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A Mind for Numbers: How to Excel at Math and Science

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Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. 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 effectively learning math and science—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 math. 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. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

336 pages, Paperback

First published July 1, 2014

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About the author

Barbara Oakley

29 books1,094 followers
Barbara Oakley, PhD, a 'female Indiana Jones,' is one of the few women to hold a doctorate in systems engineering. She chronicled her adventures on Soviet fishing boats in the Bering Sea in Hair of the Dog: Tales from Aboard a Russian Trawler. She also served as a radio operator in Antarctica and rose from private to captain in the U.S. Army. Now an associate professor of engineering at Oakland University in Michigan, Oakley is a recent vice president of the IEEE Engineering in Medicine and Biology Society. Her work has appeared in publications ranging from The New York Times to the IEEE Transactions on Nanobioscience.

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Displaying 1 - 30 of 1,873 reviews
Profile Image for Sanjay Gautam.
233 reviews443 followers
July 11, 2019
Luck favors the one who tries.

When I started reading it I never expected it to be this good. I was amazed and delighted to find this book to be exceptionally good. I have learned, which as it feels I had forgot , how to 'Learn to Learn'. It had shown me my flaws. It has shown me I was trying too hard, that it is 'easy that does it'.

She starts with learning modes, that we have two important modes of thinking, focused-mode and diffused-mode. Focused-mode are highly attentive states which are limited to pre frontal cortex and diffused-modes are diffused throughout the brain. Only one mode can be active at a time. Focused mode is related to logical, sequential, analytical process. As soon as you concentrate on some thing , you are in focused mode. Whereas, when you are not concentrating, when you let your mind just wander, you are in diffused mode. Diffused mode is related to bigger-picture. Focused mode brings you the BRICKS and diffused mode is the MORTAR.

To be attentive and try hard to get the problem inside your head is done by focused mode. Diffused-mode actually works in background under the layer of conscious awareness (and it is not that can ON and OFF, its always On whenever you are not concentrating,diffuse mode happens when you relax). Now she asserts that the learning happens when you toggle between these two modes.

And then there is Einstellung effect: It refers to getting stuck in solving a problem or understanding a concept as a result of becoming fixated on a flawed approach. Switching modes from focused to diffuse can help free you from this effect. This made me a little more flexible regarding my thinking, and more patient too. And I've also found that sometimes initial ideas about problem solving can be very misleading. To figure out new ideas and solve problems, its important not only to focus initially, but also to subsequently turn our focus away from what we want to learn.

In subsequent chapters the author deals with:
* The problems of procrastination and how to deal with it. There were four chapters dedicated for it. (And it was here I found myself, a little, dragging the book).
* Memory and how to enhance it. I remember one technique known as Memory Palace which was similar to Mind Palace shown in Sherlock TV series. It was here, once again, that I gained many insights which proved to be useful.
* In the last chapters she gives miscellaneous tips and tricks for enhancing your learning and sculpting your brain.


The central theme of this book is the paradoxical nature of learning. Focused attention is indispensable for problem solving, yet it block our ability to solve problems. Persistence is key, but it can also leave us unnecessarily pounding our heads. Memorization is a critical aspect of acquiring expertise, but it can also keep us focused on the trees instead of forest. Metaphor allows us to acquire new concepts, but it can also keep us wedded to faulty conceptions.

Our desire to figure things out right now is what prevents us from being able to figure things out. Reshaping your brain is under your control. The key is patient persistence: working knowledgeably with your brain's strengths and weaknesses. We can achieve startling insights into how to understand more simply, easily, and with less frustration: By understanding your brain's default settings- the natural way it learns and thinks, and taking advantage of this knowledge one can become an expert.

Profile Image for David Rubenstein.
816 reviews2,581 followers
September 26, 2015
I first heard of this book from an online course given by the author, Barbara Oakley. The course is called "Learning how to Learn", and you can find it at coursera.

Despite the title of the book, most of the advice here is appropriate for just about any subject. It is especially appropriate for subjects with concepts that might be difficult to grasp. And the book is most definitely geared toward students. There are highlights and questions at the end of each chapter, to reinforce the key points.

There is a useful chapter on how to prepare for tests, and how to take tests. The advice is not always intuitive, but it is all common sense. Study groups are often beneficial. There are some situations, where they may be a waste of time.

Much of the advice in the book is based on common sense. Don't cram for exams; study some each day, and don't overdo it. Lots of advice on how to make sure that you really understand the concepts. Re-reading material and highlighting key phrases is NOT very beneficial. Make up your own test questions, put them on flash cards with answers on the back. Flash cards are your friends.

