Examining the metaphoric perceptions of secondary school 8th grade students on the concepts they have about linear

In this study, it was aimed to determine the metaphorical perceptions of secondary school 8th grade students about the concepts related to linear equations and to examine the changes in these perceptions according to the gender variable and socio-economic level. In addition, it was aimed to interview the teachers in order to examine the results of the metaphors created by the students in detail. As the research model, the "phenomenology" design, one of the qualitative research methods, was used. The research consists of two dimensions. The sample of the first dimension of the study consists of 400 eighth grade students selected by the maximum diversity sampling method, studying at four public secondary schools in the province of Tokat in the 2021-2022 academic year. The sample of the second dimension of the study consists of 12 mathematics teachers working in selected schools and selected on a voluntary basis. In the research, two data collection tools were used: the Metaphoric Perception Form (MAF), which measures the perceptions of the eighth grade students about the concepts in the sub-learning field of linear equations, and the Teacher Interview Form, where the opinions of the teachers were taken according to the student perceptions. In the first dimension of the research, content analysis was used to analyze student metaphors related to concepts related to linear equations. In the second dimension of the research, the analysis of teachers' opinions was made using the descriptive analysis approach. According to the findings of the research, the metaphors related to the concept of equation were gathered under 25 conceptual categories and the metaphors of life, puzzle, human and scales were used the most. The metaphors related to the concept of the coordinate system were gathered under 17 conceptual categories and the metaphors of map, crosshair, navigation, compass, road and chess were used the most. The metaphors related to the concept of ordered pairs were gathered under 17 conceptual categories and the metaphors of friend, bro, sibling, school desk, twins, pattern and close friends were used the most. The metaphors related to the concept of origin were gathered under 16 conceptual categories and the metaphors of point, birth, equator, zero and beginning of life were used most. Metaphors related to the concept of variable were gathered under 10 conceptual categories and the metaphors of human, emotion, chameleon, dollar, weather, life, decision and stranger were used the most. The metaphors related to the concept of slope were gathered under 12 conceptual categories and the metaphors of ramp, slope, slide, stairs, road, roof, steep road and life were used most. When the metaphors related to the concepts of equation, coordinate system, ordered pair, origin, variable and slope are examined, female students developed more metaphors than male students. Regarding the concepts of equation, coordinate system, ordered pair, origin and slope, high and middle socio-economic level secondary schools developed more metaphors than lower socio-economic level secondary schools. The metaphors used by the teachers in the lesson regarding the concepts in the eighth grade linear equations sub-learning field were examined. It has been determined that the teacher metaphors used for the concepts of equation, coordinate system and slope are similar to the student metaphors developed for these concepts.