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

“Procrastination expert Rita Emmett explains: “The dread of doing a task uses up more time and energy than doing the task itself.”

“The Law of Serendipity: Lady Luck favors the one who tries”

“Focus on the process (the way you spend your time) instead of the product (what you want to accomplish).”

“Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.”

“Thiss sentence contains threee errors.”

“If you protect your routine, eventually it will protect you.”

“Befuddlement is a healthy part of the learning process. When students approach a problem and don’t know how to do it, they’ll often decide they’re no good at the subject. Brighter students, in particular, can have difficulty in this way—their breezing through high school leaves them no reason to think that being confused is normal and necessary. But the learning process is all about working your way out of confusion. Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!” —Kenneth R. Leopold, Distinguished Teaching Professor, Department of Chemistry, University of Minnesota”

“What would you do if you weren’t afraid?”

“Learning organic chemistry is not any more challenging than getting to know some new characters. The elements each have their own unique personalities. The more you understand those personalities, the more you will be able to read their situations and predict the outcomes of reactions.” —Kathleen Nolta, Ph.D., Senior Lecturer in Chemistry”

“Procrastination is like addiction. It offers temporary excitement and relief from boring reality.”

“Process, Not Product If you find yourself avoiding certain tasks because they make you uncomfortable, there is a great way to reframe things: Learn to focus on process, not product”

“The biggest lie ever is that practice makes perfect. Not true—practice makes you better.”

“Multitasking means that you are not able to make full, rich connections in your thinking, because the part of your brain that helps make connections is constantly being pulled away before neural connections can be firmed up.”

“I tell my students they can procrastinate as long as they follow three rules: 1. No going onto the computer during their procrastination time. It’s just too engrossing. 2. Before procrastinating, identify the easiest homework problem. (No solving is necessary at this point.) 3. Copy the equation or equations that are needed to solve the problem onto a small piece of paper and carry the paper around until they are ready to quit procrastinating and get back to work. “I have found this approach to be helpful because it allows the problem to linger in diffuse mode—students are working on it even while they are procrastinating.” —Elizabeth Ploughman, Lecturer of Physics, Camosun College, Victoria, British Columbia”

“There is a deep connection between technical, scientific, and artistic creativity.”

“Over the past decades, students who have blindly followed their passion, without rational analysis of whether their choice of career truly was wise, have been more unhappy with their job choices than those who coupled passion with rationality.”

“The only way to walk a journey of a thousand miles is to take one step at a time.”

“Students who are beginning to struggle in math and science often look at others who are intellectual racehorses and tell themselves they have to keep up. Then they don’t give themselves the extra time they need to truly master the material, and they fall still further behind. As a result of this uncomfortable and discouraging situation, students end up unnecessarily dropping out of math and science. Take a step back and look dispassionately at your strengths and weaknesses. If you need more time to learn 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.”

“It’s normal to sit down with a few negative feelings about beginning your work. It’s how you handle those feelings that matters.”

“You may think you really have to understand something in order to explain it. But observe what happens when you are talking to other people about what you are studying. You’ll be surprised to see how often understanding arises as a consequence of attempts to explain to others and yourself, rather than the explanation arising out of your previous understanding.”

“Deficiencies of innate ability may be compensated for through persistent hard work and concentration. One might say that work substitutes for talent, or better yet that it creates talent.”6 —Santiago Ramón y Cajal”

“This is where the Law of Serendipity comes to play: Lady Luck favors the one who tries.”

“You want your brain to become used to the idea that just knowing how to use a particular problem-solving technique isn’t enough—you also need to know when to use it.”

“From your “due date” calendar, write down a weekly to-do list of twenty or fewer key items. Each night, create the next day’s daily to-do list from the items on the weekly to-do list. Keep it to five to ten items. Try not to add to the daily list once you’ve made it unless it involves some unanticipated but important item (you don’t want to start creating endless lists). Try to avoid swapping out items on your list.”

“What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?” —David Eugene Smith, American mathematician and educator”

“Remember, research has shown that the more effort you put into recalling material, the deeper it embeds itself into your memory.”

“Internalizing problem-solving techniques enhances the neural activity that allows you to more easily hear the whispers of your growing intuition. When you know—really know—how to solve a problem just by looking at it, you’ve created a commanding chunk that sweeps like a song through your mind.”

“A synthesis—an abstraction, chunk, or gist idea—is a neural pattern. Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another. That’s why great art, poetry, music, and literature can be so compelling. When we grasp the chunk, it takes on a new life in our own minds—we form ideas that enhance and enlighten the neural patterns we already possess, allowing us to more readily see and develop other related patterns. Once we have created a chunk as a neural pattern, we can more easily pass that chunked pattern to others, as Cajal and other great artists, poets, scientists, and writers have done for millennia, Once other people grasp that chunk, not only can they use it, but also they can more easily create similar chunks that apply to other areas in their lives—an important part of the creative process.”

“Also remember that the better you get at something, the more enjoyable it can become.”

“THE IMPORTANCE OF CHUNKING “Mathematics is amazingly compressible: you may struggle a long time, step by step, to work through the same process or idea from several approaches. But once you really understand it and have the mental perspective to see it as a whole, there is often a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics.”26 —William Thurston, winner of the Fields Medal, the top award in mathematics”