Excerpt from my book The Owl Factor: Reframing your Teaching Philosophy
The Owl Factor is about teaching and learning. In SHOW, I discuss the concepts of approach, method, and technique in more detail. The question is: is there a better approach or method when it comes to teaching? The passage of the book explores the idea of inductive VS deductive teaching through two different examples: Brian Cox and his quest to investigate Galileo’s claims, and my high school physics teacher Elias.
One of my students, an environmental lawyer, lecturer, and nature enthusiast who’s obsessed with horses, showed me an incredible BBC video that can shed light on the SHOW aspect of teaching/learning. The video was an episode of a documentary that showed one of Galileo’s theories put to the test. I’m sure you studied it in your high school physics class.
In 1589, the Italian scientist Galileo Galilei, who had previously hypothesized that two objects with different masses should have the same free fall time, refuting Aristotle’s widely accepted theory that heavier objects fell faster, finally tested his experiment. Two spheres with different masses, one heavy and the other lighter, were dropped from the Leaning Tower of Pisa – this might be an apocryphal legend, like Newton and the apple – but both objects reached the ground at the same time. He then moved on to the assumption that the acceleration at which objects fall is equal. Thus, Galileo concluded that the only variable influencing the free fall time of objects is air resistance due to the objects’ surface area (Hawking, 1996).
In fact, Galileo claimed that if there were no air resistance, a hammer and a feather would fall and reach the ground at the exact same time. Obviously, this experiment could not be performed as it was not possible in the sixteenth century to remove air resistance from the equation. The first vacuum pump was not invented until the middle of the seventeenth century, and even then, making one that could remove the air from a room big enough to carry out Galileo’s experiment with the hammer and the feather would have been absolutely impossible. However, in 1971, when Apollo 15 took Commander David Scott and his team to the moon, the timing was perfect to test the idea; after all, there’s no air resistance on the Moon. He did just that: he dropped a hammer and a feather, and they fell perfectly together. After the objects hit the ground simultaneously, Commander Scott said:
How about that? Mr. Galileo was correct in his findingsCommander Dave Scott
Four decades later, the experiment was replicated on Earth. BBC’s Human Universe (2014) series and its presenter Brian Cox traveled to the USA to use the biggest vacuum chamber in the world, at the NASA Space Power Facility. This time they dropped a bowling ball and a couple of feathers at the same height from a mechanical arm. With air in the chamber, just as expected, the bowling ball fell in a straight line in a matter of one or two seconds. The big white feathers danced beautifully on their way down, spinning and gently floating in the air, reminding me of the time Hermione was mastering the Wingardium Leviosa technique at Hogwarts – perhaps using an owl’s feather. Without air – and it took the specialist 3 hours to fully remove it from the chamber – the most beautiful thing happened. The feathers fell in a perfect line side by side with the bowling ball, causing Brian Cox and everyone at NASA involved in the experiment to stand in awe.
Many might be wondering right now how an Italian scientist from the 16th century could have formulated such a theory with the lack of technological resources available at the time. I suppose the answer is that he used his reasoning, and he had a method. He had an idea, tested it, verified that his idea was correct, and he then generalized what he had discovered. He realized that the variable mass had no influence on the behavior of free-falling objects. Two spheres of approximately similar size but with different masses would fall at the same speed. However, he knew that feathers did not respect that pattern. He needed something to explain why feathers fell the way they did, so he found another variable: air resistance. This method is the scientific method that can be summarized as demonstrated below:
In the philosophical tradition, different authors employed different ways of getting to a theory. Here’s an example of a syllogism:
All humans are mortal
Socrates is human
Hence, Socrates is mortal
It starts from a general claim – all humans are mortal – and then moves to a specific situation – Socrates is human. It is deduced then that Socrates is mortal and so is every other specific case of any other human being. This is an example of deductive reasoning. Now look at the example below:
The swan I saw yesterday was white
That swan is also white
A swan my friend saw was also white
Therefore, all swans are white
This time we see how we can make inferences from what we observe – and even from what people have told us – to generalize. This is an illustration of inductive reasoning.
Let’s expand on the dichotomy of deductive versus inductive. But first, let’s revisit the idea of approach and include method and technique:
Let’s focus on teaching. An approach sets the beliefs and ideals teachers should embrace. Here we can think of words such as constructivism – when students are regarded as co-constructors of their knowledge and, thus, active agents – or behaviorism – which regards students as passive individuals who learn from external stimuli or reinforcement mechanisms (Hedlund, 2020). A method provides teachers with a set of procedures to follow in their classes, therefore it should have different stages with different aims. Finally, technique refers to the chosen activities or tasks that will be carried out in the classroom. That said, deductive and inductive are normally referred to as approaches to research or teaching, that is, the beliefs and principles that determine the methods. An example would be the following:
|Description||The teacher explains grammatical rules and students try to complete activities||The teacher repeats vocabulary, sentences, and students learn through inference|
The table above offers an example of language teaching, which may give us a clearer idea when we analyze where deductive and inductive fit in – in this case, they belong in the approach line. Nevertheless, when analyzing the scientific literature or looking at general education, it is not unusual to see approach and method used interchangeably. That means that we may choose to think of deductive and inductive as different approaches if they describe the beliefs or a philosophy that teachers or trainers should embrace, or we can think of them as different methods if they provide the step-by-step procedures of the lesson or session. Let’s illustrate the idea through my teacher Elias’s and Brian Cox’s examples:
Elias: Hello, students. Today we are going to learn how to calculate the height of a building. As you all know, objects fall at the same rate regardless of mass, shape, or size because the acceleration of gravity is a constant. So, we can calculate the velocity of free-falling objects by multiplying this constant by the time it takes them to hit the ground.
