One of the most exciting aspects of working with young children is witnessing their sense of joy and wonder in everyday objects.  I often forget that their understanding of many concepts, and their exposure to many tools, is a brand new experience for them.  As an adult, sometimes it is easy to forget this, but children remind us to see the excitement in new things, even if it is just finding new meaning and function in a familiar object.

We all know that young learners find excitement in anything novel and different.  If you ask ten children to collect five objects and create a use for them, chances are you will get many different objects and designs because all children have innovative and pioneering ideas and, rightfully so, they think their ideas are the best! Limitations, boundaries and restrictions are not yet familiar concepts to young children.  Often they are able to express their beliefs, designs and viewpoints about many aspects of their world in a more uninhibited way than adults do; their minds are free to wander, dream and plan to their heart’s content. This is the beauty of witnessing a young child explore mathematical concepts.

For young children, introduction to these new concepts is cultivated through various spontaneous activities and games.  For instance, setting out places for a tea party, counting out spaces during a game of Chutes and Ladders, finding the biggest rock, counting fingers and toes, and going down a slide all incorporate the concepts of number sense, spatial sense, measurement, estimation, and problem-solving and critical thinking skills.  Kids are constantly practicing math skills from birth!

As a stay-at-home-mom, many of the “lessons” that I find my children enmeshed in tend to begin organically.  In my experience, children are much more interested in learning something new when they initiate or present it.  To me, it always feels like they are extending an invitation to the adult to help guide the grasping of a new concept or skill that they innately feel they are ready to learn.  As educators, our learners are advancing at their own level, and our job is to encourage and support each one of them as they succeed at one step, then move onto the next.  I find the process captivating. However, many times these learning opportunities happen at inopportune times (i.e., in the car, away from home, outside) when materials that I would typically use to help supplement my teaching are not necessarily available.  Thankfully, math is all around us; and utilizing what you have or what you can find is much better (and usually more fun) than using nothing at all, or waiting and possibly missing the opportunity.  When they are ready, they are ready – jump right in!

In my last post, I discussed the process of organizing child-centered “learning boxes”  and learning spaces where children are able to explore materials on their own and practice math concepts anytime they choose.  Of course, this is helpful when they are at home or in the classroom, but learning does not just cease once they are away from these two areas. This is where being resourceful and innovative in our own right comes in handy.  Having a small set of available materials in various places (in the car, in the garage, in a bag or purse, etc.) materials are available for times when ideas spontaneously strike.

One example of this occurred recently when we were outside and my daughter excitedly decided she wanted to practice her math skills to gear up for the start of school. Naturally, her brother (preschool-age) wanted to join in as well.  Of course, I wanted to nurture this fertile idea, so I knew my responsibilities would involve keeping both engaged, allowing both ample learning opportunities, and allowing all of us to have fun. The first thing they did was to get out the chalk and a big bucket of rocks we had previously collected.  I then asked my daughter to look in her math box for other materials to assist with her vision. She came out with large foam dice.  After some discussion about our process, we came up with the idea that they could each roll a die and count out that many rocks.

After a few rolls, this proved to be a perfect task for my younger son, but my daughter bored of it quickly.  I could sense she was ready for more a challenging task.  Again, I encouraged her to practice self-reliance and creativity and referred her to her math box.  She came out with a white board and dry erase marker found in her math bin.  She had decided she wanted to practice writing out math problems, which is a new concept for her.  While her brother continued having a blast rolling his die all over the driveway,  counting that many rocks out and then putting them all back in the bucket and starting over (practicing number sense, one-to-one correspondence and problem-solving skills), we worked together on addition and subtraction problems.

She would roll her die and write that number down, then she would roll it again and add or subtract these two numbers together to get solve the problem.   Since she is just learning how to write out a mathematical equation, I helped her better understand this method by drawing two boxes side-by-side.  She rolled the die and place that many rocks in the first box.  Then, she rolled the die again and place that many rocks in the second box.  She then went to her white board, wrote out the problem using the appropriate signs and counted all of the rocks to find the answer

They did this side-by-side for quite awhile.  After a bit, this idea then morphed into both of them working together, the older child teaching the younger how to problem-solve higher-level math concepts.  My part in the learning process became unnecessary, and I was there just as a guide when help was needed, which is exactly what child-directed learning should exhibit.

There are many different ways that math can be engaging and exciting by utilizing everyday objects in a new way.  Often the most spontaneous lessons and activities turn out to be the most fun and rewarding.  Allowing children the freedom to explore math concepts in this way makes learning fun for all!

I imagine that some of you have had this same experience.  Not only do young children love boxes, they love laundry baskets, Tupperware, kitchen spoons and spatulas, a roll of toilet paper, and the Sunday paper.  You might go out and spend a whole lot of money on a set of Duplos, but when it comes right down to it, your child (ren) may be just as interested in building a pile of spoons from the kitchen drawer as they are in building a pile of Duplos.

Children are natural-born problem solvers.  Boxes present so many challenges for the young child.  Can I climb into it?  Can I stand on top of it?  Can I crawl through it?  Can somebody find me if I hide in it?  What happens when I push it down the stairs?  What happens when I put my stuffed animal into it and then push it down the stairs?  These questions and so many others come with a large empty box.  These are not questions that adults have put forth.  They are questions that arise organically from the child’s open-ended play.  There are no directions that come with the box, and nobody is asking the child to do something or make something out of it.  There is no “right” way to play with a box.  It just is.

Open-ended, found materials encourage problem solving.  That is not to say that store-bought toys do not; they do of course.  However, there is so much opportunity for discovery in the mundane.  How many hours did my oldest child spend in front of the Tupperware cabinet? He pulled them out, stuffed them back in, matched the lids with the bottoms, used the tops as frisbees, stacked them tall and knocked them over.  All of this occurred without any direction from an adult.  He solved his own problems by manipulating and playing with these materials for hours on end.  If he couldn’t find a lid, he put that piece into a bigger container one and closed it inside with a bigger lid. He figured out which ones made the most noise when banging on it with a wooden spoon.  He discovered that he could put them at various distances across the kitchen floor and jump from one to another, like stepping-stones. He played pretend, he played with space and shape, he played with number, and he played with gusto.

Next time you hear a rumor that someone you know is having a refrigerator or washing machine delivered, do everything you can to get that box that it came it.  Your children will uncover all sorts of problems with it and then they will work very, very hard to solve them.