How To Motivate A 15 Year Old Boy To Study Taking Lots of Math in High School: A Reflection

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Taking Lots of Math in High School: A Reflection

How should a world-class high school mathematics education be structured? Of course, that depends on who you ask. Many parents and students likely want an appropriate education—one that facilitates, among other outcomes, matriculation from a competitive four-year college with an internship opportunity, or an education that allows the study of different content areas (such as physics or chemistry) through a mathematical lens. Some parents, perhaps, just want their children to pass math and "get on with it" major in something applicable, treat the P, NP assumption with detached and healthy skepticism and move on to the plush business of automated trading. This article is in no way intended to offend the final camp. After all, who in the world would want their 22-year-old to make 6 figures with a healthy dose of numerical analysis or stochastics or modeling or two and get down to 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 supple – much great mathematics can be learned, and great results can be proved by effort and diligence. In addition to national and international standards (which a world-class math education will surpass) and standardized test questions (which will not be applicable to someone who completes a truly rigorous math education – they will master these tests with little effort), a truly top-notch math education must include a lot of good – math. Perhaps 10-15 courses in high school would be possible.

No, that’s not a typo. For the most rigorous modern secondary mathematics education for students who wish to pursue future studies in mathematics, engineering, theoretical physics, or computer science, it is certainly possible to accumulate this many courses (or more) in some (but by no means all) cases, and it may not be that difficult to do so , especially if your child is homeschooled or attends certain classes "classical schools" (see below). Note that I am not suggesting that a 4 or 5 course sequence is insufficient to attend a major university – many people have done brilliantly with such preparation. In my own education, it was best to start with 4 semesters of reading in analysis (advanced calculus) from scratch, doing all series results, series and approximations, then progressing to theoretical physics via vector calculus, flow theory, differential geometry and partial differentials equations (all fields of advanced mathematics that sound intimidating but are more than amenable to study by highly motivated high school students). With these foundations 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 usually taught in university and graduate courses ). What is the point of all these studies? If this question doesn’t answer itself, don’t try this at home. The point is to learn some nice math at a young age so that someone (hopefully) can contribute "conversation" of mathematical discourse discovering something beautiful. Of course, a person who is brave and interested in pursuing such a curriculum could enroll in IB, Law, Medicine, etc later in their education, since they were even better at learning a lot at a young age. It certainly wouldn’t hurt a student to get this kind of education.

But a parent may object that he could never find a syllabus for such courses. And they would be right. You won’t find any prepackaged curriculum (in my experience) that teaches beautiful math. Sorry. But this does not mean that such learning is impossible. If you’re lucky, you may have one (or more) of the following available, depending on where you live. For each option, I give you some suggestions if your family lives near that option:

If your child already attends or has been accepted to an elite day school or boarding school whose graduates routinely change the world and have been leading global trade and politics for centuries. In this case, the school will likely have some outstanding facilities in house, and will likely have some very competent teachers to manage them. You will still likely need to negotiate some independent study courses with teachers. If you live near a classical Christian school. Honestly, these are a gold mine. These schools give students the opportunity to read great books in the context of rigorous mentoring and often produce astonishingly bright graduates who attend solid universities and do well there. For full disclosure, I currently teach at one of these schools, but I am not being paid to say any of this. That’s my honest opinion. Usually the teachers at such schools have excellent math backgrounds themselves, and some of these schools may have a faculty member with a degree in pure mathematics (a comparative rarity in other types of schools) who would be happy to oversee your child’s secondary math education. Even if your children are not in school, you may be able to pay a fee directly to the teacher, who can create study materials for your student and assess 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 instructors like this. Don’t be shy: Email a pure math faculty member and ask them directly if they would be interested in mentoring and helping to build 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 a top math education. Don’t be surprised if your professors help you. They will probably be so amazed by your child’s appetite for learning that they can help you. In future articles, I (or my colleagues) will explain course by course the type of education we propose for highly oriented high school students, as well as answer current questions about rigorous high school mathematics. I will also answer questions about state standards, testing, etc.

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