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Taking Lots of Math in High School: A Reflection
How should a world-class mathematics high school education be structured? Of course, it depends on who you ask. Many parents and students may want an applicable education—one that facilitates matriculation at a competitive 4-year college with an internship, among other things, or an education that allows you to study multiple content areas (such as physics or chemistry). through a mathematical lens. Some parents may just want their kids to pass math and "get on with it" when you learn something applicable, treat P, NP assumptions with detachment and healthy skepticism and move on to plush automated trading work. This article is in no way intended to offend the definitive camp. After all, who in the world would want their 22-year-old to make 6 figures with an entire course in numerical analysis or stochastics or modeling and cope with life’s tasks?
My personal opinion is that high school math can be fun and rigorous at the same time. When the mind is young and voracious, it is especially flexible – a lot of great math can be learned, and great results can be demonstrated with effort and dedication. Aside from national and international standards (which a world-class math education will surpass) and standardized test questions (which won’t apply to someone who completes a really rigorous math education – they’ll pass those tests with little effort), really great math. education should include a lot of good – mathematics. Maybe 10-15 courses would be possible in high school.
No, that’s not a typo. For the most rigorous, state-of-the-art secondary mathematics education for students who wish to major in mathematics, engineering, theoretical physics, or computer science in the future, it is certainly possible to accumulate this many courses (or more) in some (but by no means all) cases, and in fact, probably not so hard to do, especially if your child is homeschooled or takes certain subjects "classical schools" (See below). Please note that I am not suggesting that a sequence of 4 or 5 courses is insufficient to attend a great university – many people have done great with such preparation. In my education, it was best to start with 4 semesters of reading analysis (advanced calculus) from scratch, working out all the results of sequences, series, and approximations, and then moving on to theoretical physics using vector calculus, flow theories, differential geometry, and partial differential equations (all areas of advanced mathematics, which sound scary but are more than a highly motivated high school student is exposed to). With this foundation, it was possible to study advanced topics such as manifold theory, algebraic topology, set theory, category theory, logic, module theory, measure theory, and group structure theory (all of which are mathematical concepts commonly taught in university and graduate courses). . What is the point of all this research? If this question doesn’t answer itself, don’t try it at home. The goal is to learn beautiful math at a young age so you can (hopefully) contribute "conversation" mathematical discourse, discovering something beautiful. Of course, a person who has the brains and interest to learn such a curriculum could delve into IB, law, medicine, etc. later in their education because it was better to learn a lot at a young age. It certainly couldn’t hurt a student to get that kind of education.
But a parent may argue that he or she could never find a curriculum for such courses. And they would be right. You won’t find any canned curriculum (in my experience) that teaches beautiful math. Excuse me. But this does not mean that such learning is not possible. If you’re lucky, depending on where you live, you may have one (or more) of the following at your disposal. For each option, I have some suggestions if your family lives near that option:
If your child already attends or has been accepted into an elite day or boarding school whose graduates regularly change the world and have driven global trade and politics for centuries. In this case, the school will probably have some great facilities and probably some very competent teachers to run them. You may still need to arrange some independent study courses with your teachers. If you live near a classical Christian school. Honestly, this is a goldmine. These schools provide students with the opportunity to read great books in a closely guided context, and often produce surprisingly brilliant graduates who go on to solid universities and do well there. For the record, I currently teach at one of these schools, but I’m not being paid to say so. This is my honest opinion. Usually, the teachers at such schools have excellent maths backgrounds themselves, and some of these schools might have teachers with a pure maths degree (relatively rare in other types of schools) who would be happy to supervise your child’s secondary maths education. . Even if your children do not attend school, you may be able to pay a teacher directly who can prepare study materials for your student and assess the relevant courses. If you live near a university and can find a professor who is interested in helping your child develop such a curriculum. I was especially lucky to have many such instructors. Don’t be shy: Email a pure math teacher and ask them directly if they would be interested in advising and helping to design courses for your child. Offer to pay for help. Tell them about your child’s needs and ask for advice. Tell them you want your child to have the highest math education. Don’t be surprised if professors help you. They will likely be so impressed with your child’s desire to learn that they can help you. In the following articles, I (or my colleagues) will find out, course by course, what kind of education we offer to very passionate high school students, as well as answer current questions about rigorous mathematics in high school. I will also answer questions about national standards, testing, etc.
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