Is there a “right” way to teach something?

These past few weeks, I’ve been looking up a lot of tutorials both about programming and about teaching programming to people. It made me ponder upon learning and teaching and about the latest evolutions with respect to pedagogy.

In terms of learning (and particularly self-training), Internet has been a game changer. Nowadays, there are just so many articles and Youtube videos about everything! You can get online courses on virtually any topic you want easily and quite often for free. However, it raises interesting questions: is all this content relevant? what makes your favorite science podcast so much better than the rest and so much better at popularizing these hard concepts? how come some of these lessons are clear as day while others twist your brain in a funny way? and what about this new trend of “teaching to teach” and “learning to learn”?

In 2017, the Guardian published a set of articles titled “The science of teaching and learning“. Throughout this series, they explored various ideas ranging from tips for teachers on their first day to student impostor syndrome. This example and plenty of others suggest that there is a growing interest in how we learn and how we teach, and how these skills must evolve as our world evolves too.

In this article, I’ll tell you of a personal story that generated new thoughts on pedagogy in my head, of a myth about education, of critical thinking and of the new growing trend of teaching the teachers to teach.

Did you frame your question properly?

A basic math exercise… or not?

I remember a couple of years ago, as I was doing some maths tutorship, working with a student on functions, and more precisely, “functions variations”: for the math-lovers, yup, derivatives. However, this class was not meant to go as far as actually naming and embodying the idea of derivatives, and it stopped at “increasing” and “decreasing” functions. Instead of real definitions and theorems, you would have a series of fuzzy activities to try and grasp… something about functions variations. To be honest, I’m not exactly sure what. But, in particular, I recall an exercise that presented us with a table like this one:

x f(x)
0 0
1 -3
3 -9
-2 6

And the question was: “Is f an increasing or a decreasing function?”. Hum. So my student and I were looking at this and she was completely lost. She stressfully went back a few pages in the book, pointed to a line and read something resembling: “If f is a decreasing function, then for any x and y such that x > y, f(x) <= f(y)”. This was immediately followed by her comparing the numbers on the left and on the right one by one until she eventually determined that, yes, f was a decreasing function.

It took her a good minute and a half, at which point I congratulated her and then suggested we took another example; but this time, I asked her to draw the graph of the function. So I gave another set of points (another table of x and f(x) values), and soon enough, we stared at her notebook where she’d represented our second f function:

She instantly told me that f was clearly increasing. She was way better with graphs than plain tables of numbers (like most people, I’d wager, but anyway:) so how much more helpful in solving the problem is that graph than a table such as the one above?

This highlighthed three crucial things for me, education-wise:

  • despite being perfectly accurate, the definition of a decreasing function my student took as reference to solve the problem is not intuitive for beginners and therefore doesn’t really mean anything. I am absolutely convinced that, without us drawing graphs and practising on other examples to sharpen her intuition of what an increasing function is, my student would have had to repeat this same exhausting comparison scheme anytime she was faced with a similar problem. She could learn the process by heart, it’s not difficult – but she could not derive a true understanding of the concept from it.
  • everyone has their own strengths and weaknesses, their own intuitions and their own way of approaching a problem: my student was better with graphs, so using this tool made it easier for her to understand and answer the question
  • finally, school exercises tend to focus on a very specific “ideal” context often far from reality: hypothesis specifically suit the needs of the exercise and might disregard possible difficulties, or conversely they are cleverly crafted to make for a somewhat unrealistic situation (let’s be honest, no children in their right mind would buy that many candies, or take trains at the exact same time to go across the country and meet up in the middle of nowhere)

Note: this “ideal” context can even lead you to develop wrong reflexes! Here, for example, I find it risky to have students assume that 4 points are enough to tell if a function is increasing or decreasing – you can only determine how it variates between these points but this doesn’t mean it is true for any x and y in the space…

And this specific exercise was no help: it forced you to look at things in a rather convoluted way for… what?

What’s your point?

To this day, I honestly still don’t understand the point of this exercise. Was it to check that a 15-years old teen could read a table of numbers? Was it to build some connection between the x and the f(x) column, and teach the students about function mapping? Or was it truly about increasing and decreasing functions?

