Görsel Teoremler Üzerine Matematik Öğretmenleriyle Nitel Bir Çalışma

Yıl 2018, Cilt: 7 Sayı: 2, 56 - 74, 01.07.2018

Yaşar Akkan Pınar Akkan Mesut Öztürk Ümit Demir

Öz

Farklı
disiplinlerde etkili olmasına rağmen özellikle geometri alanında daha etkili
olduğu düşünülen ve zihinsel yeteneğin bir parçası olarak kabul edilen görsel
uzamsal akıl yürütme becerisi birçok araştırmacının üzerinde durduğu bir
konudur. Bu bağlamda geleceğin bilim insanlarının öğretim için gerekli görsel
akıl yürütme becerilerini sağlayabilmede ve geliştirebilmede matematik
öğretmenlerine sorumluluk düşmektedir. Bu
çalışma ile matematik öğretmenlerinin görsel teoremleri ispatlama bağlamında,
görsel akıl yürütme becerileri ile geometrik düşünme düzeyleri ve uzamsal
görselleştirme becerileri arasındaki ilişkiyi nitel olarak özel durum
yöntemiyle inceleme amaçlanmıştır. Çalışma grubunu on lise matematik
öğretmeni oluşturmaktadır. Çalışmadan elde edilen veriler iki farklı görüşme
sürecinde elde edilmiştir. İlk görüşmede öğretmenlerden “van Hiele Geometri
Düzeyleri Testini ve Uzamsal Görselleştirme Beceri Testini” doldurmaları
istenmiş, ikinci görüşmede ise öğretmenlerle üç farklı görsel teorem üzerinden
klinik mülakatlar yürütülmüştür. Bu iki süreçten elde edilen veriler betimsel
olarak analiz edilmiştir. Sonuç olarak,  matematik öğretmenlerinin görsel akıl yürütme
becerileri ile geometrik düşünme düzeyleri ve uzamsal görselleştirme becerileri
arasında bir ilişki olduğu,  daha yüksek
geometrik düşünme düzeyine ulaşan öğretmenlerin, görsel teoremleri tanımada,
onlar üzerine akıl yürütmede ve ispatlamada daha yetenekli olduğu tespit
edilmiştir.

Anahtar Kelimeler

geometri, görsel akıl yürütme, matematik öğretmenleri

A Qualitative Study with Mathematics Teachers on Visual Theorems

Öz

The geometry that develops the aesthetic sensation of
individuals and event that allows them to think in many ways, at the same time
helping individuals to better understand the world they live in and to relate
mathematical concepts and events in life. Despite being effective in different
disciplines, visual (diagrammatic) reasoning skill that is thought to be more
effective, especially in the field of geometry, and which is considered to be
part of mental ability, it is a topic that many researchers have pointed out. Because visual reasoning is an important skill that
affects students especially to prove or solve geometric problems. Many
researchers have suggested that an individual working at a higher level of
geometric thinking should have stronger visual reasoning skills and that visual
reasoning can also be improved by geometric teaching. However, despite the considerable importance given to
geometry in recent years, it has been shown in many studies that the level of
comprehension of the geometry of students is not expected and desired. Such results indicate that the objectives of the
curriculum are not reached, such as training individuals with geometric and
spatial thinking skills. In this sense, mathematics teachers need to possess
the visual reasoning skills necessary for teaching in the training of the
individuals (mathematicians, scientists, engineers, doctors, graphic designers,
etc.) who will form the human power of the future. The aim of this study is to
qualitatively examine the relationships between math teachers' visual reasoning
skills and their level of geometric thinking and spatial visualization skills
in the context of proving visual theorems.

This research is a descriptive study conducted using the case study
method. The study group of
the study is composed of ten mathematics teachers with a postgraduate degree in
a university located in the Eastern Black Sea Region. In the selection of the study group, the maximum
diversity method was chosen from the purposive sampling methods. As a result of two different interviews with the
teachers, the data of the study were obtained. During the first interview, it was asked to answer
open-ended questions prepared by the researchers with the help of literature to
determine their geometric backgrounds. Then the teachers were asked to answer van
Hiele Geometry Thinking Level Test and Spatial Visualization Skill Test. The data obtained from these two different tests were
presented using descriptive statistics.  In this context, in order to determine the
teachers' level of geometric thinking, a criterion was used in which teachers
responded "at least 4 of 5 questions correctly" to each level. In the spatial visualization skill test, each teacher
was given a test score of 36 points by giving (1) points to the questions that
the teachers answered correctly, (0) points that they answered incorrectly or
left empty. In the
second interview, in order to reveal the problem solving or proving behaviours,
visual reasoning skills, geometrical information about visual expressions and
validation situations, clinical interviews were conducted on four different
visual theorems. Data collected with clinical interviews were analysed using descriptive
analysis technique.

In general, teachers with more geometric background
scores have been found to have higher geometric thinking levels and better
spatial visualization skills. In particular, teachers who are graduates of the
Faculty of Education and who work as permanent staff were found to have
achieved a level 4 in the van Hiele geometry thinking level test and higher
scores than the spatial visualization skill test. In addition, teachers who attain a higher level of
geometric thinking and have better spatial visualization skill scores, have
been found to be more capable in recognizing visual theorems, in reasoning
about them, and in verifying relationships. Another result is that there is a relationship between
the visual reasoning that teachers have conducted on visual theorems and the
way of thinking or behaviour attributed to van Hiele levels. However, it was
found that most of the teachers who participated in the study had lack of
knowledge about geometry and geometrical background, geometric thinking level
test and spatial visualization skill test scores. In particular, it has been determined that teachers
who have graduated from two faculties other than the Faculty of Education have
a lack of information to be gained in geometry and these deficits affect the
process of proving their visual theorems. The lack of information in the teachers has a negative
effect on the learning of the students. Because there is a positive
relationship between teacher knowledge and student achievement. In short,
teachers have to know and understand the geometry they teach in order to make
successful teaching. This work underscores some of the deficiencies in teacher
education in the context of geometry and the need to re-examine the academic
needs and curriculum changes needed to address these deficiencies.

Anahtar Kelimeler

geometry, visual reasoning, mathematics teachers

Kaynakça

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