Missing and Mis-in Concept Images of Parallelograms: the Case of Tal

Pre-Service Teachers’ Understanding of Continuity

“…These ideas are as follows: Concept image, formal concept definition, personal concept definition and conflict factors. This framework widely used in the research of mathematics education (Tirosh & Tsamir, 2021).…”

Fostering students’ definitions and images in parallelism and perpendicularity: A paper folding activity

“…Mansfield and Happs (1992) expressed that the topic of parallel lines has such a significant role in geometry since it forms a basis for the classification of polygons, an understanding of angle relationships, and geometric proofs. The findings of the latest study by Tirosh and Tsamir (2022) exemplify the role of parallel lines. Researchers observed that insufficient interpretation of parallel lines affected a student's decisions regarding parallelograms; she erroneously identified a non-example of parallelograms in the set of parallelograms.…”

“…In a recent study, Tirosh and Tsamir (2022) extended this model by adding two more constructs, missing and mis-in concept images, to describe the students' concept images. The first construct describes a situation, where an example of a concept is regarded as a non-example.…”

“…For instance, if a student identifies a trapezoid as a parallelogram, a non-example is mis(takenly) in(cluded) in the set of parallelograms. Besides, if this student states that a rhombus is not a parallelogram, then s/he has a missing concept image (Tirosh & Tsamir, 2022). The researchers suggested analysing missing and mis-in concept image situations to place and study issues about them.…”

“…Prototype examples have strong visual characteristics because of some non-critical attributes (Hershkowitz, 1989). For the parallelism and perpendicularity concepts, two horizontal or vertical parallel lines/line segments or shapes may be given as the prototype examples of parallel/perpendicular lines/line segments (Tirosh & Tsamir, 2022;Ulusoy, 2016). Although they may help initial concept formation due to their easy recognition, they may restrict the students' concept images (Hershkowitz, 1989;Wilson, 1990).…”