About Me

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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.

Sunday, August 4, 2019

Horizontal tube with holes

In 2013 I built an apparatus that I called: horizontal tube with holes.  I placed a long cardboard tube lengthwise across two sensory tables.  I supported it above the tables with two brown planter trays.  For stability, I taped the tube to the the two edges of one of the brown trays and to the lip of the clear table.
I cut and drilled multiple holes in the tube.  Those holes provided multiple points of entry for the children's operations.

This may look fairly simple, but it turned out to be a multidimensional space.  It had length: the cardboard tube spanned the two tables.  It had width: the width of the table perfectly holding the planter trays.  And it had vertical depth with three levels of play: the table, the trays and the tube, all on different levels.

There was actually a fourth level of play, namely the floor.  The level of the floor is represented by the bottom of the tub next to the table.  The following video shows how one child incorporated the bottom of the tub---a.k.a. the floor---in her operations.

Covering the bottom of the tub from Thomas Bedard on Vimeo.

She used her pail to methodically distribute the pellets to cover the bottom of the tub.  Was she cooking, gardening, ... ?

In addition to vertical depth, this apparatus provided horizontal depth, too.  The child pictured below explored that horizontal depth as he reached well into the tube to scoop out pellets.

Of course, depth also had another meaning with this apparatus.  Whether the children filled pails, the tube or the trays, the depth they experienced was volume.

The fact that this apparatus was multidimensional encouraged all kinds of operations in and around the tables.  I especially appreciated those operations that involved a certain amount of vigor.  In the video below, the child used both hands to propel the pellets out of the tube into the tub next to the table.

Horizontal blast of pellets from Thomas Bedard on Vimeo.

The child basically shot the pellets out of the tube by pushing them to the end of the tube with her right hand and thrusting them out toward the tub with her left hand.  So what if not all the pellets landed in the tub.  She created her own experiment with force and trajectory

Children are masters at exploring all the dimensions of any given apparatus.  They do it spontaneously; they do it methodically.   Sometimes they even do it with zest, and for me, that is always a bonus.

Saturday, July 27, 2019

Unique loose parts

In my last post, I wrote about children making meaningful choices around an apparatus I called the vertical tube and rope apparatus.
When I looked through my documentation on how children explored this apparatus, I noticed a couple of unique loose parts that played an integral role in their explorations.  Those loose parts were S hooks and carabiners.  In the picture above, the pail floats in midair above the table because the handle of the pail was suspended by a S hook attached to a carabiner attached to the rope strung over the table.

Here is a better view of the carabiner and S hook holding the pail in the air over the table.  That configuration allowed the child to pour hands-free.  
Contrast that operation with the child trying to hold the bucket up with one hand and pour with the other.  Of course, she could have set the pail in the bottom of the table and poured hands-free, but pouring pellets in the bucket hanging in the air was more intriguing for sure.

Not only was it intriguing to fill the bucket floating in midair, but with a little push or two, the pail easily became an experiment in pendular motion.

Pail pendulum from Thomas Bedard on Vimeo.

The child in the video above first used his left hand to push the pail four different ways.  He then used the metal bowl in his right hand to push the pail in four more different ways. 

Part of the definition of a loose parts is that they can be rearranged and combined in novel ways.  Below are some of the ways the children arranged, rearranged and combined the carabiners and S hooks.

Besides hanging pails, this child also used the carabiner to hang a metal measuring cup on the rope for easy access.

Below, the child on the left collected the carabiners and clipped them all together into a big clump.  On the right, a different child collected the carabiners and used them as a manipulative by hanging them end-to-end vertically.

Below, the child on the left combined a S hook with carabiners to carry the pail with a chain-like piece of equipment of her own making.  The child on the right took several carabiners to tie together all the ropes on one side of the apparatus.                                                                                                                                                                 

The child in the video below set a challenge for herself to connect two sets of S hooks, one set of hooks hanging from above and another set hanging lower.   To do that she had to make sure the lower hanging set stayed together as she lifted it up to meet the set hanging from above. 

Connecting the S hooks from Thomas Bedard on Vimeo.

Her actions were deliberate and cautious because she was not sure the two sets would hang together. As she stepped back to view her completed challenge, I saw a sense of accomplishment both in her face and gestures.

