Does any of that seem similar to what goes on in a classroom as teachers attempt to assess the value of student work? What goes on the mind of a child is as obscure to most observers as is the state of the Schrödinger's quantum cat.One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The (wave) psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.—Erwin Schrödinger, Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics), Naturwissenschaften
(translated by John D. Trimmer in Proceedings of the American Philosophical Society)
There are distinct challenges in teaching a classroom of students and anyone who has taken a bit of time to observe the workings of his or her own mind will know that human attention can be observed in either wave or particle states. The cat is either dead or alive to the experience of learning. The mind can fixate on a single point, or it can fade in and out, drawn hither and yon between the moment, the past and the future. When a teacher stands before a classroom of kids the likelihood of all being intellectually engaged at the very same time is small. Even the most effective and engaging teachers are challenged to keep all student attentions on that which is assumed each must be learn. But student attention is much more generally like a wave than a particle of singular focus. Within the minds of any of his or her students is Schrödinger's cat either paying attention to the lesson or dead to the moment perhaps to suddenly rewaken or then again die a thousand deaths as interests ebb and flow, wax and wane, and as connections within the brain are made either by the instructor's lessons or by other distractions in the room that lead each student's consciousness hither and yon. It seems what we've accepted in American education is at best a blurred model, a fuzzy cat neither dead nor alive.
No doubt, as you were reading this you needed to do some mind wandering of your own... what a great chance to observe how the mind works.
The teacher standing at the head of the class often has no real idea whether the cat of attention is dead or alive. And sometimes lessons learned will not really become apparent until years down the road.
Lessons are a bit different when students are directly engaged in making real objects that express useful beauty. Within each student engaged in real things, whether music, making or laboratory science, the quantum cat is most certainly alive.
Richard Bazeley, shop teacher from Australia sent a photo of his children's work and asked how we can develop an assessment process that takes account of the work's value and content.
You will recognize the Clear Spring School Math Facts Box. In it, I can observe his student's care in their making of it, persistence in its completion, creativity in its expression. These vlues do not necessarily fit a statistical assessment like that demanded in most educational environments. Fortunately, at the Clear Spring School, we can assess student performance and student engagement according to non-statistical values. With our objective of fostering life-long learning, the ability imparted to the child to reflect on one's work through self-assessment takes on greater importance than 3rd party assessment by teachers or administrators. Most assessment schemes place an incredible, almost impossible burden on teaching staff. For instance, in Richard's case, he has 24 students to shepherd through the process of making the math facts box. There more than enough for him to do just to keep his students safely engaged and to offer personal instruction where required. The ideal would be for students to develop skills of self-assessment. That is one of the important things that comes to light through the "Child as Craftsman" metaphor for education.
Make, fix and create...
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