Click on thumbnail to watch inside our video library. In this video, the children decide to act out the emergence of plants from the earth. They gather under a brown blanket meant to represent the dirt in a garden and listen for the music to guide them to grow. “Soon, the music will tell your body what to do, and it might tell your voice what to do as well. Just listen,” their teacher explains. The children are patient and listen to the music. As the music crescendos Lara begins to “grow” but stops when she notices her friends are not. They rise from the “ground” together and use their bodies to represent the plants. The children are then invited to use instruments to represent more garden sounds. While two children, Lara and Giselle, use instruments, the others take cues from the music to represent their ideas of plants growing in the garden. The children watch themselves in the mirror and seem to be in sync with one another as they do the dance of the growing garden. The unfolding of the arms could represent the blooming of a flower or the growth of buds and leaves. The swaying could represent the flexible stalk of a tall plant moving in the wind. One wonders if Lara had to decide between her interpretation of the music and her friends. We wonder what she would do in a solo. We can be impressed by the children’s delay until the music changes and the expressivity of their movements. Such moments occur when teachers help children gently move into the meaning of the music. Notice the careful choice of the teacher’s setting remarks, “The music will tell your body what to do.” Such comments will start children on the path of music interpretation.

Announcement from Videatives

You may have noticed an improvement in the quality of the video in our video streaming service. We are upgrading all of the VSS titles to play in higher resolution on your computers, even at full screen. The full screen button has been reactivated. Also note that our videos will now play on the iPad. The iPad uses a different video format so we had to convert all of our video. We are still in the process of uploading a few remaining video files, but this should all be competed in another week. We hope you will try these enhancements. The full screen option makes public viewing in classes and workshops a better experience. And viewing on the iPad will give students and staff mobile accessibility to our video library. We are not sure if we can stream the 25 or so classic videatives (text with micro-clips hyperlinked to words in the text) over the iPad, but we have a good team working on this. These titles are in the VSS under the tab that reads “Videatives.” We will let you know when the extra functionality is offered. For now, you can still watch the classic videatives on your laptops or desktop computers.

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Click on thumbnail to watch inside our video library. Truman places objects in Abby’s hands. Shall we treat this encounter as a sweet moment of fun, or consider the regularity of Truman’s actions as a foundation for logic. Let’s see what yields when we describe his action as rules, similar to the “if – then” logic of computer programming or any well stated set of instructions (see J. Langer, 1982).

Truman’s first rule begins with two empty hands and a ball. The rule states: If a hand is empty, fill it with a ball. Since each hand becomes empty when the ball is moved to the other, Truman goes back and forth between the two hands (00:00 to 00:36). Note, toward the end of this segment, that Truman holds the ball in the middle, as if he realizes he needs to get out of this endless back and forth.

In the next segment (00:36 – 00:59), Truman tries to find places for three objects in two hands. Two of the objects are similar (semi-circle blocks). For a moment it looks as though his new rule is: Place similar objects, one in each hand. But the presence of the ball confuses him. Where should the ball go? Should it be placed in an empty hand? No. On top of the semi-circle he placed earlier in Abby’s left hand? No. To establish the equivalence of the two similar semi-circles, he gives up on placing them in Abby’s hands and taps them together at the mid-line. This bilateral banging action could well be the foundation of the concept of separate-but-equal (see G. Forman, 1982).

Now (00:59 to 01:44) we have the first rule applied again with the ball: If the hand is empty, fill it. This rule was initiated when the semi-circle got in the way of placing the ball in Abby’s left hand. He removes the semi-circle (we think so he can place the ball in her left hand), but once he places the ball in Abby’s left hand he sees that her right hand is empty, so back and forth he goes.

Truman realizes he is in another endless loop, but this time he merges the right into the left in a new way. He claps his hands together (something Abby showed him some moves back). His actions almost say, “I can’t put the ball in two places at the same time, but I can represent the merging of the two sides by clapping my hands together.” Children, the world over, treat clapping as an appealing action. Even so, this action becomes a tangible method to consolidate “separate-but together/together-but-apart,” what logicians call “equivalence.” To externalize this concept beyond his own hands, Truman holds Abby’s hands and moves them together and apart (01:44, and again at 02:55). His hands are no longer the content of equivalence, but rather are the author or agent of the expression of this concept. By moving other objects, action patterns of the hands become more general and more useful in helping children organize, structure, and create rules that are a type of early math.

