CHARACTERIZING STUDENTS' ALGEBRAIC THINKING IN LINEAR PATTERN WITH PICTORIAL CONTENTS

The purpose of this paper was to explore the relation among the abilities, investigative process, generality and algebraic thinking when the fifth and sixth graders solved a linear pattern with pictorial contents. The author developed an ability model of solving pictorial patterns according to related theorems (e.g., Herbert & Brown, 1997; Ma, 2008; Orton & Orton, 1999) and 40 students' problem solving. The model denotes that there are levels of 0, 1, 2, 3a, 3b, 4a, 4b, 4c. Students are from level 0, 1 (seeing of sensory) and level 2, 3a (pattern seeking), arithmetic thinking, to level 3b (pattern recognition), arithmetic-algebraic thinking transition with understanding how to approach generality, and finally to level 4 (generalization), algebraic thinking With ability in Making a general ride. In addition the students at level 4 can achieve far generalization, While those at level 3b (:an achieve near generalization.