We see that a lot in school exercises: sometimes, they are great because they lead you down a well-constructed path of questions and reasoning that just open on your eyes on the topic at hand. On the contrary, sometimes, they drag you down by having a not-so-clear goal, suggesting wrong starting points, having you infer improper hypothesis and whatnot.

In my opinion, good exercises are like a fairytale story. For so many years our teachers kept on saying: “read the entire exercise before you start” and I would ignore them completely. I’d dive head first in the problem and tackle as many questions as possible with not much regard for a link between the questions. It took me a long time to understand the benefit of following their advice. So why am I talking about fairytales all of a sudden? The reason is that fairytales are not bunch of unrelated paragraphs on a page: they develop a (somewhat) pleasant narrative to convey a moral with a given context, some actors on stage and intermediary steps to get from the initial setup to the final scene. Similarly, a properly written exercise should focus on a topic, teach about a narrow concept, present you with a delimited toolbox and guide you with its questions.

It’s important to note that how long an exercise is does not necessarily determine how focused it is. Of course, a longer exercise has more chances of treating various topics; but a very short exercise like the one I showed above is so blurry that, to me, it could be used to teach too many things! Yes, there is a clear question that forces you to think of the situation in a specific way – but it does not build your intuition on a specific topic – “increasing and decreasing functions” is too broad a subject.

So, how can we learn?

Tailored learning styles

What I’ve proposed so far resembles the idea of creating tailored and student-customized learning styles; however, this is a myth that has been proven to be false as is pointed out for example in this Wired article by C. Jarrett (2015), this Digital Wake article (2018) or in this study by Massa and al. (2006). After being wildly spread and praised for a few years (in particular thanks to this 2009 article by Pashler and al.), the idea of every student having their own “learning style” is slowly being replaced by the concept of “learning preference”.

Note: this myth is part of the 50 Great Myths of Popular Psychology that Lilienfeld and al. debunk in their 2009 book.

This book was published in 2009 by three Professors of Psychology and aims at debunking various common myths about psychology and neuroscience, like the fact that “we only use 10% of our brains” or that “handwriting reveals our personality”…

While I’ll admit it was my first instinct, I do realize that a per-person education is nearly impossible to setup and not necessarily the best:

  • teachers are not private tutors: they cannot afford to create 40 different lessons for each of their students!
  • students themselves aren’t always the best at defining their “preferred style”
  • it encourages teachers to focus on the students’ strengths and have them avoid their difficulties which ultimately stops them from getting a complete grasp on the topic
  • school is also a place to learn to socialize and interact with others: in that respect, every child having their own math lesson is quite detrimental
  • having a standard does insure that some minimum criteria are met – if all the students are trained and assessed on the same material, you theoretically have a knowledge baseline shared by everyone that they will be able to use in their future grown-up lives
  • there is usually a “recommended way” of teaching a specific topic (i.e. a way that has been proven to work with a large number of people): learning geometry without any drawing sounds silly, picking up on German without ever hearing it doesn’t make for a great course, etc.

There should be a difference in how you teach beginners and experts, for sure – but overall, it’s not about fitting the course to your needs, but about finding the right course! What has been proven is that you learn better when you’re interested and you have fun – not much surprise there 😉

Note: this has been pointed out by several French Youtube popularizers of science I know (e-penser, DirtyBiology…): they often get comments from students saying that they are way better than their teachers – but they answer it is easier for them since their viewers are people who willingly choose to be here, and they as Youtube entertainers are free to put as many jokes and funny stuff as they want in their videos, contrary to a school teacher who has to obey some rules.

We all have a certain way of looking at things – some of us are more analytical, others more about practise and experiments… – but this initial tendency should serve as a grappling hook rather than a learning method. Associating music notes with colors is fun and all, and it works great with children, but at one point you will have to learn solfeggio if you truly wish to pursue some sort of career in music. The color-mapping is a way to ease your understanding of the topic at first but it cannot become an official way of learning music in itself.

Critical thinking

Even if tailored learning styles aren’t the right way to go, I still think we could make some changes in the current teaching methods. (Here, I’m taking the French education system as reference since it’s the one I know and grew up with.)