So often I see loose part displays that would be considered art that are aesthetically pleasing using all manner of materials both natural and man-made.  In addition to using loose parts to make art, they are also used to represent things such as flowers or buildings.  The children have helped me expand my idea of what is a loose part.   I now think there needs to be another category of loose parts, namely, functional loose parts that the children use to complete an enterprise of their own making.  Ramps, tubes and tires are common loose parts that fit into this category and are well known in ECE.  After watching the children play and explore with carabiners and S hooks, let me add those to the list of functional loose parts.

Saturday, July 13, 2019

Meaningful choices - part 2

In my last post, I wrote about children making choices.  I wondered if the choices they were making were meaningful choices or did those choices become meaningful once they made them.  Maybe it is not a question of one or the other.  Rather, it may be a combination of both.

To make some sense of this question, I looked at the choices children made in their play around an apparatus I built in 2013 that I called tall cardboard tubes and ropes.  I taped four tall cardboard tubes to each corner of the sensory table.  I drilled multiple holes in each of the tubes and strung ropes through the holes. 
I cut holes on the bottom of each tube and also placed a plastic tub under each to catch the pellets that the children poured down the tubes.  I also added a 1"x2" boards between the cardboard tubes at the top for stability.

Because there were so many holes on so many levels, the children could make meaningful choices as to which holes they wanted to work with.   Below, the child reached as high as he possible to pour pellets into the hole at the top of the tube.  Because the hole was so high and he had to reach with his full extension, his pour yielded many pellets in the hole, but also some in his face.
In a way, that choice became meaningful for him because he gained some physical knowledge about what his body could do.

The child in the following two pictures made a meaningful choice to pour pellets into one of the middle holes.   He found out the pouring directly from the pink cup did not work so well, so he found a better way to pour into the middle hole by pouring pellets from the pink cup into a small scoop that fit nicely into the middle hole. 


His choice took on more meaning when he encountered and solved a problem around pouring pellets into the middle hole.

The child below made a meaningful choice to bring the dinosaurs from the block area to the sensory table to combine them with the tub and pail on the floor. 
He created more meaning as he used the bottom hole, the tub and the green pail to establish a world in which the dinosaurs could climb, eat and fight.

Believe it or not, one of the meaningful choices the children made was to climb on this apparatus.  In the following video, two children climbed up onto the lip of the table so they could pour pellets down the top opening of the tubes.  In the process, they used and created a lot of embodied knowledge, especially in their efforts to keep their balance as they climbed onto the narrow lip of the table.  In fact, the child in the stripped shirt lost his balance on the first try and had to step back down onto the ground.  On the second try, as he stepped onto the lip of the table, he shifted his weight over the table so he would not loose his balance.  And both children knew to use their left hand to hold onto holes in the tubes for stability.

Climbing the apparatus from Thomas Bedard on Vimeo.

Up until this point, I have only talked about the children making meaningful choices.  When the children started to climb the apparatus, I had to make more conscious choices: Should I let the children climb the apparatus?  Was it safe?  Did the children have the requisite physical ability---strength, balance, etc.---to climb?  Did the children demonstrate they could assess their own risk?  Those were all moment-by-moment decisions that I was making for each child.  And those were meaningful choices because they were giving me information about myself: How do I feel about the children climbing?  What am I learning about the children's need to physically challenge themselves?  What are the children learning about themselves and their capabilities?

Even though it looked like the children had unfettered choices to explore this apparatus, there were limits.  With this apparatus, I chose not to allow the children to climb into the table.  Why?  I am not sure, but I think it had to do with the children stepping on the pellets and grinding them to sawdust.

The children honored that boundary.  One or two children did step into the table, but it was an accident and they immediately stepped out.  That said, children are great limit testers.  In the video below, the child arranged stools so she could traverse the corner of the sensory table without stepping into the table.

Making a path from Thomas Bedard on Vimeo.

He body posture at the end told me that she was quite proud of herself because she was able to define the boundary with her path over and around the corner of the table without stepping into the table.

In all these examples, both the children and I were making meaningful choices because they were were not prescribed.  We operated together in an flexible environment of rich possibilities.  And because the choices were not prescribed, they were authentic.  Those authentic choices opened up a myriad of other authentic choices that, in turn, created more meaning for all of us.