The book is filled with anecdotes and stories about educators, students, scientists, engineers, and mathematicians. These stories help make the book engaging, where otherwise it would be rather dry and uninteresting.

The main theme of the book is that there are two modes of thinking; focused and diffuse. Focused thinking is what you do when you concentrate very hard to solve some problem. You need to remove yourself from distractions during focused thinking, and you probably should only perform focused thinking for a short amount of time; 25 minutes is recommended. Diffuse thinking, however, is somewhat more relaxed and actually creative. This kind of thinking allows your mind to wander in search of "out of the box" solutions to problems.

If you are a student or even studying some subject on your own, then this book could be very helpful.
Profile Image for Moeen Sahraei.
29 reviews35 followers
May 20, 2021
I had always been frightened by mathematics since I was a child. In high school all of my grades were A or B but the highest grade i had achieved in math was D. This trend was continuing until three years ago, when I had to learn maths in order to pass the exam in university. At first I was baffled with algebra, geometry, trigonometry and most of all calculus. It was a total nightmare for me. So I realized that I had to triumph over my fear and learn it properly once and for all. I started to watch khan academy videos on any math subjects.

This was an epic moment in my life because I found out that my greatest fear was indeed my true passion in life. I just loved the harmony and beauty of algebraic expressions and calculus formulas especially the meaning behind all of these abstract symbols. With intuitive method of teaching of the khan academy and some mental exertion I managed to learn so many precious things in maths even difficult parts of calculus and I got an A in my AP exam. Since three years ago I have never stopped learning mathematics (except few months for TOEFL) and currently I am studying for the GRE test. Which I am really thrilled by this process and it is not stressful anymore at all. The most important thing is that I’ve decided to keep learning maths for the rest of my life, especially probability and statistics.

That was my personal experience. But about the book. It is a really good guide for anyone who has similar difficulties regarding math and science. And even it is so helpful for people who are good at math, it could help them get better. The author herself had been so terrible at math until she saw better job opportunities in scientific disciplines like engineering, so she learned some important principles which helped her start learning math when she was 26, she got a bachelor degree in mechanical engineering, a master in computer engineering, and finally a doctorate in system engineering. In her insightful book she collected and explained those principles. She also relate some stories of other people who had the same experiences and how they got successful in this path, and she adds some advice from math and science professors.
Profile Image for Always Pouting.
575 reviews761 followers
October 6, 2020
I have read a few of these books at this point, I bought a bunch of them when I was on my productivity kick, so a lot of the information was things I already knew. I do think just knowing what to do isn't enough, it's very much the execution that ends up being the issue. That said I think this is one of the better ones. Some of the ideas are repetitive but it's clearly done intentionally to help anyone reading the book internalize those ideas, which is probably really important if this is someone's first time encountering these things. I do also think the advice is solid and the book delivers it in an accessible and easy to internalize fashion. Probably a good book for anyone that doesn't have the best habits or relationship with long term sustained learning, including myself. Mostly its been useful as I've been studying to help get me into a place where I find it easier to do my work. It kind of serves to prime me for what I need to do which helps with execution and maybe I can try to sustain this by replacing reading books on how to be efficient with just journaling and trying to be more mindful of my behavior.
Profile Image for Amy Alkon.
Author 8 books56 followers
July 31, 2014
This book IS a book on how to excel at math and science -- even if you previously flunked them. However, it is also much more. It's a book that is transformative for anyone who does creative work that requires writing and thinking and taking in information and creating something new out of it.

The science on how to do optimal work in “A Mind For Numbers” has transformed my writing life from hellish to a tough job I love. Through what I learned from about diffuse mode thinking, I’m careful to put in daily work in reading, researching, and writing, especially on tough concepts.

Our minds, as Dr. Oakley explains in the book, seem to do a lot of work in the “background” while we’re sleeping and doing things other than working. Each day, I find that I’m enjoying my work so much more because it isn’t a struggle; I, piece by piece, simply pull together tough concepts into a coherent and far better whole. 

Dr. Oakley’s book ultimately helped me enjoy what I do in a way I never could before, when I procrastinated and was stressed out and then tried to shoehorn a bunch of information I hadn't processed into something coherent. This book was a life-changer for me.

--Amy Alkon, syndicated columnist and author, "Good Manners for Nice People Who Sometimes Say F*ck" (St. Martin's Press)
Profile Image for Chazzle.
268 reviews13 followers
February 8, 2015
Probably some of the advice in the book is good. I just wasn't in the target audience. I like math, I'm very good at math, and this book is for those who struggle.