[He goes to the board and writes v=gt]
Elias: Let’s say we drop a ball from the top of a building. We know that the ball’s velocity is 39.2m/s2. We’re not taking air resistance into account here. We now need to find the time. With that information, we can calculate how tall the building is. We need another formula to calculate the height, though.
[He writes h=1/2gt2]
Elias: So 39.2=9.8, which is the acceleration due to gravity, times t, which is the time we need to find. That gives us t=39.2/9.8. The result is 4 seconds.
[He writes everything on the board]
Elias: What’s the height of the building then? Well, we square the time, which gives us 16, that is, 4×4, and we multiply that by 9.8, our gravity constant, and then divide by two. So 16×9.8=156.8, and that divided by 2 equals 78.4 meters. That’s our height. Let’s do the activity on page 13 with more examples.
Back to Brian Cox. He went to NASA, emptied an enormous chamber of its air, thus removing air resistance, and had two objects dropped from, let’s say 30 feet or a little over 9 meters, in the vacuum. All those NASA engineers certainly had a stopwatch and checked that it took both the ball and the feathers around 1.365 seconds to hit a box on the ground. From that experiment, we can assume that other objects – since bowling balls and feathers are quite different – will fall at the same rate. We can see here that Elias started from the general rules of how objects behave when they fall and asked us to work on a specific example – the height of the building. Brian Cox did the opposite. He started with the specific example and then generalized it to other objects.
Both Elias and Brian followed a sort of recipe that went like this:
|1. Explain the topic of the lesson|
2. Give an example
3. Ask questions or assign a task
|1. Give an example |
2. Carry out a demonstration
3. Explain the topic
Since the words deductive and inductive can tell us to a certain degree of precision what our steps in the lesson will be, regardless of the resources chosen, I will consider them as methods here. As indicated in the table below, one of them is top-down, which means it relies mostly on the teacher and moves from the macro level to the micro level, whereas the other one is bottom-up, meaning it depends heavily on the audience’s reasoning skills to build from an example – the micro level – a general idea – the macro level – of how things happen.
|Example||Elias lecturing and giving us general formulas to apply in specific contexts||Brian Cox demonstrating a specific example and using the outcome to generalize|
What Galileo supposedly did was similar to Brian Cox’s experiment – except that he couldn’t create a vacuum.
So far, we’ve seen that we can show in a deductive way, which means moving from a general rule to a specific case, or in an inductive way, from the specific case to the general rule. If we distribute these two methods across a simple matrix using the two ways teachers and trainers have traditionally shown things to one another – orally and visually – we get the following:
|Deductive||Teacher lecturing on the general rule to students like: After prepositions, the verb takes the ing form||Teacher showing on a slide or in a book: After prepositions, the verb takes the ing form|
|Inductive||Teacher asking the students: What do you notice in the following sentence? He’s afraid of swimming||Teacher showing an example on a slide or in a book: He’s afraid of swimming|
Let’s assume our fictitious teacher in this matrix is a purist. They either only do things deductively or inductively – assuming that would be possible. A purely deductive teacher may overwhelm their students with abstract concepts and fail to provide any concrete examples. It might be hard for the students to understand how these concepts apply in real life. On the other hand, a purely inductive teacher who never explains any general rules might tire the students with too many examples and questions, believing that they’ll be able to work out the general rule themselves.
With that in mind, what’s the Holy Grail of SHOW then? Based on the things we’ve discussed, can we say that there is a single, one-size-fits-all, ideal, pure method? To use a Greek word, is there a panacea or a remedy for all illnesses? In Jack Richards and William Renandya’s Methodology in Language Teaching: An Anthology in Current Practice (2020), the first chapter was written by H. Douglas Brown, and it starts like this:
In the century spanning the mid-1880s to the mid-1980s, the language teaching profession was involved in what many pedagogical experts would call a search. That search was for a single, ideal method, generalizable across widely varying audiences, that would successfully teach students a foreign language in the classroom. (p. 9)H. Douglas Brown
I suppose it’s safe to assume that on reading this chapter, you will have noticed that I didn’t really say which method is the best. To be honest, I don’t think there is a best one, even though I may have hinted toward using concrete examples and demonstrations rather than direct instruction, lengthy explanations, and abstract notions. Both my teacher Elias and Brian Cox tapped into the deductive and inductive methods at times. Apparently, that is what effective teachers and trainers do based on the conditions under which they are teaching. It would be remiss of me not to compliment my teacher Elias for helping me nurture a passion for Physics because of his teaching. Mixing things up and using different resources might yield the best results. After showing us the general rule, Elias would often introduce other rules by giving us a specific example that we needed to work out based on the first general rule. Brian Cox based his demonstration on general rules given to us by the observations, experiments, and calculations of Galileo, Newton, and Einstein, and each of these he explained briefly to us. This discussion about SHOW was meant to give you a better understanding of how you can do the same thing with your audience.
If you liked it and would like to read more, make sure you get your copy of The Owl Factor: Reframing your Teaching Philosophy