# The Power of Math Manipulatives in Early Learning

## By Mallory Hansberry, Math Content Architect for ALEKS Adventure

Math can be tough and even a bit scary for many young learners, but the right tools and approaches can make a world of difference. As a former elementary school teacher and current math content writer, I’ve seen firsthand the transformative power math manipulatives have in the classroom. These hands-on tools can help students understand tricky concepts by giving them something concrete to work with. Let’s dive into why math manipulatives are so important for teaching young students and which ones work best.

## Why Are Math Manipulatives Important?

Math manipulatives are hands-on materials that help kids understand math concepts and procedures. These tools turn abstract ideas into something kids can see, touch, and play with. Based on Jerome Brunner’s theory of cognitive development, students learn best when they go through three stages: concrete, representational, and abstract.

**Concrete Stage**: At this stage, students work with physical manipulatives. For example, when learning addition, they might use counters to combine two groups and count the total. This hands-on experience is key for their initial understanding.**Representational Stage**: Once students are comfortable with the physical manipulatives, they move on to drawing or using symbols to represent those objects. For instance, they might draw circles or dots to stand in for counters and then add them up.**Abstract Stage**: Finally, students use numbers and math symbols without needing physical manipulatives or drawings. At this point, they can solve addition problems using just numbers and the plus sign, thanks to the conceptual understanding they built in the earlier stages.

## How Do Math Manipulatives Build Conceptual Understanding and Promote Problem-Solving?

Providing students with plenty of hands-on experiences is important for building a strong conceptual foundation in mathematics, especially in the early stages of learning. It is essential for students to comprehend what they are doing and why they are doing it. Students with a strong conceptual understanding of math concepts can utilize different strategies to solve problems, learning to think critically and flexibly. Using manipulatives in math instruction helps students develop a deeper understanding of mathematical concepts and promotes active engagement in learning (Moyer, 2001).

Here are some math manipulatives that enhance conceptual understanding in early math learning:

## Counters

Counters are used in early math instruction to help students grasp one-to-one correspondence and develop early number sense through counting, sorting, and basic addition and subtraction. By manipulating counters, students can represent and solve simple problems by combining and taking away quantities.

## Connecting Cubes

Connecting cubes offer students the chance to explore the composition and decomposition of numbers by snapping cubes together and breaking them apart. Students can also use these cubes to represent quantities and model addition and subtraction. This hands-on experience helps students effectively develop problem-solving strategies across various mathematical operations.

## Number Lines

Number lines provide a visual representation of numbers and their relationships, supporting math concepts like counting, comparison, addition, subtraction, and identifying patterns. Students can use number lines to solve problems by counting forward or backward, developing number sense and estimation skills.

## Base-Ten Blocks

Base-ten blocks are essential for teaching place value, addition, subtraction, and regrouping. They help students understand the relationship between digits and their values. By using these manipulatives, students can visually grasp that 10 ones make 1 ten and 10 tens make 1 hundred. This conceptual understanding of place value can then be applied to modeling and solving problems with larger numbers.

## How *ALEKS Adventure* Incorporates Math Manipulatives

We know how important physical manipulatives are in early math education, so when we set out to create our new digital personalized learning program, *ALEKS Adventure*, we carefully incorporated familiar digital manipulatives and representations into every learning experience. We’ve designed standards-based, fun, and interactive topics that help students understand math concepts and master them. Bueno et al. states that using digital manipulatives in math instruction provides students with immediate feedback and opportunities for personalized learning, enhancing their understanding and retention of mathematical concepts. (Bueno et al., 2017) Plus, with a digital program, students always have the tools they need, so there’s no digging through desks and closets looking for enough manipulatives to go around.

Math manipulatives are fantastic tools for building a strong foundation in early math learning. They turn abstract concepts into fun, hands-on experiences, helping kids understand and solve problems. *ALEKS Adventure* takes physical math manipulatives and brings them to life in a digital format, creating an interactive and engaging learning environment that makes math exciting. As teachers, we can empower our students by using these tools in our classrooms, helping them build confidence and skills for future success in math. Let’s embrace the power of manipulatives and watch our young learners thrive!

*ALEKS Adventure* is an engaging, personalized solution that invites students to learn math while they learn alongside animated sidekicks, connect with classmates, and discover new worlds. From a customizable avatar and spaceship to a powerful AI engine, *ALEKS Adventure* is a whole new way to learn math. To learn more, click here.

Mallory holds a Bachelor of Science in Early Childhood Education from The University of Dayton. With a decade-long tenure as an elementary teacher, she transitioned to become an Academic Designer for McGraw Hill’s K-5 math content team in 2016. Mallory has been instrumental in crafting both print and digital materials for McGraw Hill’s *Reveal Math* program and currently serves as a Math Content Architect for *ALEKS Adventure*, channeling her expertise to create innovative math learning experiences.

## References

Bruner, Jerome S. *Toward a Theory of Instruction*. Cambridge, MA: Harvard University Press, 1966.

Bueno, P. S., et al. (2017). “Digital manipulatives in mathematics education: A systematic review.” *Journal of Educational Technology & Society*, 20(2), 161–173.

Hand2Mind. “Benefits of manipulatives.” *hand2mind*. Accessed n.d.. https://www.hand2mind.com/media/contentmanager/content/Benefits_of_Manipulatives.pdf.

Moyer, P. S. (2001). “Are We Having Fun Yet? How Teachers Use Manipulatives to Teach Mathematics.” *Educational Studies in Mathematics*, 47(2), 175–197.

National Council of Teachers of Mathematics (NCTM). *Principles to Actions: Ensuring Mathematical Success for All.* Reston, VA: NCTM, 2014.