I liked Paul Lockhart's book "A Mathematician's Lament" much, much better. In that one, he really makes you want to DO math, to DISCOVER mathematical truth, to LOVE math. In Barbara Oakley's book, she teaches you how to "get by", and maybe even "get an A". Much, much less inspirational. Where's the fun? Where's the love?
67 reviews
January 19, 2017
This book is not at all what it says on the cover, it's just more tired "study tips" the same as you would get from any Universities student resource center. There's nothing inherently specific about learning Math and honestly I found the book to be full of an awful lot of fluff... It's a rather shockingly callous thing to do considering how many people struggle with Math to continually dance around the one fact present, it just takes a lot of time and effort and work and you may simply never crack it. Terrible book.
8 reviews
October 14, 2014
The title of the book doesn't do it justice. This is a book about how to get good at anything, not just math and science. It's a light read because it's full of simple advice. But the stuff it teaches is effective, and I wish it had been taught to me back in 1997 when I was starting graduate school.

If you find yourself checking your phone or screwing around on Facebook while you should be working, read this book. If you're having trouble learning stuff you need for work at a higher rate than you're forgetting it, read this book. Do so especially if you're young, because the longer the time you have left to reap the benefits, the more reading this book is worth to you.

Read this book, put your butt on a reasonable schedule, get your sleep and exercise, and the chances are excellent that you will never want for satisfying, well-paid employment no matter your field. This is a book about making your zombies work for you, not about learning how to fight them.
Profile Image for Stephan .
32 reviews41 followers
April 4, 2017
Fantastic learning hacks! How our brain works concerning learning, retaining. Everyone should read this, every pupil/student in school.

We learn all our lives and sometimes we have exams - this book will tell you how to prepare well.

The title "A Mind for Numbers" is misleading, it's about learning in general.
Profile Image for Mark Bao.
29 reviews221 followers
June 30, 2016
tl;dr: Read if you want to learn general study skills, skip if you're interested in skills specifically for math/science.

Why did the author write a book about getting better at numbers and math and science and not really talk specifically about how to get better at math and science? This book is 90% about general study skills with lackluster tie-ins to how it might work with math/science. Don't go into this thinking you'll learn stuff specific to math/science – you'll be disappointed.

As an introductory book to study skills, it's not too bad, though it's overshadowed by more compelling books that specifically talk about general study skills like Make It Stick: The Science of Successful Learning and Cal Newport's books. Many of the productivity and study tips it mentions are good, but they fall into the classic non-fiction personal development book trap of telling you some common-sensical thing you should be doing and adding an anecdote in there. It's OK if it's common-sense advice, but it's not really that useful if it's common-sense advice without much follow-through information on how to implement that advice.

Maybe it's just me. Admittedly, I've read a lot about productivity and study skills so most of this was a reminder at best, boring repetition at worst. If you've read books like Make It Stick or Cal Newport's books and want to get a more math- and science-focused advice on how to do better, don't pick this up. If you've read some but aren't sure, maybe pick up the audio version (which is what I did). Or go to a bookstore, skim through, and decide from there.

It's not that there aren't gems in this book. There are a few. Diffuse mode vs. focused mode thinking, a core part of the book, is pretty interesting. The fact that the memory palace technique works well for unrelated things, which I never thought about. And some other ones that weren't so memorable. It's good for reminding you about all the productivity tips that you should be doing. But for me, there was nothing novel in here.

I'm not sure what I'll read next to replace this. Here are some that I'm considering, if you're curious:

What Is Mathematics?: An Elementary Approach to Ideas and Methods
How to Solve It: A New Aspect of Mathematical Method
How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
The Princeton Companion to Mathematics
Profile Image for Daniel Clausen.
Author 11 books467 followers
May 2, 2018
I'm very fond of practical books, clearly written, that can be immediately applied.

One thing, however, does need to be mentioned from the beginning: This is not only a book for those looking to excel in math and science. These tricks and methods can be used for any subject. My suspicion is that the "math and science" aspect of the title is a marketing ploy more than anything.

That's a shame because there is a lot in this book that I hope to pass on to language learners and students of International Relations.

Getting that out of the way, let's focus on the good. The book is clearly written, easy to follow, and frequently engaging.

The book will introduce you to important concepts like:
*the difference between focused and diffuse thinking (and how to switch between these modes);
*using recall in your studying;
*the idea of chunking concepts;
*tricks for studying such as the Pomodoro technique and spaced repetition;
*the value of walks and frequent breaks; and
*ways to overcome procrastination.

The book also helps you become a deeper learner, someone more in love with education. It does so by:
*helping you understand yourself as a learner;
*promoting the virtues of teamwork and providing tips for how to use partners and teammates; *promoting broad studying and creative exploration;
*by promoting real education over vulgar grade accounting; and
*by demonstrating how much science and math are like poetry.

The book also asks you practice these methods by putting down the book and trying to recall key concepts, and by doing exercises for each chapter. Early in the book, there were also some mental exercises that I quite enjoyed.

Now, a little bit of the bad. There really isn't that much.

I felt like a lot of the "testimonials" in between the chapters and in the sidebar "success stories" gave the book a kind low-rent "kitschy" feel to it. It reminded me of self-help seminars, infomercials, the adverts of private colleges (which emphasize testimonial "successes" and overlook failures), and the other quasi-get-rich-quick, let's-find-short-cuts aesthetics of quasi-education.

I feel like that aesthetic needs to be fought at all costs. I feel like that mentality is destroying education (and America for that matter). Education is hard work. There is no getting around that. And, as several other reviewers have pointed out, by only highlighting the successes, the author is being very unscientific (she is sampling on the dependent variable, as they say).

The book is better than this. It's better than its cheap, attention-getting marketing ploys.

Still -- overall, a great book for just about anyone who wants to improve their learning!

Profile Image for Salem.
231 reviews5 followers
September 6, 2018

كتاب عظيم لا يُفوّت، وقرائته واجبة على كل متخصص في العلوم والهندسة خاصة، وكل من له اهتمام بطرق التعلم وأساليبه. وما زلت مستغرباً، كيف أن كتاباً ذائع الصيت كهذا، لم يترجم بعد للعربية !
من المباحث الرئيسية بالكتاب، إيضاح طريقة عمل الدماغ خلال عملية التعلم، وكيف بالإمكان توظيف هذه المعرفة في تكوين استراتيجيات تعلم مثمرة وفعّالة. وكذلك تفنيد عدد من المفاهيم الملتبسة عند كثير من المتعلمين، على سبيل المثال، مسألة الحفظ أو الفهم، أيهما أهم؟... وغيرها من القضايا، والتي دُعمّت بتجارب شخصية لأساتذة جامعيين وطلبة جامعات نوابغ، ومن استخلاصات البحوث الحديثة في علمي الإدراك والأعصاب
رابط الكتاب الصوتي على اليوتيوب 🔗
Profile Image for Agnes Pokorná.
23 reviews7 followers
August 13, 2016
I didn't like the way Barbara repeats over and over the same agruments for nearly trivial statements. For example she was able to write about 30 pages only about the fact that you need to sleep and relax in order to enhance your learning. For me, it seems like a 1000-year-old advice but she kept repeating it as if I haven't read it already 16 times before in this chapter. The entire book could be summarized in 5 pages. Although I must admit that I surely enjoyed reading her life story, about how she approached the math and the science which was in the beginning of the book.
Profile Image for Albert.
384 reviews26 followers
January 4, 2021
Oh my. I wish I had read this in High School or between High School and College or in College. This book is less about Math and Science and more about learning and studying. There are certainly some techniques that are specific to or a better fit for Math and Science, but most of the ideas and material will work for almost any area of study. Many of the recommendations were not new to me. I had used quite a few of them throughout my years as a student and learner. The real insight came from the overall package, putting the techniques together and most importantly, finding ways to use them persistently and with discipline. Developing the techniques and organizational methods as a complete skillset was not something I ever really accomplished. I would use a few techniques in this class and a few others in this other one, but I lacked consistency. I also lacked the discipline. My intentions were always worthy, but my execution was lacking. I would like to think I could give this book to a high school student today and they would get the benefit I missed, but I am afraid only a small percentage of those students would take the time to review the book much less read it.

Even today, I see opportunity to use what I have found in this book. As I attempt to learn something new as an adult, as I take on a new project, the opportunity is there. But first I must put aside all the opportunity missed so that I can focus on the opportunity in front of me.
Profile Image for Anatoly Leonov.
20 reviews2 followers
October 12, 2022
Книга яку варто прочитати кожній людині. Багато корисних поряд про те як сформувати знання в будь якій сфері
Profile Image for Eat.Sleep.Lift.Read..
156 reviews34 followers
March 22, 2016

Like many of 'these' books, most of the advice seems, to a stud like me, mostly common sense.

