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、發現問題、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下去。這樣大了以后一部分智商超群的學生可以做出發明創造的成績 - 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展下去。

　　當然，僅僅參加一個美國“數學大聯盟杯賽”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的數學競賽。