Search

The concept of encryption is noteworthy in terms of both familiarizing mathematically gifted students with technological developments and working with mathematically challenging tasks. Once the proper foundations are established, students can begin to formalize encryption and decryption with algebraic formulas. Encryption can be an important resource for developing functional thinking. Based on the given information, this study designed an encryption algorithm through linear patterns that can be presented as a teaching task in classroom environments to students who are learning at elementary school level and explained the implementation process. The task named "Encryption arising from patterns" is considered important in terms of both creating an encryption algorithm and providing content for the development of mathematical patterns and therefore functional thinking. In the task of "Encryption arising from patterns", the general term of the linear pattern was created by starting from two prime numbers. The numbers corresponding to the first 29 terms of this linear pattern have been calculated. The letters of the alphabet and the terms of the pattern were paired in order. Then, Caeser's Cipher was applied to the letters in the alphabet. Thus, the numbers corresponding to the key letters were assigned to the letters in plaintext. The letters of plaintext were sent to the receiver along with the numbers corresponding to the key letters and the first three steps of the linear pattern, and the encryption task was completed. [ABSTRACT FROM AUTHOR]

One of the cognitive characters emphasized by different researchers in mathematically gifted students is generalization of mathematical structures and patterns. In particular, experience with growing geometric patterns is important for initiating and developing algebraic thinking. In this context, this study aimed to explore the generalization strategies used by gifted students in the growing geometric pattern task. The study was designed in a case study. The participants of the study are five eighth grade students who were diagnosed as gifted through diagnostic tests. The data of the study were collected with the "Geometric Pattern Task Form" consisting of open-ended problems. The geometric pattern task consists of linear and quadratic patterns. Data were collected by task-based interview method and analyzed with thematic analysis. The results of the study show that gifted students exhibit figural and numerical approaches while solving pattern problems. In particular, for quadratic (nonlinear) pattern, gifted students used functional strategy in all problems of finding near, far terms, and general rule of pattern. However, in the problems of finding the number of white balls (linear pattern), different strategies (e.g., recursive, chunking, contextual) than the functional strategy were also used. Based on the results of the study, it is suggested that geometric pattern tasks involving linear and non-linear relationships may be centralized in the development of functional thinking and generalization skills of gifted students in classroom practices. [ABSTRACT FROM AUTHOR]