Challenging For All Or Just Impossible For Some? (Come back, Claude Shannon, we need you!)

Back at the start of this blog I drew up a learning and teaching diagram, which I reproduce here:

The idea is simple. We learn from inputs and, having learned, can then teach and pass this information on to other people. This diagram represents a single person and shows the benefits of learning and teaching as separate and fusion activities. But can we guarantee that our outputs will reach someone else’s inputs without distortion – without information loss?

Well, that depends very much upon us and the receiver. If we’re not prepared to explain ourselves then our transmission will be less than 100%. If the student isn’t listening then their reception will be less than 100%. Combine these (by multiplying them) and we will definitely get less than 100%. If we add the medium into the mix, the environment that the transmission moves through to get to us from them, then we introduce another potential point of loss. I now have three places to reduce my efficiency. No wonder we spend so much time on trying to engage our students, to use sensible techniques and to present our ideas clearly!

Final transfer = %age of transmission * %age of successful medium passage * %age of reception.

For example, if you have no way of getting information to your students, then the %age of successful transmission is 0 and nothing is transferred. This is not anything amazing – it’s a simple application of the product rule. This is the effective percentage of the information that you sent out that is reaching the student. How bad is this? Let’s say you have a bad day and give a lecture where everything is working except you. You give a 30% lecture. Nothing else gets in the way. Your aids all work, your students are awake. Final result: 30% * 100% * 100% = 30%. Basically, if you don’t put it into the process at the start, nothing else is going to come out. (There are many ways to think about this, including ways with mathematical proofs, that I will discuss later in this post.)

How much does a student need? Good question! Some students will get by on a small amount and go off and do excellently. Some need a lot more. Unless you have a very good understanding of your students abilities, or a very tight cohort, the line between making something challenging and making it impossible is very hard to see.

I must be frank with you in that I find that some people I have observed, over the years, have not made it easy for the students to obtain the knowledge. As you can see from the model, if you’re not communicating 100%, then it doesn’t matter if the student is desperately trying to get information out of you – they can’t get what you’re not saying. Similarly, if you put it in a form that is muddled or confused then, once again, we reduce the chances of information going across.

If you’re in engineering or ICT you’ll probably have heard of Claude Shannon. Shannon effectively founded the field of Information Theory back in 1948, but also founded both digital computer and digital circuit theory 11 years earlier, as a masters student. A lot of Shannon’s work revolved around how much information you could transmit, given the physical characteristics of the medium you were using and how noisy it was. Rather than my primitive equation above, which talks in terms of probability (or possibly efficiency), Shannon’s Channel Capacity equation very sensibly states this in terms of the largest amount of information that can be shared. If you like, you can’t fit a bowling ball through a garden hose at the same rate you can push a bowling ball through a large pipe. When the pipe is full of noise, say water or concrete, you can’t treat it like a big pipe. If it gets full enough of noise, it will be a garden hose and things slow down. (My apologies to engineers, I didn’t feel up to a discussion of mutual information and input distributions.) The medium in this case is a noisy channel – a channel where things can and do go wrong, much as happens to us every day. Because most of us are time locked (lecture time, semester duration), any decrease in efficiency that requires more time will lead to us having to omit information.

Our lives are full of noise, distraction and days when things don’t go right. Whenever I see someone who is not making it easy for their students by trying to make the students drag information out of them, I think of the noisy channel that we have every day, and the fact that students may not have the best day sometimes. And then I think of what I get paid to do, which is to try and keep my part of the system transmitting as well I can, through the least noisy channel possible. There are enough things to go wrong, without me thinking that I’m making it challenging – and I may be making it impossible.

(If you’re interested, look up Claude Shannon, Channel Capacity, Shannon-Hartley Theorem and the Noisy Channel Coding Theorem. They’re a little mathematical but, if you add Nyquist-Shannoninto the mix, you’ll find out what the maximum frequency is that CDs can store. Have fun!)