The Other Side of Math for Infants and Toddlers by Dr. Jill Uhlenberg

 

Many adults focus on numerals, counting objects, and helping young children learn the order of numbers. While these are important basics for mathematical learning, there is another side to math that is just as important; that is, learning about spatial relationships. Spatial understanding is a foundation for a substantial amount of math that we use as adults. This includes map-reading, measuring, classifying, recognizing and developing patterns, and more.

Infants and toddlers can develop spatial understanding through exploration of simple household items like plastic storage containers with lids, nesting cups and spoons, and muffin tins, along with objects to place inside these containers. Given plenty of time and adults who are willing to observe rather than direct the children’s experiences, young children can construct basic knowledge of spatial relationships. We collected 50 hours of video in order to examine how 12- to 36-month-olds used contents and containers and what they learned in the process. Adults can support this learning in the following ways:

    

Provide a variety of containers and objects for the children to explore. If possible, include a container that is large enough for the child to climb into. You will observe them placing containers on their heads, feet, and hands. Placing everything in a tub or drawer that is accessible will allow the children to engage freely, learning about the materials, then combining the materials in different ways to see what happens.

    

Spend time observing these explorations. You may want to name the materials and actions using spatial terms: you put the scarves in the bowl; I see you put the red ball beside the yellow ball; oh, the canister is on your head! You may be surprised at how the children use the materials. Over time, you will see growth in the children’s understanding of space and shapes. We also noticed that the children spent long amounts of time exploring, busting the myth of short attention spans typically attributed to toddlers.

  

 Allow the children to decide whether a problem has been solved rather than the adults expecting perfection. That is, we suggest accepting approximation. If a child is satisfied with the result of some experience, note this as a step in their development of spatial understanding, and watch for refinement in future explorations.

    

The favorite materials in our observations were plastic balls (ball pit type) of different sizes and colors. The children combined these balls with muffin tins (we had three sizes from mini-muffin to large muffin sizes). Using these materials, very young children began by testing whether one ball would fit in each of the 12 cups of the muffin tin. As adults we know these sizes are constant, but at 12 months of age, this is new knowledge. Other spatial understandings/math learning constructed with muffin tins and balls included these examples:

• One-to-one correspondence—one ball fits in one cup;

• Estimating space—using the medium ball in the medium-sized muffin tin; noticing which balls fit and which did not; pouring a bowl full of balls into a too-small canister; trying to place a lid on a too-full container;

• Classification—sorting balls by color or size; older preschoolers may use two characteristics, but infants and toddlers can generally only sort on one attribute;

• Patterns—placing balls in the muffin cups in a particular order (color, size, selected cup, etc.) that is repeated;

• Distribution—performing the same act on the same materials repeatedly, like placing the same ball in each of the muffin cups one by one; this mathematical process shows up later when adults are calculating equations.

    

The more experiences, the more advanced the children’s use of materials became. Eventually they began
combining materials in creative ways by constructing towers of bowls, canisters, nesting containers, and other objects. These explorations lead logically into the use of blocks, another strong component of spatial understanding. When you recognize and celebrate infants’ and toddlers’ bent for objects and containers, you are supporting their beginning spatial understanding. You will be surprised at the wealth of knowledge they construct over their first three years.