. I told them that I was going to be looking for students that were on task and showing the behaviors that we all agreed upon in workshop expectations. Then I explained that I would be getting my mobile device out to take photos of them doing these things. I told them I would use the photos to make something special. Suddenly they sat up straighter, got immediately to work, and were perfect tiny little angels. For real. Angelic.
So here is the special thing I made them:
I looked at each part of the teacher’s workshop and about what the students needed to look like to be successful. I targeted my photos to be able to show them exactly what they look like when on task. When the expectations were crystal clear, and they were in the photos…that’s when we started to see more focused behaviors.
I believe this can be adapted to any grade level. Children love to be validated and honored for doing great work. I think that we all do in some way or another. This gives them great recognition for being on task, with the added benefit of reinforcing your math workshop expectations.
Yes, I know. The R word. Ugh. I’m only starting to hate it because it sounds like a buzz word that you hear over and over, yet it’s like some kind of mystery to classroom teachers.
When I began teaching I thought that raising the rigor in my math classroom meant using bigger numbers, more problems, or homework projects.
And the kids hated it. They didn’t feel energized or motivated in math. They felt bogged down and I pretty much sucked all the joy out of their little faces.
Nice going Ms. Smith.
Instead now I know that rigor has a different definition. It might mean solving open ended problems, finding multiple solutions, connecting math to real life situations, using visual models, and thinking deeper instead of faster. And I’ve realized that sometimes rigor can be injected in very simple ways. Take this example (used in a second grade classroom early in the year):
This is really quite a simple idea, and almost any number (or number sentence!) could be put in there to adapt it to any grade level. Notice how open ended it is? The teacher is not telling them to use: tallies, ten frames or cubes. We started with 10 to show the routine and the process, allowing them to find more and more ways and share their thinking. Students are given a number and need to think of how many ways to build it and show representations of it. The beauty is they begin to see the need for shortcuts in math more naturally. It doesn’t make sense to show the number 110 with 110 individual cubes, we can group them into packs (rods/sticks..whatever you call them) of 10 or 100!
The more students can use tools and visuals, the stronger their mathematical thinking will become!
That’s the question I would dread the most during math class…
“Mrs. Smith, what do I do when I’m done?”
In the early days I didn’t have any clue what to do with students when they were finished with their work. During Readers Workshop, they could read. What could they do when they were done with their work in math? Fact fluency games were a great option, but I wanted fact fluency instruction and game time for all students. What could I do with these early finishers that would be engaging?
Enter deep math tasks. There are so many out there that it can be overwhelming to try to find them. But my favorite math tasks I find for free at Youcubed.org. Here is just one example called Nine Colors that can work for just about any age. It can be a station in your math centers, or it can be a challenge that is open for those who finish early.
This is what we call a “low floor high ceiling task”. This means that anyone can attempt it, but it’s challenging and rigorous for any student.
You can find this one and much more at Youcubed.org!
I am so thrilled that Laura Candler asked me to guest post over at her blog Corkboard Connections. I’m a long time reader of her blog and feel so honored!
In my post I talk about my favorite group work strategy to help elevate all students in your math class. Click the photo below to read more!