Saturday, June 22, 2019

Meaningful choices

As of late, my go-to book for thinking about early childhood education is The Informed Vision, by David Hawkins. In his book, Hawkins often talks about setting up the classroom for children so they can make meaningful choices.  What constitutes meaningful choices? And, more specifically, what constitutes make meaningful choices in the sensory table?

What complicates any answer to the question of meaningful choices is the following quote.  Early on in the book, Hawkins wrote:

           "The product number, of possible congenital patterns multiplied by possible early 
            biographies of children, is of higher arithmetical order than the total number of 
            children past, present, or future.  The probability is effectively zero that there 
            would be two children presenting the same educational challenges and opportunities." (p. 25).

In other words, every child who enters the classroom is different from every other child.  How, then, can a teacher set up any area of the classroom so every child can make meaningful choices?

My answer is a simple answer: every child has to be able to find their place in the classroom.  That would be a place in which they feel valued for who they are and the choices they make about how to engage with the environment.

As an example, let me show you choices that children could and did make around one apparatus set up at the sensory table in 2015.  I chose to build an apparatus in which I embedded the sensory table halfway into a big box that I called table embedded in a big box.

I chose to add a second box that was tall.  I inserted two tubes in the box that went from the top the box, down into the box and then out of the box. One tube emptied into the table and the other emptied down into the bottom of the big box.

The first meaningful choice children made was to not engage with the apparatus at all.  Because children were not required to move to stations around the room, some children chose to work in other areas of the room that included the writing table, the large muscle area, the building area, the housekeeping area, the manipulative area and the book area.   Even though I myself had chosen to put a lot of effort into building the apparatus, I still had to honor a child's choice not to engage with it and to engage with something more meaningful to them on that day.

One child chose to arrange the loose pails, pots and bowls on top of the apparatus so he could use the plastic serving spoon to deliberately test the different sound each object made. 

Percussion play on top of the box from Thomas Bedard on Vimeo.

He gathered the pails, pots and bowls and arranged them almost like a drum set on top of the big box.  No other child did this with this apparatus.  In essence, he played with an idea of his own making/choosing that resulted in new meaning for him.

It was not unusual to see a child actually go into the box itself.  That was likely since I purposefully chose to leave some room as an invitation for a child to crawl in.  The child in the video below crawled in and situated herself as she gleefully exclaimed: "I fit in even though I am taller than this whole thing!"

I fit in the box from Thomas Bedard on Vimeo.

In essence, the child has chosen to use her body and her emotions to make meaning of this complicated apparatus.

If one child fit inside the box, why not two?  However, when two children chose to be in such a small space their choice took on a much different meaning.  It was not just figuring out a complicated structure, but it was also about how to negotiate movement in a very tight space.
These two children chose to be in the box together.  They also chose to constantly move, even go so far as to as to switch places a couple of times.   In essence, they were socially constructing what it means to accommodate another child in a very confined space.

Many children decided to engage with the second box with the tubes.   Because the tubes were inserted into the box, the children could not see the path of the pellets that were poured into the holes at the top.  Instead, they had to experiment to see where the pellets exited when pour into one of the holes at the top.   The child below did just such an experiment.  He chose one of the holes into which he poured the pellets.  He had an idea where the pellets would come out and looked to see if his hypothesis was right.

Hypothesis from Thomas Bedard on Vimeo.

In essence, the child chose to experiment with the apparatus, not only to make sense of it, but also to understand the properties of the material he was working with and the forces acting upon that very material.

Children often decided to act together.  Below, five children poured pellets down two holes.  They may not have been as interested about where the pellets went as they were in the frenzy to pour as fast and as many pellets as they could as a group.
In essence, they were socially constructing what it meant to work as a group in self-chosen task.

I began with the question: What constitutes meaningful choices for children?  In almost every example I gave, I actually reversed the order to show that children were making choices and that they were meaningful to them.  That was true if they worked alone or with others.

For me this raises several questions.  If children are truly given the freedom to make choices, are all their choices meaningful?  Can a child even make a choice that is not meaningful in some way? Who gets to decide what is a meaningful choice?  Are some choices more meaningful than others?  

