## Zone of Proximal Development

The photo above shows 3 levels of task demands for children based on Vygotsky’s levels of development.

• On the left is a level in which the student can readily perform the task independently, i.e. he is doing something he already knows how to do. (This is a not a student with special needs but some guy having fun.)
• On the right is a level that is too challenging for the student to accomplish independently. It is something he cannot do and does not know how to do.
• In the middle is a sweet spot. The level involves tasks that are accessible to the student but with support – scaffolding.

In reading this is known as the “instructional level” – see photo below. Reading material is evaluated by determining how challenging it is for a student. Material that the student can read independently may allow for some growth in reading ability, but not at the level of growth desired. Material that the student finds too challenging would not allow for substantive growth. In the middle is the sweet spot – the Zone of Proximal Development. This is where growth in reading can be maximized.

We can do the same with math using scaffolding. In the photo below is work performed by a former 7th grade student of mine with Asperger’s who tested at a 1st grade math level. I used colored pencils and 2 sided tokens to support his work with integers (red for negative and yellow for positive) in a CRA approach. The color coding and tokens were like the swimmies in the photo above of the child in the ZPD. Eventually these supports were faded. Throughout this process I was constantly pressing him to do more with a little less assistance.

I want to emphasize 2 major points regarding this.

• Substantive learning occurs when a student has to step beyond his or her current ability level – the ZPD.
• Often in schools educators avoid this (including me at times), especially for students with special needs, because we want students to be engaged and successful (in the short term). We often confuse being active with learning. The guy on the tricycle in the top photo was performing a task but was he learning?

Here’s are a video that fleshes out this idea.

## Art = Critical Thinking

In my MATH class I use Picasso’s GuernicaÂ to get students to think – shaping critical thinking. This is a tribute to my art and architecture class which was the coolest class I had as an undergrad – the act of art speaking to life blew me away. I show them a photo with the following directions:

What do you notice in this painting? Write any ideas at all on your own paper.

I find that after prompting, prodding and not accepting “I don’t know” almost all will share something, e.g. “people look sad.” That singular effort alone is a big step for many. Here is information about the painting that I share afterwards (credit to Wikipedia):

Guernica is a painting by Pablo Picasso, in response to the bombing of Guernica, Basque Country, by German and Italian warplanes at the behest of the Spanish Nationalist forces, on 26 April 1937, during the Spanish Civil War.

Â Guernica shows suffering people, animals, and buildings wrenched by violence and chaos.

• The overall scene is within a room where, at an open end on the left, a wide-eyed bull stands over a woman grieving over a dead child in her arms.
• The centre is occupied by a horse falling in agony as it had just been run through by a spear or javelin. It is important to note that the large gaping wound in the horse’s side is a major focus of the painting.
• The bull’s tail forms the image of a flame with smoke rising from it, seemingly appearing in a window created by the lighter shade of gray surrounding it.
• Under the horse is a dead, apparently dismembered soldier; his hand on a severed arm still grasps a shattered sword from which a flower grows.
• A light bulb blazes in the shape of an evil eye over the suffering horse’s head (the bare bulb of the torturer’s cell.) Picasso’s intended symbolism in regards to this object is related to the Spanish word for lightbulb; “bombilla”, which makes an allusion to “bomb” and therefore signifies the destructive effect which technology can have on society.
• To the upper right of the horse, a frightened female figure, who seems to be witnessing the scenes before her, appears to have floated into the room through a window. Her arm, also floating in, carries a flame-lit lamp. The lamp is positioned very close to the bulb, and is a symbol of hope, clashing with the lightbulb.
• From the right, an awe-struck woman staggers towards the center below the floating female figure. She looks up blankly into the blazing light bulb.
• Daggers that suggest screaming replace the tongues of the bull, grieving woman, and horse.
• A bird, possibly a dove, stands on a shelf behind the bull in panic.