Many first-time parents wonder whether the wooden blocks and magnetic tiles in their lounge room are doing anything beyond keeping a toddler busy. Worksheets, counting apps, and flashcards can feel more productive. The research suggests the opposite. Open-ended toys, used consistently in everyday play, are quietly building the foundations of how a child will think mathematically for the rest of their life.
What open-ended actually means
Open-ended toys are objects with no fixed outcome. Magnetic tiles, wooden blocks, loose parts like pebbles and discs, and nesting or stacking sets can be combined, sorted, balanced, and rebuilt in countless ways. Unlike battery-operated toys with one button to press, open-ended toys ask the child to do the thinking. That thinking is mostly mathematical.
What the research shows
Spatial reasoning, the ability to mentally picture and manipulate shapes, is one of the strongest early predictors of later maths achievement. Research published in Psychological Science found that spatial reasoning measured in babies as young as six months predicted maths ability at age four (Lauer & Lourenco, 2016). This is the skill being trained when a toddler turns a magnetic tile to fit a square edge or stacks blocks to keep a tower upright.
Block play in particular has been studied for decades. A randomised controlled trial of preschool-aged children found that free block play produced statistically significant gains in geometry skills compared with no intervention (Schmitt et al., 2018). Earlier longitudinal research linked the complexity of preschool block constructions to standardised maths scores in later schooling (Wolfgang, Stannard, & Jones, 2003).
Loose parts research is newer but consistent. A 2025 experimental study published in Communications Psychology found that preschoolers showed significantly more spontaneous science, technology, engineering, and maths behaviours during play with loose parts than with single-purpose toys.
What this looks like in practice
Children working with open-ended materials are running through several mathematical processes at once:
- Counting and one-to-one correspondence when sorting pebbles into baskets
- Classification when grouping discs by colour or shape
- Spatial transformation when rotating a tile to fit a build
- Part-whole reasoning when splitting a stack of blocks evenly
- Estimation and measurement when comparing taller, shorter, heavier, lighter
- Pattern recognition when repeating colour or shape sequences
The Raising Children Network notes that toddlers begin sorting objects by colour, shape, or size from around 16 months, and that this hands-on play is what builds early maths thinking, not formal instruction (Raising Children Network, 2023).
Practical strategies for first-time parents
1. Choose fewer toys, but better ones. A small rotation of magnetic tiles, wooden blocks, and a basket of loose parts will outperform a cupboard full of single-purpose plastic toys. Open-endedness is what creates the maths.
2. Use spatial language during play. Words like taller, shorter, under, between, half, equal, and more turn play into maths vocabulary. Research shows parental spatial language during play predicts later spatial skill in children (Levine et al., 2012).
3. Avoid directing the play. Let the child build, knock down, and rebuild without correction. Free play with blocks produced the strongest geometry gains in the Schmitt et al. trial, more than adult-led structured tasks.
4. Add gentle prompts, not solutions. Instead of fixing a wobbly tower, ask “What do you notice about this side?” Open questions invite reasoning.
5. Include natural loose parts. Pebbles, gum nuts, shells, and pinecones cost nothing and offer the same mathematical affordances as expensive sets. Variety in size, weight, and colour is what matters.
6. Tidy-up time counts too. Sorting blocks back into baskets by shape or size is genuine classification work. The packing away is part of the learning.
What this looks like in real life
A two-year-old sits on the lounge room rug with a small basket of wooden blocks and a handful of round wooden discs. She lines six discs along the edge of the rug, then picks them up one by one and drops them into a tin. She knocks over a tower, watches it fall, then tries to rebuild it taller. Her mum sits beside her and says, “That one is bigger than the other one.” No worksheet, no app, no instruction. The maths is already happening.
A reassuring close
First-time parents do not need to choose between play and learning. The toys already in the basket, used slowly and without pressure, are doing more for early numeracy than most structured programmes designed for the same age group. The research is clear that open-ended materials, plenty of time, and a parent who notices and names what is happening together build the foundation that formal maths will later sit on.
For a deeper look at this approach, see the related post on the benefits of Montessori play-based learning.
References
Communications Psychology. (2025). Loose parts play encourages spontaneous science, technology, engineering, and mathematics (STEM) behaviours. https://www.nature.com/articles/s44271-025-00362-y
Lauer, J. E., & Lourenco, S. F. (2016). Spatial processing in infancy predicts both spatial and mathematical aptitude in childhood. Psychological Science, 27(10), 1291–1298.
Levine, S. C., Ratliff, K. R., Huttenlocher, J., & Cannon, J. (2012). Early puzzle play: A predictor of preschoolers’ spatial transformation skill. Developmental Psychology, 48(2), 530–542.
Raising Children Network. (2023). Play ideas for toddler cognitive development. https://raisingchildren.net.au/toddlers/play-learning/play-toddler-development/thinking-play-toddlers
Schmitt, S. A., Korucu, I., Napoli, A. R., Bryant, L. M., & Purpura, D. J. (2018). Using block play to enhance preschool children’s mathematics and executive functioning: A randomized controlled trial. Early Childhood Research Quarterly, 44, 181–191.
Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2014). Deconstructing building blocks: Preschoolers’ spatial assembly performance relates to early mathematics skills. Child Development, 85(3), 1062–1076.
Wolfgang, C. H., Stannard, L. L., & Jones, I. (2003). Advanced constructional play with LEGOs among preschoolers as a predictor of later school achievement in mathematics. Early Child Development and Care, 173(5), 467–475.
