Eighth grade students' mathematical language usage in the context of quadrilaterals: Syntax and semantic components

The main purpose of this study was to investigate the syntax and semantic components of eighth grade students' mathematical language usage in the context of quadrilaterals. Qualitative research methodology was used for the purpose of this study. This research was conducted with eight, eight-grade students in the 2014-2015 academic year at the middle schools in the center of Eskişehir. Clinical interview was used to explore the purpose of this study. Clinical interviews were video-recorded and students' activity sheets were also used as a data source. To analyze data, the three phases consisting of "data reduction", "data display" and conclusion drawing and verification were considered. The results revealed that students have insufficient mathematical language and misconceptions about quadrilaterals without noticing the students' achievement levels and gender. It was seen that students were able to define quadrilaterals but they insufficiently describe the properties of the quadrilaterals because of their ignorance of the diagonal. Moreover, results of this study showed that students were not aware of the distinction between definition and properties, they were able to define the quadrilaterals when the symbols were given, however they were not able to define the quadrilateral class. As a result of this, they were not able to describe the hierarchical relationship between quadrilaterals based on the given symbolic statement. On the other hand, they defined the class of the quadrilaterals based on the verbal inclusive definitions of quadrilaterals; hence it was revealed that they thought the hierarchical relationship between quadrilaterals and they semantically detected the verbal expressions better than the symbolic expressions. Although students should be on Level 2 (analysis) in the van Hiele model of geometric development when their grade levels were considered, it was seen that they have shown Level 0 and Level 1 characteristics in terms of using mathematical language. Key Words: Mathematical language, geometry, syntax, semantic, van Hiele geometrical thinking levels