But, A Mind for Numbers, has more 'takeaway' value than most.

If you want to grow ya brain (the one up top) then give this book a whirl.

If you want to grow the other one, I have a plethora of www. recommendations.

Either way, stay sexy.
Profile Image for Giuseppe D.
274 reviews51 followers
November 20, 2014
Got to this book after reading about it in the Coursera course "Learning how to learn". Some very good ideas not at all obvious, at least not to me, that make perfect sense. Go have a look at the author's website for the 10 principles of learning and, if you find them interesting, grab a copy!
Profile Image for Bryn.
29 reviews1 follower
January 1, 2015
A fantastic book for understanding how we best learn complex concepts. Initially I thought because I already have college degrees in Math and CS that I didn't need to read this book. I though I already knew how to learn match and science. I was wrong.

In retrospect, the subjects and classes that came easily to me were the classes in which I was practicing many of the good habits prescribed in this book. The subjects in which I struggled, were plagued by many of the bad habits and pitfalls outlined by Dr Oakley.

In fact, I have resolved to revisit some of those subjects that proved difficult in school using these techniques.

The book is written at a very easy reading level, making it very approachable for readers as young as 12. I will be testing this theory by making this book required reading for my kids before they start middle school.

This is the companion book to the Coursera course taught by Dr Barbara Oakley. https://www.coursera.org/course/learning
Profile Image for Seyed-Sajad Hamedheydari.
Author 5 books17 followers
September 21, 2021
دقیقاً یادم نیست برای چی سراغ این کتاب رفتم، فقط یک جورایی از لیست خرید کتابم سردرآورده بود (البته نشر چترنگ کتاب‌های باکیفیتی ترجمه می‌کنه و یکی از دلیل‌هاش می‌تونه این باشه).
ولی با این حال کتاب بدی نبود. مخاطب اصلی این کتاب دانش‌آموزها و دانشجوها هستند که در یادگیری درس‌هایی مثل ریاضی، فیزیک، شیمی و درس‌های حفظی مشکل دارن. اما غیر از مواردی که به‌صورت اختصاصی برای این دسته از مخاطبین نوشته شده بود (مثل روش امتحان دادن و یادگیری با امتحان)، بقیه‌ی مطالب برای افرادی که همچنان بعد از مدرسه و دانشگاه دنبال یادگیری مطالب هستند مفیده و کمک می‌کنه به‌طور موثرتری مطالعه کنند.
Profile Image for Sadra Aliabadi.
45 reviews77 followers
October 30, 2017
من درواقع این کتاب رو نخوندم. کورسش رو که با توجه به متریال کتاب توسط نویسنده در کورس‌ارا بود رو گذروندم.
کتاب ظاهرا بیشتر از این که در مورد یادگیری ریاضی باشه به شکل عمومی تر در مورد یادگیری هست. نویسنده به خوبی از آنالوژی‌های متفاوت استفاده کرده تا حرفش رو برسونه.
اگر به یادگیری علاقه مند هستید من یک خلاصه سه هزار کلمه ای از کتاب رو در وبلاگم منتشر کردم:
میتونید اینجا بخونیدش.
30 reviews5 followers
January 26, 2015
A Mind for Numbers is a worthy addition to the "owner's manual for the brain" genre. It's billed as a description of how people who did not do well in math or science in school can learn to effectively study topics within those fields.

As someone who did well in math and science in school, this book reminded me of many successful study habits, some cultivated on purpose and some by accident during my preprofessional academic career. The book also has some great ideas that run counter to the conventional wisdom (in this case, foolishness) of our day. I'll list these separately:

Good study habits:
- Building my ability to memorize scripts, movies, jokes, etc. (on purpose: I still love quoting things)
- Not cramming (accidental: I never had the need, though I procrastinated on projects)
- Reviewing before bed (on purpose, but only for subjects I was particularly interested in)
- Reading ahead (on purpose, but driven by annoyance at how similar arithmetic lessons were from grades 1 through 3)
- Focusing on the edge of my understanding rather than burning study time on mastered material (on purpose: I didn't like "studying," so why would I waste "study" time on stuff I already knew?)
- Teaching others (on purpose: helping someone understand new concepts makes you feel like a boss)
- Paraphrasing (accidental: I never enjoyed the physical act of writing longhand, so I was often annoyed by any hint of verbosity in definitions or descriptions. I actually got in trouble once for not copying sections of my science textbook's glossary verbatim for an assignment!)
- Joking about the material (accidental: you have to have a sense of humor)
- Interleaving material (accidental: it just felt right. I never thought of myself as "studying" because "studying" was something that was supposed to feel miserable. I did my homework and I reviewed the syllabus before tests.)

