Research questions:

1.      What is the effect of peer instruction method on the 8^th grade students’ mathematics achievement in transformation geometry in crowded classrooms (more than 50 students)?

2.      What is the effect of peer instruction method on the 8^th grade students’ mathematics attitude in transformation geometry in crowded classrooms (more than 50 students)?

The study of transformation geometry consists of the motions such as translation, reflection and rotation (Karakuş, 2008). According to Klein (1870), the transformational geometry is the basic subject of learning geometry (as cited in Junius, 2002).

Harper (2002) asserted that transformation geometry should take place in K-12 mathematics curriculum. Especially for students between the 9^th and 12^th grades transformations should be a significant tool to solve geometric and non-geometric problems (Harper, 2002). In addition to these, according to Gürbüz (2008), students discover the relationship among the geometric shapes by constructing, drawing, measuring, comparing, changing the shapes and classifying them and they develop spatial intuition.

Beside these, there are several research studies on transformational geometry teaching techniques which are convenient for the class structure. Boulter (1992) said that in order to provide conceptual understanding of students in transformational geometry topic, instructors must create an environment where the motions can be simulated and alternative teaching methods should be used. However, some teachers think that this will require too much work, time and preparation to afford (Niemi, 2002). At this point peer instruction method may be an alternative way for teachers.

The definition of peer instruction varies in the research, but the basis of all the definitions is the same- children help children cooperatively in a classroom in order to reveal a common product (Lindboe, 1998). For centuries educators have been using peer teaching in order to disseminate information to the large number of students by breaking them into small groups (Lindboe, 1998). The advantage of the small group is that it gives opportunity of being involved to every student (Hooker, 2010). In Turkey, in some public schools classrooms are too crowded and peer instruction method is thought to be an effective teaching method. In the literature, peer instruction method has been studied in different areas such as science, and laboratory instruction and population education. However, there are very limited studies conducted related to this method.

This research administered in Turkey but it is also important issue in many different countries’ curriculum. For instance, Webb and Mastergeorge (2003) claimed that in smaller groups students may help each other and learn through collaboration. Further, understanding one another’s mathematical ideas is provided by mathematical communication in discourse practices like reasoning, argumentation, conjecture, and proof (Lerman, 2000). Moreover, according to Johnson and Johnson (1999) cooperative work with peers, have positive effects on psychological health, self-confidence and social proficiency. One reason of this could be the collaboration offers a free area without fear of failure or criticism where the students put out their abilities (Hooker, 2010). Eventually, different methods should take place since teaching and learning mathematics is a hot issue throughout the world. Therefore, it is worthwhile to study.

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