Now watch the remaining two and a half minutes to see if you can figure out the rules Truman uses as he plays with Abby. Look for repeated actions with two or more steps. Look for aborted actions (change of mind). Look for the onset of sound as a marker for an action sequence or an expression of equivalence. Also appreciate how responsive Abby is to Truman’s intentions. Notice how responsive she is to Truman’s cue to make her open hands available (00:16) and how steady she holds her open hands, patiently smiling at Truman to signal her willingness to play according to his rules. This is an excellent example of an adult and child in perfect synchrony and a profound example of the development of the early logic of empty sets, full sets, and equivalent sets.

References

Jonas Langer, 1980. The Origins of Logic: Six to Twelve Months, New York: Academic Press

George Forman (Ed.), 1982. Action and Thought, From Sensorimotor Schemes to Symbolic Operations, New York: Academic Press.

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Click on thumbnail to watch inside our video library. Two boys, almost three, spend 15 minutes of playing with small toy cars. Can we find value in such ordinary moments, that is, from a learning perspective? One hears general claims about learning to play together, taking turns, pretending, being creative, and figuring out inclines. Too often the claims are not mapped to specific actions; they are simply made as if common sense. Even if these claims do make sense, we still do not know what any of them mean unless we use actual behaviors to define them. Furthermore, when we take the time to specify the behavior, we learn that there are dozens of different ways to play together, to take turns, to pretend, etc. and the differences in these ways begin to reveal what we call development, as opposed to learning.

We have analyzed and edited seven minutes of this play episode with a eye toward important dimensions of development – inventing symbols, maintaining co-play, and finding function in form. We take note of how the cars, as small replica objects, are particularly suited for the variations in play that we see, and we differentiate cognitive styles that may be gender related. Please download our analysis by clicking here, view the clip, and then read the text. We hope you will see their familiar actions in a new light.
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Click on thumbnail to watch inside our video library. This video clip begins with three children and two adults exploring MadPad™, an iPad app that allows children to create sound tracks to a set of twelve images arranged in a 3 by 4 matrix. The children can use the front video camera on the iPad to create a short video of themselves making sounds, or they can use the rear camera to take snap shots or video clips to go with sounds. When they touch any one of the twelve images, the respective audio loop plays once. The app also includes a large number of prefabricated images with sounds that the children can touch.

After an open-ended experience with MadPad the teacher (off camera) asks the children how this device could help them play music in the theater. Brian initially confirms that they could use funny sounds. Perhaps the children require more time with MadPad before they can generalize the formal properties of this device in order to suggest new uses for it. The adults move the experience forward by responding to the children’s wish to use the iPad to make their own sounds.

At 1:02 Brian has a funny sound ready to add to an image. At a minimum the MadPad app causes the children to explore the “funny” side of sounds. After Brian records a nasal whine, Sam, the technology teacher, taps the image so that Brian can hear that sound almost immediately. Then Sam touches the image rapidly, and the single sound becomes a phrase. The children laugh at the recognition of the repeated whine so similar to a baby’s, “Waaa waaa waaa.” (01:23). Would they have laughed had the pitch changed with each “waa?” Probably not. Such are the syntactical rules children use to “read” sounds.

At 01:37 Sam invites Maia to choose a category of sounds in advance of making the sound (funny, serious or musical). When this seems too complicated for her, her teacher (off camera) offers Maia the option to tap the table. Maia does so in a slow rhythmical manner as Sam records and then plays back the rhythm. Maia listens but does not react. Now the children know how MadPad functions, so Sam suggests that they create an entire 12 image matrix of self-made sounds.

The children shift into a more reflective mode to consider what sounds to make that are not ordinary, that is, sounds that are worth recording. What is funny? What combinations of sounds can two children make? They also like to video their faces as they are making sounds and words that they deliberately distort or truncate. The device encourages them to play with phonetic variations that they would not otherwise consider.

