# Pre-Service Mathematics Teachers’ Understanding of Quadrilaterals and the Internal Relationships between Quadrilaterals: The Case of Parallelograms

Tugce Kozakli Ulger, Menekse Seden Tapan Broutin

**APA 6th edition**

Ulger, T.K., & Broutin, M.S.T. (2017). Pre-Service Mathematics Teachers’ Understanding of Quadrilaterals and the Internal Relationships between Quadrilaterals: The Case of Parallelograms.

*European Journal of Educational Research, 6*(3), 331 - 345. doi:10.12973/eu-jer.6.3.331

**Harvard**

Ulger T.K., and Broutin M.S.T. 2017 'Pre-Service Mathematics Teachers’ Understanding of Quadrilaterals and the Internal Relationships between Quadrilaterals: The Case of Parallelograms',

*European Journal of Educational Research*, vol. 6, no. 3, pp. 331 - 345. Available from: http://dx.doi.org/10.12973/eu-jer.6.3.331

**Chicago 16th edition**

Ulger, Tugce Kozakli and Broutin, Menekse Seden Tapan . "Pre-Service Mathematics Teachers’ Understanding of Quadrilaterals and the Internal Relationships between Quadrilaterals: The Case of Parallelograms". (2017)

*European Journal of Educational Research*6, no. 3(2017): 331 - 345. doi:10.12973/eu-jer.6.3.331

### Abstract

This study attempts to reveal pre-service teachers’ conceptions, definitions, and understanding of quadrilaterals and their internal relationships in terms of personal and formal figural concepts via case of the parallelograms. To collect data, an open-ended question was addressed to 27 pre-service mathematics teachers, and clinical interviews were conducted with them. The factors influential on pre-service teachers’ definitions of parallelograms and conceptions regarding internal relationships between quadrilaterals were analyzed. The strongest result involved definitions based on prototype figures and partially seeing internal relationships between quadrilaterals via these definitions. As a different result from what is reported in the literature, it was found that the fact that rectangle remains as a special case of parallelogram in pre-service teachers’ figural concepts leads them not to adopt the hierarchical relationship. The findings suggested that learners were likely to recognize quadrilaterals by a special case of them and prototypical figures, even though they knew the formal definition in general. This led learners to have difficulty in understanding the inclusion relations of quadrilaterals.

**Keywords:*** Internal relationships between quadrilaterals, personal-formal-figural concept, pre-service mathematics teachers.*

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