This is the third of the five steps of efficient learning that are outlined here.
Understand: Some things you’ll understand straight away and the ‘understand’ step will easily fit in right between acquire and link. But sometimes this is a huge challenge. This is the step where we often are challenged in moving from concrete to abstract ideas, or the other way around. We can think of understanding the lynchpin or keystone of learning. It needs to be there otherwise learning hasn’t really taken place.
But sometimes it’s unrealistic to expect understanding to come straight away. Sometimes the content is just so hard that it’s going to take a while to sink in. In this kind of a scenario we may have to be patient and follow through with the next two steps (link and train) before we truly understand. Regardless, there are things we can do to boost our chances of understanding, and make it happen faster. This article details some excellent methods.
But first, Here’s my top tip for understanding: DON’T LIE!!!
This may sound like a strange place to start when we’re discussing understanding but it really is the basis. What I’m talking about here is lying to yourself or to your teacher. If you tell yourself that you understand before you do, or tell your teacher that you understand before you do, then the next piece of content will be moved on to and that just doesn’t help anyone.
I can’t stress this enough. It’s a lesson that has taken me a long time to learn. But not for myself, It’s never made any sense to me to lie about whether I understand or not. But it appears to be pretty common for lots of people*.
As a teacher I’ve been in the following situation countless times: I’ll explain a concept and a student says ‘aha‘ or ‘oh, I get it now‘ or ‘yeah, that makes sense‘. I think ‘great, we’ve really had an aha moment!’, only to discover that they fail the test and when I ask them ‘what happened’ they tell me they didn’t really understand in the first place.
As such, now if a student says ‘aha’ or another such exclamation I’ll say ‘great, now you explain it to me’….
Half the time, that’s what I hear. Which is great. It’s honest feedback. We can’t learn without honest feedback. If you tell me you don’t understand then I can take a different tack and approach explaining it from a different direction. Honesty: This is the first and most crucial step to understanding!
*I’ve learnt that students behaving this way is probably because they have are performance goal orientated student rather than a mastery goal orientated student. This means that they are more concerned about other peopling thinking that they understand than they are about actually understanding. Therefore they’ll go to lengths to keep up the charade that they understand, even to the detriment of their education!
What is understanding?
Good question!!! At this point it’s important for me to comment on the connection between step 3: Understand, and step 4: Link. In many ways understanding is simply linking new things that you learn to things that you already know in a way that is going to help you remember. More links to things you already understand represents deeper understanding. Here’s an example.
-In year 10 you may learn about the derivative. You learn that the derivative tells you the slope of a line, and that for a straight line, the derivative is only a number.
-Then in year 11 you might learn that the concept of the derivative is more broad, it actually gives you the slope of the original function (whether it be linear or quadratic, etc) for any x value (don’t worry if you don’t know what I’m talking about, just keep reading).
-Then in year 12 you do a physics unit and find out that the derivative links displacement to velocity, and that acceleration is the derivative of velocity!
-Then years later someone points out to you that the formula for the surface area of a sphere is actually also the derivative of the formula for its volume! WOW!!!
Perhaps in year 10 you did understand the derivative as it was taught to you, but every additional link that you made to other things you knew about (velocity, displacement, area, volume, etc) represented an increase in your understanding of the concept of a derivative. It broadened your understanding and increased your ability to transfer. Transfer is the ability to apply the concept to new situations where you haven’t seen it used before. This is the basis of creativity and is one true tests of understanding.
This concept map of derivatives can be found on Darylin Barney’s page here. My derivative analogy can be found here.
How do I get understanding?
As mentioned, linking is understanding, but sometimes the concepts that you’re trying to understand are so foreign that your brain doesn’t manage to naturally make any links. In situations like these there are a couple of things you can do.
Find an Analogy:
Maybe you’re trying to understand electrical circuits and you find it helpful to think of them as rivers, maybe you’re trying to understand what goes on in an atom and you think of how the planets orbit around the sun to try to understand how electrons orbit around the nucleus. Analogies are powerful tools for understanding. You can find analogies by googling ‘analogy for electrical circuit’ or ‘analogy for the atom’ and this can set you on track to better understanding. A good teacher should help you out with this! A good teacher or tutor can also introduce you to helpful analogies. Click here for a bit more info about analogies and to see an example of how analogies can be used to understand a complex concept like the derivative.
The Pokemon Card Method:
This is to be used when you’re really clutching at straws (as I have been many times). The idea of the pokemon card method is that when you’re a kid (and assuming you collected pokemon cards) you don’t really know why certain pokemon are good, or why they would make a good addition to playing deck, you just know that they’re good. You know they’re good because you’ve probably heard it from your friends (maybe they even tricked you, sorry younger brother…). So you do your best to collect a card of that particular ‘good’ pokemon. Over time you collect more and more pokemon and you learn how they can work together to win pokemon battles. Through the relations that you see between the cards (link), and how they interact with each other you get a better understanding of why the cards you collected in the first place were good (or you realise you were fooled!). In this analogy pokemon cards represent facts or phrases that you know are important, but you just don’t understand yet. So that’s basically the pokemon card method. You collect up key bits of info, even though you don’t understand them yet. As an example, here are some pokemon cards (key phrases) that I collected when I was trying to understand Wave Mechanics at Uni.
-Probability density: Is the probability of finding a particle at a given position. It is the wave function multiplied by the complex conjugate of the wave function
–Eigenfunctions are: Solutions to the Time Independent Schrodinger Equation (TISE)
–Eigenvalues are: allowed total energy values that are possible in conjunction to solns to the Time Independent Schrodinger Equation
–Any linear combination of wave functions: is also a solution to the Time Independent Schrodinger Equation
Now, I can guarantee that when I wrote these things down I only knew 2 things. 1: It was important. 2: I had no idea what it meant. Then I went away, and I tried to get these phrases in my head**, I also brought them along with me to lecture (along with about 100 more of them) on my computer and when the lecturer said one of those words (eg: eigenfunction’) I could use the search function in my word document to pull up that line. Over time my brain started to see the words such as ‘eigenfunction’ as cues to bring up phrases such as ‘solution to the TISE’. As I began to internalise these ‘facts’ my brain began to automatically build connections between the concepts. This happened till eventually I was able to explicitly talk about the connections between these concepts, at which point I began to feel like I was ‘understanding’ wave mechanics! At the end of the semester, I understood enough for transfer to occur. Ie: I was able to apply the concepts that I now ‘understood’ to situations that were unfamiliar… questions in the exam! Understanding success!
Since that time I’ve come to a better understanding of why this method actually worked. It’s because facts are the foundations of critical and scientific thinking.
**What I was doing to memorise them at the time was to print out two lists of them. One was the complete list and the other was a list with just the parts in bold on it. I’d staple the only-bold-bits page in front of the complete-sentences page and try to recall the full sentence from the cues on the only-bold-bits page. This method was pretty effective, but at the time I hadn’t heard about Anki. If I had have I would have used it to get these phrases into my head as it’s much more efficient.
Don’t lie, and keep trying! Ideally you’ll begin to understand after steps 1: Survey and 2: Acquire. But if you can’t, try to use the analogy or the pokemon card method, or just move straight on to step 4: Link then 5: Train. Understanding WILL come later if you keep on working and following through with the process. In the words of the great Physicist Erwin Schrödinger.
“In an honest search for knowledge you quite often have to abide by ignorance for an indefinite period… The steadfastness in standing up to [this requirement], nay in appreciating it as a stimulus and a signpost to further quest, is a natural and indispensable disposition in the mind of a scientist.”
Check out the next of the five steps, Link.