Learning: A Better Way
Recently, I’ve realized I need to overhaul my study habits. This was mainly brought on by reading Barbara Oakley’s fabulous book A Mind For Numbers. Though book is designed to help cultivate an effective mindset for learning math/science, these concepts are just as applicable to learning in general.
There is such a treasure trove of thought provoking material that I’ve decided to create a new series of blog posts, probably one for each chapter.
Rather than try to completely summarize each chapter, I’ll be going over some of my resulting thoughts about the concepts presented.
I should also mention that this book is based off an awesome Coursera course which you can follow along with, which might make these posts a little more meaningful. But I’ll try to make these posts free-standing so even if you haven’t read the book (or seen the lectures) they’ll be helpful.
There are a few realizations that made me very anxious to start my learning overhaul, and I think sharing why I felt I needed to change my study habits:
- Repeatedly reviewing notes and the textbook is a terrible way to learn:
I think this is something we all sort of intuitively know, but it scares me that my “default” study mode is to think, “Well, let me just go and reread my notes…and reread them again…” Part of this is because doing “real learning” can be tiring (read: painful) for your brain. But if the alternative is not learning, I think I need to learn to put in more effort.
- My current study habits weren’t designed to maximize learning:
If you think back, the methods you currently have for comprehension and information are most likely cobbled together from years of experience. This makes them usable, but probably not optimal. If I didn’t actively decide to create study habits that promote learning, I find it highly unlikely that what I’m using is the best I there is–so spending some time thinking about what sorts of skills I want to be in my mental toolkit seems very appealing.
- These posts are part of the learning process:
By trying to convey the gist of what I’ve read, I’m actively mapping the areas in my own head for how these concepts involved fit together. This way, I can see what I’m explaining well, what I understand, and what’s tricky for me to break down –perhaps because it’s shaky in my own mind as well. (Writing about learning to learn is a way to learn how much you’ve learned about learning to learn, it seems.)
The Introduction: How We Think
AMFN begins by describing two models of thinking that Oakley refers back to throughout the book: focused-mode thinking and diffuse-mode thinking.
Focused-mode thinking is supposed to refer to the sequential thinking mode when we utilize analysis and critical thinking. The prefrontal cortex is also involved, which makes this seem similar conceptually to Kahneman’s System Two.
I liken this to when I directly try to solve a math problem. I start out by asking what the problem is looking for. Then, I begin to list out manipulations between the numbers to take me to the answer. This is very step-by-step.
In contrast, diffuse-mode thinking refers to a more “spread-out” or “bigger-picture” state of mind. I confess that I am having trouble grasping this idea as one concept. I think it’s easier to see it as a few related things:
One is the “free association” that my mind goes through when I’m doing a “mindless” task like exercising. Thoughts are flying around, and I feel more like a passive observer.
Second is the unconscious “background” work my brain does when I’m not directly thinking about a problem. This is the progress that we might see when we come back to something after a break–the sort of “aha” moments when things click together.
Thirdly is “meta-level” thinking, which looks at the bigger picture of things. Being able to “zoom-out” and abstract levels also seems connected. For example, I could be looking at finding the area of a triangle as an interaction between its “base” and “height”. But on a higher level, it’s also one more tool in my math-solving toolkit. Now, I can split things up into triangles to solve trickier area problems.
Oakley uses “diffuse-mode” to mean a combination of the above.
While we’re on the idea of “zooming-out”, I think this would be a good time to give a powerful general tip for learning that Oakley mentions early on:
TIP: When reading through any piece of work, it pays to look over the entire chapter first, taking note of the headings, titles, and pictures. This helps to see where concepts fit into a larger picture, so it makes more sense as you read individual passages.
Though I’ve personally liked the “surprise” of encountering new information on a page, I think this is much less valid when reading nonfiction/textbooks. (Somewhat related is the aversion to reviewing things I “already know”, and “ugh” feeling that we’ll also have to tackle later on)
Oakley also discusses the question of what can make math/science more challenging than other subjects.
Abstraction and generalizing are also involved here. In other subjects, symbols tend to have real-life referrents– a “duck” can be shown in the real world, but the “+” symbol is an idea; there are no wild plus signs we can use as an “anchor” in reality.
Related to this is the idea of encryption. Often, complex mathematical ideas are represented by simple symbols, like how πr² represents a circle’s area. There are a lot of ideas going on behind the scenes here– what the exponent on the r means, what the r stands for, what π is, and so forth.
These ideas might not always be familiar to us, especially if they don’t blatantly show up in everyday life.
I think that having these concepts down as fundamentals should make the manipulation of such abstract ideas easier– sort of like how thinking in a foreign language is a big step to fluency.
It seems like it could help to be able to not have to ask yourself “what does the ‘+’ refer to?” and instead just feel that “plus-ness” is a basic, intuitive idea of the world, like “cause-and-effect” or “thoughts”, which seem indivisibly simple.
Otherwise, it seems that much of the work in math/science involves trying lots of different solutions, which can be harmed by sticking only to one approach. Oakley calls this an Einstellung, which is German for “mindset”, an incorrect way of looking at the problem that doesn’t allow you to consider alternate solutions.
TIP: Before starting problems, to help counter Einstellung, it seems like making a list of different ways you can tackle the problem before starting can improve the variety of approaches you take.
Below is a basic algorithm I’ve decided to implement whenever I decide to study/learn. This is very much a first draft and I suspect I will revise it many times along the way: