The purpose of this study is to investigate which factors
affect problem solving processes and psychological traits of
these factors during problem solving. The study selected 6
samples from 5-th & 6-th grade students, and classify
them by low, average, high abilities ,and used non-
synchronic thinking-aloud method to obtain problem
solvers'''' information in short term memory during problem
solving processes. The study designed a model of five
components of mathematical problem solving processes
that are used analytical framework. According to these
components, the findings of the study have: 1. Perception,
understanding and representation of the problem. (1) High
abilities tend to observing relations of problem context and
evaluating availability of these relations , but low abilities
only tend to perceiving single or few relations. (2) To
the same problem, different problem solver often formulate
different and various meaning. (3) To low abilities, it is
enough to assist him successful problem solving by making a
graph or a diagram. 2. Understanding of math concepts. Low
abiities tend to apply some similar context or keywords of
the problem, and math knowledge of low abilities is
often formula for incantation or surface understanding.
3. Design and perform strategy. Effective problem-solving
strategies are almost from high abilities. 4. Awareness and
control. Awareness can be distinct from five levels:
unawareness; unrelational awareness; unclear
awareness; relational awareness; reflective awareness. 5.
Looking back. Problem solvers of the study have few looking
back. In particular, average or low abilities often reprent
them to dislike check or unknow how to check.