平面几何问题解决过程中的元认知实验研究

This study was based on the cognitive-metacognitive model of mathematical problem solving established by Lester & Garofalo(1985). The method of protocal analysis was used and 19 excellent students(9 male and 10 female) & 19 learning-disabled students(11 male and 8 female) in middle school(grade 3)were tested and interviewed during they solved plane geometry problems. The main results showed as follows: (1) There was a significant difference between excellent students and learning-disabled students on time-assignment when they solved plane geometry problems. Excellent students used more time on phase organization and less time on phase execution. There was no difference on phases orientation and verification. (2) Excellent students showed higher metacognitive level than learning-disabled students. The deference existed in phases orientation and organization. Excellent students reported more metacognitive sentences in phases orientation and organization than learning-disabled students. They had more self-awareness and goal-awareness. They had more "knowledge about what they know" and "knowledge about what they should use". They designed more globle goal and subgoals and made more self-evaluation. (3) Both the excellent students' and learning-disabled students' self-checking level should be improved.

Two-Point Closure Strategy in the Mapping Closure Approximation Approach

A two-point closure strategy in mapping closure approximation (MCA) approach is developed for the evolution of the probability density function (PDF) of a scalar advected by stochastic velocity fields. The MCA approach is based on multipoint statistics. We formulate a MCA modeled system using the one-point PDFs and two-point correlations. The MCA models can describe both the evolution of the PDF shape and the rate at which the PDF evolves.