Good ideas:
- Creativity is retrieving from long-term memory something that was never there
- The necessary ping-pong between the brain's focused and diffuse modes
- It's not a coincidence that we experience "aha!" insights when we step away from a problem we've been working hard for a while. Harness this phenomenon.
- Memorization as critical to creativity and effective problem-solving. This is a big one for two reasons:
1. Some nonsense started getting popular around the turn of the 21st century that knowing facts is inconsequential so long as you know where to find them.
2. Memorization assignments fell out of fashion since they're confused with rote-learning. In fact, perfect memorization of longer scenes is *only* possible by "chunking" the details into an outline of overall concepts.
Profile Image for Olga.
17 reviews16 followers
October 31, 2018
Гадаю, я буду не єдиною, хто після прочитання цієї книги (або проходження відповідних курсів на Coursera/Prometheus) подумає: "Чому, чому ніхто не розповідає про всі ці штуки ще у школі?" ;)
Інструменти, прийоми та техніки навчання, до яких багато людей приходять інтуїтивно, повільно, з досвідом, методом проб та помилок, викладені тут чітко та структуровано, причому йдеться не тільки про "як", а й про "чому" і "як це працює", а це дуже важливо і дає більше мотивації все-таки спробувати. Крім аргументованого викладу з прикладами та посиланнями на джерела, дуже сподобалося те, що сама побудова книги відповідає принципам, про які розповідає: вчитися маленькими порціями, з перервами на інші заняття - маєте розділи та підрозділи, розмежовані невеликими історіями; асоціації та метафори дуже важливі - нате яскравий приклад чи порівняння до кожної теми; ефективне навчання базується на регулярному повторенні, поглибленні та самоперевірці - вкінці кожного розділу є підсумки та контрольні запитання, та й навіть сам порядок розділів відповідає цій логічній спіралі, і т.д.
Попри те, що оригінальна назва та чимало акцентів у тексті - про вивчення математики та природничих наук, ця книга - чудовий помічник в опануванні будь-чого.
Ставлю високу оцінку не тому, що вся інформація в книзі була для мене зовсім нова, а тому, що якби я дізналася про це раніше, вчитися в школі та університеті було б набагато легше та цікавіше. Меншій сестрі обов'язково подарую, і вам раджу. ;)
Profile Image for FOYSOL MAHMUD.
13 reviews21 followers
December 23, 2020
This should be a text book for every high school (8th grade or 9th grade) students. Additionally, there should be a mandatory course in the first semester of every undergraduate program which will teach the students how to study well. In schools and colleges students are only taught what to study, however its important to teach them how to study.
A very well written book.
Profile Image for Kitty.
1,205 reviews77 followers
March 9, 2021
täiesti asjalik raamat, kuigi üldse mitte selline, nagu ma oleks kaanedisaini ja pealkirja ja alapealkirja põhjal oodanud. jääb ju mulje, et see raamat on... numbritest, matemaatikast ja loodusteadustest? aga on hoopis sellest, kuidas õppida. ükskõik, mida.

eessõnas autor kirjeldab, kuidas ta ise oli veendunud, et tal ei ole reaalainetele annet ja need ei meeldi talle, ja hakkas vene filoloogiks. aga elu näitas, et reaalainete oskajate järele oli tema valitud töökohal (USA armee, kui te juba küsisite) rohkem vajadust, nii et tuli tal oma vastumeelsusest üle saada. selle käigus selgus, et kui matemaatika juba hästi välja tuleb, on ta ka tunduvalt meeldivam, kui siis, kui millestki aru ei saa. nüüd on tal mingis reaalaines doktorikraad ja ta õhutab meidki mõistma, et anne ei puutu siin asjasse, tuleb lihtsalt õigesti läheneda ja veidi tööd teha.

siiski, kuigi tal tuleb iga natukese aja tagant meelde, et ta pidi ju matemaatikat, füüsikat, keemiat ja inseneriteadusi promoma, ja seda siis kohusetundlikult teeb, räägib see raamat ikkagi õppimisest üldiselt. ilma liigselt ajuteadusesse süvenemata, aga üldiselt ikkagi neidsamu asju, mida ajuteadlased meile juba tükk aega räägivad - et mälust ammutamine, enesetestimine ja ülesannete läbilahendamine on paremad õppimisviisid kui tuimalt raamatulugemine; et tasub teha erinevaid ülesandeid vaheldumisi, mitte kogu aeg ühesuguseid järjest; et enne kontrolltööd tuleb korralikult magada; et viimasele hetkele ei ole õppimist mõtet jätta ja et mõned asjad tuleb ikkagi pähe ka õppida. ja kõik see kehtib minu meelest küll ühtviisi nii matemaatika kui näiteks keelte õppimisel.

