The article explores six dimensions of quantitative research : its possibility and feasibility , its substances and functions , its subjective and objective characters , its contents and forms , the superficiality of the behaviors in the process of the measurement and the concealment of the thought and motivation , the abstractness of the scores in the measurement reports and the concreteness of the characteristic reflections 本文从量化的可能性与可行性，实质与功能，主观性与客观性，内容与形式，以及测评过程中行为的表面性与思想动机的隐蔽性，测评报告中分数的抽象性与特点反映的具体性等六个方面进行了探讨。
( 2 ) instructional design of mathematical problem solving should be built on psychology theory , learning theory , teaching theory and consider the principle of clarity , matheaiality , enlightenty , expansibility and integrity of the design . ( 3 ) instructional design of mathematical problem solving consists of four closely related steps : to set up and to present teaching objectives , to analyze learning tasks , to design instructional strategy and instructional media and to evaluate learning outcomes ( 2 )数学问题解决的教学设计应以心理学理论、学习理论、教学理论为基础，遵循明确性、具体性、启发性、发展性、整体性原则。 ( 3 )数学问题解决的教学设计由紧密联系的四个环节组成：设置与陈述教学目标；分析学习任务；设计教学策略与教学媒体；评价学习结果。
