PDF Summary:A Mind for Numbers, by Barbara Oakley

You may not realize it, but your brain has an extraordinary capacity for complex calculations. Simple tasks like stepping over a garden hose as you walk across your lawn require elaborate computations, and yet they seem easy because your brain does them intuitively.

Barbara Oakley wrote A Mind for Numbers to help you learn math and science well enough that they, too, become intuitive. In this guide, we will examine Oakley’s explanation of your brain’s natural capabilities, her strategies for remembering complex concepts more easily, her recommendations for building good study habits and avoiding procrastination, and a few other tips for succeeding in your studies. We’ll also examine the scientific basis of her recommendations and compare her strategies to those of other experts in learning and memory.

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• The information stands out as novel or unique (Novelty Factor).

• You can relate the information to your own experiences (Personal Factor).

• It’s concrete rather than abstract (Concreteness Factor).

• It displays patterns or structure, like rhyme or repetition (Structure Factor).

Techniques for Making Information More Memorable

But what if you need to remember something that, by itself, isn’t all that memorable? As Oakley explains, you could come up with an acronym or a sentence composed of words that symbolize the ideas you need to remember. Oakley notes that if you say it out loud or set it to music and sing it, you can also take advantage of the speech and song factors.

Another technique that Oakley discusses consists of developing a “visual metaphor,” or mental image that represents what you need to remember. She also discusses the “memory palace,” which is a powerful extension of visual metaphors to take advantage of the spatial factor and potentially the story factor. As Oakley explains, you first think of a place that you know well, such as your home or college campus. Then you imagine yourself moving through the place, interacting with objects. Each object is a visual metaphor for something you need to remember.

For example, suppose you need to memorize the hierarchy of taxonomy for biology class: Kingdom>Phylum>Class>Order>Family>Genus>Species. In your mind’s eye, you are walking across campus when you suddenly bump into the King of England, who happens to be visiting your college that day (Kingdom). Next, you stop at the cafeteria, where you order a Philly steak-and-cheese sandwich (phylum). Then you go to class (class).

After class, you head back to your dorm room, but you have to take a detour because a drill sergeant is parading his troops on the campus lawn and shouting a lot of orders (order). When you arrive at your dorm room, you discover your family has come to visit (family). After your family leaves, you notice that your laundry basket is full of jeans, so you head over to the campus laundry room to wash your jeans (genus). However, in the laundry room, you discover that your jeans are covered with tiny yellow specks (species) that won’t wash off.

Foer’s Techniques for Making Information More Memorable

Unlike Oakley, Foer doesn’t discuss singing or speaking out loud as a way of making information more memorable. Perhaps this is because when you’re taking an exam and need to remember something, you’re generally not allowed to break out in song or get up and dance around the classroom.

However, Foer does discuss the use of visual metaphors and the memory palace. He explains that the term “memory palace” is a modern name, while earlier sources refer to it as the “method of loci.” In these early descriptions, each imaginary location where you place a visual metaphor was called a locus (and loci is the plural of locus).

In Foer’s description, the memory palace is the master technique to which all other methods are subservient. You populate your memory palace with visual metaphors, and in some cases, you may use symbolic sentences to generate visual metaphors for abstract concepts or develop more memorable images.

For example, if you are building a memory palace for your biology class and you want to consolidate the hierarchy of taxonomy into a single image, you could symbolize it with the sentence, “King Phillip cleaned orange fungus off Jenny’s spectacles,” where King = Kingdom, Phillip = Phylum, cleaned = class, orange = order, Jenny = genus, spectacles = species. You then place the mental image of this scene at one location in your memory palace.

Review Information to Keep it Accessible

Now, let’s discuss strategies for recalling information. Oakley cautions that even a memorable fact may soon become unretrievable if it is not reviewed. She presents some strategies you can use to make your review sessions more effective:

• Test yourself with intentional recall. If you just finished a reading assignment, Oakley recommends closing the book and trying to recall the essence of what you just read. She asserts that this is the most effective way to embed the content in your memory.

(Shortform note: William James documented that active repetition (or intentional recall) is more effective for learning than methods of passive repetition, such as rereading the material, over a hundred years ago. Numerous studies since then have confirmed this effect.)

• Oakley suggests practicing “spaced repetition,” where you repeatedly revisit material at designated intervals. She recommends revisiting any new information within one day, so you don’t forget it completely.

