For children to feel connected to their own learning experiences, artistic activities should be open-ended with a variety of questioning opportunities. Observation and guidance in nondirective ways help children feel supported yet independent.  Asking questions such as, “what else could you add?” and “what could we do if we take these away?” allow for children to problem solve and support one another.  Vygotsky (1933) called this observation and questioning technique the scaffolding process.  This supportive process enables children to take their knowledge deeper. By encouraging children with open-ended questions, they will play an important role in designing their own experiences.  This process allows for purposeful, independent play which increases knowledge along with encouraging the joy of learning.

When I am looking for connections that can be found between math, art, and sand, I think about how children tend to resolve problems.  Children will try challenges that are puzzling enough to be fascinating yet not completely beyond their abilities to resolve.  I invite children to think about the natural relationships between math and art while they are engaged in activities.  The range of children’s questions are impressive when they are involved in this style of play. I hear them ask questions such as “how tall should we make the castle?”  Children will often consult other children about design ideas and materials to use.  They will ask each other to help find pretty rocks or decide how many items to add.  It’s the beauty of math in collaboration, investigation, and social skills all naturally occurring from the basis of play.

Math is all around us- we simply have to look for it.  Consider this scenario.

Johnny is playing at the sand table.  He is filling and dumping a small bucket of sand into a sand castle mold.  He presses the sand into the mold  and then flips it over and all of the sand spills out.  Bea, the teacher, comes over and begins playing beside him.  She too, fills a bucket with sand and then pours it out.  A few minutes into this parallel play, Bea asks Johnny about what he is doing.  He tells her that he is making sand castles. 

Bea sees an opportunity to use math vocabulary and spatial reasoning to discuss Johnny’s play with him.  She uses words like, “heavy and light” to describe the weight of the mold when it is full and when it is empty.  She talks about “turning over” the sand mold so that it is upside-down.  She asks if he prefers “a lot of sand” or “less sand” when filling the mold. She offers suggestions about how to make the sand stick together.  They fill the bucket with water at the sink and add water to the sand to experiment with making the sand stick.

This “incidental” math moment happens during free play.  Often, these opportunities occur and we miss them.  Keep your eyes open and look for a chance to deepen and extend a child’s play.  When seized, these moments are golden.