Watch the last 20 seconds of this clip carefully. The iPad has become a keyboard of animated images with corresponding sounds. All three children play and build on each other’s discoveries. If you look carefully you will see that they are testing paired sequences of two images; the first one followed by a similar sound or variation on the first. In summary, this device provides a method to create an alphabet of sounds, supported by relevant visual animation, in a keyboard matrix that can be used to compose interesting sequences – what we could call symbol literacy.

We will post more video clips on this application in the near future. If you have suggestions for its use in a school setting, please reply on our blog. For example, how could MadPad be used to revisit the sounds recorded on a nature walk? How could it be used to create a set of facial expressions that show a range of emotions and meanings, not in still photographs, but in short video clips with representative sounds (laughs, groans, whoops, etc.)? After all, aren’t emotions represented by how the face moves and not by some split second still shot? We welcome your suggestions.

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Click on thumbnail to watch inside our video library. Matthew and Angus work together for 45 minutes, drawing railroad tracks on a papered tabletop, connecting sites (and states) so their train can deliver candy cargo. In offering this setup, the teacher understands that drawing tracks eliminates the limits of using plastic or wooden track segments. The boys draw well and can easily change the direction and interconnection of an inexhaustible “supply” of tracks.

In this video sample of their work we suggest you think about the items below in order to decide if their 45 minutes contain value and learning moments.

* Each boy takes a turn drawing short segments of track toward the next city, instead of drawing a long segment all the way to the next city (00:54). This strategy assures the collaborative nature of their work. The rule emerged naturally from their desire to participate as equals.

* The boys look ahead from where the train is now to where it needs to go and calculate the direction and angle required to draw a curved section of track (01:49). The medium, drawing, makes these calculations necessary since there are no pre-formed sections of wooden tracks. The fact that the boys recognize the need to curve the track, even some distance from the destination, reveals their spatial intelligence.

* The teacher wants to help increase the complexity of the children’s thinking. Initially they are working to link one track to the closest dot (city). The teacher senses that the boys might be able to mentally step back and study the track as a system of interconnected routes, as opposed to thinking only about the direction the track should point to reach a dot. At several points she asks them, “It there an easier way to get to that city?” (02:50) “Could you use a track you already have?” (03:03)

* To the degree that the boys are successful in responding to the teacher’s question (03:35), they shift from relating one track to one dot and think about the relation of one track to another track and eventually another dot. This new way of thinking requires stepping back to mentally reframe what they are looking at. They are not looking at a list of separate tracks, each with an exclusive connection to one dot. Some tracks may be connections between tracks to create some economy in the system, and some may be used for traveling to more than one city, such as a main line that has spurs to outlying small towns.

* At one point Matthew works on a section that is separate from Angus’ work. Angus is keen to draw Matthew back into taking turns on the same track. Notice how Angus is careful to leave enough of the track unfinished so Matthew will have something to do (03:50). Angus calls out, “Matthew, it’s your turn.” Angus is also keen to say, “We are almost there,” (03:57) perhaps to maintain Matthew’s interest in working together on one track.

* Consider the value of having the toy trains as moveable objects that travel over the drawn tracks. Quite possibly the moveable trains add narrative and emotion to the game and help to sustain the boys’ interest (04:08). Also, the toys add purpose for the drawing and a way to confirm that the tracks create a useable system.

* Finally, consider the scale of this large drawing and the obvious complexity of what the children have produced during these 45 minutes. Most marks were done with a focus on a local objective, but when the boys sit back they are amazed and proud of creating an entire city. Matthew first calls their work a town, but then expands the category to “the whole country” (02:15). Similarly, note the brief discussion of the difference between a city and a state (04:20). Did the idea of a state, “not just cities,” come from the boys’ appreciation of the large scale of their work? Of course the class extension of “state” includes the subclass “city.” The fact that Angus points to a dot and calls it a state indicates that the class inclusion relation between state and city does not exist in his thinking. But it is through these games that such understandings are gradually constructed. Matthew knows that his city is called Boulder and learns that his state is called Colorado. But it will take a while longer for him to understand that he lives in both places at the same time.