(Shortform note: Psychological studies have determined that students who practice intermediate spacing between study sessions tend to perform better than those who do all their studying at once, and also better than those who break it up into smaller sessions and study too frequently. Other experts assert that the optimal time for a recall session is when the information in your mind gets fuzzy—it’s no longer fresh, but it’s not gone yet either.)

Take Control of Your Habits to Make the Most of Study Time

Understand the Habit Chunk

According to Oakley, your study habits (good or bad) will have a strong impact on your ability to learn math and science. She explains that habits develop via the same chunking process that condenses information in your brain and facilitates storage in your memory. A habit chunk consists of four pieces of information:

1. The Cue: Oakley identifies this as the stimulus that your brain responds to by performing the habitual action. She notes that cues can be linked to people, places, time, feelings, or events.
2. The Routine: This is the action or sequence of actions that you perform when the habit is triggered by the cue.
3. The Reward: Oakley asserts that you have to derive some kind of benefit from executing the routine for a habit to develop. Your brain executes the routine in response to the cue because it expects the reward. She also points out that only immediate consequences of the routine are stored as part of the habit chunk. This is why bad habits are possible: The reward is immediate but transient and the long-term consequences are negative, but the long-term consequences are not processed as part of the habit chunk, and thus do not automatically cancel out the reward.
4. The Belief: According to Oakley, your habits are grounded in your perception of reality and of your own identity.

For example, suppose you make a habit of reading your text messages immediately:

1. The cue is the ringtone your phone plays when you get a text.
2. The routine might consist of retrieving your phone from your pocket and accessing the text-messaging app.
3. The reward is the pleasure that you derive from reading text messages.
4. The underlying belief could vary: Maybe you believe responding promptly to communications is an important part of being respectful toward others, or maybe you identify as a social person and believe in staying connected with others through text.

Comparing Habit Models

Charles Duhigg, author of The Power of Habit, and James Clear, author of Atomic Habits, offer descriptions of the make-up of a habit that are similar to Oakley’s model (although both omit the “belief” element of Oakley’s model). However, BJ Fogg, author of Tiny Habits, provides an alternative model.

According to Fogg’s behavioral model, you perform an action or behavior when a prompt alerts you to the opportunity to do so, and the combination of your ability to complete that action and motivation to do so is above a certain threshold. Fogg’s model applies both to habits and to non-habitual actions.

Fogg conceives habits as self-perpetuating. The more often you do something, the better you get at doing it, so your ability to do it increases. Further, the habit reward provides motivation to keep doing it. This combination of increasing ability and increasing motivation makes a behavior more likely to exceed the threshold the next time you receive the prompt—thus making you more likely to engage in the habit again.

Strategies for Changing Habits

As Oakley explains, you can modify your habits by making changes to any part of the habit chunk:

1) Oakley suggests that you can prevent bad habits from triggering by isolating yourself from their cues. For instance, if hearing a certain song while driving triggers you to habitually speed, remove this song from your driving playlist.

(Shortform note: Clear corroborates this suggestion of Oakley’s. He proposes four “laws” of forming new habits, each with an inverse form for breaking bad habits. His first law is to make cues obvious, and inversely, to prevent bad habits from triggering by making their cues invisible.)

2) Overwrite the habit routine by changing how you react to the cue. Oakley notes that this strategy requires a deliberate plan and an exertion of willpower, but that it plays a key role in optimizing your study habits.

(Shortform note: Fogg identifies this same strategy of changing the behavior associated with a certain prompt. However, instead of highlighting the need for willpower, he advises designing the replacement behavior to take as little willpower as possible. To do this, he advises you to make the replacement behavior easier and more desirable (higher ability and motivation) than the old one.)

3) According to Oakley, sometimes you can modify the habit by manipulating the reward. If you understand what reward is tied to a certain habit, you may be able to change the reward to either reinforce or dismantle the habit. For instance, creating rewards for sticking to good habits can keep you on the right track.

(Shortform note: In Fogg’s model, rewards primarily influence motivation. He cautions you to avoid basing habit changes too much on motivation, because motivation is often complex and can be fickle. Nevertheless, he presents celebrating small victories as a key strategy for reinforcing changes that you are trying to make to your habits.)

4) Address underlying beliefs fueling the habit. Oakley asserts that to change a habit, you must believe that you can change and that the change will be an improvement.

(Shortform note: Clear observes that it is particularly easy to pick up habits from people you are close to or look up to because these people influence your beliefs. This implies that you can sometimes prompt a change in your habits by changing the company you keep and thus changing your beliefs.)

