100 books like Understanding How We Learn

I think about this book every day, even though it was written almost 25 years ago, and the edition I read explained how to manage your paper file folders! (One of my most-used apps, the to-do manager Things, is built on this system.)

I love how much time this book has saved me as I juggle running several businesses, staying active in my hobbies, and running a household. Allen’s approach to capturing your ideas and then deciding how to organize them so that you can keep track of what needs your attention is both simple and really profound.

For athletes who need to be as efficient as possible to reserve time and energy for training, this book is a lifesaver.

This book provides a systematic account of how to understand and structure mathematical proofs. Its approach is almost entirely syntactic, which is the opposite of how I naturally think – I tend to generate arguments based on examples, diagrams, and conceptual understanding. But that difference, for me, is precisely what makes this book so valuable. Solow gives a no-nonsense, practical, almost algorithmic approach to interpreting logical language and to tackling the associated reasoning. His book thereby provides the best answer I know of to the “How do I start?” problem so often encountered when students begin constructing proofs.  

Many undergraduate mathematics books – even those aimed at new students – are dense, technical, and difficult to read at any sort of speed. This is a natural feature of books in a deductive science, but it can be very discouraging, even for dedicated students. Houston’s book covers many ideas useful at the transition to proof-based mathematics, and he has worked extensively and attentively with students at that stage. Consequently, his book maintains high mathematical integrity and has lots of useful exercises while also being an unusually friendly read.

Mathematics requires accurate calculation, and students sometimes think that getting the right answer is enough. But mathematics is also about valid logical arguments, and the demand for clear communication increases through an undergraduate degree. Students, therefore, need to learn to write professionally, with attention to general issues like good grammar, and mathematics-specific issues like accuracy in notation, precision in logical language, and structure in extended arguments. Vivaldi’s book has a great many examples and exercises, and students could benefit from studying it systematically or from dipping into it occasionally and reflecting on small ways to improve.

Harvard-educated cognitive scientist Daniel Willingham is one of the foremost experts in educational psychology. While the title of this book may not sound so appealing, it’s really a tight summary of some of the most important principles of psychology to learning more effectively. Willingham’s blog and other books are also excellent resources for someone who wants to understand how to learn well.

It’s impossible, as a parent, not to marvel at the miracle of learning that occurs in very young children. Indeed, parents have experienced this sense of awe for time immemorial, and some have gone so far as to venture explanations for how it works. John Dewey, the American philosopher and psychologist, argued at the dawn of the twentieth century that children are like young scientists as they go about their day, subtly testing the things and people around them to see how they work. We now know, in no small part due to the work of researchers including The Scientist in the Crib author Alison Gopnik, that Dewey was right. Children are compelled to experiment; what’s more, they make the most of the limited data they produce with a powerful logic invisible to the untrained eye. Parents—but also anyone with a sense of wonder—will find answers to deep mysteries in… show more.

An evolutionary psychologist, Gray argues that human children, like all mammals, learn best through play. He advocates for a learning process that is kid- and play-driven. Using an innovative school as a model, Gray makes a compelling case for revolutionizing education by putting it in the hands of the kids themselves. Even if you can’t send your child to one of these schools, this book will give you many ideas on how to let your kids take charge of their own academic interests and pursuits which will ultimately help them grow up to take better charge of their own lives and happiness.

Here is another game-changing book that is a few decades old, but has spanned a worldwide movement in the knowledge, research, and growth of self-directed education. This book addresses how children learn everything they need to know through self-directed play, projects, and exploration for grades 1 to 12. It also shows the damaging effects of institutional school, bullying, and how direct teaching can stop a child’s curiosity and creativity needed for 20th-century careers. Children do not need school to learn. Learning is everywhere, anytime, and is available to everyone.

Alright, alright. There should be at least one book that actually helps with the practice of teaching. And this is the one. Countless books admonish specific programs and practices, chock full of the fanciest edu-buzz words. But rarely do they discuss why a strategy works based on the science of human cognition and development. Even less frequently do they back the why with multiple peer-reviewed studies. 

Jensen and McConchie combine an absurd level of nerd as researchers and veteran educators. This book and its predecessors helped me gain a deep understanding of why a strategy worked (or how to make it work), whether it was something new or something tried-and-true. The job of a teacher is to mold human brains. We should probably know everything we can about how those brains work.

I’m interested in how mathematicians create mathematics but this book made me realize that learning mathematics is also a form of creativity. Each of us has created our understanding of mathematics as we were growing up. We are all creative!  

What is amazing about this book is that even children as young as six months possess rudimentary mathematical concepts, in particular, the concept of number. (Actually, Carey shows children have two distinct ways of thinking about numbers). The concept of number is built-in. That’s amazing to me! The mastery of counting numbers, 1,2,3,… is a great creative leap in the development of the child. This leap is followed by a series of further amazing accomplishments, for example, the insight that a fraction like 2/3, is a completely new kind of number (and not just a problem in division). How do kids manage to accomplish such radical changes in their concept… show more.