Examination of mathematical proficiencies of 7th grade students in the context of algebra content area

The purpose of this study is to examine the mathematical proficiency of secondary school students in the context of algebra content area. To this end, multiple case study design, which is one of the qualitative research designs, was employed. Students in different levels of productive disposition and mathematics achievement were used as the cases of the study and mathematical proficiency strands were used as the analysis unit of the study. The research was carried out in one of the Grade 7 classes, which was determined by accessible sampling, of a middle school in the Central Anatolia Region. The productive disposition (high, medium, low) and mathematics achievement levels (high, medium, low) of the students were determined, and crossing the achievement levels and productive disposition of students resulted in 6 categories. Considering these categories, 7 students who would provide maximum diversity were determined as participants. Chelsea Diagnostic Algebra Test and the students' 6th grade mathematics scores used to decide on the achievement levels of the students. In order to determine the productive disposition levels of the participants, "Productive Disposition Scale Toward Algebraic Expressions" was developed by the researcher. Lastly, Cronbach Alpha value of 36 Likert scale items, consisting of four factors which are "self-efficacy, enjoyment, anxiety and usefulness", was calculated as 0.919. Total variance explained by four factors is 48.509. The data of the research were collected through observations, audio-recorded interviews and documents, such as student's notebook, written exams papers and homework, in fall-semester of 2018-2019 academic year. With the researcher's field notes, all data were analysed using qualitative methods and the mathematical proficiencies of the students were evaluated in a holistic perspective. The framework created by Kilpatrick, Swafford and Findell (2001) was used as a base for the evaluation of mathematical proficiency of students. In this context, students' mathematical proficiencies examined in terms of procedural fluency, conceptual understanding, strategic competence, adaptive reasoning and productive disposition. The results showed that although the participants have certain proficiency strands according to their achievement and productive disposition levels, their mathematical proficiency strands and levels differ according to subject areas and individual differences. Although all students have succeeded in various proficiency strands in the content of equality and solving equation, in the content of problem solving by equation it was seen that the participants with a high productive disposition and achievement level were more successful than the others. It was revealed that the high-achieving and average-achieving participants mostly showed sufficient adaptive reasoning to check the accuracy of their results. It was seen that the majority of the participants maintain productive dispositions that they have towards learning algebraic expressions at first. Result also indicated that, students with low-productive disposition avoid trying and making efforts to solve the questions. Compared to other mathematical proficiency strands, it can be concluded that students are more proficient in procedural fluency. It can be said that the strategic competence of participants in using algebraic methods is low. It can be deduced that the problems experienced by the participants at the point of strategic competence stemmed from their lack of conceptual understanding. In addition, based on research results showed that the 5 mathematical proficiency strands can positively/negatively affect each other. That is, a positive/negative development in one of the mathematical proficiency strands may support the development of other strands or that a deficiency in one of them may negatively affect other strands. At the end of the research, some suggestions were made based on the research findings.