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This study investigates the learning of the concept of functions in an adidactic learning environment, explains the five phases of the adidactic learning environments defined in the Didactic Situation Theory and their interactions with the milieu generated within the given problem state of the students. It was carried out with 33 ninth grade students from an Anatolian high school in Balıkesir. This qualitative study was designed as a case study. Descriptive analysis was used to analyze the data from students’ worksheets, and the transcriptions of video records in order to investigate the outcomes of an adidactic learning environment in detail. Students’ performances in the teaching process were evaluated with a checklist for problem-solving, construction of function knowledge and interaction with the milieu. The results showed that the basic conditions of an adidactic learning environment were provided, the students with a high interaction with the milieu constructed function knowledge by completing each stage. The students’ display rates for the indicators on the checklist were 70.90 % for problem-solving, 77.77% for construction of function knowledge, and 80.00% for interaction with the milieu.

This study aims to assess eight grade students' algebra knowledge and algebraic thinking levels with regard to problem posing. The study sample included 200 eighth graders that were selected using simple random sampling method in Bursa province. This is a survey. Problem Posing Test and Scale on Algebraic Thinking Level were used as data collection tools. Problems posed by students were scored based on data coding scheme developed by Silver and Cai in data analysis. One-way analysis of variance (ANOVA) was used to determine whether problem posing skill scores showed a significant difference by algebraic thinking levels of students. In addition, student's algebra knowledge was analyzed by the rubric developed to determine whether student's algebra knowledge reflect on the problems they posed, and data regarding each level were presented in a descriptive manner. As a result of the study, a significant difference was found between mean scores of students' problem posing skill and algebraic thinking levels. It was found in the examination performed using posed problems on algebra knowledge that 18% of the students described mathematical, symbol and formula knowledge correctly when posing problems, 5.5% were able to pose problem transforming knowledge and skills regarding how to use algebra knowledge in daily life, and 14% were able to make judgment regarding given situation when posing problem and pose a suitable problem.

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