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Click on thumbnail to watch inside our video library. Young children often imitate an action that they see. This action could be an early form of representation; that is, making a symbol that “stands for” a referent that happened in the immediate past. By imitating the event, the child in a sense “puts a handle” on the event so that she can mentally “grasp” it. Using two short clips, we have added more granularity to these metaphors. The text first describes what occurred, and then in italics presents our interpretation of what the child and the teacher might have been thinking, not literally as explicit thoughts, but rather as some intuitive level of their intentions.

00:03
The teacher spins a lid like a top. Blake, 14 months, sees the spin, rocks his shoulders back and forth while looking at teacher. [I want to share with you the excitement of this movement. I will move my body back and forth and look at you to see if you too are excited. My movement is my way of letting you know what it is in the world that excites me.]
00:04
The teacher looks at Blake, who is rocking back and forth. She rocks back and forth, while maintaining steady eye contact with Blake [I see you rocking. I know you are trying to share something with me. I will rock just like you are rocking to let you know that I understand you are sharing a referent (the spinning) with me.]
00:08
The teacher spins the lid again. Blake smiles and looks up at the teacher. Almost at the exact same time, Blake and the teacher rock their shoulders as they maintain steady eye contact with each other. The rocking is now the game: look at the spinning lid, look at the teacher (child) immediately, and rock your shoulders back and forth. [Blake: There is the spin. I need to look at the teacher quickly to see if she is looking back at me. I will rock back and forth to see if she will rock back and forth. We are playing a game.] [Teacher: I will rock back and forth when Blake looks at me. Perhaps he will know that I am doing the same thing that he is doing. That will augment the strength of his feeling that we are sharing ].
00:16
Blake moves to catch the spinning lid. He misses. Then he moves his hand back and forth. [Blake: This thing was moving when I tried to grab it. I will move my hand to indicate that the movement of this thing was what I noticed most ]. The teacher makes a circular movement with her finger and says, “Yes it does go round and round and round.” Blake watches her finger intently. [Teacher: Perhaps if I move my hand in a circular way and say round and round, Blake will associate the words with the shape of the movement. My gesture might help him "abstract," from all the many things he sees, the event that I am speaking about. I am not certain that he will think of the lid going round and round, but at the very least he might think that the words are related to the shape of my gesture].
00:20
The teacher spins the lid for a third time, but it does not spin well. When the lid falls, the teacher says, “Oops, silly.” Blake looks up at the teacher when she speaks but does not rock his shoulders back and forth. [Teacher: I want Blake to know that I did not expect the lid to fall, that this time the lid "did not work." It is important for children to classify events as either "done well" or "done poorly." This might help him to think about why ].
00:26
Blake throws the lid to the floor; it does not spin on its vertical axis, but it does rotate rapidly on its circumference. When it stops, he smiles and rocks back and forth while still looking at the lid. He vocalizes an expression of joy. [Blake: I know that movement. It is not exactly the same as before, but it is a movement that continues after I let go of the object. It is a movement that stays mostly in one place. To indicate what I abstract from what is going on around me, I will rock back and forth. I am moving in a way similar to the movement of that thing in front of me. That similarity makes me smile ].
00:31
The teacher spins another lid, smaller and silver. Blake watches this lid spin but does not wait for it to come to a stop. He crawls away from the play space toward another part of the room. [Teacher: It might be useful for Blake to see that the spinning action is not inherent to a particular object, but rather can be created using different objects that have the same basic round and flat shape ]. [Blake: Okay, I have seen this movement before. I would like to go elsewhere and do something new ].

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Click on thumbnail to watch inside our video library. Children, when in the comfortable presence of a loving adult, will allow themselves to go with the flow of spontaneous ideas while telling a story and even explain their story when asked. In this particular episode, Milena’s mom asks Milena to clarify story elements Milena has offered. Milena, who just turned four years old, knows the game and can switch back and forth between describing the events of the story and explaining her choices to her mom. Some of her remarks tell the story of swimming underwater and riding a dolphin. Some of her comments explain the motive or meaning of what she has already said. The combination of her creative imagery and her meta-linguistic comments makes this experience a learning encounter, an encounter that fosters Milena’s language development. She imagines, “I put on my sunglasses (probably means goggles), and they are going to stay on me, and they are gonna go under here (gestures around back of her head), and I am going under the water and swim in the deepest water.” She explains, “Far away means nobody is there.”

