Investigation of Turkish and libyan students' algebraic thinking skills in quadratic equations with one unknown according to SOLO taxonomy

Mathematics grows alongside the evolution of human life. Mathematics being an essential element in all areas of life, it is one of the most important essential sciences to solve everyday life problems. In addition, it plays a fundamental role in scientific development and its application to most of the sciences, for example physics, biology etc. For this reason, mathematics is a science that should be taught and implemented in education stages. Mathematics is one of the subjects in which the level of students' achievement is low in different educational stages, where some of whom feel unwilling to study, lack of motivation, fear and worry, and sometimes they try to avoid learning mathematics. Mathematics considered by very nature a fertile field for the development of thinking in its different forms and that due to its objectivity and logic. Mathematics with its different branches is a necessary and it has a role in the development of thinking skills and the ability to overcome with life problems. Algebraic thinking plays an important role in mathematics. Many studies have indicated that there is low level of students in algebra. For this reason, the purpose of this study is to investigation of the algebraic thinking skills of Turkish and Libyan students in quadratic equations with one unknown by formulating generalizations, using symbols and algebraic relationships, and using multiple representations. In this study, scanning model is used to reveal an existing situation without any intervention. The participants of the study consisted of 112 students from Libya at 3 high schools in the city of Tripoli and 129 students from Turkey at 3 high schools in the city of Kastamonu. The data obtained by algebraic thinking test. This test consisted of 16 questions. The test was applied to students in the 2018-2019 academic year. In the analysis and assessment of student responses to algebraic thinking questions SOLO (Structure of the Observed Learning Outcomes) taxonomy was used. Thinking stages of the SOLO taxonomy consists of 5 levels which classify the students' answers to questions by its structural complexity (Pre-structural, Uni-structural, Multi-structural, Relational- structural and Extended abstract). According to the SOLO taxonomy, the results show that both the Libyan and Turkish students could reach the uni-structural, multi-structural, and relational levels. 26.3% of Libyan students are at the relational-structural level, 24.1% of are at the multi-structural level and 28.7% of are at the uni-structural level. 25.7% of Turkish students are at the relational-structural level, 28.3% of are at the multi-structural level, and 25.9% of are at the uni-structural level. In addition, there are a small number of Libyan and Turkish students at pre structural level. 7.0% of Libyan students are at pre-structural thinking levels and 12.7 % of Turkish students are at pre-structural thinking levels. 13.9% of Libyan students and 7.4% of Turkish students did not try to answer the questions. The data obtained were analysed with SPSS program. Mann-Whitney U Test was used to analyse the data. Results obtained after use Mann-Whitney U Test showed, there is not a significant difference between the level of Libyan and Turkish students in algebraic thinking test in formulating generalizations and using multiple representations skill. But there is statistically significant difference between Libyan and Turkish students' in algebraic thinking test of using symbols and algebraic relation skill, but it was not a big difference. So, students can be supported to develop their thinking skills by solving problems. Students must involve in different activities that are aimed to promote their skills and improving their ability in algebraic thinking. In addition, mathematics teachers should create opportunities for students to relate their mathematical ideas and concept to enable the students promote their ability in algebraic thinking.