Analysis of the students' errors related to numbers and operations

The purpose of this study is to determine the errors of the eighth and ninth grade students regarding to rational numbers, exponential numbers, root numbers and mathematical operations and to evaluate these errors based on teacher's opinions. The cluster sampling method was used for the determining schools which are the members of Turkish Ministry of National Education in Ceyhan/ADANA. This study was applied to 611 students which 302 of them are eight grade students in 3 schools among 37 Elementary schools and 309 of them are ninth grade students in 3 schools among 33 High Schools and 11 mathematics teachers in the 2017-2018 of academic year. As a data collection tool, Diognosis Test was applied for the determine the density, operation and size of numbers which are rational numbers, exponential numbers, root numbers. In the test in this research there are 24 questions was formed by density, operation and size parts in rational numbers, exponential numbers, root numbers in naturel numbers bias. Totally 44 questions were asked with their lower entry items. Interview form has been applied to teachers to understand what type of errors students do. In this context, SPSS 16 package program was used in the analysis of data. The method of descriptive statistics (frequency, percentage calculation) and t-test have been used in analysis of quantitative data. Content analysis was used in qualitative data analysis. According to the datas which are collected by the data collection tools, the succeed of the students are observed on medium level for rational numbers, exponential numbers, root numbers. Although generally students pass their class, they have errors in next levels, too. There was significant difference between the achievements of students in the eighth and ninth grades in the questions about rational numbers, exponential numbers, root numbers. It is seen that the students generally think that the numbers in the rational numbers, exponential numbers, root numbers can always be whole numbers, and when collecting the rational numbers with the same shares, it is seen that instead of equaling the denominator, the same share is written and the borrowers collect as if they are collecting with natural numbers. Besides this, it has been seen that students have error about the density of rational numbers. Teacher views also support these findings. Keywords: Rational numbers, exponential numbers, root numbers, mathematic teaching