Saturday, June 8, 2019

Big box and cardboard tube with opposing inclines

For 28 years, I built apparatus that fit in and around the sand and water table .  Children arrived in my classroom already with a set of competencies that could be expressed while playing with those structures.  I always wondered how those structures would shape children's play and exploration given their competencies.

As I have done over the past couple of posts, let me infuse my musings with a context.  The context I wish to use is an apparatus I built in 2012.  The apparatus was a long narrow box set on an incline.  Children poured wooden fuel pellets down the box through various holes I cut in the box.  The pellets exited the bottom of the box through a slit that directed them down and into the blue tub next to the sensory table.  Here is the original post: big box incline with added element.

The reason I cut multiple holes in the box was to give children multiple points of entry for their operations.  In addition, I partially embedded a cardboard tube in the top area of the box on an opposing incline.  Pellets poured down the tube exited into a small sensory table at the end of the cardboard tube.

Let me start with a couple of competencies that the children brought to the apparatus; scooping and pouring.  Those may sound simple but I wonder if they really are.  I do not know enough about motor development, balance and proprioception to understand how complex those operations really are.  However, given those competencies, how did the incline apparatus shape the children's play and exploration.

In the video below two children poured wood pellets down the box incline through the hole at the top end of the apparatus.  The child on the right poured first.  As he poured, he looked down at the bottom of the box incline because he expected the pellets to exit from there.  He did see some pellets fall out the bottom of the box, but most of his pellets went down the cardboard tube in the opposite direction.  When the child on the left poured his pellets into the box, he seemed to aim his pour so he could direct as many pellets as possible into the cardboard tube.  Both children poured pellets a second time.  The child on the left did a careful pour again making sure to get as many pellets as possible to fall into the cardboard tube.  The child on the right decided to pour pellets through the hole on the top of the apparatus.  He again looked to the bottom of the box for the pellets even though most of them went down the cardboard tube, not down the box.

Aiming for the tube from Thomas Bedard on Vimeo.

In a way, I think the apparatus gave a novel purpose to their scooping and pouring.  For the child on the left, it was to see how many pellets could he get to disappear down the cardboard tube.  Was he working on his aim or was he fascinated with how the pellets tumbled and disappeared down the tube?  For the child on the right, it was to see where the pellets he poured actually went.  Did he notice the disconnect between how many pellets he poured and how many dropped out of the box at the bottom?  

Another competency that the children brought to the apparatus was an insatiable curiosity of how it worked.  That was true for the two children in the first video and it was also true for the children in the following video.

Two children brought little cars from the block area to use with this apparatus.   One child made ambulance sounds as he positioned his little ambulance in the opening on the top end of the box.  Before letting it go, he moved his head to the hole on the side of the box so he could get a closer look at what happened to the ambulance when he let it go.  He let it go and watched it drop into the cardboard tube.  He knew immediately that it changed directions and went down the tube.  He even told a child at the end of the tube that he caught an ambulance, his ambulance.  A second child in red repeated this experiment but watched his actions through the opening in the top end of the box.  This child knew that his race car changed directions when it entered the tube because he, too, immediately looked to the bottom of the cardboard tube to see where it went.

You caught an ambulance from Thomas Bedard on Vimeo.

In this case, the apparatus offered the children a challenge: What happened to their cars when they fell into the tube?  That challenge fed their curiosity to figure out the trajectory of the cars they put in motion down the box.

Yet another competency the children brought to the apparatus was the ability to give the apparatus a novel purpose.  In the video below, the same two children who brought the cars to the sensory table were asked to collect the cars at cleanup time.  To collect the cars into the car container, they decided to place the car container at the bottom of the cardboard tube.  In that way, they were able to send all the cars down the tube right into the container. 

Fun way to cleanup the cars from Thomas Bedard on Vimeo.

I suppose they could have just collected the cars and put them in the container, but by using their ingenuity, they decided there was a more engaging way to collect the cars.  It may not have been the most efficient way to collect the cars because some cars bounced out of the container, but the apparatus afforded an opportunity for them to figure out an original way to collect the cars.  And as the child in the orange stated: "Who knew picking up the cars could be so much fun!"

