Thoughts on high school activities

High school is an important time in your development. It represents 4 years during which you're growing rapidly, and what you do in high school plays a major role in shaping your future prospects.

Your high school experience will include:

• Coursework
• Extracurricular activities
• Standardized tests
• College applications

Coursework

The basics

High schools have graduation requirements. Depending on your high school's requirements and your future ambitions, your coursework will likely include at least the courses required for admission by the University of California:

• World history and United States history
• Four years of English
• Three years of math, including Algebra 1, Geometry and Algebra 2.
• Two of biology, chemistry and physics.
• Two years of foreign language.
• One year of visual or performing arts.

In order to get into prestigious colleges, you'll almost certainly have to take more demanding courses than the minimal requirements for University of California admission. For example, Stanford University's department of admissions says:

We expect freshman applicants have engaged in a rigorous curriculum and chosen from among the most demanding courses available in secondary school. It is not necessary to have loaded your schedule with every advanced course offered; but if such courses are available to you, we expect you have taken advantage of many of them. Our most competitive freshman applicants often have four years (grades 9-12) of English, four years of math (including calculus), four years of social studies, four years of science (including biology, chemistry and physics) and four years of a foreign language.

The importance of learning math well

Out of the subjects that you'll study in high school, it's unusually important to learn math well. You should consider learning math well beyond what's necessary to get an A in a course.

Some reasons for this are:

• The main reason why learning math well is important is that many courses depend on mathematical knowledge, so that learning math well improves your ability to perform well across the board. With the exception of geometry, the high school math curriculum is very hierarchical, so that doing well in a given course requires solid knowledge of earlier courses. The main limiting factor to students doing well in chemistry and physics is often mathematical subject matter knowledge. Knowing math well makes economics easier. If you end up majoring in engineering, you'll benefit substantially from a solid knowledge of calculus (which hinges on a solid knowledge of the math that's covered earlier in the curriculum, with the exception of geometry).

• Other subjects have more limited applicability than math does. Doing well in United States history isn't highly dependent on having learned world history well. English classes can build general reading and writing skills, but aside from that are not very hierarchical — understanding a book that's covered in a given English course seldom depends on knowledge of books that have been covered in previous courses. High school chemistry doesn't depend on high school biology, and while knowledge of high school chemistry helps with high school physics (and vice versa), the interdependence isn't strong. Foreign language courses are hierarchical, and it's important to learn the material in a given course well enough to do well in subsequent courses, but in contrast with math, learning a foreign language doesn't help much with learning subjects other than foreign language. Studying an art won't help very much with courses outside of art.

• Knowing math well helps with the math section of the SAT, and the math SAT subject tests. There are high school math competitions that offer students the opportunity to stand out. So learning math well offers you unusually good opportunities to showcase your abilities.

• Mathematical thinking is closely connected with general reasoning ability. Many subjects outside of math depend more on memorization and less on abstract reasoning than math does. Math is often taught in a way that requires students to memorize and regurgitate, but this is because of poor teaching rather than an inherent feature of math. By using [math learning resources] such as select books and videos, you can learn math in a way that disproportionately develops your abstract thinking skills, which can then be transferred to other subjects.

Of high school math courses, geometry is the least important to learn well. The material in high school geometry seldom shows up much less frequently in other contexts than subjects such as algebra, trigonometry, and calculus.

Balancing personal growth and looking good to colleges

Some courses help you grow more than others. Some courses look better to colleges than others. In an ideal world, the courses that help you grow the most would be the same as the courses that look best to colleges. Unfortunately, this is not the world that we live in. Some examples:

• Many students will take AP Art History to fulfill their art requirement, not because they're interested in or will benefit from learning art history, but because taking an AP course looks better to colleges than taking a non-AP course.
• Taking a course with a bad teacher, who you won't learn much from, but who's an easy grader may give you a better chance of getting a high grade than taking a course with a good teacher, who you'll learn a lot from, but who's a hard grader. Some easy graders are good teachers, and some hard graders are bad teachers, but there can be a conflict between getting a good grade and learning.