My approach: Zero rote learning and memorization (which don’t work anyway). Instead, genuine understanding (which works).
I teach my students to genuinely understand the material and think critically.
Not accept anything as truth just because I or their teachers or anyone else said so. Make sure every assertion or argument makes sense. Understand its flaws. Recreate it from first principles.
Sapere aude—dare to know. Dare also to question and criticize others, weigh the merits and flaws of opposing arguments, think for yourself, make your own arguments (and then criticize them).
The Cambridge Examiner Reports (written by those marking A-Level Economics exams) make these criticisms of candidates:
- Responses tended to consist of a long list of briefly stated reasons … whereas what was needed was the use of analysis to support the choices given.
- candidates frequently are not able to access the highest marks, as their answers tend to be descriptive in nature or lack the required depth of analytic explanation
- Most candidates also appeared well coached … but unfortunately all too frequently these tended to be listed … rather than well explained, leading invariably to only Level 2 responses.
- All too often, … candidates stated the observation … without using analysis to explain why
The student of mine learns to avoid the above criticisms. She writes down a clear and concise answer that (i) actually answers the question, (ii) provides in-depth analysis, (iii) demonstrates her understanding; and (iv) skilfully weaves together all available evidence and arguments.
No “Correct” Answer
There’s often no “correct” answer in Economics, the General Paper, or indeed any form of writing, communication, thought, or reasoning.
Markers care less about “correct” answers than critical thinking, well-reasoned arguments, and signs of understanding and intelligence. Again from the Examiner Reports:
It is important to stress that the conclusion reached was not important here. What mattered was the way in which the candidate used the evidence to assess the validity of the argument. A questioning approach in which the candidate showed good understanding of the opposing views and used evidence with skill was well rewarded.
Not Answering the Question
The candidate who memorizes lists of definitions, formulae, catchphrases, and examples rushes blindly into regurgitating her memorized (and limited) store of content. She’s unable to understand what the question is asking for and so wastes time writing irrelevant rubbish.
More from the Examiner Reports:
- rehearsed answer[s] which … [do] not address the question as set;
- tended to concentrate on ‘textbook’ explanations … without applying relevant … concepts to the question set;
- tendency to attempt to apply the formula mechanically to the data with no evidence of understanding.
Understanding + Practice = Mastery
To learn economics, mathematics, writing, or any other “school subject” is to learn a new skill.
Hence, it is no different from learning to swim, cycle, or play a computer game. With sufficient guidance and practice, you learn to automatically put one arm, foot, or mouse click ahead of the next when swimming, cycling, or gaming. Memorization is neither needed nor desirable.
Likewise, you can learn to do well on the exams without memorization. With sufficient guidance and practice, well-reasoned arguments flow naturally and relevant real-world examples spring to mind.
Wah Lao, You Think Everyone So Smart Issit? Growth vs Fixed Mindsets
I’m sometimes told that many or most students are simply stupid. There’s no point trying to teach them critical thinking. The only way they’ll ever get an A is through rote memorization and relentless drills.
In my experience, this pessimistic view is false. All material taught at the high-school level (including the IB and the Singapore A-Levels) can be genuinely understood and even mastered by most human beings. Most humans can also acquire at least some degree of critical thinking.
Unfortunately, in the Singapore education system, students are sorted and labelled as “clever” or “stupid” from a very young age. Teachers often believe some students are so stupid they couldn’t possibly do well on the exam (or later on in life). Not surprisingly, this is often a self-fulfilling prophecy: Neither teacher nor student believes the student can do well, neither tries very hard, and we get the predicted poor results.
I do get some (admittedly childish) pleasure from taking such supposedly “stupid” students and proving their teachers wrong.
But my greater pleasure is from transforming the student’s self-confidence and self-image. Starting as a poor student grasping at lists of definitions and formulae learnt by rote, she transforms into a true student with an active interest in understanding the material. Starting as a child who does only what’s forced upon her by parents and teachers, she transforms into a young adult who understands she alone is fully responsible for her own life and her own learning.
She comes to realise that while some of the material may be difficult, it’s far from impossible. With some effort, she can and will gain a genuine understanding of the material.
I try to instil in every student a growth mindset. Contrary to what the Singapore education system tells them, their brains are not fixed at some particular PSLE or O-Level L1R5 score from X years ago. With a little belief and effort, every one of them (along with their brain) can grow from a mere rote learner into an intelligent, critical, and confident thinker.
Make Obvious (and Non-Obvious) Connections
Robotic and inflexible rote learners are often unable to draw even the most obvious, simple, and common-sense connections. Again from the Examiner Reports:
Many did not see that [concept X] was significant, even where they had themselves used [concept X] to answer another question on the paper.
