Abstract:

Algebraic reasoning plays a foundational role in mathematics education and STEAM fields. Algebraic reasoning encompasses recognizing and generalizing patterns, justifying generalizations, and using different representations. This study aims to investigate seventh-grade students’ generalizations of patterns using arithmetical generalization, algebraic generalization, and naïve induction. This study tries to answer the following research question:

How do seventh-grade students generalize patterns across the different algebraic levels of factual, contextual, and symbolic generalization?

Data was gathered through a mathematical task centered on a real-life modeling scenario. This task required students to identify pattern and determine both near and far terms, as well as the general term within the linear-numeric pattern. Two 7th-grade students volunteered for an in-depth investigation of their generalization strategies. The data set for this study includes the students' written solutions, video recordings, and transcripts from interviews conducted with the two seventh-graders. The transcripts and written student solutions were analyzed based on the students’ pattern generalizations, utilizing algebraic generalization levels: factual, contextual, and symbolic generalization.

Both participants generally employed multiple generalization approaches, as reported in the literature. Students used their own generalization strategies, and both of the participants were able to find near-term, far-term, and general terms by using different generalization types.

Keywords:

Factual generalization, contextual generalization, symbolic generalization, middle school.