Teacher's Specialized Content Knowledge on the Concept of Square: A Vignette Approach

In learning geometry, the discussion about the definition of quadrilateral is a material that is difficult and not easily taught by the teacher. This study aims to explore the teacher's specialized content knowledge about square. This is a descriptive-qualitative research. The process of selecting subjects begins with searching prospective subject data according to the level of the teacher through a portfolio of 82 teachers in South East of Sulawesi: (33 First Teachers, 33 Young Teachers, and 16 Intermediate Teachers). The research subjects consisted of three teachers, namely: First Teacher, Young Teacher dan Intermediate Teacher with score > 50. Data were taken using vignette. The results show that there is a difference when the teacher is asked to define a square with when given a definition of a square. First Teacher is accurate when given a square definition with the symmetry and diagonal axis attributes; the side attribute is not accurate in giving arguments to the square definition. Young Teacher is inaccurate when given the definition of a square with side and angle attributes; accurate with symmetry and diagonal axis attributes; but it is not accurate when given a square definition. Regarding attributes of side; Intermediate Teacher revealed that the side and angle attributes are inaccurate but accurate with the symmetry and diagonal axis attributes but do not appear / are not used when asked to define a square. Specialized content knowledge First Teacher is better because it has been able to reconstruct concepts from a square, but Young Teacher and Intermediate Teacher are still influenced by concept images and figural concepts.

Use of theories and models in geometry education research: A critical review

The aim of this article is to provide a critical review of the theories and the model used in the field of geometry education research. The article critically discusses van Hiele’s theory, Fischbein’s theory of figural concepts, Duval’ s theory of figural apprehension, the Spatial Operational Capacity (SOC) model by Wessels and van Niekerk, and the Sfard’s commognition theory. The van Hiele’s theory proposed a sequential order of development through which the learners construct their understanding of geometry concepts. Fischbein’ s theory of figural concepts suggested that a geometric figure is always comprised of a visible representation and a concept. Duval’s theory of figural apprehension underscored the heuristic value of a geometry figure for solving geometry problems. The SOC model by Wessels and van Niekerk emphasised the importance of instructional design incorporating a variety of physical and mental objects to work with to develop geometry concepts. Finally, the article discusses Sfard’s commognition theory that emphasises the communicative function of language in developing geometry concepts. There are two major concerns highlighted with respect to these theories and the model. Firstly, these theories and model emphasise the development of the two-dimensional geometry concepts, neglecting the development of the concepts of three-dimensional geometry. Secondly, these theories and the model fail to acknowledge the multilingual context of geometry class. The article aims to highlight the dearth of studies that explore the multilingual context of geometry class and calls for future studies in this direction.