Concrete learning is a game-changer when teaching math to little learners. By using hands-on tools and real-world examples, students can grasp abstract concepts more easily. In this blog, we’ll explore why concrete learning is crucial in building a solid math foundation and how it helps students thrive in the classroom.
Why Concrete Learning is So Important
I want you to think about your experience learning math as a child. Did you love it, or did you dread it? Did it come naturally to you, or did you struggle like many of our little learners do? Now, think about the students you have today. How many of them are excited about math, and how many of them dread it?
Personally, I remember tensing up every time a teacher mentioned math. Throughout high school, I felt immediate anxiety whenever math was involved. It wasn’t that I thought I was unintelligent, but math made me feel that way. I began to label myself as “not a math person” and avoided it altogether. I mastered the basics to get through life and didn’t push further—until I became a teacher. Suddenly, I had to teach something I had struggled with. That’s when I began to question: What does it even mean to be a “math person”?
If you’ve always loved math and consider yourself a “math person,” I commend you. I realized later in life that the secret to loving math is confidence. When students feel confident in their math abilities, they begin to love it too. Having taught first through third grade, I’ve seen the importance of concrete learning for young students. Especially in first grade, building a solid foundation is key to long-term success.
Math instruction in your classroom has the power to shape how students feel about math for years to come. The key is using a CRA (Concrete-Representational-Abstract) model, which supports students by meeting them where they are in their learning. This model makes it easy to differentiate instruction and cater to the needs of all your students, giving everyone the tools to thrive in math!
The CRA Model and Concrete Learning
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 encourages students to take charge of their own learning. After all, who knows best what they need? They do! The same goes for our little learners. Students naturally understand what helps them learn—they just need the opportunity to figure it out. And if they don’t know yet, that’s great! There’s power in struggle. Let them struggle! If a student tries to create a representation but isn’t quite ready, let them attempt it. They’ll quickly realize it’s not working and go back to using concrete methods for support. This approach makes math lessons more fun and engaging while giving students the chance to feel successful. It helps them discover what learning strategies work best for them. Plus, it gives educators a fresh perspective on how to guide and challenge each student in the areas they need it most.
What Concrete Learning 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?”
DIFFERENTIATED QR CODE TASK CARDS
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 a 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! Now we have instant engagement PLUS we begin to eliminate some of those math worries.
I’m a strong advocate of gradual release (I do, We do, You do), and we use that model consistently. I begin each lesson by modeling a subtraction equation, showing students how to solve it using manipulatives. I do this a few times, encouraging students to observe my strategies and how I check my work. Then, it’s time for us to practice together, which is when the excitement kicks in. They get to use their own manipulatives, which takes away the pressure of “heavy” math. This phase is crucial because it gives students a solid foundation before moving on to representations and abstract thinking. Next, I introduce drawings and mental math strategies. This is where differentiation plays a big role—students can choose the approach that works best for them as they solve problems, making the learning process more engaging and tailored to their needs.
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.
The Power of Concrete Learning
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.
HANDS ON PLACE VALUE ACTIVITIES
Just like in reading, math builds upon itself. If students don’t understand counting, how can they learn to add? If they can’t subtract, how will they divide? Scaffolding is essential for building that foundation and helping students not only feel successful but also enjoy math. Give your students time to play. Let them touch and manipulate objects to grasp what math truly means. Don’t skip or rush through concrete learning!
Think about the next math skill you’ll teach. How can you make it concrete for your students? What manipulatives can you use to support them? For those ready for representations, provide various drawings and strategies. If some students already have a solid understanding of math, challenge them with abstract problems to practice mental strategies. By supporting all levels, you help every student become a “math person.” 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!
MATH WORKSHOP AND GUIDED MATH ESSENTIALS
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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Collaboration is essential to learning, and distance hasn’t changed that it’s probably more essential than ever. Students benefit from sharing their ideas and considering and building on the ideas of others.
Yes! That is so true!
This is awesome!! So helpful!!
I am so glad to hear that!!