mulle tundub, et selle raamatu hea sihtgrupp oleks koolilapsed alates põhikoolist ja võibolla ka tudengid - kõik on kirjas väga lihtsas keeles ja lisatud on meeldejätmist ja arusaamist soodustavad peatükikokkuvõtted, kordamisküsimused jms. aga samuti võib ära kuluda igaühele, kes on sunnitud ilma suurema pedagoogilise ettevalmistuseta kedagi teist õppimisel abistama (khmkhm, distants- ja koduõpe).

mis puutub pealkirjas lubatud numbritesse, siis kui leheküljenumbreid mitte arvestada, siis esimest ja viimast korda kohtume numbritega 12. peatükis ja seal ei lähe asi ka keerulisemaks kui kaks näidet: 10*10=100 ja 10^4*10^5=10^9. kõik, rohkem pole! mina isiklikult oleks täitsa hea meelega tahtnud mingeid reaalseid ülesandeid kasvõi illustratsioonidena juurde kogu sellele värgile. aga mulle isiklikult ka matemaatika ja füüsika kohutavalt meeldivad.
Profile Image for محمد الحسين.
Author 4 books449 followers
June 21, 2018
كتاب رائع يعلم كيفية التعلّم بفاعلية. الكثير من الطلاب يواجه صعوبة في فهم الرياضيات والمواد العلمية لأسباب مختلفة، أغلبها عائد لخلل في عملية التعلم في مراحل مبكرة. ولأن هذه المواد هي ذات طبيعة تراكمية (فهم دروس الصف الثاني يعتمد على فهم دروس الصف الأول... وهكذا) فإن معاناة أولئك الطلاب تصبح تراكمية أيضاً، وتستمر إلى عمر متقدم، فيعتقد الطالب أنه غير مؤهل لفهم هذه المواد، فضلاً عن التفوق فيها.

يأتي كتاب (عقل للأرقام) بفكرة صادمة وهي أن الجميع يستطيع أن يتعلم الرياضيات والمواد العلمية إذا عرفنا الطريقة الملائمة لتعلم هذه المواد. ويفكك الكتاب عملية التعلم بشكل علمي مرتكزاً على نتائج دراسات في علم النفس وعلم الأعصاب. ثم يصب هذه النتائج في قوالب من سلوكيات بسيطة وواضحة يستطيع أي طالب أن يمارسها. فالكتاب يسد الفجوة بين النتائج العلمية والنصائح السلوكية العملية (وهو أمر ضروري للغاية في نظري)!

أعجبني في الكتاب أن المؤلفة (د. بربرة أوكلي) كانت تعاني كثيرا من الرياضيات في الصغر وتكرهها بشدة: "كنت أفكر أن الأرقام والمعادلات يجب تجنبها، كما نتجنب الأمراض القاتلة". لذلك هربت من كل ما له علاقة بالرياضيات وتخصصت في اللغات والترجمة. ولكن أثناء عملها، تمت ترقيتها لمنصب يتطلب فهما جيدا لأساسيات الرياضيات، فاضطرت لتعلمها، ثم أكملت دراستها لتحصل على بكلريوس في الهندسة الكهربائية، ثم ماجستير في الهندسة، فدكتوراة في هندسة النظم! والآن هي بروفيسورة في الهندسة!

من المواضيع الهامة التي أسهب الكتاب في الحديث عنها (مثالان فقط):

* العقل المركز والعقل المنتشر: يشرح الكتاب أن التعلم الفعال يكون بالتنقل بين نوعين من التفكير (المركز والمنتشر). فالطالب الذي يحاول أن يحل مسألة صعبة لمدة 3 ساعات (تفكير مركز)، من الأفضل له أن يترك المسألة لبرهة من الزمن، أن يحاول حلها في اليوم التالي. غالباً سيجد أن المسأله صارت أسهل أو أنه أصبح ينظر لها من منظور مختلف. لماذا؟ لأن العقل المنتشر (diffused mind) كان يعمل بصمت على ربط الأفكار واستخلاص النتائج. (أعتقد أكثرنا مر بهذا الموقف).

