The Lasting Impact of Math Manipulatives in Early Childhood Education

This research overview shows that early use of math manipulatives and math packs at home and school significantly boosts young children’s mathematical understanding, engagement, and confidence.

Introduction:

How important are manipulatives in transforming early childhood math experiences at home and school?

Many parents and educators recognize the importance of early math skills but may not know how to make mathematics engaging, accessible, and meaningful for young children. Math packs curated sets of manipulatives and activities offer a research-based approach to nurturing mathematical thinking at home and in the classroom. These packs include materials such as blocks, dice, counting chips, and pattern blocks, designed to support growth across foundational domains such as: counting, numeration, addition and subtraction, geometry/spatial reasoning, measurement, and patterning (NRC, 2009; Brendefur et al., 2018). By supporting active exploration and bridging the gap between home and school, manipulatives lay the groundwork for school readiness and lifelong confidence in mathematics (Anders et al., 2022).

Theoretical Foundations

Why do hands-on models and developmental progressions matter in early math learning?

Many adults might not realize that young children first understand mathematical ideas through physical actions and concrete experiences, not abstract symbols. Manipulatives are grounded in learning theory, particularly Bruner’s (1966) framework of enactive (physical), iconic (visual), and symbolic (abstract) representations. This progression is essential: children manipulate objects, see and create patterns, and later connect these experiences to formal symbols and procedures (Bruner, 1966; Gravemeijer, 1999). Manipulatives serve as a bridge, making abstract concepts tangible and accessible.

Research highlights the importance of moving from concrete to pictorial to abstract understanding a process known as progressive formalization (Gravemeijer, 1999). This approach supports deep conceptual learning and helps children build the foundation for later mathematical achievement. By providing structured opportunities for handson exploration, specific manipulatives ensure that children’s early math experiences are developmentally appropriate and rooted in best practice (National Research Council, 2009)..

Key Components and Practical Uses

What are the foundational math domains that foster deeper mathematical thinking?

Families and educators often wonder which activities are most effective for supporting early math learning. Drawing on research, six foundational domains have been identified as critical for developing deep mathematical understanding in young children: counting, numeration, addition and subtraction, relational thinking, geometry/spatial reasoning, and measurement (NRC, 2009; Brendefur et al., 2018). Math packs typically include a variety of manipulatives such as wooden blocks, dice, counting chips, pattern blocks, connecting cubes, and cards paired with structured activities that target these domains. Contrary to common assumptions, measurement and spatial reasoning are especially influential, with research indicating that early experiences in these areas are strongly correlated with long-term mathematical achievement and understanding (NRC, 2009).

Activities should be designed to be playful, adaptable, and accessible to various skill levels, making them valuable tools for classrooms, homes, and tutoring contexts. For example, children might use blocks to compare heights, which develops measurement skills and comparative language, or roll dice to practice addition and subtraction, building number sense and fluency. Pattern blocks can create shapes and repeat patterns, supporting geometry and spatial reasoning. Research consistently shows that when children manipulate objects and represent their thinking with physical and visual models, they develop deeper and longer-lasting mathematical understanding (Carbonneau, Marley, & Selig, 2013).

Research Evidence: Impact on Learning and Engagement.

What does the evidence say about the impact of math packs on student learning and family engagement?

Many may wonder if manipulatives affect children’s math achievement. The evidence is clear: structured interventions using manipulatives at home and in classrooms lead to measurable gains in early numeracy, subitizing, patterning, and geometry compared to control groups (Anders et al., 2022). Children who participate in math pack activities show increased mathematical talk, more open-ended questioning by parents, and greater engagement in reasoning and problem-solving (Anders et al., 2022; Carbonneau et al., 2013).

Randomized controlled trials provide compelling evidence that distributing math packs to families increases the frequency of parent-child math interactions and enhances their quality, significantly improving children’s mathematical achievement (Berkowitz et al., 2015; Young et al., 2023). These studies reveal that when parents receive structured guidance on using the materials such as activity suggestions, conversation prompts, or supportive messaging they are more likely to engage in rich, meaningful mathematical discussions and problem solving activities with their children.

Math packs also support family engagement and help bridge the divide between home and school learning. When families use math packs, children develop stronger skills and positive attitudes toward mathematics (Civil, 2016). These benefits are especially pronounced for children from disadvantaged backgrounds or those with parents who are anxious about math (Maloney et al., 2015).

