Pattern Generalization Problem Solving Strategies and Explanation Methods of Elementary Gifted Students

Abstract

The purpose of this paper is to examine the differences in problem solving strategies and solution explanations for solving pattern generalization problems by ability groups among gifted mathematics students in elementary schools in Korea. In the process of generalizing the algebraic-geometric problem of the least numbers of moved stones from triangular arrays to inverted triangular arrays, several types of problem-solving strategies are identified as (1) recursive relation (2) functional relations(guesswork-based, singular, compound) (3) perception of situational structure can make the difference in finding general formulas. Many students try to generalize from numerical patterns in recursive or singular functional relations but some gifted students go beyond numerical patterns and generalize based on situational structures. Having grasped the geometric situation one of our best students outlines the problem solving process with a generic example. We found that Korean gifted students' pattern recognition strategies in situational structures and their ability to generalize high-level mathematical knowledge determined their problem solving success.