Day 2

This is the second in a series of three interviews with Prof. Frieda Gufthausen.

Frieda Gufthausen

CC: Good morning, professor.

Gufthausen: Good morning, child. How are you today?

CC: Well, thank you.

Gufthausen: Shall we continue?

CC: Yes, please. You said that experts have forgotten what it is like to learn. So, what is learning?

Gufthausen: It is too complex to describe directly. Only through metaphor.


Gufthausen: A path through an n-dimensional state space, where each dimension is itself a state of knowledge of some simpler concept. The number of dimensions is large, in the thousands for even basic learning. The number of states is very large, infinite for all practical purposes.

The dimensions are highly interdependent, although the dependencies are not fully known. The cost of a state transition is influenced by yet another set of factors, that change during learning. The probability of many transitions is zero, because of constraints on motivation, time, prerequisite understanding, and other things.

Of course, this is just a metaphor, oversimplified. Oh, we haven't talked about the objective function.

CC: Er, I'm totally lost.

Gufthausen: I don't blame you. It's not a useful metaphor for most people. The mathematical metaphor suggests a degree of precision that isn't present.

Let's try again. Think of learning as a journey across a landscape. The journey is made one step at a time. Some steps are easier than others. Walking up a steep slope is harder than walking on a plain.

The course designer chooses a destination that is worth getting to. That destination includes knowledge of skills, as well as facts.

CC: OK. That's deep learning.

Gufthausen: Yes.

The course designer chooses a path for the students. Sometimes more than one, but let's stick with one. The designer chooses a path that can be traveled in the time available, and with the resource available.

The path is a sequence of steps. For every step, the designer makes sure that, first, the step leads towards the destination, and that the student is able to make the step easily. For example, a path that leads up a rock cliff is OK if the students are rock climbers. But for other students, a slower path with more steps that goes around the cliff will be better.

CC: But that path will take longer. There is only so much time in a semester.

Gufthausen Gufthausen: Yes! Good thinking. This is one of the tradeoffs of course design. Many designers put the destination too far away from the starting point. Students must run to get there, and they don't have time to examine the land along the way.

CC: But they will have seen the land.

Gufthausen: True, but not enough to understand the landscape. If they wander off the defined path, they'll quickly get lost. Deep learning helps students learn how to make their own paths. That is the goal, after all.

CC: Hmm. A useful way of thinking.

Gufthausen: You must also ask: what makes a step on the path difficult? Think of the cognitive cost of making a step. For example, if the language of a lesson is overly complicated, the learner will waste time deciphering the text. So, make the language easy to understand.

CC: Makes sense.

Gufthausen: There are other ways to make the walk easier. For example, if you watch someone else on the path ahead of you, you can see where they stumble, and where they make good time.

CC: How is that done in learning?

Gufthausen Gufthausen: Modeling. Show learners how other learners work, including the mistakes they make. And, very important, how they recover from those mistakes.

You should also consider the learner's training and general level of fitness. A learner who is used to walking can take bigger steps and move more quickly.

So, prepare learners with basic skills. For example, show them how to use tools like calculators or software.

CC: As the journey goes, do the students get stronger? Can they take bigger steps?

Gufthausen: Very good! They can. If they've been keeping up.

CC: You've given me a lot to think about. Same time tomorrow?

Gufthausen: We will speak then.