An examination of misconceptions regarding rational numbers in 7th grade mathematics lesson within the context of teaching with mathematical modeling activities

The purpose of this study; to analyze the misconceptions that may occur in the teaching of rational numbers, which is the sub-learning area of the numbers and operations learning area of the 7^th grade mathematics course in secondary school and to examine the effect of the use of mathematical modeling activities on eliminating misconceptions. In this study, mixed methods research was used, in which qualitative and quantitative researches were used together. Working group; It consist of 24 (twenty-four) students, studying at the 7^th grade level of secondary school in Çaldıran burgh of Van province in the 2023-2024 academic year. "Misconception Detection Test 1" and "Misconception Detection Test 2" were applied to determine students' misconceptions about rational numbers. Then, mathematical modeling activities were generated taking into consideration the achievements and were carried out after the lesson. After the three weeks performing, the last test was applied to the students and interviews were had with 9 students representing the group. While obtained quantitative data were analyzed with the SPSS package program, the qualitative data were analyzed with content analysis. The students' pre-test and post-test results were compared and the percentage and frequency values were examined. As a result of the research, writing the numerator part of the rational number to the whole part and writing the denominator part to the decimal part, converting decimal numbers to rational numbers by thinking of them as decimal numbers, ignoring the minus when sorting, adding the numerators among themselves and the denominators among themselves, equaling the denominator in multiplication and division operations and negative whole numbers, six misconceptions were identified, including subtraction instead of addition when converting a numbered fraction to a compound fraction. At the end of mathematical modeling activities, the students rose from "medium level" to the "good level" in terms of academic success. It was observed the misconceptions that occurred were partially eliminated.