Creative Thinking, Critical Thinking, and Problem Solving Skills:

　　Creative thinking that focuses on the skills of fluency, flexibility, elaboration, and originality coupled with the affective characteristics associated with creativity such as curiosity and risk-taking.

　　Critical thinking as the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and evaluating information to reach an answer or conclusion; a reasonable, reflective thinking focused on deciding what to believe or do.

　　Inductive and deductive reasoning skills such as analysis, evaluation, and predicting.

　　Problem-solving skills, using a math heuristic to outline the process.

　　我们的理解是西方包括美国教育的“好处”不在于教了学生多少“知识”及会解多少“难题”， 而是在于教了学生很多观察事物、究根求源、发现问题、解决问题的能力和动手能力， 同时鼓励学生按照自己的兴趣继续下去。这样大了以后一部分智商超群的学生可以做出发明创造的成绩 - 像教授、科学家等; 另一部分智商不是那么杰出的大多数人可以踏踏实实地做好自己平凡的工作 - 像工程师、技术工人、职员等， 从而各尽所能、整个社会有秩序地发展下去。

　　当然，仅仅参加一个美国“数学大联盟杯赛”的初赛、复赛、甚至决赛， 不足以了解美国教育的精髓和“博大精深”， 我们鼓励和倡导学生多多学习、比较、体验各种先进的教学方法和实践，“海纳百川”。

　　复赛的题目和形式有别于中国传统的数学竞赛。