Below (left) was the frontpage of The Straits Times (Singapore’s flagship newspaper) from 2021-07-20. The day before, a student had (allegedly) killed another student with an axe. Yet the journalists and editors at The Straits Times failed to notice that it might be inappropriate to place on the frontpage both this news item and an Axe Brand ad. Apologies had to be issued (right).
In part the result of years of rote learning, the typical Singaporean is unable to make even the most obvious connection. She emerges from the education system a rigidly inflexible robot that is unable to think for itself, draw analogies, detect patterns, make connections, or come up with a single original thought.
An obedient rule-follower may have done well enough 50 years ago. But it certainly isn’t good enough today. As the Stanford mathematician Keith Devlin writes (2010),
In the nineteenth century and for much of the twentieth, most industrial workers did work silently on their own, in large open offices or on production lines, under the supervision of a manager. Schools, which have always been designed to prepare children for life as adults, were structured similarly. An important life lesson was to be able to follow rules and think inside the box. But today’s world is very different – at least for those of us living in highly developed societies. Companies long ago adopted new, more collaborative ways of working, where creative problem solving is the key to success – the ones that did not went out of business – but by and large the schools have not yet realized they need to change and start to operate in a similar fashion.
All Learning Should Be Fun and Interesting
Otherwise the learner will just hate everything she learns and forget everything two weeks after the final exam. Which may be fine for some (provided the learner gets her A), but not for me.
I don’t believe in teaching one damned fact or formula after another. Instead, I properly motivate all material. I ensure students fully appreciate, understand, and believe that what they’re learning is interesting, relevant, important, useful, and fun.
This way they are motivated by the prospects of genuine understanding of something true and important, the joy of seeing the world in a new light, and the possibility of using what they’ve learnt outside the classroom. In contrast, relying solely on the prospect of an A or 7 is a rather weak and depressing way to motivate students.
Preparation for Life
All of the above is great for ensuring students get their As.
But what I value more is teaching my students something true, important, relevant, and useful that they’ll remember and have a good chance of using years after their final exam.
I also place great value on preparing my students for life. This means preparing them for their future studies, professional lives, personal lives, and also their role as citizen of their society and the world. By teaching my students to think critically and reason better, I hope I better prepare them to enjoy better, happier, and more productive lives and make greater positive contributions to the world.
For a few more of my thoughts on education, see the Prefaces/Rants in my H2 Mathematics Textbook and H2 Economics Textbook.
Some concrete examples of how I teach
Example 1 (maths). To find the distance between a point and a line, one can teach students to memorize some formula or algorithm.
I instead teach students to understand what this actually means and the many possible methods one can use to solve such a problem.
This way, memorization is unnecessary. The student fully and confidently understands what’s going on and so can, even under stressful exam conditions, quickly recreate for herself any one of the many possible methods for solving the problem.
Even from a purely cynical utilitarian view, rote memorization of a formula or algorithm can often go wrong. Misremember just one little subscript or superscript symbol and you’ll get zero credit. In contrast, when you demonstrate your understanding, even with small mistakes, you’ll still get the bulk of the credit.
I sometimes also teach that an accurate drawing is a perfectly correct method for finding the distance between a point and a line (even though the rigid and inflexible writers and markers of exams may disagree). In so doing, I convey to the student that contrary to how maths is usually taught at the pre-tertiary level around the world, maths does not consist solely of mere mindless manipulations to be memorized and mimicked. Instead, maths is about seeing the same thing from many different angles, finding connections, creativity, experimentation, discovery, conjecture, beauty, and many forms of intuition.
Example 2 (econs). In national income accounting, one learns that Y = C + I + G + X – M.
From this equation, many are led to this common fallacy: If M↑, then Y↓.
Unfortunately, the above common fallacy is often taught by high-school econs teachers around the world (including IB and A-Levels)! This fallacy follows from the mechanical and mindless interpretation of the above equation.
The problem is that most teachers (and their teachers who taught them) jump too quickly to the above equation without carefully explaining where it comes from.
My approach is to instead take an additional 10 minutes or so to explain a few basic and plausible accounting principles. I then use these principles to derive the above equation. This way students understand where the equation comes from, not take it as some mindless mechanical formula, and so avoid the erroneous manipulations commonly made even by high-school econs teachers.
By the way, this fallacy is no academic matter. It helped Trump get elected in 2016! (Considering how slim Trump’s margin of victory was, it’s probably safe to say that the 2016 election result would have been different had economics teachers around the US done a better job.) I’ve previously written about this fallacy here and here.
(First posted: 2022-01-19. Edits made: 2022-01-21.)