I has just occurred to me that as teachers we work a piece of un-physical magic as we lead or guide a class through a course.

My reasoning goes as follows. At the start of the class, all the students are unknowns. We don't know how well they learn, how hard they are going to work, or what their ability is.

So if we define the entropy of the system in terms of all the possible outcomes, any student could potentially end up at any point in our class and the entropy is high.

in formula S = k Log(n)

where n is the number of possible states of the system, that is the number of different potential outcomes.

If I have 30 students in the class, and I mark out of 100, then this comes to

S = k 30 Log (100) = 60 k.

After the first mid term, when 30% of the marks have been decided,

S = k 30 Log (70) = 55.4 k.

After the second midterm with only 40% of the marks to be decided by the final,

S = k 30 Log (40) = 48.1 k.

After the final, when all outcomes are clear,

S = 0.

As the semester (term) goes on the probable trajectory of each student becomes more constrained. with the system eventually resolving into one final configuration, the final marks, and the uncertainty about the progress of any given student has reduced to zero. In thermodynamic terms, we have cooled the system by removing the entropy and condensed the educational gas which the students represented, into a set of distinct phases, one for each possible student outcome (mark)..

We have reduced the entropy of the system Can I say cool?

## Wednesday, March 28, 2012

## Saturday, March 24, 2012

### Learning is one dimensional

Not all of it. But I have encountered a problem and its made me think of learning in a new way. I wanted to use Moodle to asses student learning styles, this would involve asking the questions from a test bank, and then rating their answers along a number of different dimensions of learning preference.

I have not solved this problem. We normally assign students to a point along a one dimensional continuum which runs from didn't understand a thing I taught them in class to has complete understanding of everything covered.

Our aspiration as teachers is to move student along that scale, with the hope that they will end up at the I know everything end of it.

We are neglecting the possibility that their learning is moving in several different dimensions at once. They may be failing my maths course, but becoming more reflective and capable persons through knowing their limitations.

They may be learning a lot about the interpretation of data and the application of geometry, but failing to pick up on the abstractions of algebra.

In most subjects, if I think about it, I can find several different strands or dimensions of learning, but we insist that at all times is all part of one bag which we judge solely by how full it is.

Maybe its time to make our subjects more multidimensional.

I have not solved this problem. We normally assign students to a point along a one dimensional continuum which runs from didn't understand a thing I taught them in class to has complete understanding of everything covered.

Our aspiration as teachers is to move student along that scale, with the hope that they will end up at the I know everything end of it.

We are neglecting the possibility that their learning is moving in several different dimensions at once. They may be failing my maths course, but becoming more reflective and capable persons through knowing their limitations.

They may be learning a lot about the interpretation of data and the application of geometry, but failing to pick up on the abstractions of algebra.

In most subjects, if I think about it, I can find several different strands or dimensions of learning, but we insist that at all times is all part of one bag which we judge solely by how full it is.

Maybe its time to make our subjects more multidimensional.

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