Taking a look at math fields and age levels in math education is very broad topic. In order to be as concise as possible, this article will divide this topic into its two natural parts. The first will be based on the wide scope of influence that mathematics brings on many disciplines. The second will be to briefly outline the time line for math education.
Numbers appear everywhere in life. How tall are you? How old are you? How long will it take? How much will it cost? These few questions give a feel for the way most of us encounter math everyday. Almost every field could be described as a math field. We use math when we build, buy, travel, and grow. For the sake of brevity, let's just consider those fields that are mostly math based or that cannot be studied without a strong math background.
Obviously, a math teacher or professor would be the first field that comes to mind. After that, those who are involved in the nuts and bolts of the computer industry need strong math skills to develop hardware and software. Physics and chemistry both sit as strongly related to the math field. Without math, neither would have a basis to exist.
While not considered math exactly, accounting deals with math from the basics to some of the more complex formulas when projections are needed. Economics is a math based field. The military uses math heavily in mapping, weapons guidance and targeting, and logistical areas. The largest single field when considered as a whole to use mathematics would be engineering. This can be stretched to encompass architecture and survey work.
Math education often begins with the toddler at home learning that their body has two eyes, two ears, one mouth, one nose, ten fingers, and ten toes. Most youngsters by the age of 4 or so have master some simple addition of single digits. This is expanded a little in kindergarten. By the age of 7 or 8 most children have learned to subtract with borrowing.
Moving on with their education, at 8 or 9 children enter the world of multiplication and easy division. Within a year or so, long division is introduced. At the age of 10 or 11 most young people encounter decimals and fractions with addition, subtraction, multiplication, division, and fraction to decimal conversions. If their teachers are good, they learn that division is a short form of subtraction and multiplication shortens addition.
At around 12, most children encounter sets, larger fractions and mixed numbers, and easy algebra-style problems. At 13-14 more difficult algebra is introduced and depending on abilities graphing straight lines and conic sections come on the scene. The understanding of exponents and roots is developed. Simple to difficult geometry is brought into play. By 16, most young people who are able to perform acceptably beyond general math begin to tackle trig and more advanced math including vectors.
By completing high school, most college-bound students will have mastered early calculus, some physics, the gas laws, and will be ready to move toward more advanced calculus and integration. How far students go at this point is related directly to ability, motivation, and interest.