Via her mother’s questions she learns to think about the story as a structure with a beginning and ending; a story that is finished or not finished. She learns to think of genre: scary story, happy story, or short story. She knows that stories have openings, but the opening itself is not the story (“No, you’re supposed to tell it (the story),” she tells her mom who stopped after saying, “Once upon a time.”). She learns how to extend the complexity of a story by adding a second character (Mom asks, “And Buyla (grandmother) will jump in the water too?). She is asked to consider how one event precipitates the next event (Mom asks, “So how can she get a ride then?”). She learns how to find dramatic tension by focusing on elements of danger (Mom asks, “And then you’re going to swim… how far?).

Watch the video and listen for the comments from Milena’s mom. Notice how she adds voice quality when repeating Milena’s scary story, adding expressivity to the story telling. Consider how she helps Milena think about the concept of story. She co-constructs the story with Milena by offering specific suggestions, not simply saying to Milena, “Tell me more.” Here is a sample of her questions during this story telling encounter.

00:06 And what should we do (next)?

00:40 And Buyla (grandmother) will jump in the water too?

01:03 And Buyla with be right there with you, right, swimming?

01:09 What if you meet a dolphin? What would you do?

01:26 If you go on the dolphin, what would Buyla go on, a whale?

01:38 So how can she get a ride then (if the whale swallows Buyla)?

01:50 And then you’re going to swim…. how far?

02:00 Do you know what’s far away?

02:21 And what do you do if someone is not there?

02:30 And will that be the end of the story or only the beginning of the story?

03:48 Oh, that’s a very happy story.

03:53 What’s so scary about that story?

04:29 And he was afraid of the ghost and what’s next?

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Click on thumbnail to watch inside our video library. Watch this 2-year-old child explore the buttons on a music synthesizer and take note of what she learns about the conditional logic of the button functions; that is, how the lower button, B will turn on the drum cadence or turn it off but only if the power button, A is in the “on” position. We can define this conditional logic as follows: If A is x then B can be x or y. If A is y then B can only be y. By reflecting carefully on her play she discovers this conditional function (B’s function is conditional on, or determined by, the settings on A).

Piaget would call this video an example of “self-regulated learning.” We should not reduce this form of learning to the common phrase “trial and error.” To the child’s credit she understands which “trials” will give her the most information. So her trials are not random. What she decides to try comes from her assumptions about possible patterns, possible contingencies.

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If you subscribe to our streaming video library, look at “Not Just Play” as another example of self-regulated learning.

Notes from the Field

Boulder Journey School early childhood educator, Alex Cruickshank, recently shared her views on the current state of education in the US. Her riveting speech was presented to an audience of 1,700 at a TEDxBoulder event that was held on the University of Colorado Boulder campus. TEDxBoulder organizers, recognizing the relevance of Alex’s message, rewarded her with a donation of $1000, payable to Hawkins Centers of Learning, a non-profit organization that inspires educators world-wide. To view this presentation, click here.

Click on thumbnail to watch inside our video library. Young children will understand a book, as a cultural artifact, at different levels. We might call these early levels a form of pre-literacy. Is a book an interestingly hinged object to fold open and shut or pages that carry information in a sequence? Are the color patterns pretty decorations or pictures that refer to real things? Does the cover of a book have a different purpose than the inside of the book?

What actions do we look for to answer some of these questions? This clip shows two children at slightly different levels of treating a book as more than a physical object. The young girl finds the side of the book that allows her to pry it open. She does not try to pry it open from the spine. Notice how she lifts the open book toward her face and utters a sound (00:09). Is this sound an imitation of what she has seen others do, or is she expressing her recognition of a picture? Her line of gaze seems to be directed more at the blue on the page of print. As she continues to open pages she takes less and less time to process what is printed on the pages. As she switches to a second book we credit her again with knowing how to search for the side that opens. But instead of studying the pictures on the page, she tries to lift an edge with her thumb (00:26). She works to turn the pages and even over-applies this goal when she gets to the picture glued to the front of the book (00:52). When this picture resists folding over she reverses her strategy and folds the adjacent page toward the front (01:00). We can credit her with knowing how a book works as a physical object, but we have little reason to conclude that she is thinking that a book carries information. The teacher captions the picture, “a duck.” This labeling of the pictures will eventually help the child treat books as a source of information.