Since each child is unique who enters our classroom, how do we come to know their competencies?  I contend we can only come to know their competencies in a context that allows them to express their competencies.  If that sounds circular, it probably is.  If we take the time to observe children's play and exploration---not for checklists---we can see that a context can nurture children's competencies and children's competencies can give shape to that very same context.  


Saturday, June 1, 2019

Intentionality and spontaneity

I have been thinking a lot about intentionality and spontaneity and where they fit in an early childhood classroom.  Intentionality seems to carry a lot of gravity these days.  Teachers are suppose to be deliberate and purposeful in their teaching.  They are asked to know what they are teaching (think curriculum); how are they teaching it (think fidelity to the curriculum); and to test their students to see if they have learned it (think checklists). What does not seem to carry a lot of gravity in early education is spontaneity.  So much of what happens in an early ed classroom is directed by the teacher leaving little room for spontaneous ideas and actions to emerge from the children themselves.

I would like to give my thoughts context using an apparatus I built back in 2015 I called horizontal tubes in boxes.  This apparatus consisted of four long cardboard tubes embedded horizontally through two boxes.

I intentionally constructed this apparatus to offer children an opportunity to work on a horizontal plane.   My intention was to create a challenge for the children to move the wood fuel pellets through the long tubes.   (I also intentionally embedded the tubes on different levels.)

Since the tubes were so long, I intentionally offered different points of entry so the children could move the pellets inside the tubes with their hands.

In addition to multiple entry points, I also fabricated homemade plungers by attaching a metal jar lids on the end of a dowels.   And I intentionally made them different lengths... 
so children could explore how deeply they would have to reach into the tubes to move the pellets all the way through the tubes.

Finally, I intentionally handed the apparatus, along with the implements, over to the children so they could make it their own.  My intentions at this point went as far as setting up this classroom space for play and exploration.

What were the children to learn from their play and exploration?  I honestly did not and still do not know.   I do know that the children created numerous ways to move the the pellets and other things through the tubes horizontally.  And many of those trials included a good dose of spontaneity.  Below are just three examples.

The child in the video below pushed the plunger all the way through the cardboard tube.  The plunger got stuck on the lip of the tube on the other side.  The child, by looking in the mirror, could see how the plunger was stuck and he told the child on that end that he "needed it."  The child off to the left of the screen then lifted the plunger so it was no longer stuck.  The child seen in the video was then able to pull the plunger out.  After getting the plunger out, he reinserted the plunger and pushed it through the tube again.

Referencing his own actions from Thomas Bedard on Vimeo.

What made this child's actions so intriguing was that he completed his actions by looking in the mirror on the wall next to the sensory table.  He may have purposefully moved the pellets through the tube, but because he offhandedly saw himself in the mirror, he spontaneously referenced his actions in the mirror.

The child in the video below created a different mode of moving the pellets through the tube: he blasted them by thrusting the plunger with force and speed through the tube.  Some of the pellets moved into the tube, but many went flying.  At the end of his actions, he turned to me and basically said that it was funny how he "blasted it."

Blasting the pellets from Thomas Bedard on Vimeo.

This child was the only one who introduced speed and force to move the pellets with the plunger through the tube.  He used the word funny to characterize his actions that blasted the pellets.  However,  I think he was also surprised and delighted at the result of his spontaneous actions of jamming the plunger with force through the tube.  What surprised me was how he reversed his operation by pulling out the pellets from the tube, not with speed and force, but with measured speed and deliberation so the pellets dropped nicely into the bin below the tube without spillage on the floor.  Did he intentionally reverse his operation or was that spontaneous, too?

In the video below, the child on the left of the screen inserted a plunger into one of the cardboard tubes.  She turned to the camera and said: "I am pushing."  Her actions actually pushed a second plunger out the other end of the tube.  The child on the right of the screen squeals when that second plunger suddenly popped out of the tube on her end.  She used her hand and measuring cup to block the plunger from going any further out of the tube.  Then she pushed it as far as she could back into the tube.  The child on the left pulled her plunger back.  After a brief pause, she thrust her plunger back into the tube as far as she could.  As she did that, she looked through the hole in the top of the tube to see why she encountered resistance.  The reason, of course, was that the child on the other side was expecting the second plunger to come out of the tube again, but this time she was ready and she blocked it with her measuring cup again.

Pushing from both ends from Thomas Bedard on Vimeo.

