An investigation of the transformation from taught knowledge to learned knowledge about eighth grade greatest common divisor (GCD) - least common multiple (LCM) subject in ecological context

As a result of the interaction of the individual with the information, the information undergoes a transformation. The "Didactic Transformation Theory" [DDT] explains how the processes of transforming the scientific knowledge produced into knowledge to be learned and from the knowledge taught at school to the knowledge that the student assimilates take place. According to DDT, the information presented to the student by the teachers using appropriate materials in the classroom environment is the information taught, while the learning products consisting of the student's studies are the learned or assimilated information. Educational institutions are the environments where the transformation of information takes place. The environment in which the information is transferred and transformed by changing means the ecology of the information. The aim of this research is to examine the transformation from the knowledge taught to the learned knowledge related to the eighth grade GCD-LCM in an ecological context. The research was designed as a holistic multiple case study. In the study, three public secondary schools (according to LGS success rankings and socio-economic levels) were selected from Erzin district of Hatay, with different socio-economic levels and achievement levels, as the ecological context. Participants were determined by maximum diversity sampling. The participants of the study are 54 volunteer eighth grade students with parental consent and 6 volunteer math teachers who teach mathematics to eighth grade students from three secondary schools. GCD-LCM academic achievement test with 15 questions prepared by the researcher in order to examine the data in the research, the transformation from taught knowledge to learned knowledge, were collected through interview forms and lesson observations (with videos). The answers in the academic achievement test of the students were scored with the rubric developed by the researcher and analyzed in the SPSS program. Interviews were conducted with the students and teachers who scored the highest and lowest scores of each teacher in the academic achievement test. Qualitative data in the research were analyzed with inductive content analysis. As a result of the research, it has been determined that there are low-income parents in all three socio-economic schools. When the techniques used by the teachers in the presentation of the taught information were compared, it was determined that the teachers in the upper SES school frequently used question-solving strategies, whereas the teachers in the lower SES school mostly resorted to making sense of the information and focusing on important information about the subject. Again, it was determined that the teachers in the school in the upper SES did the operations without emphasizing the rules on GCD-LCM, but the teachers in the school in the lower and middle SES solved the questions by emphasizing the rules and explaining the steps and purpose of the operations. According to the findings obtained from the academic achievement test, regardless of SES, the majority of the students are partially sufficient (2nd Level) and sufficient (3rd Level). It has been determined that they perform at the level). However, when the students' mistakes were examined, it was determined that the students in the middle SES school made more conceptual errors, operational errors, and both conceptual and procedural errors. The reasons for the mistakes made by the students were determined as carelessness and difficulty in understanding the question. By making use of the results of this research, teachers can design instructional activities for errors, sources (reasons) of errors and eliminating these errors. Keywords: Ecological context, taught knowledge, learned knowledge