# Discovery teaching: my doubts

Say you want to teach someone what the Fibonacci series is.

## Two approaches

### Inductive

You show a kid this sequence of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21

You ask what the pattern is. The kid has a guess. If they get it right, you say so and tell them it’s called the Fibonacci series. If they get it wrong, you give them some clues until they get it right. These clues could take the form of Socratic questioning, scaffolding towards a moment of discovery. If they still don’t get it, you explicitly tell them what the pattern is.

### Deductive

Alternatively, you could show them the same sequence of numbers, cut out the guesswork stage and say: “This is called the Fibonacci series. Each number is the sum of the previous two.”

## How these two approaches compare

I used to lean heavily towards inductive teaching, not least because of the subtext it carries. It presents the world as a puzzle, and treats the student as someone who is able to solve it. I also accepted that a rule you have figured out is more likely to be remembered than a rule you have been told. Finally, the inductive method seems to encourage a more independent state of mind on the part of the student. The mood of this teaching style is implicitly anti-authoritarian. You are not told; you discover.

Inductive teaching is an example of the discovery method at work. Years would pass before I came to doubt the supremacy of discovery teaching, but two problems now stand out:

(1) It is an inefficient use of time. It takes a lot longer to discover than to be shown.

(2) It reduces the importance of the teacher’s expertise. Presumably you are in the role of teacher because you know more than your student. Yet in discovery teaching, as long as you can facilitate well, this expertise is only an added, non-essential benefit.

Example: a student is sitting at their computer. They put their hand up and the teacher comes over. The student asks a factual question, like “What’s the capital of Peru?”

The teacher immediately reaches a fork in the road (to avoid false dichotomies, let’s say it’s a fork with 25 prongs). One choice might be to answer the factual question straight out. Discovery choices are numerous, but let’s say the teacher holds back on answering the question, and says “How would you answer that if I wasn’t here?” The student turns to Google and types in their factual question. A list of results come up. The teacher watches as the student chooses one and looks for the answer. If the student finds it, great. If not, the teacher tells them.

In my first few years as a teacher, I leaned heavily towards the latter approach. In the above situation, nine times out of ten I would have got the student to ask Google. Now, having been teaching for six years, I’m leaning more towards just answering their questions outright. Why is that?

First, I know more. When a student asked what the present perfect was in my first year of teaching, I could say “Let’s look at the textbook together”. Bingo: all the benefits of a discovery approach, and I save myself the embarrassment of admitting that I don’t know myself. This benefit of discovery teaching is frequently underplayed by its proponents. That is, it allows underskilled people to fill the role of teacher. If you have good facilitation skills, you don’t even need to know your subject. Tangentially related to this, check out Tom Friedman in the New York Times last week, dropping this howler:

“Because increasingly the world does not care what you know. Everything is on Google. The world only cares, and will only pay for, what you can do with what you know.”

Right – because no-one cares if a doctor knows anything, do they. Or engineers. “Everything is on Google.” This attitude is pernicious, because if it takes hold, we are going to end up with teachers who don’t know their subject.

Second, I have undergone that metamorphosis which comes over teachers as they become more experienced: class time becomes valuable, rather than something which must be filled. If I can save time when dealing with factual questions, the class can move on to the activities which apply that knowledge.

Discovery teaching has a lot of benefits, and I wouldn’t suggest anyone stops using it. However, if you do use it, you have to consider whether the extra time spent is worth it, and whether covering up deficiencies in your own knowledge is one of your motivations. Once your conscience is clear, go nuts.