### Abstract:

The purpose of this study was to examine the problem solving processes of
Thai gifted students when they solved non-routine mathematical problems. The
research questions guiding the study were: (1) What is the nature of the problem
solving processes that Thai gifted students use as they engage in solving non-routine
mathematical problems? (2) What metacognitive behaviors do Thai gifted students
exhibit when engaged in mathematical problem solving?
Five Thai gifted students who were eligible for the Thai Mathematical
Olympiad project and met the selection criteria participated in this study. Each student
practiced the think aloud method before solving three mathematical problems
individually. The problems were non-routine problems that focused on number theory,
combinatorics, and geometry, respectively. The subjects worked on each problem
separately and were interviewed at the end of each problem solving session. Data
sources included videotapes of the think aloud and the interview sessions, students’
written solutions, and researcher’s field notes. These data were analyzed using the
within-case and cross-case techniques. Data gathered were also categorized using a
constant comparative method to conceptualize a model of problem solving process.Overall, the participants solved Problem One and Problem Two without
hesitation, although some did not completely solve Problem One. In spite of the fact
that two students had some difficulty searching for a solution for Problem Three, all of
the students eventually succeeded. The results generated a Thai model of problem
solving process that detailed the students’ behaviors in each of four stages:
understanding, planning, executing, and verifying. Their behaviors occurred in this
model cycled back and forth among the four stages. It was apparent in each stage that
the students understood when and how to apply their mathematical knowledge and
strategies in their solutions. They also applied self-evaluation statements to monitor
and evaluate themselves as problem solvers. The findings also provided five
categories of emerging evidence related to the students’ problem solving processes:
advanced mathematical knowledge, willingness to consider multiple alternative
solution methods, recollection and willingness to consider prior knowledge and
experiences, reliance on affect, and parental and teacher support.