A Mind for Numbers - A Review

I have heard many people argue they can never succeed in a certain field of study because, they say, “I’m just not a math person.” The idea is that there are fields of knowledge that it requires some innate set of skills to gain any sort of foothold.

For the sake of debate, we might set aside those who are obviously especially gifted at some academic skill. One may, indeed, need to be specially gifted and then extensively trained to discover new proofs of mathematical ideas or originate create solutions to scientific problems. However, not having the capacity to be at the top of a field should not be confused with being unable to grasp the rudimentary aspects of it.

One of the central theses of Barbara Oakley’s book, A Mind for Numbers: How to Excel at Math and Science Even if You Flunked Algebra is that with due diligence, anyone can do well at Math and Science.

The examples tend to be oriented toward technical disciplines, but the reality is that this book is simply trying to teach habits that lead to academic success in any field. In fact, to someone who has done any significant research in metalearning or study habits, there is very little that is not known. Most of the information Oakley outlines is fairly intuitive for the experienced student.

That qualification is the key, though. Experienced students may have struggled through difficulties on their own, had a mentor who provided them guidance (like a parent, sibling, or neighbor), or simply have naturally fallen into a helpful set of habits related to study because of their environment.

Not everyone has the advantage of being homeschooled, having parents who teach and emphasize learning, or that have excelled in school and are able to help break down mental barriers when they arise. A Mind for Numbers is a treasure for those who are trying to figure out studying on their own, attempting to help a student grow when they aren’t really good students themselves, or looking for ways to restructure curriculum to set students up for success. The target audience of the book is high schoolers, but this is the sort of volume that is useful for college students or adult learners trying to retool for a better career, get a new certificate, or conquer a challenge that previously defeated them.

Oakley’s story is intriguing. Though she is now and engineering professor, she once believed she was incapable of doing math. At some point along the way, a family crisis led to an untimely move with an unhelpful teacher in a new school, all of which resulted in Oakley missing some key links in her mathematical understanding that made it hard for her to follow along in later efforts in the subject. Her natural reaction was the “sour grapes” approach, where she decided that math just wasn’t her thing and that was ok because it was a dumb subject anyway. She later enlisted in the Army, became a language specialist, earned a degree in Slavic languages, but came to realize that the career opportunities in that narrow field were quite limited. So, she decided to see if she could retrain herself to love math, and she pursued a degree in engineering. The end result being a lot of work to learn how to learn, a PhD in engineering, and a deep interested in the learning process.

Much of A Mind for Numbers is really just a plan to become a better student through better time management and prioritization techniques. There are no gimmicks about doing special online puzzles to improve spatial reasoning or whatever. Oakley offers explanations on why starting with easy problems, working examples in the textbook, and doing least-liked jobs first are part of getting through new or difficult subjects. There is a mix of practical wisdom and scientific data, along with the fact that the advice does not come from a parent or teacher who is already in an adversarial role. As a result, this might be a book that a struggling student may find helpful. Oakley digs into the brain science of procrastination, of test stress, and overconfidence. She offers some real, proven processes that will benefit most students in most subjects, even if it does not open up doors to a PhD for everyone.

The trick with any methodology is that the individual who needs the new technique has to want to apply it. There is no magic wand to shake over a student who is entirely uninterested in learning or overtly hostile to it. However, in many cases, those who are obstinate about studies often got that way because they weren’t particularly good at it, so Oakley’s book may offer a way to break a stalemate. Or, for the marginal student in a difficult situation, finding A Mind for Numbers in the library (or having it presented by a well-meaning mentor) may provide the beginning of a framework that can change their life.

One of the things I most appreciate about this book is that it does not make excessive promises. Oakley doesn’t promise that everyone can be a quantum physicist. She does, however, offer real hope that everyone can master even difficult scientific and mathematical concepts if they are willing to exert due diligence, apply themselves systematically, and given some of the basic resources necessary to be successful. That’s an honest claim that the book is entirely capable of delivering on.

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

By Oakley PhD, Barbara

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Another Sort of Learning - A Review

The Preacher who gave us Ecclesiastes famously wrote, “What has been is what will be, and what has been done is what will be done, and there is nothing new under the sun.” (Ecc 1:9)

This is true in many arenas, but those who read old books will find it true of controversies, antagonisms, and the general feel of cultural unrest. C. S. Lewis recommends reading old books “to keep the clean sea breeze of the centuries blowing through our minds.” (Lewis, “On Reading Old Books”) It is by reading old books that we gain a corrective to the characteristic blind spots of our own culture.

