Reflections from the gifted students' generalization processes of patterns: Strategies and cognitive demand

The aim of this study is to explore the strategies used by gifted students in the process of generalizing the pattern tasks presented with different representations and the cognitive demand levels they reveal. This study, which adopts a qualitative approach, was designed in a case study. The participants are nine middle school students who were identified as gifted. Data were collected with the Pattern Tasks Form consisting of open-ended pattern tasks. Pattern tasks are designed in linear, quadratic, and other pattern types within the scope of the growing pattern presented with number and geometric representations. Task-based interview was used as the data collection method. Data analysis was carried out with deductive thematic analysis. According to the results of the study, gifted students used recursive, interval counting, prediction-control, contextual, and functional strategies in the generalization processes of pattern tasks. The most commonly used strategy in inverse problems is "statement and solution of an equation". The results of the study show that students mostly exhibit cognitive demand at the level of "procedures with connections" in linear geometric, number and other pattern tasks. However, in the quadratic geometric and other number pattern tasks, the students showed intense cognitive demand at the level of "doing mathematics".