Investigation of 12th grade science high school students' mathematical thinking skills within the contexts of specialization, conjecturing, proving, and generalization steps

The aim of this study was to investigate mathematical thinking skills of 12th grade science high school students within the contexts of specialization, conjecturing, proving, and generalization steps. The sample of the study was 9 twelfth grades students who were studying in a science high school in centre district of Uşak city on 2015-2016 academic years. The study group was identified through one of the purposeful sampling strategies, maximum variation sampling. Data were collected with a "Mathematical Thinking Scale" developed by the researcher, consisting of 9 problems requiring written answers and interviews with the students about their answers to the problems. Data were analyzed with descriptive and content analysis method. At the end of the study, it was determined that as the difficulty levels of the questions increase, students specialization tendency also increased and achievements of the students decreased especially in generalization and proving steps. The steps students performed well were specialization, conjecturing, generalization and proving in decreasing order respectively. Among five types of conjectures mentioned in the study, students used only two types of them; Empirical Induction from a Finite Number of Discrete Cases and Perceptually Based Conjecturing. Results also revealed that students had the best achievement level in specialization step and they had the highest level in generalization step. Almost all of the students who were successful in generalization step, made Symbolic Generalization type generalizations which is the highest level in generalization hierarchy defined by Radford and Peirce (2006).