A Mind for Numbers – Barbara A. Oakley
How to Excel at Maths and Science
Focused thinking and diffused thinking
Focused mode is used to concentrate on something that’s already tightly connected in your mind because you are familiar and comfortable with the underlying concepts.
The diffuse approach involves a big-picture perspective. useful when you are learning and understanding something new. As long as we are consciously focusing on a problem, we are blocking the diffuse mode. Do something else until your brain is consciously free of any thought of the problem.
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You need to use both big-picture, or focused mode, and detail-oriented, or diffuse mode, to get good at math and science.
Create the best conditions for focused and diffuse thinking
Focused thinking needs meaningful stretches of undisturbed time to focus and think.
- Prioritize making distraction-free time and space to think deeply
- (SQ3R: Survey, Question, Read, Recall, Review)
- Practice purposefully (Work the hardest bits, generalize through variation)
- Think on paper, there’s magic between the hand and the brain
- Diffuse thinking occurs subconsciously by temporarily loosening attention.
- Relax/disengage attention: Sleep, walk, drive, blink, exercise
- Recall and test frequently (e.g., spaced repetition techniques).
- Actively build time into each day to alternate between both modes.
One of the first steps towards gaining expertise in math and science is to create conceptual chunks.
Once you chunk an idea or concept, you don’t need to remember all the little underlying details; you’ve got the main idea—the chunk—and that’s enough.
Basic steps to forming a chunk:
Focus your attention on the information you want to chunk.
No television on in the background, don’t look at your phone, etc.
Understand the basic idea you are trying to convey.
Gaining context so you see not just how, but also when to use this chunk.
Focus on process instead of product
Unfortunately, many of us find it too easy to procrastinate even starting our math homework because we see it as boring and difficult. This thinking comes from focusing on the idea that we only want to finish our work.
If we instead look at our goal as “For the next 15 minutes I’ll work on this math assignment,” it becomes a lot easier to just begin. When we center our mind on only the process of learning, it’s easier to just go with the flow and relax.
Interleaving versus overlearning
Interleaving means practicing by doing a mixture of different kinds of problems requiring different strategies.
Overlearning means continuing to study or practice a problem immediately after some criterion has been achieved. For example, correctly solving a certain type of math problem and then immediately solving several more problems of the same kind.
Overlearning provides diminishing returns.
Enhancing your memory
Learning to use your memory in a more disciplined yet creative manner helps you learn to focus your attention.
- One of the best things you can do to remember and understand concepts in math and science is to create a metaphor or analogy for them.
- Use spaced repetition to help lodge ideas in memory.
- Create meaningful groups that simplify the material you are trying to remember.
- If you are memorizing something commonly used, search online to see if someone has already come up with a particularly memorable memory trick.
- Beware of mistaking a memory trick for actual knowledge.
Writing to improve your memory
There is a direct connection between your hand and your brain. The act of organizing and rewriting your notes is essential to breaking down large amounts of information into smaller, digestible chunks.
Writing and saying what you are trying to learn seems to enhance retention.
The Einstellung effect
The Einstellung effect is a phenomenon in psychology and cognitive science that refers to the tendency of people to be influenced by their prior experiences and knowledge when solving problems or making decisions. This can sometimes lead to a “mental set” or a tendency to approach problems in a particular way, which can be both helpful and hindering depending on the situation.
Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!
The Learning Paradox
Learning is often paradoxical. The very thing we need in order to learn impedes our ability to learn. We need to focus intently to be able to solve problems – yet that focus can also block us from accessing the fresh approach we may need. Success is important, but critically, so is failure. Persistence is key – but misplaced persistence causes needless frustration.