I’ve already mentioned it but something that often struck me throughout my studies was how single-voiced courses were. It is logical that there should be national standard all teachers convey so as to insure the aforementioned “baseline knowledge”, and I do agree teachers should not tint the lessons with their own beliefs. But what I’m finding harmful is the fact that we don’t even discuss the idea of multiple points of view.

If we go back to my maths tutorship example, remember how my student had not even thought of drawing a graph? I had had the same feeling before: what was written in the book had to be the (entire) truth, right? I think we weren’t at fault here; the issue is to me that, in France, and especially in science class (math, chemistry, physics, computer science…), you are told to stick to the rules and learn the “right solution”. One problem, one answer. Straight and simple. (You only discover there could be such things as “alternatives” when you do math-oriented college studies – yay.)

Note: since I didn’t study humanities as much, I can’t judge as aptly how they are taught nowadays – but my French and history teachers in high school were doing the same.

Endorsing this method of teaching means agreeing to severely limit our learning of critical thinking. By getting used to the idea that there is always one perfect unique solution for any problem, you gradually stop reflecting upon the question you’re asked. You just assume the situation that was described contains all the necessary information, you apply a routine process to go through it and you hand back your results. This leads to two main issues:

  • one, you don’t analyze anything anymore and the people who describe the situation have inimaginable power over you, given they effectively shape and control your understanding of this piece of the world
  • two, if you don’t have an exact process for this situation in your toolbox, you won’t be able to “improvise” and come up with your own solution

The first point is particularly visible with something seemingly straight-forward: word definitions. Your first instinct with word definitions may be that it’s easy: the definition of a word is the paragraph next to it in the dictionary. But there is way more than that in the definition of a word! This video on cybersecurity is a great example of why understanding the various acceptions of a term is paramount: definitions are used in laws and policies, they are used in debates and in the media, they are used in scientific congresses… Agreeing on a common signification is mandatory if you wish to have healthy discussions, else you run the risk of everyone talking of something different and conveying different ideas with the same word. If someone gives you a biased definition of something and tells you to use that to decide on a national policy, if you are not able to apply critical thinking to the situation you will be forced to rely on their biased assessment to solve the problem.

Aretha Franklin and Louis Armstrong’s “You Say Tomato, I Say Tomato” song may have more to it than just a catchy melody and funny lyrics… 🙂

The second point follows from the “ideal situation” syndrome I talked about in the first section. Because school teaches you about neatly crafted use cases where everything falls into place perfectly, you only learn how to interact with such a perfect machinery. But the world rarely runs like clockwork, it’s more about bumps on the road and unexpected deviations. If you are not prepared for this, if you are not able to take a step off the road to go around the wall you’re facing, you’re gonna be stuck there for a while. Critical thinking is crucial in that matter because it allows you to take distance from the specific problem you have to solve and examine the situation more globally. Then, you can compare it to other problems you know how to solve and derive a new process to answer new questions.

Today, you can find pretty much anything you want on the Internet, and in many forms. In the domains I’m interested in, there are online journals like Medium that are filled with written programming tutorials, Youtube channels entirely dedicated to discovering computer science or maths, forums and threads for coding advice (like Stack Overflow)… Even big companies like Google are taking advantage of this new channel of communication to spread their content and offer free online courses (see for example this Youtube channel that gathers lots of their videos).

It is then up to you to assess for the quality of the content, for how relevant the sources and authors are in this domain, for how up-to-date and accurate the syllabus is, etc. This requires skills and abilities that we haven’t always developed as much as is necessary, although the will to teach critical thinking is starting to spread around and next generations might (hopefully!) have a better grasp on it than we do.

Critical thinking is primarily about examining and analysing a situation to solve problems.

At the age of Internet, where every piece of “pure” knowledge can be found easily (you don’t need to remember the exact date of this battle, or the middle name of a foreign prince anymore: Google has the answer!), it is no longer a question of “can you get this information?” but rather “can you verify this information is correct?”.

This in turn changes the way we think of teaching and, for the last few years, more and more conferences or courses have focused on teaching teachers to teach.

Teaching learners… and teachers!

Learn-by-heart? Practise first? Stick to the theory?

