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.

　　我們的理解是西方包括美國教育的“好處”不在于教了學生多少“知識”及會解多少“難題”， 而是在于教了學生很多觀察事物、究根求源、發(fā)現(xiàn)問題、解決問題的能力和動手能力， 同時鼓勵學生按照自己的興趣繼續(xù)下去。這樣大了以后一部分智商超群的學生可以做出發(fā)明創(chuàng)造的成績 - 像教授、科學家等; 另一部分智商不是那么杰出的大多數(shù)人可以踏踏實實地做好自己平凡的工作 - 像工程師、技術工人、職員等， 從而各盡所能、整個社會有秩序地發(fā)展下去。

　　當然，僅僅參加一個美國“數(shù)學大聯(lián)盟杯賽”的初賽、復賽、甚至決賽， 不足以了解美國教育的精髓和“博大精深”， 我們鼓勵和倡導學生多多學習、比較、體驗各種先進的教學方法和實踐，“海納百川”。

　　復賽的題目和形式有別于中國傳統(tǒng)的數(shù)學競賽。