Making sense of qualitative geometry: The case of Amanda

Mathematics teacher candidates’ approaches to using topology in geometry

“…In this study, the teacher candidates' geometric thinking abilities and opinions about their undergraduate courses were examined in order to determine what they thought of their topology course. Although children acquire an instinctive grasp of topology before they begin formal education, the teaching process unfortunately eliminates the effectiveness of this system of thought over time (Greenstein, 2014). Topology is perceived as a high-level mathematics subject that most students do encounter until they begin university life.…”

“…The aim of this study was to examine the thoughts and opinions of the teacher candidates regarding topology and topological thought in detail. It is stated that the topology will enable to see the relationships between different geometries and to provide a different view of geometric relations (Delice & Karaaslan, 2016;Greenstein, 2014). To accomplish this aim, the following research questions were answered:…”

“…The more detailed framework of geometric thought that is expected to emerge from the research performed will contribute significantly to how students are taught to think about geometry. More importantly, this framework will help teachers guide their students in connecting with other ways of thinking, allowing them to conceptualize geometry-related concepts in more detail and in various ways (Greenstein, 2014).…”

“…In this sense, a non-square, rectangle, or even a triangle or a square can be seen as an image that can be converted. Thus, the square, rectangular, and triangle appear to have the same rather than distinct qualities (Greenstein, 2014). According to Piaget, children can only recognize and distinguish between Euclidean forms such as triangles, rectangles, and squares at the second stage of learning (Piaget & Inhelder, 1967).…”

Bringing van Hiele and Piaget Together: A Case for Topology in Early Mathematics Learning

“…Lastly, I would like to convince the reader that there is a need to do research to see the effects of teaching topological concepts to young children. While researchers such as Piaget and Inhelder have done studies that suggest that children understand topological concepts, I have not heard of a complete early education curriculum which explicitly teaches topological concepts, though also see [5] for the case study of a seven-year-old girl who participated in an eighteen-week teaching experiment aiming to model the development of her intuitive and informal topological ideas. Educators who work with young children often observe misunderstandings of certain concepts.…”