Investigation of the 7th grade students' proportional thinking skills with SOLO Taxonomy

The aim of this study is to examine the proportional reasoning skills of secondary school students and their mistakes in the process with the help of SOLO Taxonomy. The study is a case study. In the 2016-2017 academic years, 33 students in a public school in a district in the Middle Black Sea Region participated in the study for the first phase. By purposeful sampling method 10 students were selected to have detailed information about the students for the second phase. Data collection tool was Proportional Reasoning Test with the reliability coefficient .86 and item discrimination indexes between 0.50 to 0.71. In order to collect more detailed information about the students' reasoning skills, 5 problem situations were identified in which the students made the most mistakes from the questions in the test and semi-structured interviews were conducted with the students about their solutions. Interviews were recorded and evaluated as research data. It is seen that students have difficulty in understanding terms and concepts such as ratio, proportion, direct proportion and inverse ratio and using them appropriately in problem solving process. It is observed that the students have an additive relationship in cases requiring multiplicative relations and multiplicative relations in cases where they need to establish an additive relationship. It was observed that the students used 5 different misconceptions while solving the problems requiring proportional thinking skills. These are defined as the additive strategy, relating the only one variable by ignoring part of the data strategy, responding to the numbers but not the context of a given strategy, affective responses to numerical data strategy and failure to identify non-proportional states. In addition to these findings, the interview data were analyzed with the SOLO Taxonomy Rubric which was developed by the researcher for proportional thinking skills. It is observed that the students who are accepted as high scores according to the proportional thinking ability scores are generally in relational and extended abstract levels in the SOLO Taxonomy evaluation criteria. One of the students who were accepted as intermediate scores was not in the extended abstract level of SOLO Taxonomy. The students in the mid-point group mostly responded to the problems of proportional reasoning skills at the level of uni-structural and multi-structural. Similarly, students who were accepted at low level were also found to have low levels in the criteria of SOLO Taxonomy criterion. None of the four students at the low grade level were able to take part in extended abstract and relational taxonomy levels. In particular, all of the students in the problem that should determine non-proportional relationship, 0 points in the ratio of proportional thinking and in the SOLO Taxonomy were 1 point uni-structural level. According to the findings obtained from the study, it was seen that the students made fewer mistakes and had better reasoning in the questions involving daily life situations. Therefore, it is recommended that daily life problems should be used in teaching the ratio and proportion of teachers. In the student interviews, it was observed that the students who think aloud and are encouraged to express their ideas have noticed and compensated their mistakes much faster. For this reason, it is suggested that students expressing their thoughts by voice are important in preventing false learning and are recommended to be used in mathematics lessons.