I’m not sure if James Schall’s book, Another Sort of Learning, counts as an old book, since it was published in 1988, but it had a revealing effect for me. Schall’s book is worth considering on its own, but it also provides evidence that today’s cultural battles are not really that new. More than thirty years ago, Schall was calling out the same problems that might be the source of concern in The American Conservative, First Things, or National Review today. That doesn’t mean that the concern is not warranted, but rather that we might be better served by recognizing that this election or this court case or this movie may not actually be the straw that broke the camels back. It may be, but that seems less and less likely the older I get. There is nothing new under the sun.

In Another Sort of Learning, Schall writes “about being a student, about reading, about the fact that each of us is called to understand. . . ‘the truth about our lives.’” This is a book that discusses other books that can help shape the mind. It is a book about thinking well, appreciation of the transcendentals, and recommendations of others who are thinking along the same vein.

Contents

The book is divided into three parts. The first is addressed to college students, pointing them toward what their goal as students ought to be. Schall expresses concern that students seek to answers to the big questions of life, rather than simply learning a trade. The whole of this section is framed around that. In his first essay, “Another Sort of Learning,” Schall commends used book stores for being able to find the right sorts of books that are often not in as regular circulation. A lovely way to begin an engaging book.

The second part of the volume recommends “Books You Will Never Be Assigned.” Here offers to “provide reviews of certain books that I think help us gain some insight into the heart of reality.” These are mainly modern books with an ancient soul. They are the sorts of secondary literature that take the Great Conversation seriously and try to engage it meaningfully rather than demonstrate why it is a foolish attempt. For those with a hefty book budget, these are chapters ripe with suggestion.

Part Three seeks to provide an alternative viewpoint to the most common modern perspective. Schall states, “I want to discuss rather substantive things, both intellectual and spiritual. Here I want to say something about the humanities, about devotion, prayer, something more, again, about permanent things.” Here he again is recommending volumes that pull readers deeper into the idea of reality about the universe, rather than directing them to their own reality.

Conclusion

Another Sort of Learning is a deeply conservative book. Not the sort of conservatism that produces strong tweets or rages against the right enemies, but the sort of conservatism that digs deep into the intellectual realities of the world and seeks to find truth, goodness, and beauty. It is a sort of reactionary perspective that is revulsed by the evils of modernity, looking to the solidity of the past for a conversation of substance.

One of the interesting benefits of reading a book like this over thirty years old is that it skips a generation. The authors that I recognize are mainly the ones still being discussed today, so Schall’s reading lists can point us back to older books of substances that may further help clear away the cobwebs of the contemporary cacophony. There is nothing new under the sun, but Schall provides access to the ongoing debates that doesn’t include the gaps and blind spots of the latest cycle of blogs.

Another benefit of Another Sort of Learning is that Schall describes the same sorts of problems being lamented by thoughtful people today. There is, indeed, nothing new under the sun. On one hand, the continuance of this concern about the loss of the transcendentals is discouraging because we have not made much progress. On the other hand, the continuance of concern on this issue shows that we have not altogether lost the fight. This is an encouraging volume that is worth the time to read. The essays are no worse for being more than thirty years old. Maybe they are even better for it.  Overall, the collection is well-written and engaging, perfect for taking a chapter at a time after a long day at work.

Another Sort of Learning

By James V. Schall

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Learning How to Learn - A Review

Learning how to learn has always been a struggle, I think. Ancient philosophers invested significant time and energy into thinking about pedagogy. Though we have advanced in many ways, our struggle to learn has not changed that much, since we are still humans with the same basic traits as the ancients.

The difference in our age is that everyone promises easy ways to learn with half the effort. Usually, those new ways to learn are ineffective in the long run. Meanwhile, the sheer number of distractions and their addictiveness have increased. While there is nothing new under the sun, I think that Nicholas Carr is on to something with his book, The Shallows.

As an instructor, I am seeing a generation rise that tends to struggle with focus and learning in ways that are changing. This is not as much as “kids these days” comment as it is an awareness that the ubiquity of digital entertainment and information overload has made it more difficult for people to make connections between concepts, retain that information, and see the value in knowing anything that can be looked up. Since by federal law the end of the training course I supervise is a closed book exam, there is no escape from the informational demands, just a greater struggle to get to the finish line.

My wife found and enjoyed Barbara Oakley’s 2014 book, A Mind for Numbers, in which she talks about how she went from being a very verbal person to an engineering professor over a number of years. In 2018, along with Terrence Sejnowski and Alistair McConville, she published a volume for kids, Learning How to Learn: How to Succeed in School without Spending All Your Time Studying.

