There is a concept in mathematics called “Mathematical Maturity.” It means that, over time, someone becomes more able to think like a mathematician. This change may be gradual, like emotional maturity, and its emergence may not be linear or straightforward.
Many students have difficulty with word problems. They might be able to do every step in the problem if you put the steps in front of them one at a time. However, they can’t actually understand the problem as a whole and organize those steps themselves as a way to solve it.
It may be that after a couple of years, this capacity for looking at the problem, for putting the pieces together into a coherent image may develop. The process may be completely out of the hands of the teacher, and may happen over the summer, or over a longer period of time. That’s Mathematical Maturity.
A student may never reach their mathematical maturity, or may never realize he or she has gained it, because the cost of making mistakes in math feels so incredibly high. In mathematics one mistake at any point in the chain will result in a wrong answer and, from a student’s perspective, will be a waste of time. Only students who are tenacious and love the process, or who are forced to persevere, will put enough time into learning math for the maturity to kick in.
Music and math are not so far apart. Certain kinds of musicians do think more like mathematicians than, say, writers. And musical maturity is a real and necessary part of musical growth.
Unlike mathematical maturity, the road to musical maturity, while sometimes painful, need not feel so futile. True, no one likes to make a mistake while practicing that Chopin Prelude on the piano…how embarrassing. But one mistake in a piece does not invalidate a performance.
In ensembles the forgiveness of mistakes is even greater. Unless you are in a high-powered group where one mistake will stand out and get you expelled, most ensembles are designed to bolster the errors of an individual. If I’m singing in a chorus and I drop out for a second because I forgot a phrase, no one is likely even to notice.
The best news is that musical maturity can foster the same types of thinking as mathematical maturity: a capacity for seeing how the parts fit into the whole. If the specific tools of music and math are different, they are often used in the same way. So if a student lacks in mathematical maturity they very well might be able to back into it by increasing their musical maturity.
Maturity comes with the process of making mistakes, as a means to understanding a bigger idea. Whether in learning to walk as a baby, or mastering differential equations as a mathematician, it is vital to be in an environment where mistakes, at an early level, are welcomed. Good music teachers (and good math teachers) will offer that.
Many students have difficulty with word problems. They might be able to do every step in the problem if you put the steps in front of them one at a time. However, they can’t actually understand the problem as a whole and organize those steps themselves as a way to solve it.
It may be that after a couple of years, this capacity for looking at the problem, for putting the pieces together into a coherent image may develop. The process may be completely out of the hands of the teacher, and may happen over the summer, or over a longer period of time. That’s Mathematical Maturity.
A student may never reach their mathematical maturity, or may never realize he or she has gained it, because the cost of making mistakes in math feels so incredibly high. In mathematics one mistake at any point in the chain will result in a wrong answer and, from a student’s perspective, will be a waste of time. Only students who are tenacious and love the process, or who are forced to persevere, will put enough time into learning math for the maturity to kick in.
Music and math are not so far apart. Certain kinds of musicians do think more like mathematicians than, say, writers. And musical maturity is a real and necessary part of musical growth.
Unlike mathematical maturity, the road to musical maturity, while sometimes painful, need not feel so futile. True, no one likes to make a mistake while practicing that Chopin Prelude on the piano…how embarrassing. But one mistake in a piece does not invalidate a performance.
In ensembles the forgiveness of mistakes is even greater. Unless you are in a high-powered group where one mistake will stand out and get you expelled, most ensembles are designed to bolster the errors of an individual. If I’m singing in a chorus and I drop out for a second because I forgot a phrase, no one is likely even to notice.
The best news is that musical maturity can foster the same types of thinking as mathematical maturity: a capacity for seeing how the parts fit into the whole. If the specific tools of music and math are different, they are often used in the same way. So if a student lacks in mathematical maturity they very well might be able to back into it by increasing their musical maturity.
Maturity comes with the process of making mistakes, as a means to understanding a bigger idea. Whether in learning to walk as a baby, or mastering differential equations as a mathematician, it is vital to be in an environment where mistakes, at an early level, are welcomed. Good music teachers (and good math teachers) will offer that.