Abstract:

Pattern is one of the most important topics of mathematics education in all degrees. Some researchers asserted that pattern is the heart and soul of mathematics. Many skills and mathematical knowledge of students can be developed through pattern activities. In this study analyzing the structures of figural patterns/situations produced by middle school students based on number patterns was investigated. In total, 474 middle school students (254 were girls and 220 were boys) attended to study. Data were collected from a pattern task including linear and quadratic (non-linear) number patterns, in which participants were asked to generate figural patterns based on those number patterns. The obtained data were analyzed at two levels. The results of the study indicated that participants created 18 linear forms and 33 non-linear forms for linear number pattern and 13 linear forms and 20 non-linear forms for quadratic number pattern. During the study participants preferred to use the same geometric shapes such as circles, triangles and squares, etc. Creating figural patterns. Moreover, participants created many more figural patterns for the 3,5,7,9,11,... number pattern than for the 2,6,12,20,30,... number pattern. Some of the participants had problems while generating figural patterns such as producing non pattern forms, no answer, creating an irrelevant pattern and extending number patterns.

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