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High school coursework

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Key takeaways

  • Coursework and grades appear to be the most important input into college admissions. If you want to get into a prestigious college, you should give very high priority to getting high grades in challenging courses.
  • Your study habits play a major role in determining how well and quickly you learn course material. You'll learn better and more efficiently if you think about how the material that you're learning relates to other things, rather than practicing rote memorization.
  • Seriously consider spending more time and energy on your math courses than you do on your other courses.
  • Plan ahead for SAT subject tests, and place high emphasis on learning the material that will be tested on them well.
  • When you choose courses, consider both about how they'll affect your college admissions prospects and how much they'll help you grow.
  • Select teachers based on how much you'll learn from them rather than how entertaining they are.
  • If your school's courses are inadequate, consider online 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. The courses that you take, and the grades that you get in them, are said to be the most important input into college admissions decisions. As such, if you want to go to a prestigious college, you should give heavy weight to getting good grades in challenging high school courses. You can see supporting evidence for the claim(s) made here at the page college statements on the importance of grades and coursework.

KEEP IN MIND: Make sure that you don't bite off more than you can chew by overloading your schedule with challenging courses. If you take more challenging courses than you can handle, you run the risk of performing worse across the board.

Good study habits

Further information: Good study habits

KEEP IN MIND: Working as much as possible often isn't the key to success. How efficiently you study can matter more than how much you study.

The importance of learning math well

Further information: Learn math well

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

KEEP IN MIND: People often incorrectly believe that they don't have the ability to develop mastery of high school math. Most high schoolers fall short of their mathematical potential. If you use good study habits and work hard, you can learn math significantly better than most high schoolers of your innate ability.
  • The main reason that 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 some parts of geometry, the high school math curriculum is very hierarchical, so that doing well in a given math course requires solid knowledge of earlier courses. The main limiting factor to students doing well in chemistry and physics is often mathematical subject 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 some parts 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. Knowledge of high school chemistry helps with high school physics (and vice versa), but he 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 plausibly doesn't help much with learning subjects other than foreign language. Similarly, studying an art plausibly doesn'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 also 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.
KEEP IN MIND: 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 studying good math books and videos, you can learn math in a way that builds your reasoning skills.

Of high school math courses, geometry is the least important to learn well. The material taught in high school geometry shows up less in other contexts than the material taught in algebra, trigonometry, and calculus does.

Coursework and SAT subject tests

If you're applying to selective colleges, you'll probably need to take a couple of SAT subject tests. In preparation for these, you should pick out two tests early on, and commit to learning the material in the corresponding courses really well (possibly beyond the level of mastery needed for A's in the courses), and take the SAT subject tests immediately after completing the courses.

For example, if your favorite subjects are history and science, you could pick US history and chemistry to be your two SAT subject tests, and then them like the back of your hand. This would maximize your chances of getting outstanding scores on the SAT subject tests in US history and chemistry.

Balancing personal growth and looking good to colleges in course selection

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. A couple of examples of this are:

  • Many students will take AP Art History to fulfill their art requirement, not because they're interested in art history, and not because they'll use it later on, but because taking an AP course looks better to colleges than taking a non-AP course.
  • Some teachers are easier graders than others, and some teachers are better teachers than others. The best teacher often won't be the easiest grader, and the easiest grader often won't be the best teacher. So taking the course where you'll learn the most doesn't necessarily guarantee you the best grade, and vice versa.

You probably want to grow personally and get into a good college. In order to do so as well as possible, you'll have to think about how to balance the two things when choosing courses.

KEEP IN MIND: You'll be faced with the problem of simultaneously achieving two different goals throughout your life. The earlier you develop skills to do this well, the better.

In general, when balancing, you should try to make the smallest sacrifices possible. You should place high priority on personal growth when it comes to taking classes on subjects that you're interested in, or that you'll use in the future. If you're not interested in United States history, and don't plan on doing anything that requires knowledge of it, then it might be good to take it with the easiest grader possible, even if he or she isn't the best teacher. Similarly, if you're planning on becoming a historian, it might be good to take US history with the best teacher possible, even if he or she isn't the easiest grader.

Our page on course selection offers more guidance on the relevant considerations, and how to weigh them.

Selecting good teachers

In choosing courses, you should give careful consideration to who's teaching them. Teachers differ significantly from one another in terms of their quality of teaching and ease of grading. Teachers are also candidates for writing recommendations for colleges, scholarships and summer programs.

KEEP IN MIND: Students often choose teachers based on what will make them happy in the short run, rather than based on what will improve their lives in the long run. If you're prepared to delay gratification, you'll be better positioned for success later in life.

Some points to consider:

  • Try not to judge a teacher primarily based on how entertaining he or she is. Entertaining teachers aren't necessarily the ones who you can learn the most from: some entertaining teachers offer a very superficial coverage of the course material, and some dull teachers challenge students to absorb the material deeply and think about it. You may enjoy an entertaining teacher's class more, but depending on the teacher, you may not grow as much as you could have if you had taken a class with another teacher.
  • Just because you find a teacher easy to understand doesn't mean that you're learning a lot, and just because you find a teacher hard to understand doesn't mean that you're not learning. Some teachers appear to be clear precisely because they don't spend time on the parts of the material that are hardest to understand — they teach students material that they don't need help with rather than material that they do need help with. Some of the teachers who are hard to understand are ones who you can learn the most from. Of course, there are teachers who are hard to understand who you can't learn from even if you try, and you should avoid them, but you should be aware that this isn't always the case.
  • Students often incorrectly believe that teachers who are harder in terms of the material covered or in terms of the work they assign will be harder in terms of the final letter grades they assign. This is not necessarily true: it can happen that a teacher challenges students while grading leniently, and it can happen that a teacher who doesn't challenge students grades harshly.
  • Give more weight to reviews from students who have already taken the class than reviews from students who are currently taking the class. Students who took the course one or more years ago know whether the teacher prepared them well for subsequent courses. Similarly, students who have already completed a given course are better able to assess whether the teacher is an easy grader or a hard grader, because they've received their final grade.

Online coursework

Aside from taking courses at your high school, you can also take courses online. You may be able to find more challenging versions of your high school's courses online. In such instances, your high school may allow you to substitute online courses for the courses offered at your high school. You may be able to find online courses that you're interested in taking, that your high school doesn't offer.

KEEP IN MIND: High school staff sometimes claim that they're not allowed to give students credit for courses taken elsewhere, even when it's not true, because they don't want you to take fewer courses at your high school. Don't be discouraged too easily – if a teacher or your parents advocate for you, your school may allow you to, even if it's initially resistant.

Some organizations that offer online courses are:

Stanford University Online High School

Stanford University Online High School is an accredited online school situated at Stanford University.

It offers some courses that are rarely available in high school. For example, it offers math courses in linear algebra, multivariable calculus, differential equations, complex analysis, modern algebra, real analysis, partial differential equations, number theory, and logic. It also hosts a rich variety of student clubs.

In order to take classes there, you have to apply and be admitted. The cost of the program is high: ~$3500 for single course enrollment.

Art of Problem Solving

Art of Problem Solving is a company that serves high performing math students. It's accredited by the Western Association of Schools and Colleges. It offers challenging versions of courses in the standard high school curriculum. It also offers math contest preparation courses.

Any students may sign up for courses with Art of Problem Solving. The courses are considerably less expensive than Stanford Online High School's courses: the most expensive of them run no more than $600.

Disclosure: I'm currently teaching an online course for Art of Problem Solving.