During my programming refresher tutorials, I was especially fascinated to see some teachers vividly preach for an hands-on on-the-computer training while others would snap it on your fingers to have you first write down the algorithms. I myself have always had trouble with on-paper programming exercises because I like to feel the code grow under my fingers; still, I get the point of crafting your algorithm beforehand: it cements your understanding of the task to perform and helps you make sure you’ve actually taken into account the entire scope of it.

Once again, it’s about giving in your “initial tendency” or fighting it to develop new skills. The two aren’t necessarily exclusive: instead, I believe you should trust your instinct to navigate the sea of content that’s offered to you and find the courses you really want to take – but then, strap on and be prepared to let go of the colored music notes!

Note: truth is, for programming stuff, I guess I’m sort of a bad student: I usually trust that my experience will prevent me from taking too wrong a turn early on, start coding, and hope I’ll be able to reshape my program a bit later if need be… – oops! Yet this is how I work and this is how I work best – not to say I didn’t pass my programming exams during my studies, but I often felt like they were harder than they had to be because of this on-paper constraint. This is why finding the online courses that best match my way of learning is hugely beneficial to help me get into the topic; then, when I’m touching on the hard concepts of the course, there probably is a recommended way of learning it and I trust the persons making the course are aware of it.

I also stumbled upon a variety of programming courses that were about the language core concepts or documentation tools rather than precise syntax, the point being that if you know what you’re searching for and where to search it, then you don’t need to learn it by heart. What I like with this approach is that it is more scalable: there is only so much pure information you can store in your head, but humans are really good at learning patterns and processes. So, instead of learning 100 specific solutions, learn 1 process you can apply to 100 questions! Plus, I find it more satisfactory to come up with my own solution than just repeating a lesson I learnt by heart.

Education sciences

We have been teaching the next generation and using pedagogy for centuries and people already tried to understand and improve learning methods in Antiquity – however, it’s only in the second half of the 19th century we started branding an actual field as “education sciences“. This domain was born with the recent progress in psychology, sociology and neurosciences and it aims at studying and possibly prescribing better education policies.

In other words: we are now learning to learn, and teaching to teach. We study the brain with MRIs while it’s learning to try and understand the biological mechanisms at play, we work on the relationship between culture and education, we use communication or management concepts to improve teaching abilities… It is quite a recent movement, with regard to the long tradition of teaching we have. For example, a 2001 paper by Weinberg, Nichols and Stich named “Normativity and Epistemic Intuitions” focused on whether or not different backgrounds could lead to different notions of epistemology (i.e. knowledge). In spite of some flaws from a technical standpoint (in particular not enough diversity in the experiment subjects’ backgrounds) that have since been pointed out to discredit the authors, this article is nonetheless considered as one of the starting point of experimental philosophy.

The very fact that we discuss how to teach is to me a very positive thing because it confirms and supports the idea that teaching is not an innate ability, that some are born with “the gift of transmitting to others”. While it’s true wanting to teach is important and usually makes for a better teacher, teaching skills can – and must – still be learnt and trained. It emphasizes that knowing the topic and knowing how to teach it are two different abilities, too; thus a young teacher might be more aware of the latest advancements in their domain but they should not be expected to naturally be as good at teaching as experimented ones. In my opinion, this skill should be recognized and taught as well as the topic itself to teachers in training to make sure they indeed are able to talk a class of students by the end of their formation.

Conclusion

With the rise of Internet, over the course of twenty years, we have created new places of knowledge. Today, online course platforms like Coursera or Skillshare or Youtube educational channels are offering official certificates and propose a complementary form of education next to traditional schools. By broadening the access to some of their educational content, universities such as the MIT hope to spread knowledge further and faster than ever before and to reach otherwise too isolated students. But these new forms of teaching are different from the previous models in different ways:

  • because of the tools involved they require you to be familiar with new technologies, to be digitally literate, which is sadly not yet true for all world-wide (digital illiteracy doesn’t curse only the elderly)
  • anyone is allowed to become a teacher and publish their content which increases the risk of having self-entitled inapt educators: I’ve praised how open and full of great things the net is in this article; the drawback is that anyone may share their own online course and, if they advertise it well, they will sell it to a broad audience no matter how well-structured it truly is

Of course, the bright side is that you can find tutorials on almost any topic you want (be it cooking lessons, Spanish courses, mobile app programming, woodcrafting techniques…) more easily, from anywhere as long as you have a computer, any time of the day or night and in lots of languages.

