I want you to think about learning math as a child. Did you love it or did you hate it? Did it come naturally to you or did you struggle like so many of our little learners? Now I want you to think about the group of students you have in front of you today. What is math like for them? How many of them get excited about learning math? How many of them dread it?
When I think about my math learning journey, I remember that EVERY time a teacher mentioned the word math, I tensed up. I felt this way all throughout high school. That’s a lot of years being scared of math. For me, math immediately triggered me into knowing I was going to have a hard time. I knew I wasn’t stupid, but math definitely made me feel like I was. Eventually I began to feel like I could never get math and labeled myself as “not a math person”. I shooed it all away. I mastered my basics to function in life and went no further. Until I became a teacher of course. I had to teach kids to understand something I struggled with. Talk about a challenge. I questioned what does it even mean to be a “math person”?
If you have always loved math and deemed yourself this unicorn I call a “math person”, I commend you. It wasn’t until later in life that I realized there was a secret to mastering math. And when you feel like you can do math, you can actually LOVE IT! You too can be a unicorn math person and lover! I have taught first, second, and third grades so I have experienced several different age groups interact with math. I’ve seen how much students need CONCRETE learning when it comes to this subject. With the bulk of my time in first grade, I realized just how crucial it was for those little learners to build a strong foundation for those later grades. Math instruction in your classroom is powerful. It can be the determining factor on how your little learners feel about math for years to come. The power is in using a CRA model. Have you ever heard of this model? It is a process that can easily support ALL students depending on their needs. This makes it SO easy to differentiate for ALL of your students!
The CRA Model
The CRA model breaks down math into three components: Concrete, Representations, and Abstract. This is where the power lies. All students start with concrete practice. As we practice our concrete skills together, THEN drawings, or representations (R) and mental math, or A-abstract, concepts are introduced. With all of these components, not only are students given choices on how to interact with the skill, it also is differentiating for their needs.
I went to a training last year with Graham Fletcher that really opened my eyes on the way we teach math. He talked about giving students the options to use manipulatives (concrete learning) all the way through elementary school, not just in primary grades. He spoke about how schools too quickly push students right through concrete learning into representational concepts or abstract thinking before they are ready. Instead of looking at manipulatives as the concrete part of learning, oftentimes there is an opinion that using manipulatives is too “baby-ish”. But if we don’t allow students the time to learn concretely, how will they ever be ready for more? They won’t be. Students will end up like me. Sitting in math and feeling lost and overwhelmed by numbers.
This model supports students learning themselves. Who knows best on what YOU need to learn? YOU of course! It’s the same with our littles. Students innately know what they need for them to learn- they just have to figure it out. And if they don’t know yet what works best for them, perfect. There is power in struggle. Let them struggle! Maybe a student really wants to create a representation but isn’t quite ready yet. Let them try and struggle with it. I guarantee you they will quickly realize it’s not working for them and they will move back into using those concrete methods to help them. Using this model to construct your math lessons opens it up to be more fun, engaging, while allowing students to feel successful. It gives students the opportunities to see what they need and how best they learn. It also gives us educators a different perspective on how to guide and challenge them where and when they need it.
What It Looks Like
So the components sound great right, but I can’t wait to share with you how to implement it! Think about a skill you teach that you know students struggle with. For example, subtraction, fractions, or multiplying. The first component is to plan out how to make that skill concrete for our learners. Ask yourself, “What type of concrete objects can I use to allow students to manipulate with their hands to understand this skill?”
Let me paint a picture for you using subtraction. When I teach ANY skill, I always start concrete for all my students. Do all of them need it? No, but I offer it to all to start. So imagine we’re getting ready for our subtraction lesson and I explain types of problems we’re going to be solving today. I can see some anxious looks and nervous students in front of me. But then I add in that we’re using manipulatives and I SHOW them the “toys” they get to play with during math. We know kids LOVE to play with manipulatives and it is usually a sad moment for them when they are “no longer needed” in the lesson. So you can picture the excitement of seeing counters, mini erasers, or even food as their manipulatives! So now we have instant engagement PLUS I have begun to eliminate some of those math worries.
I am a HUGE proponent of gradual release (I do, We do, You do) so we follow that model. While going through our lesson I model for students a subtraction equation and show how I can solve it using my manipulatives. I do this a few times while having students notice my strategies that I use and how I check my work. After I’ve modeled for students, now it’s time for US to practice. This is where they get really excited! They get to use their manipulatives and it has taken away so much of the burden of heavy math. This concrete phase is SO important because it gives students a better foundation for those representations and abstract thinking of math to stand on. After we spend time with our concrete stage, I introduce those drawings and mental math strategies. This is where your differentiation comes in. Students are given those choices on how best to begin solving their problems.
When I’m planning out my math lessons and what these components will look like, I like to use the standards from the grade directly above me and below me to see how best to differentiate for students. If students are struggling, I will use the lower grade standards to teach in small groups. If students have already mastered the skill we’re doing, I will look at the higher grade standards to challenge them. But no matter what, we start out concrete before representations and abstract concepts. They are given ample strategies, materials, and proper scaffolding to help them be successful. This is what our math looks like.
I think of the exact time I began to hate math as a child. It was in third grade when we began learning about fractions. I had no idea what was going on and I didn’t feel like anyone cared. If my teacher would have allowed me the time to sit and understand fractions CONCRETELY, using fraction tiles or some sort of manipulative, I would have felt much more successful. Not only have I found TONS of success teaching students this way, but it really hit home when I was able to share this model with a teaching partner of mine. She began planning her math lessons, allowing her students ample time of concrete learning. After a few skills taught, she told me how much better her students performed and she noticed they had less unintentional gaps. However, the real power was when the next school year started. She got all of my first graders in her class for second grade because that was the way our school looped up. She came back to tell me that it was the first time EVER that her group of second graders were truly ready to go right into second grade skills. Those rising first graders really knew their stuff and clearly understood the concepts and she was able go right into second grade skills. It was a great feeling knowing all my babies were math masters. I knew I was doing what was best for my students.
Just like in reading, math builds upon itself. If you can’t understand counting, how will you be able to add? If you can’t subtract, how will you learn to divide? Providing scaffolds for students helps build that foundation and allows students to not only feel successful, but to ENJOY math. Give those babies time to play. Let them touch and manipulate those objects so they can deeply understand what math means. Don’t skip or skimp on concrete learning! I hope you walk away reading this understanding how simple little adjustments can really deepen your students’ understanding. Think about your next skill coming up. Figure out how you can make that concrete for students. What manipulatives can you include to support them? For your students who are ready for representations, think about all the different drawings and strategies you can give them for support. Got students who already have a deep understanding of math? Begin to challenge them abstractly so they can practice using their quick mental strategies. Help them be math people!! Want to learn more about teaching through play? Click HERE!
If you love organization and having binders to help store all your important papers for planning, observation notes, center activities, and more, I’ve got you covered! Grab THIS comprehensive resource that prepares you with all the templates for planning whole groups, small groups, and centers all in one place! Simply print, grab a binder, and start marvelously making math fun!
Do you feel like you would love to know more about transforming your math instruction? I would love to support you while planning! Please email me and let me know where you get stuck! Have different ideas? I would love to hear those too! Coming up, look for how I teach math using math workshop. You’ll also find a how to video walk through of the template in use housed in the free resource library.
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