Barbara A. Oakley

An engineering professor who started out doing poorly in mathematical and technical subjects in school offers tools, tips and techniques to learning the creative and analytical thought processes that will lead to achievement in math and science. Original.

How to Excel at Math and Science (even If You Flunked Algebra)

A Mind for Numbers

matej yangwao

Book starts with nice explaining on memorization techniques and continues with few tactics how you can raise your knowledge income.

You won't miss if you apply it in your learning process.

≥Learning can be an adventure rather than hard labor.

 ≥At first, you focus on the situation. Then, you turn away from the new learning to use the diffuse way of thinking.

≥The Einstellung effect refers to getting stuck because you’re fixated on an approach that’s not working.

≥Distracting yourself from a problem opens the door to big-picture thinking for a solution.

≥To learn about and be creative in math and science, we need to strengthen and use both the focused and diffuse modes.

≥Chunking requires a combination of thoughts into a smooth neural pattern that describes a concept. The best language programs combine focused-mode learning of the language with more diffuse-life free speech for native speakers.

≥The glue that holds the underlying memory or chunks together is understanding.

≥Chunking increases the size of your working memory.

≥The first step is to focus your attention on the information you want to chunk.

The second step in chunking is understanding the basic idea you are trying to chunk. Gaining context is the third step. Context means gaining a broad perspective on the problem at hand, so you see not only when to use the chunk but when not to use it.

≥Research has shown that writing appears to help you to more deeply encode (that is, convert into neural memory structures) what you are trying to learn.

≥Write the symbol on an index card and write the remaining information on its other side. Then, at intervals, try to remember what is on the other side of the card when you see the density symbol. If you can’t remember, flip the card and remind yourself. Practice this at increasing time intervals.

≥Using recall — mental retrieval of the key ideas — rather than passive rereading will make your study time more focused and effective.

≥Interleaving means employing different strategies to solve related problems.

≥Laser-focusing on a single task within a short period of time will produce better results than trying to juggle several tasks within the same time frame. When learning a concept, focus on it and completely avoid distractions. Then you can try to remember what you've learned while doing something less important to be sure the concept has been mastered.

≥Things become automatic as you chunk material by writing and memorizing.

≥If you switch from fear to excitement, your performance will improve.

A great read. The author is able to transmit difficult ideas in a really abstract way, making them easier to understand. 

I learnt a lot, and it's made me rethink my note-taking style and improve the way I revisit content. 

jason birchall

A great read. The author is able to transmit difficult ideas in a really abstract way, making them easier to understand. 

I learnt a lot, and it's made me rethink my note-taking style and improve the way I revisit content. 

Gavin

Lovely. She pitches it at anxious people - and just mentioning the difficulty, just treating a block as a normal problem with normal solutions, dissolves half the problem. The chapters are tiny and repetitive and cutesy, no doubt also intended.

The other side of being humanistic is that she draws on theories from the dodgiest sciences: social psychology, pedagogy and a bit of pop neuroscience. But unlike similar books by Baumeister and Dweck, the dubious results are like rhetorical ornament rather than the crux. I give it a pass. Also she's a good teacher, so gets plenty of feedback from students about what actually works. 

She accounts for human variance, obviously vital for any good advice:

  Take a step back and look dispassionately at your strengths and weaknesses. If you need more time to learn [a given amount of] math and science, that’s simply the reality. If you’re in high school, try to arrange your schedule to give yourself the time you need to focus on the more difficult materials, and limit these materials to manageable proportions. If you’re in college, try to avoid a full load of heavy courses, especially if you are working on the side. A lighter load of math and science courses can, for many, be the equivalent of a heavy load of other types of courses. Especially in the early stages of college, avoid the temptation to keep up with your peers... learning slowly can mean you learn more deeply than your fast-thinking classmates.


Maybe won't do much for you if you've ever had a good maths teacher.

---

Claims

- Two disjoint brain modes: focused ("studying") and diffuse ("shower thoughts"). Mixture of the two is needed for problem solving: focus, then unfocus. Sleep is [diffuse](https://www.bytestart.co.uk/relaxing-...).

- Einstellung effect: anchoring on the first flawed approach. Focus as the opposite of exploring.

- You need lots of time: time to switch modes, time to chunk content into strong abstractions, time to form long-term memory.

- Spaced repetition duh

- "Chunk creation" (learning suitable abstractions): focus on it, get the gist, practice (how to use it), work out applicable contexts (when to use it), test recall

- Worked examples are good

- But seeing the answer leads to the illusion of competence (hindsight bias). 

- Re-reading the formula also leads to illusion of recall ("it's in my head")

- Go walk and chew it over

- Some overlearning ("continuing the study or practice after it is well understood"), not too much

- "If you don’t understand a method, stop and work backward. Go to the Internet and discover who first figured out the method or some of the earliest people to use it. Try to understand how the creative inventor arrived at the idea and why the idea is used"



---

Misc

* Not sure about the examples here: 

  the brain is designed to do extraordinary mental calculations. We do them every time we catch a ball, or rock our body to the beat of a song, or maneuver our car around a pothole in the road. We often do complex calculations, solving complex equations unconsciously, unaware that we sometimes already know the solution as we slowly work toward it

This is a classic modelling mistake of physicists. I think motor coordination is done by simple rule of thumb plus a control loop (see motion, move hand, predict path, see motion, move hand) rather than unconscious calculus or ODEs.

* One place she overdoes the weak psych is insisting that the world is just when it comes to mental power. 

  A superb working memory can hold its thoughts so tightly that new thoughts can’t easily peek through. Such tightly controlled attention could use an occasional whiff of ADHD-like fresh air—the ability, in other words, to have your attention shift even if you don’t want it to shift. Your ability to solve complex problems may make you overthink simple problems... their slower way of thinking can allow them to see confusing subtleties that others aren’t aware of. 


* Happy to see the late Seth Roberts show up. He went too far and dogmatic, but his impulse towards self-experiments is great. 

  first self-experiment involved his acne. A dermatologist had prescribed tetracycline, so Roberts simply counted the number of pimples he had on his face with varying doses of tetracycline. The result? The tetracycline made no difference on the number of pimples he had! Roberts had stumbled across a finding that would take medicine another decade to discover—that seemingly powerful tetracycline, which has unsafe side effects, doesn’t necessarily work on acne...

Felipe Saldarriaga 

Read it, even if you think you love maths or if you hate it, this book goes far far beyond that

Guillermo Rodas

Amazing book! I watched the course but this book is a MUST read after the Coursera course. I agree as the author describes in the afterword that I wished to have a book like this in my early days at the university. Totally recommended!

Barbara Oakley

The companion book to COURSERA®'s wildly popular massive open online course "Learning How to Learn" Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a new skill set, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating material. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. The learning strategies in this book apply not only to math and science, but to any subject in which we struggle. We all have what it takes to excel in areas that don't seem to come naturally to us at first, and learning them does not have to be as painful as we might think! From the Trade Paperback edition.

A Mind for Numbers How to Excel at Math and Science (even If You Flunked Algebra)

Reviews