The topic of “learning and teaching well” is also put more under scrutiny than it used to: while articles and videos help us self-learn better (by teaching us to learn effectively), educators themselves are getting formations on how to teach in this new world of technology and communication.

I’d like to conclude by mentioning something obvious: teaching is hard. It is something you have to be dedicated about and, in addition to mastering the content you are teaching, you need to know how to convey information about it properly. I think we’ve all had some teachers that had this amazing charisma, a twinkle in their eyes, a voice filled with energy – those were the ones you wanted to listen to and learnt the most from. I’m not saying others are bad: I have the upmost respect for teachers, I think it’s among the most difficult jobs nowadays! Plenty of them are doing their best given the situation and are actually doing pretty well. But I do have an issue with people who assume that because they know about something, they can simply teach it.

References
  1. Medium’s website: https://medium.com/
  2. Stack Overflow’s website: https://stackoverflow.com/
  3. Coursera’s website: https://www.coursera.org/
  4. Skillshare’s website: https://www.skillshare.com/
  5. e-penser’s Youtube channel (in French): https://www.youtube.com/user/epenser1
  6. DirtyBiology’s Youtube channel (in French): https://www.youtube.com/user/dirtybiology
  7. MyCS’s Youtube channel: https://www.youtube.com/channel/UCq8JbYayUHvKvjimPV0TCqQ
  8. 3Blue1Brown’s Youtube channel: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
  9. Geek’s Lesson’s Youtube channel: https://www.youtube.com/channel/UCKXx22vOENUyHrVAADq7Z_g
  10. “Cyber Security for beginners || Introduction to Cybersecurity” by MyCS: https://www.youtube.com/watch?v=y9LJoa79GEk
  11. About experimental philosophy: https://plato.stanford.edu/entries/experimental-philosophy/
  12. S. O. Lilienfeld, S. J. Lynn, J. Ruscio and B. L. Beyerstein, “50 Great Myths of Popular Psychology: Shattering Widespread Misconceptions about Human Behavior” (https://www.wiley.com/en-gb/50+Great+Myths+of+Popular+Psychology%3A+Shattering+Widespread+Misconceptions+about+Human+Behavior-p-9781405131124), 2009. [Online; last access 16-August-2020].
  13. J. M. Weinberg, S. Nichols, S. Stich, “Normativity and Epistemic Intuitions” (https://sites.ualberta.ca/~francisp/Phil488/WeinbergNicholsStichEpistemicIntn01.pdf), 2001. [Online; last access 16-August-2020].
  14. The Guardian’s “The science of teaching and learning” articles series: https://www.theguardian.com/teacher-network/series/the-science-of-teaching-and-learning
  15. C. Jarrett, “All You Need to Know About the ‘Learning Styles’ Myth, in Two Minutes” (https://www.wired.com/2015/01/need-know-learning-styles-myth-two-minutes/), Jan. 2015. [Online; last access 16-August-2020].
  16. DigitalWake, “Demystifying learning styles and tailored instruction” (https://www.digiwake.com/learning-styles-tailored-instruction-2/), Aug. 2018. [Online; last access 16-August-2020].
  17. SilverEco, “Illectronism: 57% of over 70s are not comfortable with digital formats” (http://www.silvereco.org/en/illectronism-57-of-over-70s-are-not-comfortable-with-digital-formats/), July 2018. [Online; last access 16-August-2020].
  18. I. Wikimedia Foundation, “Education studies” (https://en.wikipedia.org/wiki/Education_sciences), March 2020. [Online; last access 16-August-2020].
  19. I. Wikimedia Foundation, “Epistemology” (https://en.wikipedia.org/wiki/Epistemology), Aug. 2020. [Online; last access 16-August-2020].
  20. I. Wikimedia Foundation, “Digital literacy” (https://en.wikipedia.org/wiki/Digital_literacy), July 2020. [Online; last access 16-August-2020].

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