Teacher's opinions on the perceptions of equivalence of 7th grade students

The aim of this study is to examine the opinions of secondary school mathematics teachers on how 7th grade students perceive equivalence and equality concepts, how students' perceptions of equivalence affect their understanding of equivalence-related issues, as well as how their perceptions of equivalence affect ratio-ratio problem solving strategies and performance. The sample of the study consisted of 24 mathematics teachers teaching 7th grade classes in the central district of Siirt province in the 2020-2021 academic fall semester. In this study, which was carried out with the phenomenological pattern and qualitative method, the data were collected with a semi-structured interview form. The semi-structured interview form was created by re-arranging the questions written by the researcher within the scope of expert suggestions, after going through the opinion of field experts. The interviews with the teachers were carried out through the zoom program or face to face, and the interviews were recorded. The collected data were analyzed using the content analysis method. As a result of the analyzes made, it was concluded from the opinions of the teachers that the 7th grade students mainly lack conceptual knowledge and misconceptions in their definitions of equivalence and equality, and that there are also definitions close to the truth, and that the students as a whole are not completely unfamiliar with the concept of equivalence. Similarly, it has been observed that there are incomplete or erroneous information in teachers' definitions of the concepts of equality and equivalence. Again, from the opinions of the teachers, it was determined that the students were able to base some information on some subjects such as equivalent fractions, ratio-proportional equations, and they also partially noticed the similarity between the equivalent fraction and ratio subjects. It was determined that the students could not distinguish the concepts of equality and equivalence, so they used them interchangeably, and the operational understanding of equality continued even in the 7th grade. From the statements of the teachers, it was found that the majority of the students used rote methods (inside-out product, linear multiplication) in ratio-proportion problems, however, students with a sense of equivalence tended to reach the answer by reasoning proportionally and to use intuitive strategies (unit ratio, equivalent fraction, change multiplier). Finally, it was determined that students' equivalence perceptions positively affected their performance in ratio proportionality problems and accordingly their success.