Implications for Practice: Supporting all Learners

How can educators and families use math packs to maximize student growth and confidence?

Math packs provide visual and tactile learning experiences that make abstract concepts concrete, improving comprehension and retention for all learners (Carbonneau et al., 2013). These hands-on activities and family involvement can reduce math anxiety and foster positive attitudes toward mathematics, making learning enjoyable and memorable (Maloney et al., 2015).

Even with evidence, some may be unsure how to implement math packs effectively. For educators, math packs offer ready-to-use, research-backed tools that can be integrated into classroom routines, homework, or family engagement events. They support differentiated instruction, address specific learning needs, and encourage collaborative problem-solving and discussion (Webb, 2009).

For families, math packs provide structured, playful opportunities to engage with math at home. Regular use of math packs supports skill development, builds confidence, and fosters curiosity (Epstein, 2018). When families and teachers work in partnership using these tools, children experience consistent support and encouragement, leading to stronger skills and a lifelong love of mathematics.

Conclusion:

Why are manipulatives and math packs essential for early childhood math experiences at home and school?
When thoughtfully designed and supported, math packs are powerful tools for enriching early math learning. They promote family engagement, bridge home and school experiences, support growth mindsets, and yield measurable gains in children’s mathematical knowledge and confidence (Anders et al., 2022; NRC, 2009). Math packs lay the groundwork for school readiness and a lifelong love of math by equipping families and educators to nurture foundational domains. The research is clear: every child deserves access to these hands-on, engaging resources that make learning mathematics meaningful, enjoyable, and effective.

References

Anders, Y., Grosse, C., Roßbach, H.-G., Ebert, S., & Weinert, S. (2022). Home and preschool learning environments and their relations to the development of early numeracy skills. Early Childhood Research Quarterly, 59, 1–14. https://doi.org/10.1016/j.ecresq.2021.11.002

Berkowitz, T., Schaeffer, M. W., Maloney, E. A., Peterson, L., Gregor, C., Levine, S. C., & Beilock, S. L. (2015). Math at home adds up to achievement in school. Science, 350(6257), 196–198. https://doi.org/10.1126/science.aac4628

Brendefur, J., Strother, S., Thiede, K., Lane, D., & Surges-Prokop, M. (2018). A professional development program to improve math skills among preschool children in the United States. International Journal of STEM Education, 5(1), 1– 12. https://doi.org/10.1186/s40594-018-0120-2

Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.

Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084

Civil, M. (2016). Family engagement in mathematics: A review of the literature. Journal of Urban Mathematics Education, 9(2), 108–118. https://eric.ed.gov/?id=EJ1117179

Epstein, J. L. (2018). School, family, and community partnerships: Preparing educators and improving schools (2nd ed.). Routledge.

Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177. https://doi.org/10.1207/s15327833mtl0102_4

Maloney, E. A., Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2015). Intergenerational effects of parents’ math anxiety on children’s math achievement and anxiety. Psychological Science, 26(9), 1480–1488. https://doi.org/10.1177/0956797615592630

National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. The National Academies Press. https://doi.org/10.17226/12519

Webb, N. L. (2009). The role of professional learning communities in mathematics education. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), Mathematics education: Perspectives on learning, teaching, and curriculum (pp. 95–108). Information Age Publishing.

Young, L. K., Levine, S. C., Berkowitz, T., & Huttenlocher, J. (2023). Parent-guided math activities and children’s math achievement: Evidence from a randomized controlled trial. Journal of Educational Psychology, 115(4), 678–692. https://doi.org/10.1037/edu0000732.

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Want to spark a lifelong love of math in young children? Research shows that hands-on math packs filled with blocks, dice, pattern blocks, and more make early math engaging and meaningful for families and classrooms. These playful tools help children explore counting, addition, geometry, measurement, and patterns through active discovery and conversation.

Key math words like “count,” “compare,” “pattern,” “measure,” and “shape” empower children to talk about their thinking and deepen their understanding. When parents and caregivers use math packs with guided activities and prompts, kids practice important skills and build confidence and curiosity about math (www.dmtinstitute.com).

Math packs bridge the gap between home and school, making math accessible to all learners and supporting positive attitudes, even for families anxious about math.

Let’s transform early math from worksheets into hands-on adventures that prepare every child for success!