The ability of second graders to identify solids in different positions and to justify their answer

Abstract

From a young age children feel the need to identify two-dimensional geometric figures (shapes) and three-dimensional geometric figures (solids). The National Council of Teachers of Mathematics indicates the importance of being able to identify and name various geometric figures by kindergarten age. One of the objectives of this study was to learn the ability of second graders to identify examples and non-examples of three generally known solids: cylinder, cone and pyramid, and to justify their identification based on the attributes (critical and non-critical) of those solids. Another objective was to find out whether changing the position of the solids would result in those children maintaining their decisions regarding the name or changing their identification of the solids, giving arguments accordingly. Findings of this study illustrate that children can identify and characterise solids presented to them in a typical position. However, they find it difficult to correctly identify the same solids in another position. An interesting finding was that most of the arguments given to justify their identification were based on the specific attributes of the solid rather than on the perception of the solids in general. Findings of the present study suggest that it is highly important for learners to be acquainted with a variety of both non-examples and examples of solids. Moreover, it is recommended that solids are presented to learners not only in the typical position, in order to improve their ability to identify them and understand that the name of the figure does not change when its position changes

8. Sınıf Öğrencilerinin Cisimleri Görsel Tanıma Ve Tanımlamaları: Cisim İmgeleri

“…Prototipleri oluşturan bir veya birçok örnek olabilir. Bu nedenle kavramı örneklendiren modellerin sunumu farkında olunması gereken bir konudur (Sarfaty ve Patkin, 2013). Cunningham ve Roberts (2010) tarafından yapılan çalışmada öğretmen adaylarının çokgenlerin köşegenlerini belirlerken prototipler dışındaki örneklerde başarısız oldukları saptanmıştır.…”

Middle school mathematics teachers pedagogical content knowledge regarding teaching strategies on quadrilaterals

“…Informal definitions are used in addition to formal definitions and that in general a personal definition is given by listing the various properties of quadrilaterals. When studies on understanding quadrilaterals and the concept image are examined, it has been observed that individuals define geometric concepts by way of an image they form of the concept and that they use personal definitions instead of formal ones (Sarfaty and Patkin, 2013;Turnuklu et al, 2013;Hershkowitz, 1989;Burger and Shaughnessy, 1986). To this end, it can be stated that the definitions used by mathematics teachers who participated in this study are shaped pursuant to their perceptions.…”

Middle School Mathematics Teachers’ Pedagogical Content Knowledge Regarding Student Knowledge about Quadrilaterals

“…In many other studies carried out on comprehending and defining quadrilaterals, it was also noted that students have difficulties in defining quadrilaterals and use arbitrary definitions instead of formal definitions in their attempts to express the image of concepts and geometrical concepts (Akkas and Türnüklü, 2014;Sarfaty and Patkin, 2013;Türnüklü, Alaylı and Akkas, 2013;Hershkowitz, 1989;Burger and Shaughnessy, 1986). As far as teachers' responses reveal in this study, it can be suggested that students make definitions within the framework of their individual perceptions, thus they make mistakes in relation with definitions of quadrilaterals.…”