The young boy’s actions are rather different. He opens a new page, pauses, and looks at the pictures for a few seconds. Notice that at 02:16, when he sees the picture of a gorilla, he recognizes that the same picture appears on the cover. He flips the pages to reveal the cover, confirming his observation. He leaves his thumb in the place he left, perhaps as a way to more easily return to the interior page containing the gorilla’s picture.

He makes some vocalizations that are punctuated to match the full opening of a new page, as if he knows that this is what you do to introduce new information on a new page. He goes both forward and backward through the book, so he probably does not know that pages are turned from right to left for a reason. Each new page has something new to see and study, but he does not value the sequence. When he finishes turning all the pages from back to front, he goes back the other way. But he does not try to turn just one page at a time(03:14) as he did when he went from back to front. Perhaps he simply does not want to miss viewing any of the pictures. It is unlikely that he knows that a story has a sequence.

The early strategies described above are more than imitations to be forgotten as the child learns to read. They are components of the conventions that make books work: searching for the edge that is not hinged; turning one page at a time; turning from front to back only; pausing to scan the visual patterns on the page; treating the cover as a clue for the contents, and eventually using the sequence of the pages as relevant to the meaning of the presentation.

Runtime 4 minutes 2 seconds

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Click on thumbnail to watch inside our video library. Truman, 11 months, rotates, probes, and rubs a white shell. Let’s try and figure out what he might be thinking. By reading his actions as high level thinking we reveal the incredible intelligence manifest during the first year of life, intelligence that is sadly often reduced to phrases like “hand-eye coordination” or “using the five senses.” This shell has two contrasting sides, one convex, one concave; one smooth, the other ribbed. Watch this video and decide if you agree that Truman is actually comparing these two sides. In other words, is he thinking how one side is not like the other?

00:06 Truman turns the shell over, convex side facing him. He pushes on the surface with his right thumb. This occurs immediately after he looks into the concave side of the shell and probes its depth with his right index finger. These two actions look like a pair, one done because of the other, one done to see how it differs from the other. These actions confirm that this paradoxical object is both convex and concave.

00:12 During these six seconds he flips the shell several times, looking at it, perhaps confirming that the differences he feels with his fingers are corroborated by what he sees.

00:20 The camera zooms in to capture the small movements of his fingers. He presses hard on the shell with both thumbs, pressing on the relief created by a ribbing on the convex surface of the shell.

00:38 He changes his firm press downward into a sort of scraping over the ribbed surface of the shell. In this manner he gathers more information about the texture of the ribbing on the shell.

He frequently changes which side is up by pronating his wrist. 00:24 and 00:43 During these inversions, his finger tips are more fully in contact with the smooth inside of the shell. While we do not know if this contrast has entered his thinking, we do know that his hands have created this contrast for him to use. Much of early learning results coincidental to unintentional events. These events, once created, move into the consciousness of the child who subsequently makes the effect happen again with forethought.

At 00:48 we witness another contrast. His right hand releases his grip on the shell while his left hand holds it securely. At this moment, notice how he flexes his fingers, as if to say, “I have nothing in my right hand.” He has discovered the contrast between the substantial and the non-substantial.

Watch the rest of the clip and think about what you see this child do that reveals what he might be thinking. Place this thinking both in terms of what he discovers that the shell is and what he determines the shell (or a side) is not. The emergence of the concept “not,” as in “not smooth” serves as a foundation for even more abstract thinking. This way of marking development represents so much more than learning that something is smooth. Indeed, smooth itself has little meaning if it remains alone rather than compared to something that is not smooth. Paradoxically, a comparison, literally, is not “in” the shell but created by the working intelligence of a child. How can the senses feel something that is not literally there? They don’t. The child’s intelligence constructs a relation between the sensations.

Runtime 2 minutes 2 seconds

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