Overcome Procrastination

Understand the Procrastination Chunk

Oakley asserts that habitual procrastination is often your most significant barrier to learning math and science. She explains that procrastination is a special kind of habit, but it has the same basic components as any habit chunk:

1. The Cue: According to Oakley, the procrastination cue comes in two parts. The first part is the unpleasant feeling that you get from anticipating an activity that makes you uncomfortable. The second part is the “distraction,” which is any stimulus that you can shift your focus to in order to escape the pain of anticipation.
2. The Routine: Oakley explains that the procrastination chunk in your brain generally doesn’t have just one routine, but rather several sub-routines. The type of distraction that completes the cue determines which sub-routine gets triggered. For example, if the distraction is a new email from an online retailer, maybe the sub-routine consists of following the link in the email and mindlessly browsing the retailer’s website.
3. The Reward: According to Oakley, the reward that allows a procrastination habit to develop is temporary relief from the pain of anticipation.
4. The Belief: Oakley reiterates that one of the keys to changing any habit is believing that you can change. If you’ve been procrastinating habitually for a long time, it might be tempting to believe procrastination is an innate part of who you are, but understanding the makeup of the procrastination habit can help you change this belief.

Oakley and Eyal: Procrastination vs Distraction

Some authors discuss a process similar to Oakley’s “procrastination” using different terms. For instance, Nir Eyal uses the term “distraction” to define any behavior that draws you away from the tasks that you need to focus on to accomplish your goals. He asserts that we are all fundamentally motivated to free ourselves from discomfort, and we get distracted because distractions offer temporary relief from mental discomfort.

Furthermore, he states that distractions start with “triggers” and distinguishes between internal and external triggers. He equates internal triggers to the sense of discomfort or dissatisfaction that prompts you to look for an escape. External triggers, then, are environmental stimuli that interrupt your concentration and/or offer an opportunity for escape.

Thus, “distraction” as used by Eyal seems to be functionally synonymous with “procrastination” as used by Oakley, and Eyal’s description of the root cause of distraction is compatible with Oakley’s description of the procrastination habit model. As such, we can compare Oakley’s strategies for avoiding procrastination to Eyal’s for additional perspective. We’ll discuss both Oakley’s and Eyal’s strategies in the next section.

Strategies for Overcoming Procrastination

In addition to her general strategies for changing habits, Oakley provides strategies specifically for combating procrastination:

1) Plan your time. According to Oakley, just having a plan for how to spend your time can reduce the temptation to procrastinate, and tracking your time can help you identify specific procrastination habits. To this end, she recommends keeping a daily to-do list in a journal planner or on a conspicuous whiteboard.

(Shortform note: Eyal also identifies building the right schedule as one of the key strategies for overcoming distraction. However, he asserts that just making a to-do list of daily tasks is not enough, because it’s too easy to move uncompleted tasks to tomorrow’s list if you slip into distraction. Instead, he prescribes “timeboxing,” where you split up your entire day into blocks (or boxes) of time, all of which are allocated to specific activities. This way, if you find yourself doing anything other than what you planned to be doing at that time of the day or night, you can identify exactly when you were distracted. Eyal recommends scheduling one 20-minute box each week to reflect on the times you got distracted and consider how you could adjust your schedule to avoid such distractions in the future.)

2) Eliminate distractions. Oakley points out that avoiding distractions can prevent your procrastination sub-routines from triggering.

(Shortform note: Eyal likewise identifies “eliminating triggers'' as one of the keys to conquering distraction. He presents a list of triggers to manage, including in-person interruptions, incoming email, text, or social media media, and desktop clutter. By letting people know when you are and are not available, disabling notifications for most incoming communications, establishing set time-boxes for responding to communications, and keeping an organized desktop, Eyal says you can greatly reduce distractions.)

3) Ignore distractions. Oakley acknowledges that this requires an exertion of willpower, much like overwriting a habit routine, but she says this is a key strategy for overcoming procrastination habits. She notes that you can use meditation techniques to let distractions pass.

(Shortform note: Author Bhante Gunaratana describes “mindfulness” meditation as a state of mental awareness in which you listen to your thoughts without getting caught up in them. You just observe what’s going on in your mind, without expecting, reacting, pondering, analyzing, or passing judgment on any of it. Medical studies affirm that this meditation technique tends to reduce susceptibility to distraction. Presumably, every time you observe a distraction without responding to it, the association between the distraction and its procrastination sub-routine grows weaker.)