The Case for Concrete: Making Early Math Stick with Real Objects
After over twenty years in the early childhood classroom, I’ve seen every kind of math curriculum come and go. Some promise faster learning; others claim to align with the latest standards. But what most have in common is this: they jump too quickly into the abstract. First graders, and young children in general, are concrete thinkers. They learn best when they can touch, see, and experience something. Yet, many math programs start with pencil-and-paper tasks that expect children to grasp big ideas without ever putting their hands on real materials. That’s a recipe for confusion.
The Disconnect Between Curriculum and Cognitive Development
Research shows that young learners are not developmentally ready to understand abstract math concepts without first engaging with them in a concrete way. According to developmental psychologist Jean Piaget, children in the early elementary years are in what he called the “preoperational” or “concrete operational” stages of cognitive development, where hands-on learning is not just helpful—it’s necessary1. Yet, many current math programs dive into symbolic representation—like numbers and equations—before children have built a foundation of understanding through manipulation and exploration.
Recent data from the National Assessment of Educational Progress (NAEP) reveals that only 40% of fourth-grade students performed at or above the proficient level in math in 20222. That’s a startling number. While multiple factors play into this, one major reason is that we’re asking children to memorize rules and symbols before they ever understand what those symbols mean.
Why Touch and Talk Make All the Difference
Children need to handle real objects in order to make sense of numbers and quantities. Whether it’s counting buttons, sorting rocks, or building towers with cubes, these actions give meaning to the numbers they will later write and manipulate on paper. When adults talk through these processes with children—saying things like, “Let’s see how many blocks tall this tower is,” or “We have two socks here and two more—how many in all?”—they give language to the thinking, which deepens understanding3.
In my classroom, I’ve seen the difference this makes. Give a child a worksheet with ten drawn apples and ask them to circle the even ones, and you’ll get blank stares. Give them ten real apples and ask them to make pairs, and suddenly the concept of “even” becomes clear. It’s not just about getting the right answer; it’s about building a mental model that they can carry forward.
Strategies That Work: From Classroom to Home
1. Use Real Manipulatives, Not Just Drawings
There’s no substitute for the real thing. In my classroom, we use linking cubes, plastic bears, leaves from outside, and even bottle caps. When students can build, sort, and rearrange, they see math in action. Research confirms that manipulative-based instruction improves math achievement, especially among younger learners4. While drawings can be helpful later, they should come only after children have had plenty of experience with real objects.
2. Connect Math to Everyday Routines
Math is happening every day, all around us. One of my favorite suggestions for parents is to use laundry time to teach counting by twos. Ask your child to find matching socks and count the pairs out loud. This reinforces the concept of grouping and skip counting—skills that are foundational for multiplication later on. It also shows kids that math isn’t just something we do at school; it’s part of life.
3. Make Board Games Count
Games like Chutes and Ladders aren’t just fun—they’re full of learning opportunities. When playing, I encourage adults to count the moves out loud with their children, saying, “One, two, three—now you’re on square 12!” This type of verbal reasoning supports number sense and sequencing. Researchers have found that board games with numbered spaces can significantly improve children’s numerical skills5.
4. Create Math Stories and Role-Play
Children love stories, and incorporating math into storytelling can make abstract concepts come alive. For example, I might tell a story about a hungry bunny who finds five carrots and eats two. “How many are left?” I ask, and we act it out with paper carrots or real baby carrots. This bridges the gap between narrative reasoning and numerical understanding, an essential step for many young learners6.
5. Use Open-Ended Questions and Encourage Explanation
When a child solves a problem, I always ask, “Can you show me how you figured that out?” or “What did you do first?” This gives insight into their thinking and allows misconceptions to surface. It also builds a habit of reflection and explanation, which research links to deeper mathematical understanding7.
6. Encourage Math Talk at Every Opportunity
Whether at home or in the classroom, talking about math is critical. Adults should model thinking out loud, such as, “I need three more forks for dinner. Let’s count how many we already have.” These moments show children that math is useful and conversational, not just a subject in a workbook. According to one study, children whose families engage in regular math-related talk show stronger number skills by kindergarten8.
Support from Educational Leaders is Key
For early education leaders and administrators, supporting teachers in this approach means more than just providing materials. It means creating professional development opportunities that focus on child development, recommending curricula that start with concrete experiences, and encouraging classroom environments where exploration is valued over rote performance. Leaders can also model these practices during teacher training sessions and family engagement events.
We also need to rethink assessment. If our testing methods only measure what children can write on paper, we’ll never truly know what they understand. Observational assessments, student interviews, and performance tasks provide a fuller picture of a child’s math thinking and should be part of every early learning program.
Let’s Make Math Meaningful
When we teach math in a way that makes sense to young children—through touch, talk, and real-life experience—we’re not just teaching them numbers. We’re helping them build confidence, curiosity, and a genuine love for learning. No worksheet can do that on its own. So let’s get out the blocks, the buttons, and the board games. Let’s count socks and carrots and footsteps. And let’s keep asking, “What do you notice? What do you wonder?” Because math is not just something to be taught—it’s something to be experienced. And every child deserves the chance to experience it with their hands, their eyes, and their hearts.
Ready to transform your math instruction? Head to your classroom or your kitchen and start counting something real. The numbers are waiting.
Baroody, Arthur J., and Herbert P. Ginsburg. “The Effects of Instruction on Children’s Understanding of the ‘Equals’ Sign.” Elementary School Journal 84, no. 2 (1983): 199–212.
National Center for Education Statistics. “NAEP Report Card: Mathematics 2022.” U.S. Department of Education, Institute of Education Sciences. https://www.nationsreportcard.gov/mathematics/
Gelman, Rochel, and C.R. Gallistel. The Child’s Understanding of Number. Cambridge, MA: Harvard University Press, 1978.
Sowell, Evelyn J. “Effects of Manipulative Materials in Mathematics Instruction.” Journal for Research in Mathematics Education 20, no. 5 (1989): 498–505.
Ramani, Geetha B., and Robert S. Siegler. “Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games.” Child Development 79, no. 2 (2008): 375–394.
Perry, Maria, et al. “The Role of Narrative in Young Children’s Understanding of Mathematics.” Early Child Development and Care 182, no. 7 (2012): 951–962.
Carpenter, Thomas P., et al. Cognitively Guided Instruction: A Research-Based Teacher Professional Development Program for Elementary School Mathematics. Madison: University of Wisconsin, 2000.
Levine, Susan C., et al. “What Counts in the Development of Young Children’s Number Knowledge?” Developmental Psychology 46, no. 5 (2010): 1309–1319.
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