As the subtitle hints, the selling point on this is instrumental. Read this book and you’ll get smarter faster. However, given that a book advertising the benefits of learning for its own sake is less likely to sell, I can’t really fault the publisher for their choice in titles. In the end, the book is helpful whether you are learning how to learn to get ahead or simply for the value of learning on its own.

Summary

The book opens with an introduction to the main authors. More significantly, the book tells students that “follow your passion” is bad advice. It’s a good way to start. Their point is that just because something is hard or unpleasant does not mean that it is not a good thing that you come to enjoy. In Chapter Two, the authors shift to describing types of thinking, noting that we need to practice both focused thinking when we are zeroed in on solving a problem or getting information, but we also need to use diffuse thinking, where we allow ideas to bounce around in the back of our head. A lot of creative thought and connection of ideas comes during diffuse thinking. The issue is that its not enough to try to blast through studying in one chunk, there has to be time for multiple focused hits and diffuse mulling to get things embedded. So this is not a book that simply tells you to work harder, it is intended to help teach how to study smarter for better results.

The third chapter wrestles with focus and procrastination. The authors provide some hints to help overcome the hard start as well as to increase focus. One big tip they recommend is the Pomodoro method. Chapter Four drills into some neuroscience, describing how many scientists believe information is stored and provided some tips on how to strengthen neural pathways. The visual aids in this chapter help with understanding, and the understanding can be useful in providing motivation for study. The fifth chapter offers an exhortation to take up subjects that are new, even at the risk of being bad at it. Chapter Six emphasizes the need for proper sleep so that the brain can be restored. It also introduces the concept of “spaced retrieval” where a learner looks at material multiple times, preferably with sleep in between. This is the anti-cramming chapter.

Chapter Seven deals with the way our memories work and describes the processes for getting things from short term (working) memory to long-term memory. This is an encouraging chapter for those that struggle with focus, as the authors highlight the potential for people with weaker working memories often have higher capabilities in creativity. The eighth chapter provides to tips and tricks for improving one’s memory. There is nothing earth shattering, but the techniques have been validated, which is encouraging. Chapter Nine talks about building brain links, which elsewhere is called chunking. This is the process of connecting ideas together to strengthen their hold in our minds. The authors recommend focus, repetition, and understanding as key means of retaining knowledge and skills.

The tenth chapter recommends learning in groups, especially exploring more in-depth topics beyond the typical curriculum. Chapter Eleven commends the benefits of both exercise and good nutrition as part of improved learning. The twelfth chapter returns to the construction of brain links and encourages practice over an extended period. The authors commend both deliberate practice (focused study) and interleaving (doing something different between practice or study sessions). Both can be helpful means of solidifying knowledge in the brain.  Chapter Thirteen recommends being truthful about how distractions affect a student and then eliminating them. The fourteenth chapter notes that tests are actually some of the best ways to learn and thus commends quizzing and self-testing as a means to ingrain knowledge.  Chapter Fifteen provides some helpful tips on being better prepared for tests. And the book concludes in the sixteenth chapter tying many of the concepts together.

Analysis and Conclusion

Learning has not changed drastically over the course of documented human history. There are no real shortcuts to learning, but Learning How to Learn helps to identify roadblocks so they can be removed. In other words, there is not a lot of original content in this volume, but it has been structured and presented in a way that it is accessible to kids.

The target audience of this volume is tweens and teens. There are cartoons and diagrams throughout. The language is simple and plain. On of my children didn’t appreciate the zombie cartoons or analogies, but others might find this makes the book more interesting.

This is the sort of book that will help a motivated student get better. For the kid that is convinced that everything is going to pan out and that video games are enough of a career goal that real learning can be foregone, this book will probably not cross the threshold of engagement. Learning How to Learn isn’t a promise of an easy path to success. For students that want to learn more effectively, this can be an excellent resource. For parents of kids who have some desire to improve, but whose kids are resistant to their input, this book offers a sly way to get good advice into the hands that need it.

I commend this book as a helpful resource. As we try to prepare out children to learn on their own, this sort of book has the potential to assist them in the quest to be successful in their studies and become lifelong learners. It may also begin to form habits of persistence and perseverance that transcend academic success, often bleeding over into so many other venues.

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 As a bonus, here is Barbara Oakley speaking at Google. This is based on her Mind for Numbers book, but it has basically the same content as the book translated for teens.

Learning How to Learn: How to Succeed in School Without Spending All Your Time Studying; A Guide for Kids and Teens

By Oakley PhD, Barbara, Sejnowski PhD, Terrence, McConville, Alistair

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Ultralearning - A Review

There is a temptation in our world to try to find a quicker, easier, and better way to do everything. How can I lose 20 pounds without actually dieting? How can I earn a huge income without working? How can I make everyone think I am more intelligent without actually studying? We are a culture of convenience that hasn’t eliminated our preference for appearance—we want microwave dinners that don’t really taste like it. It’s a form of dishonesty.

