Mastery Maths Quotes

Persistence is often more important than intelligence.1 Approaching material with a goal of learning it on your own gives you a unique path to mastery. Often,

Mathematicians need to understand a problem only for themselves; math teachers need both to know the math and to know how 30 different minds might understand (or misunderstand) it. Then they need to take each mind from not getting it to mastery. And they need to do this in 45 minutes or less.

As you can see from the following “top-down, bottom-up” illustration, learning takes place in two ways. There is a bottom-up chunking process where practice and repetition can help you both build and strengthen each chunk, so you can easily gain access to it when needed. And there is a top-down “big picture” process that allows you to see where what you are learning fits in. Both processes are vital in gaining mastery over the material.

In one study, elite violinists had separated themselves from all others by each accumulating more than 10,000 hours of practice by age 20. Thus the rule. Many elite performers complete their journey in about ten years, which, if you do the math, is an average of about three hours of deliberate practice a day, every day, 365 days a year. Now, if your ONE Thing relates to work and you put in 250 workdays a year (five days a week for 50 weeks), to keep pace on your mastery journey you’ll need to average four hours a day. Sound familiar? It’s not a random number. That’s the amount of time you need to time block every day for your ONE Thing. More than anything else, expertise tracks with hours invested. Michelangelo once said, “If the people knew how hard I had to work to gain my mastery, it wouldn’t seem wonderful at all.” His point is obvious. Time on a task, over time, eventually beats talent every time. I’d say you can “book that,” but actually you should “block it.

A Chinese proverb says that the mastery of three things will make you fearless anywhere in the world. They are math, physics, and chemistry.

AI is set to universalize the access to intellectual tools that otherwise require years of study, training and practice.

First, to be useful, learning requires memory, so what we’ve learned is still there later when we need it. Second, we need to keep learning and remembering all our lives. We can’t advance through middle school without some mastery of language arts, math, science, and social studies. Getting ahead at work takes mastery of job skills and difficult colleagues. In retirement, we pick up new interests. In our dotage, we move into simpler housing while we’re still able to adapt.

Many people believe overlearning means studying or practicing until mastery is achieved. However, in the research literature, overlearning refers to a learning strategy in which a student continues to study or practice immediately after some criterion has been achieved. An example might be correctly solving a certain kind of math problem and then immediately working several more problems of the same kind. Although working more problems of the same kind (rather than fewer) often boosts scores on a subsequent test, doing too many problems of the same kind in immediate succession provides diminishing returns. “In the classroom and elsewhere, students should maximize the amount they learn per unit time spent studying or practicing—that is, they should get the most bang for the buck. How can students do this? The scientific literature provides an unequivocal answer: Rather than devote a long session to the study or practice of the same skill or concept so that overlearning occurs, students should divide their effort across several shorter sessions. This doesn’t mean that long study sessions are necessarily a bad idea. Long sessions are fine as long as students don’t devote too much time to any one skill or concept. Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day.

Teaching is a surprisingly powerful method of learning. In a meta-analysis of 16 studies, students who were randomly assigned to tutor their peers7 ended up earning higher scores in the material they were teaching. Students who taught reading improved in reading; those who taught math got dramatically better at math. The more time they spent tutoring, the more they learned. As one group of researchers concluded, “Like the children they helped, the tutors gained a better understanding of and developed more positive attitudes toward the subject matter covered in the tutorial program.”8,fn2 Psychologists call this the tutor effect.9 It’s even effective for novices: the best way to learn something is to teach it. You remember it better after you recall it10—and you understand it better after you explain it. All it takes is embracing the discomfort of putting yourself in the instructor’s seat before you’ve reached mastery. Even just being told you’re going to teach11 something is enough to boost your learning.

In one study of U.S. eighth graders, for example, the best predictor of academic performance was not the children’s IQ scores—but their self-discipline. Mastery of math never made anyone get to work on time, finish a thesis, or use a condom.

Great teachers focus on what the student is saying or doing,” he says, “and are able, by being so focused and by their deep knowledge of the subject matter, to see and recognize the inarticulate stumbling, fumbling effort of the student who's reaching toward mastery, and then connect to them with a targeted message.

Repetition until Your Learning Becomes Unconscious (Outsourced to Environment) While I implemented what I learned, my teacher would watch me from a distance. He let me struggle as I tried to remember what he had just shown me. The first time, applying what he taught took a lot of time and effort. So we did it again, and again, and again. Over time, I became competent and thus confident. Learning something new is all about memory and how you use it. At first, your prefrontal cortex—which stores your working (or short-term) memory—is really busy figuring out how the task is done. But once you’re proficient, the prefrontal cortex gets a break. In fact, it’s freed up by as much as 90 percent. Once this happens, you can perform that skill automatically, leaving your conscious mind to focus on other things. This level of performance is called automaticity, and reaching it depends on what psychologists call overlearning or overtraining. The process of getting a skill to automaticity involves four steps, or stages: Repeated learning of a small set of information. If you’re playing basketball, for instance, that might mean shooting the same shot over and over. The key here is to go beyond the initial point of mastery. Make your training progressively more difficult. You want to make the task harder and harder until it’s too hard. Then you bring the difficulty back down slightly, in order to stay near the upper limit of your current ability. Add time constraints. For example, some math teachers ask students to work on difficult problems with increasingly shortened timelines. Adding the component of time challenges you in two ways. First, it forces you to work quickly, and second, it saps a portion of your working memory by forcing it to remain conscious of the ticking clock. Practice with increasing memory load—that is, trying to do a mental task with other things on your mind. Put simply, it’s purposefully adding distractions to your training regimen.