the point is to discover them.
The Yau Tsinghua Mathcamp is a summer camp for mathematically talented and strongly motivated secondary school students from China and all over the world. A highly selected group of students are invited to join a rigorous month-long program to explore the art of creative problem solving with masters. Mathcamp also offers a great opportunity for students to work on research projects through collaborative discoveries guided by their coaches and teachers.
Running the Mathcamp was an idea born out of a little chat S.-T. Yau and Bong H. Lian had in 2010 about Chinese high schools. After a number of false starts, we finally got it off the ground as a pilot program in the summer of 2014. It was also the very first of its kind in Mainland China. We had an exciting 3-week camp in 2014, and we were lucky to have 32 students of superb caliber participating.
Our Mathcampers are a group of uniquely talented students, who come to us equipped with tremendous potential and natural curiosity. They are generally quick, inquisitive, and some of them very knowledgeable indeed. More importantly, they generally have immense raw talent waiting to be transformed into real one, and are very eager to see how real math and science are done.
One might say that our singular purpose is this:
At Mathcamp, we would like to offer campers a truly unique learning experience that is fun and genuinely different from their regular high school classes in China. The idea is that at Mathcamp, knowledge acquisition and problem solving are viewed as a creative process which is discovery based, as opposed to just fact gathering and fact applying. Thus, knowledge is more often created by the student themselves, and less often conveyed upon to them by someone else or other sources. They are driven and motivated by nothing other than their natural curiosity. We ask our Mathcamp teachers to serve as the campers’ mentors. In a nutshell, they inspire campers by helping them ask the ‘right question’ in formulating the ‘right definition’ and the ‘right conjecture,’ starting from simple (natural) questions, intuition, and examples. They guide campers toward solving questions and conjectures by helping them discover the ‘right idea’ and heuristics, and if necessary suggesting a pathway towards a verification or proof.
We hope to achieve four primary goals in each of the courses we offer:
To cover the basics of one math or science subject up to an advanced undergraduate level, a near equivalent of a college junior or senior level course at a top university.
To open the door to some advanced graduate or research level topics in that subject, by challenging students with selected problems in those topics, in the form of research projects.
To prime each Mathcamper with the basic tools needed to start on one or more research projects or lines of inquiry along those topics introduced.
To instill a sense that curiosity-driven creative discoveries in problem solving is not only fun, but far outweighs a fact-gathering/applying approach.
Although to finish covering a pre-set course syllabus may be a desirable outcome, it does not have to be the top priority for the Lecturer. Thus, some built-in flexibility in the prepared syllabus of the Lecturer would be helpful. With that in mind, we try to structure our curriculum within each course to emphasize the creative process leading to each topic, problem, conjecture; and ultimately the process leading to discovery of each fact, idea, answer, and solution as well.
On day one of the camp, we expect our campers are coming to us with high hopes, great enthusiasm, and very ready to learn. We expect everyone is fully proficient in almost all aspects of Chinese twelfth grade math curriculum, including algebra, geometry, and calculus. However, most campers are probably unfamiliar with the notion of creative learning, or have never practiced it. To them, knowledge is mostly existing, and is conveyed or endowed to them by others. When faced with a math or science question, most often their modus operandi is either look to their memory to see if it is something similar/related to what they know. If that fails, their natural instinct is to turn quickly to another source – someone (a teacher, a colleague, or a friend) or something (a book, a website, or a lecture note), to either look up an answer or remind themselves of a way to reach an answer that they might have seen. In other words, they take for granted that an answer has already been created, and locating is the most natural thing to do. We know that answering a question by sourcing, no doubt, is a skill that has an important role to play in all forms of learning. But it is not what we hope to develop in these bright students in this summer camp. We wish our campers to experience a ‘new dimension’ in learning: we show them that an answer to a question is often locked within the question itself – if only you can unlock it. To take this metaphor even further, we as Mathcamp teachers are viewed as master locksmiths, showing the young apprentices nothing but the art of unlocking a question. It is not so much by sourcing, but by asking the right question in making each incremental step. And it's also fun and it's minimalist. We encourage our apprentices to work with other apprentices. Collaborative discovery is a spirit we wish to instill in them, because collaborating with others not only can be a better and faster way to solve a problem than working solo, but explaining your thoughts to a collaborator can itself be a creative process. It can help uncover ideas you miss, while clarifying your own understanding of the problem at hand. By the last day of the camp, we wish our campers to reach the following milestones:
From problems to elements: To acquire the instinct and skills to deconstruct a question or a research problem we pose into elemental terms.
From heuristics to solutions: To be able to create a pathway toward a solution or a partial solution to such a problem.
From knowing to telling: To be able to present their findings to their peers in clear and thoughtful ways.
February 14, 2023