These two children could not see each other but they were still able to create a spontaneous game of "push-of-war," the reverse of tug-of-war.

I have only scratched the surface of how the children made this space their own.  They may have been purposeful in the exploration and play, but the purposes they created were fueled by their ability to spontaneously interact with the setup, the materials and each other.   By intentionally offering them the space, the materials and the time to play, I was free to document their spontaneity---intentionally.

Saturday, May 11, 2019

Honoring their operations

Children's operations might look simple but are really quite complex.  Take for instance the operations of filling, pouring and transporting.  To understand how complex these operations can be, I need to put them in a context.  The context I will put them in is an apparatus I built back in 2011: vertical boxes.  I built the apparatus using four boxes.  Box 1 was the base. I attached it to one end of the blue sensory table.  Boxes 2 and 3 were partially embedded in the base box.  Box 4 was attached to box 3.
Holes of different sizes and orientations were cut in all the boxes except box 4.  I even cut a hole on top of the orange box in the section that was partially embedded in the base box.  (That hole is important to understand the last video in this post.)
Those holes provided different pathways to move wooden fuel pellets around and through the apparatus. 

For example, in the video below a child transported pellets from the bottom on one side of the large narrow box to the blue sensory tub on the other side of the box.  He did that by scooping pellets with a spoon through a window on his side and then reaching over the box to deposit the pellets into the blue sensory table.

From side to side from Thomas Bedard on Vimeo.

His operation turned out to be quite complex.  To get the pellets on his spoon out of the big box without spilling them, he had to carefully navigate the narrow verticality of the base box.  That took good eye-to-hand coordination and good muscle control.  Next, to reach over the box, he had to lift the spoon to shoulder height.  Because he still did not want spill any pellets, he had to keep the spoon horizontal.   Once he cleared the top of the box, he dropped the head of the spoon to deposit the pellets in the blue sensory table.  A nice added touch to his operation was when he monitored his operation by stretching his head over the top of the big box to see where the pellets dropped.  

Here is a slightly more complicated operation of filling, pouring and transporting the wood pellets.  The child started his operation much like the previous child.  He scooped pellets into a small metal measuring cup by reaching deep into the window on his side of the large narrow box. He did not pour the pellets over the box like the first child.  Instead, he poured his cup of pellets into a five gallon pail.  Then he lifted the pail over the top of the box to pour his pellets into the blue sensory table.

Big pour from Thomas Bedard on Vimeo.

There are several actions that added to the complexity of this child's operation.  First, he grabbed the hole on the top of the orange box with his left hand for body balance and stability.  Second he had to use both his hands to lift the five gallon pail to the top of the big box.  Third, because of the size of the five gallon pail, he used the top of the box as a fulcrum to help empty the pail of pellets into the blue sensory table.  In essence it was a three stage operation with specific challenges accompanying each stage.

A filling, pouring and transporting operation can often times work in reverse.  In the picture below, a child used a big white scoop to pour pellets from the table into the hole on the top of the orange box partially embedded in the big box (the hole can be seen in the second picture of this post).  The orange box was full, so as he poured, pellets spilled into the small box next to orange box.  Below, he observed the results of his actions.

Here is a video that shows his operation.  It is interesting to note, that a child who heard the flow of pellets on the opposite side of the box, came over to watch the pellets tumble out of the orange box into the smaller box.  At the very end of the video, that child looked up at the boy on the other side of the box in an attempt to understand the connection between the boy pouring and the pellets dropping out of the orange box.

Novel path to fill the box from Thomas Bedard on Vimeo.

The child pouring the pellets added complexity to his operation by creating a novel path for transporting the pellets from the blue sensory table into the small box on the floor attached to a window of the orange box.  Not only was it a novel path---through the big box, through the full orange box and into the small box next to the orange box---it was partially hidden.  The child had to connect his actions on one side of the box with the overflow of pellets on the other side of the box even though he could not see full path of the flowing pellets.

I have just scratched the surface of examples of how children's operations that may look simple are really quite complex.  A structure like the vertical boxes invites the children to explore its complexity.  In that way, the vertical boxes---or any other apparatus at the sensory table---honors the children's capacity to come up with new and complex operations to carry out self-selected challenges as they claim ownership of the apparatus.