The traffic lights metaphor
When my students first meet me, I tell them that I am usually criticized for not explaining the maths I teach. I assure them, with a smile, that those critics are about right, but I also tell them not to worry, that they are going to learn, but by their own means.
There are always a few worried students that want to talk to me after that first class, concerned, because they want to success in maths but they can’t imagine how to do so “by their own means”.
A few years ago I came up with an easy-to-understand example that throws some light upon those concerns and helps them understand. My older son (and only one by that time) was more or less 18 months old, we were in the car waiting for the traffic light to turn green and when it did, he screamed: "Green! Come on!" and after the next turn another traffic light was orange changing into red and screamed: "Red! Stop!".
I'm almost sure we have never told him how traffic lights work, I do recall talking about their colors when he started to learn their names. So this got me thinking.
Imagine that you want to tell a little child how a traffic light works, how would you do that?
Usually, the answer is something like: “When the light is green, you can pass through, if it is red, you can’t and have to stop, and if the light is orange, be careful as it is going to turn red.”
With this in mind, I tell my students that this is not what I would do, I would ask the child to observe a crossroad with traffic lights for a few minutes and then I’ll ask about how the traffic light works.
If the child is a fast learner, the answer might be: “When the light is green, the cars go on, when it is red, they stop and when it is orange, they go fast because it is going to turn red.”
Or, maybe the child says “I saw a red SUV, a white motorbike, two police cars and an ambulance”, in this case I’ll insist about observing the Traffic lights and allow a few more minutes.
Chances are that the child says: “The traffic lights goes from green to orange, then to red and back to green again”, then I’ll celebrate those findings and encourage some further observation of the crossroad while paying attention to the traffic lights.
Hopefully, the child finds it now, but if not, then I would scaffold by asking
What happens when the light is green?
What when it is red?
What if it is orange?
Then I’ll ask the kid to formulate a whole sentence describing how the traffic light works.
In case that I run out of, whatever comes first, ideas or patience, I would eventually tell the child how the traffic light works, but this is something earned that won’t come free of effort.
And this is how I torture my students by making them think (I know, so evil of me...).
Learning by discovery takes time, for sure, more than a traditional lesson. However, the learning outcomes are more meaningful (there has been research done about it), aside from the thinking skills being developed.
In their article Does Discovery-Based Instruction Enhance Learning? (Alfieri et al., 2011), the authors warn that, for being more effective than explicit instruction, the discovery learning must be guided. Lauren Margulieux (assistant professor at Georgia State University in the Department of Learning Sciences) did a very good summary of the article and concludes:
The second analysis compared enhanced discovery learning to other types of learning, including unguided discovery and direct instruction. In this comparison, enhanced discovery performed better than other types of instruction.
The results also emphasize that younger learners need more guidance in discovery learning.
Update before publishing:
A student, recently, openly complained in class "Why are you making us think?" to which I answered "I'll take that as a compliment 😊".
It is, in fact, the biggest compliment I could receive.