Knowledge Construction Schemata of Teachers in Solving Real World Non-Routine Problem Situation: Their Implications to Mathematics Education

Abstract

The study investigated the nature of Knowledge Construction Schemata (KCS) that teacher-solvers use to solve a real-world non-routine problem situation. Eighteen Math teachers in different schools of Region I and the Cordillera Administrative Region were given a carefully selected power problem, which they solved in at most two hours. Results showed that rigid procedural framework of thought characterizes respondents’ KCS in solving problems. Based on this framework, solvers see solutions to a problem situation as purely routine or algorithmic procedures, a condition that makes them selective in interpreting data. They give meaning only to quantitative data while ignoring the qualitative ones, resulting in incomplete solution steps and failure to solve the problem. The influence of the routine type of problem solving appears to be so entrenched that solvers could not find meaning in qualitative data and venture to alternative solution steps that do not necessarily address the problem situation. An important component of problem solving, which is making necessary adjustments in response to a new problem situation (accommodation process), remains a great challenge among the teacher-solvers. Their KCS nature is heavily confined to assimilation processes, which seem responsible for keeping solvers from making exploratory attempts that could have paved the way for more productive problem solving. The study recommends that real-world non-routine type of problem-solving be integrated with school mathematics to develop among the students flexible, reflective, and transformational KCS.