In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students’ concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition–concept image as reported by Tall and Vinner (Educational Studies in Mathematics 12:151–169, 1981), a theory that is widely used in mathematics education. The occurrences during our interviews with one of the first students that we interviewed led us to identify a need to extend this theory. This manuscript suggests to add two new constructs to the theory of concept definition–concept image: missing concept images and mis-in concept images. Missing concept image defines a situation in which an example of a concept is erroneously categorized as a non-example of the concept. Mis-in concept image is the somewhat complementary case, in which a non-example of the concept is mis(takenly) in(cluded) in the set of examples of the concept and consequently this non-example is erroneously identified as an example of the concept. In this manuscript, we introduce these two constructs. We also describe two possible sources of students’ decisions regarding their ways of sorting figures into examples and non-examples of parallelograms that were detected during the interviews. To the best of our knowledge, these sources were not reported in the related literature.

在本文中，我们描述了一个案例研究，该案例旨在诊断5年级学生的平行四边形概念图像。我们为这项研究采用的理论框架是概念定义的概念图像，如Tall和Vinner所报道的（数学教育研究12：151–169，1981 ），该理论在数学教育中得到了广泛使用。在与我们采访的第一批学生之一的访谈中发生的事情使我们发现有必要扩展这一理论。该手稿建议在概念定义理论上增加两个新的概念概念图像：缺失的概念图像和误入概念的图像。缺少概念图片定义了一种情况，其中概念的示例被错误地分类为该概念的非示例。误入概念图像是一种互补的情况，其中概念的非示例误入（包含）在概念的示例集合中，因此，该非示例被错误地标识为以下示例：这个概念。在本手稿中，我们介绍了这两种构造。我们还描述了学生做出决定的两种可能来源，即他们在访谈中发现的将图形分类为平行四边形的示例和非示例的方式。据我们所知，相关文献中未报告这些来源。