When I first picked up Scott Young’s book, Ultralearning, I expected to find a microwave dinner that advertised itself as fine cuisine. But what I actually found was a microwave dinner than that advertised accurately and notes the benefits and the drawbacks of what it is. The potatoes may be a little soggy and the meat a little tough, but it takes ok and is reasonably nutritious. A little candor is a good thing, because sometimes a microwave dinner is good enough.

Young’s book falls into the airport book genre, which I commented on in my review of Rolf Dobelli’s, The Art of Thinking Clearly. It is reasonably short, lucidly written, relies on the research of others, provides clear steps to success, and is the sort of self-improvement volume that can provide light conversation and make the reader sound intelligent.

That Young’s book is designed to sell well should not be considered a severe criticism, however, because he has put together some helpful advice in an easily absorbed presentation.

Young has done the round of podcasts and presented at a TEDx event and some other self-help, inspirational, big-idea sort of stages. His writing style, ideas, and approach fit well within that genre of thought.

The majority of what he advertises, though, is simply a way to become a better learner. The lack of originality is no sign of a lack of value. Every generation needs champions of ideas and contextualizers that can help translate older ideas for newer audiences. The weakness in Young’s approach is that he does not really recognize that what he is doing is translating older ideas, but presents much of what he offers as being derived from contemporary science, rather than simply repackaging older methologies.

Ultralearning is “a strategy for acquiring skills and knowledge that is both self-directed and intense.” It is, in essence, the process of becoming an efficient autodidact. It is an approach that Young has put to the test by working his way through MIT’s computer programming curriculum on his own and by learning four languages in a year. Ultralearning is about becoming competent quickly at a particular skill.

There are nine principles that Young recognizes for ultralearners:

• Principle #1 – Metalaerning – Figuring out the way that the subject or skill should be learned.

• Principle #2 – Focus – Zooming in on the subject to the neglect of many other things. Making a job of getting good at whatever the goal is.

• Principle #3 – Directness – Seeking to gain the information or skill in as close to the setting as it can be applied.

• Principle #4 – Drill – Figuring out where the choke points are in learning or proficiency, breaking those down, and practicing them until proficiency is achieved.

• Principle #5 – Retrieval – Using testing (of various sorts) to embed information well so that skills and knowledge are retained and progress can be made.

• Principle #6 – Feedback – Going through the discomfort of feedback so that problems can be corrected as quickly as possible.

• Principle #7 – Retention – Creating a plan to maintain important proficiencies, depending on the nature of the skill.

• Principle #8 – Intuition – Making the “why” connections on the topic to help make further learning on the subject easier.

• Principle #9 – Experimentation – Changing methods when something isn’t working, even if it worked earlier on.

As I noted, there is nothing that is truly remarkable about any of these steps for those that been engaged in the study of pedagogy. But Young packages them in a way that prevents having to dig through the literature of the field. He also shows some ways that some of the “quick fix” learning methods that are advertised are doomed to failure.

Ultralearning is not a “quick and easy” approach to becoming an expert in something. Rather, it is “hard and fast” approach to becoming reasonably proficient at something. It does not advertise cheap, fast, gourmet food. It advertises reasonably healthy, reasonably tasty, microwave food. On that front it delivers.

I think there is value in the Ultralearning approach for those that are trying to gain knowledge in a new field. For the pastor seeking to learn New Testament Greek without going to seminary, something like an ultralearning approach would probably work well. If someone could carve out three hours a day for a few months to jam through a common Koine textbook, memorize the most common vocabulary, and develop a plan to use it daily, they will be more likely to be successful than by trying to do Greek drills 20 minutes a day for years. There is a realism to Young’s approach that I find attractive.

This, of course, does not mean that someone can become an expert in something nearly instantly. While the internet tends to make people feel they can be experts on constitutional law one day, international politics another, and health sciences on the next, the reality is that most of us have a limited bandwidth to develop competencies. The ultralearning approach intentionally neglects a lot of the background work that is typical of more conventional learning approaches.

If you want to be able to paint something you find attractive and don’t expect to become a stellar artist, then it can be helpful to learn to paint from Bob Ross. If you want to become more proficient at a skill or in a limited area of knowledge that can develop you personally or improve your career options, then Scott Young’s approach is beneficial. In neither case will you be the best at something or the expert in a field, but it can certainly add tools to a toolbox that can make a huge difference.

Ultralearning: Master Hard Skills, Outsmart the Competition, and Accelerate Your Career

By Young, Scott

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