Do not memorize before you understand
This text is a part of a series of articles about SuperMemo, a pioneer of spaced repetition software since 1987
Understanding should precede memorization
The first rule of effective learning is obvious and universal:
The rule comes from the mnemonic power of coherent memories, which dramatically reduce the cost of learning. In short, you should never try to cram this sentence: "Вы никогда не должны запоминать то, что не понимаете" unless you know Cyrillic and know what the sentence means. Memorizing the sentence "as is" is wasteful and useless. Hoping the sentence might be useful one day is a weak bet.
Rule #1 is actually derived from the Fundamental law of learning. Developing coherent memories is pleasurable. Cramming nonsense violates the call for the pleasure of learning.
Bad teacher's advice
Most of kids learn or should learn the value of understanding at school. However, even the most obvious rule can find its detractors who can even call it nonsense. Apparently, you can even be a teacher of physics at college, and still call Rule #1 nonsense.
Here is an actual complaint about Rule #1:
guizzmo wrote on Nov 27, 2016
The first rule "do not learn what you do not understand" is nonsense in the context of learning mathematics, physics, and hard sciences. If you understand a subject, then it means that you have learned it effectively.
In my experience with teaching at university, I have found that the wish of students to understand before learning is actually a great barrier to comprehend a subject.
In order to build intuition on a subject, a student should first try to apply it, play with it (without understanding it) and then understanding will come. But I have yet to witness a student which understand a subject without being able to use/apply the subject.
Take the notion of electric field. You could try to understand it before learning how to use it. Good luck. You are not a fish, so you probably have no sensors of electric field on your skin, and thus you have no prior notion to cling to. I contend that it is virtually impossible. Or you could try to use the concept of electric field to compute forces on charged particle, or compute the electric field created by a charge, or you could build a program that represent the electric field in space. Doing this requires no understanding, just boring substitutions in the definition of the electric field. But doing that forces you to build understanding (its a vector, it changes direction with the sign of the charges, etc, etc)
Another example is understanding how to bike. You could try to understand how balancing on a bike so that it stay upright, understand how moving the handlebar right makes you turn left or, you could just try to bike, and then understand how it works out.
So my advice: don't try to understand. Do, and do again until you have learned. Not the other way around
The teacher's advice may lead to disastrous consequences at school. It can lead to cramming, toxic memories, hate of school, and more. What is worse, the advice is dished out pretty often by lesser teachers.
Correct reasoning, wrong advice
The drama of the bad advice comes from not truly understanding Rule #1. Paradoxically, the teacher is not wrong (apart from using a biking example from procedural learning domain)! The teacher simply used his own advice, and acted upon knowledge (of Rule #1) before understanding it (or even reading my explanatory examples). The teacher does not understand Rule #1 for terminological reasons.
The apparent contradiction between the first rule of effective learning and the claims of the teacher comes from the interpretation of the word understanding and the word learning. In the context of developing long-term memories, the term learning may be used in place of committing knowledge to memory, while understanding is the ability to represent knowledge as simple coherent models that (1) explain the subject matter, (2) contain low amount of information (even for complex subjects), and (3) are well integrated with the student's body of knowledge. The simplest test for this type of understanding is the ability to use the knowledge in practical applications. In the said definition of understanding, we see that:
Our teacher uses a different terminology though. Learning is used to mean the process that leads to understanding, while understanding is a coherent, but not necessarily minimal representation of knowledge. The use of the words is legitimate, and the claim of the teacher is correct. It is true that good understanding leads to good applicability.
However, teachers negation of Rule #1 comes from simply not understanding it.
No wonder, the professor puts the cart in front of the horse terminologically, and formulates his own rule that may lead to disastrous consequences at school.
At school, the wish to understand it not a barrier. It is a barrier for a teacher who needs to rush his curriculum. Students are right to demand clear explanations, and delay memorization until it leads to meaningful associations that are bound to send pleasure signals in a student's learn drive system.
How can a child surpass a college student?
It is true that a student can memorize Coulomb's law without a deeper understanding of the electric field. All he needs is the understanding of charge, distance, and ABC of mathematics. This minimal understanding may later lead to deeper understanding, when the new knowledge is used to build up larger semantic framework, and richer associations. The teacher is right. However, the student will need to do a lot of computing, tinkering, and pondering.
