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Early childhood education has been my life for over 30 years. I have taught all age groups from infants to 5-year-olds. I was a director for five years in the 1980s, but I returned to the classroom 22 years ago. My passion is watching the ways children explore and discover their world. In the classroom, everything starts with the reciprocal relationships between adults and children and between the children themselves. With that in mind, I plan and set up activities. But that is just the beginning. What actually happens is a flow that includes my efforts to invite, respond and support children's interface with those activities and with others in the room. Oh yeh, and along the way, the children change the activities to suit their own inventiveness and creativity. Now the processes become reciprocal with the children doing the inviting, responding and supporting. Young children are the best learners and teachers. I am truly fortunate to be a part of their journey.

Saturday, December 12, 2015

HOLES AND MATH

Holes are important to children.  So important that I have included them in the right-hand column of the blog twice.  Under dimension and elements, holes are listed under #5:  Children need to put things in holes; include holes of various sizes and shapes on various levels.  Under axioms, holes are also listed under #5: Children are compelled by nature to put things in holes; they will find every hole and even try to alter the shape and function of holes.

The Concrete Forming Tube apparatus is a study in holes.  Let's start with the long, cardboard tube that rests on top of the concrete forming tubes.  There are seven holes: a top hole and a bottom hole, two rectangular holes and three smaller, round holes.  Thus, the holes vary in size and shape on multiple levels.
Essentially, this cardboard tube is one long hole with various holes along the way so children get glimpses of pellets racing down the tube.  In addition, the holes along the way offer the children multiple entrees into the tube for their own operations.

There are actually more holes in the concrete forming tubes.  There the three large holes at the top of each concrete tube.  Each concrete tube also has two small holes at the bottom.   You can only see one in the picture, but believe me, they each have them as outlets for pellets dumped into the top of the big tube.  There are also the holes that accommodate the clear plastic tube, which can be thought of as one long hole with a top and a bottom.
There is one more hole in the tallest concrete tube that is hidden.  It is a small round hole just below the silver rod.   And no matter where it is or what size it is, the children will find it.
I originally made this hole to stabilize the large tube.  I did not need it, so I forgot about it until I saw this child reaching through the hole for pellets to put in his plastic measuring cup?  Why did he reach through the hole to get pellets when it would have been easier just to reach down to grab some pellets from the table?

Do you know that children measure holes? They measure holes in many different ways.  One way they measure is to use their own body.  

Here are pictures of two boys using their hands and arms to measure the respective holes.  The one on the left reaches across two holes.  The child on the right reaches down into the clear tube.  Both are measuring size and length of the holes.  Can a hole have a length?
Another way they measure holes is with the loose parts they find on shelves near the sensory table.  An example is the child who finds a bottle that fits nicely into one of one of the holes so he can empty the pellets from his bottle.
In a way, this is like a 3-D puzzle.  Will the bottle fit into this hole?  And like a puzzle, when it fits, there is a certain satisfaction and a foundational experience with geometry.

Two other children find a clear plastic tube and discover that it fits through two holes horizontally. 
Besides measuring the holes, these children are also altering them.  The two holes in the cardboard tube have now become one long hole with two ends.   Of course, they measure each end of the hole with their hands as they reach in to retrieve pellets.

Not only do children measure the size and shape of holes, but they also use holes to measure volume.  The children pictured below filled up the shortest concrete tube. 

They are able to do that because the holes at the bottom of this concrete tube are buried in pellets.  How many pellets fit in the big tube?  A lot!

The clear tube embedded in the two taller concrete tubes is easier to fill.  Also, because the tube is clear, the children are able to follow the progress of the tube filling up. 
Adding volume becomes a dynamic process.  The opposite is true, too.  Watch as one child empties the clear tube of pellets.  She starts out slow, but once she realizes her progress, she is going to get every last pellet out of the tube.


If we are using math terms, this could be considered subtracting volume. 

Children need holes.  They do not need holes for math, but holes and math go together quite nicely.  If you do not believe me, I took an informal poll and the "eyes" have it.











2 comments:

  1. Hello Tom

    I totally agree with your regarding the mathematical value of holes and the need to learn through physical exploration. Without these experiences children fail to understand not just geometric concepts such as shape and space but also numerical concepts linked to measurement. Thanks for a fabulous blog post.

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    1. Hi Juliet. Since I have read your book, Dirty Teaching, I know that children can measure with natural elements such as sticks. In fact, that probably gives them a better understanding of measurement than a ruler. That is especially true for young children for whom numbers are too abstract. Thanks again Juliet for your kind words. Tom

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