Analysis of the pattern problems posed by prospective elementary school mathematics teachers using different forms of representation on their own and student level

This study examined the pattern problems created by the prospective elementary school mathematics teachers by means of different forms of representation and attempted to identify their problem posing skills on the subject of patterns both at their own level and at the level of middle school students whom they will lecture. The study utilized a mixed method. The sample of the study consisted of a total of 137 people, who are 3rd and 4th grade prospective elementary school mathematics teachers. The Test of Forming Pattern Problems by means of Multiple Representations, which was prepared by the researcher, was used as the data collection tool of the study. The prospective elementary school mathematics teachers were asked to form 4 different problems based on these forms of representation: "Figure", "Table", "Verbal" and "Symbolic" in the Test of Forming Pattern Problems by means of Multiple Representations with two different parts. The study concluded that the performances of the prospective elementary school mathematics teachers in forming pattern problems based on different forms of representation varied depending on their own levels and the levels of middle school students whom they will lecture. While figure was the form of representation in which the prospective elementary school mathematics teachers achieved the highest performance levels in the different forms of representations both in their own levels and in the levels of middle school students whom they will lecture, symbolism proved to be the form of representation where they had the poorest performance levels. The prospective teachers showed performances also in other forms of representations, which were respectively verbal and table. The findings of the study indicated that the average performance score of both 3rd and 4th grade prospective elementary school mathematics teachers in the different forms of representations formed for the levels of middle school students whom they will lecture proved to be higher than the average performance score that they obtained in the forms of representations formed for their own levels. A significant relationship was found between the performances of the prospective elementary school mathematics teachers in forming patterns problems for their own level in all forms of representations, except for the pair of the forms of figure-verbal representations. On the other hand, the study revealed a significant relationship in the performances of the prospective elementary school mathematics teachers in forming patterns problems for the levels of middle school students whom they will lecture only between the pairs of the forms of figure-table and verbal-symbolic representations. Furthermore, there was a significant relationship between all forms of representations except for the form of verbal representation, in regard to the performances of the prospective elementary school mathematics teachers in forming pattern problems for their own levels and for the levels of middle school students whom they will lecture in the forms of figure, table, verbal and symbolic representations. There was no significant relationship between the performances of 3rd and 4th grade prospective elementary school mathematics teachers in forming pattern problems for their own levels and for the levels of middle school students whom they will lecture in different forms of representations. As a result of the interviews, the prospective elementary school mathematics teachers' lower performances in the tests were determined about not understanding related test, posing the problem with simple thinking, unable to pose problems accessible for their student's thinking level and similar situations. Key Words: Pattern, forms of representation, problem solving, problem posing, prospective elementary school mathematics teacher