In contrast, the electric field can also be explained to a four year old who never heard of constants, charges, or multiplication. The kid does not need to be a fish with electric field sensors. All she needs is a PhET simulation of the electric field:
Figure: Even if this picture may seem to illustrate complex science of electric fields, it can actually be understood by a pre-schooler. This is a PhET simulation of the electric field. All a child needs is to move around the charges and see how the arrows change. The simulation makes it possible to build an understanding that can later be used in memorizing formulas with pleasure. This is an example of why understanding should precede memorization
By placing charges in the field, moving them around, and having fun, the kid can develop a playground understanding of the electric field without the need to cram formulas. The field is illustrated with arrows and voltage shading. The kid can also play with a sensor vector to see the change in its length when approaching a charge (see the picture). This is learning with pleasure, and this is usually not happening at school. This is almost definitely not happening in the quoted teacher's place of employment. Bad teachers tend to dish out formulas and claim "you will understand later". Doing hours of calculations without understanding their meanings is a sheer waste of time. Formulas are a tool and should serve a purpose.
As for Rule #1, in SuperMemo, the kid who understands the electric field at Phet simulation level, will have an easier life when it comes to formulas, perhaps 4-10 years later. The formulas will actually bream with understanding. And this is how we want kids and students to learn: at low cost, while having fun. We will forever be grateful to Carl Wieman for his approach to teaching physics. Bad teachers have been conditioned by their own bad learning habits, which then get worse via routine, poor understanding of the efficient learning methods, and the need to hurry with the curriculum.
Bad mnemonist's advice
Anthony Metivier is a self-styled "memory expert". He is pretty knowledgeable about mnemonic techniques. However, he is also a poster boy for the abuse of the power of mnemonic techniques.
Anthony claims that he enjoys memorizing ancient poetry in Sanskrit even if he does not understand the underlying text. I never have issues with joyful learning. However, Sebastian Lisinski (quoting "Ancient Indian Education: Brahmanical and Buddhist", by Radhakumud Mookerji p. 31) suggested that traditional Sanskrit texts, such as Saṁhitopaniṣad Brāhmaṇa emphasize that understanding is more important than recitation: “He is only the bearer of a burden, the blockhead, who having studied the Veda does not understand its meaning”, or “Learning without understanding is called cramming; like dry wood on ashes, which can never blaze”.
The meaning of the texts comes to Anthony during his mediation sessions. This sounds like an interesting exercise for a connoisseur of Sanskrit, poetry, arts, or philosophy. If he finds fun and meaning in this effort, it must make sense. However, Metivier takes his reasoning a step too far when he adds: "I've heard people tell me they've had similar experiences with memorizing mathematical concepts".
Metivier is right. Millions of kids are force-fed mathematical formulas at school. This often happens with minimum understanding of the implications of the formulas. On occasion, the meaning of formulas emerges through reasoning, related reading, problems solving, etc. However, predominantly, this is how we generate millions of adults who hate math, hate school and its futility, and cannot possibly ever dream of employing the formulas in real life. Once you memorize that cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b), you will likely forget the formula in a week. Naturally, you can use spaced repetition, which Metivier calls a hoax, or even invest in a nice memory palace. The chance that you will find the meaning behind the formula before forgetting is negligible. You would need the time and the mind of Ptolemy. Most likely though, you will keep cramming formulas (or poems) for the next test, and the entire memorization effort will go up in smoke.
Metivier proposition is wasteful and ancient. It reminds me of an effort to memorize a phone book to be truly able to spot identical numbers assigned to different users. Possible and utterly futile.
Metivier's error can be best understood by the contrast between semantic and asemantic learning.
Programmer's shortcut
Arkadiy Kossakovsky suggested that instead of using incremental reading, we might associate ready-made items with all texts and courses on the web. This is a very old idea, but it would rather only benefit the speed of the consumption of knowledge (not even the long-term acquisition rate). It would not be beneficial to knowledge structure, semantics, knowledge coherence, knowledge darwinism, or intelligence. Only rigid knowledge sets taken from the curriculum would benefit. However, we all know that schools are not a good model for learning. For details see: Spaced repetition courses with associated ready-made items
Cramming is a waste of life
Students should never listen to teachers who recommend cramming, memorization without understanding, calculations without a good purpose, etc.
Rely on your own learn drive!
Here is a short illustration of how learning without understanding affects the love of learning: Unpleasant learning at school
This text is a part of a series of articles about SuperMemo, a pioneer of spaced repetition software since 1987