A Mind For Numbers: How To Excel At Math and Science

Barbara Oakley, “A Mind For Numbers: How To Excel At Math and Science” The Penguin Group, 2014, 269 pp.

This book is for anyone interested in math, although the techniques work well for any subject or skill.   It is especially useful for students.  The author explains how it is important to alternate between focused thinking and diffuse thinking, both modes are important to the learning process. 

The author, 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, she returned to school with to master the very subjects that had given her so much trouble throughout her entire life.

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.  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.

My Notes:

Pg. 11:  The brain has two different types of networks from which it switches back-and-forth: the focused mode and the diffuse mode, respectively—these modes are highly important for learning.  The diffuse mode does seem to be able to work quietly in the background on something you are not actively focusing on.  Focused-mode thinking is essential for studying math and science.  It involves a direct approach to solving problems using rational, sequential, analytical approaches.  The focused mode is associated with the concentrating abilities of the brain’s prefrontal cortex, located right behind your forehead. 

Diffuse mode thinking is also essential for learning math and science.  It allows us to suddenly gain a new insight on a problem we’ve been struggling with and is associated with ‘big-picture’ perspectives.  Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander.  Unlike the focused mode, the diffuse mode seems less affiliated with any one area of the brain.  (A good example of diffuse thinking occurs when you are trying to remember a name, just can’t, and give up.  Later, when doing something entirely unrelated, the name pops into your head.  The brain has been processing this in the background all the time.  Another good reason to study complex subjects just before going to bed—let the brain work on it all night.)

Pg. 38:  Figuring out a difficult problem or learning a new concept almost always requires one or more periods when you aren’t consciously working on the problem.  Each interlude in which you are not directly focused on the problem allows your diffuse mode to look at it in a fresh way.  When you turn your focused attention back to the problem, you consolidate new ideas and patterns that the diffuse mode has delivered.  A good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day.

Pg. 42:  Working memory is the part of memory that has to do with what you are immediately and consciously processing in your mind.  It used to be thought that our working memory could hold around seven items, or ‘chunks,’ but it’s now believed that the working memory holds only about four chunks of information.

Pg. 43:  Research has shown that if you try to glue things into your memory by repeating something twenty times in one evening, for example, it won’t stick nearly as well as it will if you practice it the same number of times over several days or weeks.

Pg. 106:  The author strongly recommends incorporating the use of Pomodoro sessions when learning complex subjects.

The Pomodoro Technique is a time management method developed by Francesco Cirillo in the late 1980s.  The technique uses a timer to break down work into intervals traditionally 25 minutes in length, separated by short breaks. The method is based on the idea that frequent breaks can improve mental agility.  It is essential that all electronic devices be turned off and no multi-tasking is going on, such as listening to music, etc.

Pg. 257:  Ten Rules For Good Studying:

1.      Use recall.  After you read a page, look away and recall the main ideas.

2.     Test yourself.  Flash cards are your friend

3.     Chunk your problems.  Chunking is understanding and practicing with a problem solution so that it can all come to mind in a flash. 

4.     Space your repetition.  Spread out your learning in any subject a little every day.  Your brain can handle only a limited amount of exercise on one subject at a time.

5.     Alternate different problem-solving techniques during your practice.

6.     Take breaks.  When you get frustrated with a math or science problem, take a break so that another part of your mind can take over and work in the background.

7.     Use explanatory questioning and simple analogies.  Explain your explanation out-loud. Write it down (not type it).

8.     Focus.  All distractions must be shut off for a period of time (no multi-tasking).

9.     Eat your frogs first.  Do the hardest thing earliest in the day when you are fresh.

10.                        Make a mental contrast.