Free Exploration, or How Not to Be a Nag

by Alysia Krafel

I recall an incident years ago when my six-year- old nephew was learning to set the table.  Dinner was almost ready and there he was popping his fists down onto fork tines to flip them into the air.  The stage was set for an unpleasant confrontation.  I see now that the problem is one of time frames.  We needed him to get the job done; he needed to explore.  When we press a child to use a tool seriously and with skill before we have provided fiddle time, we set him up to be seen as a behavior problem and ourselves to be seen as nags.  If a child can do his necessary playing and exploring with materials when he is not under pressure or expectations, before he needs to use them as we wish him to use them, not only will he learn the new skill faster and with more understanding, he will learn it with more delight (or at least with less complaining).  The first association will be of joy and competence rather than frustration and forced anxiety.

Learning to use math manipulatives is like learning to use other tools.  An adult will look at a screwdriver and use it to drive screws.  A child will roll it on the floor, listening intently as the grooves in the plastic handle thump.  She will roll it over her tongue, poke it into cracks, bang it on the table, spin it, or balance it on her finger.  When finally satisfied with the investigation, she will watch you screw in the screws and then try it herself.  And so it is with all of our doodads.

Play, unhindered exploration, is very important to  children.  At the Farm School, we came to realize that this self-directed learning style was not an impediment but a boon to our aims.  We found that children who had enough time to fiddle with the plexiglass tiles came to their first fractions lessons knowing that the smaller the pieces there were, the more of them they had; that you could cover the  black (1/2) tile1 with the yellow (1/4) tile or orange (1/6) pieces, but you couldn't with the clear ones (1/3).  When they began to work with the formal fractions lessons, they brought into action all that their senses already knew about these tiles.  As soon as the labels "halves" and "fourths" were attached to the colored tiles, they knew that 1/2  = 2/4.  They found the patterns very quickly and mastered the materials faster than the previous children who had not been allowed fiddle time.

The problem the teachers at the Farm School  had encountered was that we wanted to teach x amount of material in a certain time frame.  When the children needed three weeks of fiddle time with the fraction tiles, we experienced that as a delay,  a delay that made us nervous.  We just had to teach and have the children master fractions by the end of the school term.  The solution was to introduce the materials long, long before (in many cases years before) we intended to use them as teaching tools.  After ample free exploration time, not only did the children not resist the use of the materials in the specific way that the formal lessons demanded, they eagerly attended to the new way to interact with the now familiar materials.  The new work was for them a  continuation of the old play.  The experience did not feel all that different to them.  Since the struggle between teacher and child had been eased, the adversarial relationship became a co-worker relationship.  The instruction then proceeded easily.  The children and the teachers learned together  to truly understand the world of numbers and enjoyed doing it.