GENERALIZATION OF PATTERNS: THE TENSION BETWEEN ALGEBRAIC THINKING AND ALGEBRAIC NOTATION (original) (raw)
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Factors Affecting Students' Performance in Generalizing Algebraic Patterns
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Pattern generalization is indispensable to the development of algebraic thinking; however, students in early and even in late middle school are struggling in generalizing patterns. This study identifies the students' perceived factors that affect their performance in generalizing algebraic patterns and describes how each factor affects their process of generalization. This study used the qualitative descriptive design. The students were given open-ended problems which require them to generalize patterns. Results show that the factor which greatly influences the students' performance was associated to the structure of the task such as the size of the values and problem presentation. The ability to derive algebraic symbol influences students' thinking of getting better result while lacking this ability despite their complete and accurate solution leaves them the feeling of arriving at incorrect answer. With these results, teachers should help students to structure and organize their informal methods rather than focus on how to use mathematical formulas. Teachers should expose them to pattern-based problem solving with considerations to the elements that influences their performance.
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This paper explores how a group of pre-service elementary school teachers training to become mathematics teachers for elementary schools arrived at generalizations based on patterns. Two representative problems were investigated with these preservice teachers. The focus of this study was how these preservice teachers analyze and symbolize algebraically their generalizations during a problem-solving process. The results indicate that the preservice teachers had difficulty making use of input-output (having two variables in the table) relationships in a generalization process associated with developing symbolic functions. This study identifies the crucial need for introducing students to pattern activities early on in their lives.