![]() The findings obtained from the semi-structured clinical interviews with the selected students were analyzed in depth with content analysis. 12 students were selected with maximum diversity sampling. 4 open-ended questions developed in order to determine the concept images of teacher candidates for the concept were applied. The layout of the study, the plan as a case study model from qualitative research methods. ![]() The study was carried out with a third-year undergraduate student enrolled in the Department of Elementary Mathematics Teaching at a state university in Izmir in the 2019-2020 academic year. The aim of this research is to determine the concept images of pre-service mathematics teachers towards the concept of plane in three-dimensional Euclidean space. Ayrıca günlük yaşam deneyimleriyle oluşmuş kavram imajlarının daha kalıcı olduğu sonucuna varılmıştır. Yapılan veri analizi sonucuna göre öğretmen adaylarının düzlem kavramını genellikle Ax + By + Cz + D = 0 düzlem kapalı formülü çerçevesinde zihinlerinde yer edindirdikleri görülmüştür. Öğretmen adaylarının düzlem kavramına yönelik kavram imajları belirlenirken Tall ve Vinner'ın (1981) kavram tanımı-kavram imajı yapısı ışığında hareket edilmiştir. Seçilen öğrencilerle yapılan yarı yapılandırılmış klinik görüşmelerden elde edilen bulgular içerik analiziyle derinlemesine incelenmiştir. Maksimum çeşitlilik örneklemesi ile 12 öğrenci seçilmiş. Öğretmen adaylarının düzlem kavramına yönelik kavram imajlarının tespiti için araştırmacının geliştirdiği 4 adet açık uçlu soru uygulanmıştır. Çalışmanın deseni, nitel araştırma yöntemlerinden durum çalışması modeli olarak belirlenmiştir. Çalışma 2019-2020 eğitim-öğretim yılında İzmir ilinin bir devlet üniversitesinin İlköğretim Matematik Öğretmenliği Programında üçüncü sınıfa kayıtlı 80 lisans öğrencisi ile gerçekleştirilmiştir. After shifting from two to three dimensions, students symbolized all possible linear combinations with a parametric vector equation and reasoned about how this could represent particular points on the corresponding lines or planes.īu araştırmanın amacı, ilköğretim matematik öğretmen adaylarının üç boyutlu Öklid uzayında düzlem kavramına yönelik kavram imajlarını tespit etmektir. We found students' use of sliders supported their reasoning about individual linear combinations the trace function and slider animation supported their intuition for all possible linear combinations of vectors. We analyzed these with a lens of mathematization, with a particular focus on tool use. Data sources come from six individual task-based interviews with two linear algebra students. ![]() ![]() Considering tools and functions of a digital environment (specifically of GeoGebra) with design heuristics of Realistic Mathematics Education, we introduce four tasks (in R 2 and R 3) and results of pilot studies. In this paper, we focus on students' symbolizing activity and mathematization relating to linear combination and span in the context of a task sequence designed with digital tools. We conclude with a discussion of this and how it may be leveraged to inform teaching in a productive, student-centered manner. Furthermore, we found that all students interviewed expressed, to some extent, the technically inaccurate “nested subspace” conception that Rįor k < n. We also present results regarding the coordination between students’ concept image and how they interpret the formal definition, situations in which students recognized a need for the formal definition, and qualities of subspace that students noted were consequences of the formal definition. Through grounded analysis, we identified recurring concept imagery that students provided for subspace, namely, geometric object, part of whole, and algebraic object. We used the analytical tools of concept image and concept definition of Tall and Vinner (Educational Studies in Mathematics, 12(2):151–169, 1981) in order to highlight this distinction in student responses. This is consistent with literature in other mathematical content domains that indicates that a learner’s primary understanding of a concept is not necessarily informed by that concept’s formal definition. In interviews conducted with eight undergraduates, we found students’ initial descriptions of subspace often varied substantially from the language of the concept’s formal definition, which is very algebraic in nature. This paper reports on a study investigating students’ ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace.
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