Examining the Relationship between Geometric Habits of Mind and the Mathematics Achievement: The case of Mathematics Preservice Teachers

Abstract

Öz: Geometrik düşünme alışkanlıklarının matematik dersleri üzerindeki etkisini ortaya çıkarmak, kavramsal boyutta öğretimin nasıl gerçekleşeceğine etkileyebilir. Bu kapsamda çalışmanın amacı matematik öğretmeni adaylarının geometrik düşünme alışkanlıkları ile matematik başarıları arasındaki ilişkiyi belirlemektir. Bu amaç doğrultusunda çalışma, bir devlet üniversitesinde matematik öğretmenliği dördüncü sınıfta öğrenim gören 30 öğretmen adayı ile ilişkisel desen yöntemi kullanılarak yürütülmüştür. Çalışmada öğretmen adaylarının geometrik düşünme alışkanlıkları başarı testinden aldığı puanlar ile dördüncü sınıfa kadar olan matematik derslerinden aldığı puanlar arasındaki ilişki analiz edilmiştir. Çalışma sonucunda öğretmen adaylarının Geometri, Analitik Geometri 2 ve Matematiksel Yazılımlar dersleri ile geometrik düşünme alışkanlıkları puanları arasında yüksek düzeyde, pozitif ve anlamlı bir ilişki bulunmuştur. Bu durum öğretmen adaylarının karşılaştığı problemlerin üstesinden gelirken aslında geometrik düşünme alışkanlıklarını da kullandığı anlamına gelmektedir.

Can Geometry Achievement and Geometric Habits of Mind Be Improved Online? Reflections From a Computer-Aided Intervention

“…To evaluate the PTs’ progress in geometry and their habits of mind, a GHoM test developed by Bülbül (2016) was implemented before and after the intervention. In addition, at the end of the term, when the treatment ended, the PTs were asked for their views about the implementation process.…”

“…If a PT drew and explained the new shape, he or she was also considered to apply the habit of exploration and reflection , because an additional drawing was made. Validity and reliability studies of the test, as well as additional test items, can be found in Bülbül (2016).…”

“…First, supporting the development of individuals’ ability to solve problems is among the principles and standards for school mathematics (National Council of Teachers of Mathematics, 2000). Second, certain fundamental skills are necessary to the main goals of geometry teaching such as reasoning and proofing, associating, communication, critical thinking, and creative thinking; a large proportion of these skills are addressed in the problem-solving process (Bülbül, 2016). Finally, this study was particularly focused on the prospective teachers’ geometric habits of mind (GHoM); these habits are defined as intellectual problem-solving skills (Yavuzsoy-Köse & Tanışlı, 2014).…”

“…(2007) focused on elementary level students and was limited to activities carried out in a pencil–paper environment. Thus, in order to account for higher level cognitive processes, as well as for teaching geometry in a computer-aided environment, an adaptation study was carried out by Bülbül (2016) in consideration of current research (see Figure 1). For example, Driscoll et al.…”

“…defined basic indicators such as comparison of two geometric shapes given for the reasoning with relationship habit and classification of geometric shapes in the reasoning with relationship habit. In the revised framework (Bülbül, 2016), in addition to the basic indicators determined by Driscoll et al., high-level indicators—such as similarities in triangles and making connections between the areas of geometric shapes, their edge lengths, and their perimeter lengths—are included in the same habit. Going beyond the emphasis of Driscoll et al.…”