* التخلص من التسويف: هنا يشرح الكتاب لماذا نحب التسويف، وكيف أنه نوع من أنواع الإدمان، وعادة يمكن التخلص منها بفهم مكوناتها وتغيير بعض الظروف. يحلل الكتاب المكونات الثلاثة للعادات (الإشارة، الروتين، الجائزة) ويشرح كيف يمكن كسرها بسهولة. على سبيل المثال، الطالب الذي يسوف البدء بالمذاكرة لساعات بسبب الانشغال بالجوال، هو يستجيب لإشارة (cue) عبارة عن تنبيهات أو نغمات الجوال، فيقوم بروتين معين (وتساب يوتيوب ....إلخ) لأن هناك جائزة تعوّد على الحصول عليها وهي متعة وسائل التواصل والتخلص من ألم المذاكرة. يستطيع هذا الطالب أن يقلل من أثر الجوال بتركه خارج الغرفة، وبالتالي يقضي على فرصة أن تسرقه منبهات الجوال (إشارة cue). لماذا نتحدث عن التسويف في سياق ت��لم الرياضيات والعلوم بالذات؟ لأن هذه المواد – كما أسلفت – تراكمية. بالتالي فإن للتسويف أثر سلبي مضاعف (هل رأيت طالباً يحاول أن يفهم منهج الفيزياء كله في ليلة الإمتحان؟)

كما تحدث الكتاب بإسهاب عن مواضيع أخرى مثل: وسائل تقوية الذاكرة، الاستعداد الأمثل للإمتحانات، الطريقة المثلى للمذاكرة الجماعية، أهمية النوم، التخلص من القلق، كيفية الإجابة أثناء الامتحان، وغيرها.

في رأيي هذا الكتاب رائع لكل من يريد أن يضاعف قدرته على التعلم. تقييمي له هو 4 من 5، فقط لأن أسلوب المؤلفة في الشرح كان متعب قليلاً، ولأن هناك مواضيع متعلقة هامة لم يتم التطرق لها.
Profile Image for GridGirl.
281 reviews26 followers
July 6, 2018
“This is where the Law of Serendipity comes to play: Lady Luck favors the one who tries.”

Wow! I wanna read this book over and over and over again! But actually, that is something this book told me not to do… The struggle is real!
This is an excellent book for everyone who struggles with math. It doesn’t matter if it’s a 7-year old’s problem with multiplication tables or a physics master student trying to understand thermodynamics in quantum systems.
This is also a great book for everyone trying to learn anything new in their life. I am convinced that the majority of people would take a benefit in their personal and professional life from reading this book.
I can’t say that every concept in this book was completely mind-blowing and new to me, but Barbara Oakley manages to explain why things that have worked for you for years are actually excellent learning strategies. This book also inspired me to use my planner more and it had a positive effect on my self-esteem (especially before and during exams). I am completely sure that, would I go through this book again, I’d notice advice that I haven’t put to practice yet and I’m planning to implement more of it to my life. For now I’m just happy with all the help this book provided me with.

Profile Image for GT.
94 reviews118 followers
December 11, 2016
Haven't finished yet... So far so good. Very applicable and readable.

The book is not only for undergrads learning math and science but also for anyone who wants to learn any subjects that require more mental power. It's also good for grad students, faculty, researchers who want to stay productive.

P.S. Finished.
Profile Image for Ahmed Tharwat.
102 reviews151 followers
July 26, 2019
هذا هو النوع من الكتب الذي يجب أن يكون محفوظاً في قلب كل مدرس قبل أن يشرع في عمله في التدريس!!
Profile Image for Gavin.
1,090 reviews342 followers
November 5, 2021
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.



- 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"



* 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...
Author 2 books109 followers
January 4, 2016
It’s amazing that majority of people (at least white collars) are spending tons of time dealing with new information but has very limited experience in doing this efficiently. This book is about your personal productivity in tackling new concepts. This book is about your brain and tips and tricks about improving you “brain muscles” by doing well-established techniques like chunking, interleaving, space repetition, memory palaces and more.

Here is a small example: how are you reading books? Are you highlighting key ideas? Maybe you’re like me and trying to highlight every useful piece of information. But study had shown that this technique not only useless, but could be harmful. You should try to understand the basic idea, try to recall it without looking into the book and only after that, you may highlight key pieced with some insightful notes on the martins.

This is book is really well written and I highly recommend it for everyone who wants to be more efficient in their learning journeys.
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