The strategies of using a special kind of number patterns in different stages of education

Patterns and generalization are one of the most fundamental aspects of mathematics, which makes  recent decades, mathematical tasks which include patterns, whether they are numerical or graphical, are mostly used, for example researching generalization. The aim of this paper is to investigate how a special kind of task concerning well-known palindromes can diversify the process of generalization in three different age groups of students. More precisely, the paper includes the analysis of solutions of one task concerning counting of numbers of palindromes by middle school, high school and university students with the special attention for finding similarities and differences among advance of process of generalization and using methods of solving in researched groups. The researched groups chosen randomly from two distant part of Poland, were consisted of 44 middle school students, 102 high school students and 51 university students (including 42 pre-service teachers). All students solved the same task in limited time without any assistance of teachers. The research was carried out between 2013 and 2015. Key words: Strategies, patterns, palindromes, mathematics.