# A Structural Equation Model for Factors Affecting Eighth Graders' Geometry Achievement *

## Article excerpt

Geometry is an important branch of mathematics that explores the characteristics and relationships of angles, lines, and shapes (Üstün & Ubuz, 2004). Students learn geometric shapes and structures, their basic properties, and their relationship to each other in geometry lessons, which is very important for school mathematics (National Council of Teachers of Mathematics [NCTM], 2000). This course also develops their decisionmaking and judgment skills. Moreover, students who master the concepts of geometry and possess strong spatial awareness are ready to learn advanced mathematical subjects as well as subjects on numbers and measurement (Cantürk-Günhan, 2006). Though geometry as a discipline has rather great importance, the research reveals students' geometry achievement to be generally low and the students unable to sufficiently succeed in geometry-related topics (Battista & Clements, 1988; Carroll, 1998).

Thirty-eight countries participated in the 1999 Trends in International Mathematics and Science Study (TIMSS); Turkey came in 34th place on the geometry test, which had 21 questions (Toluk-Uçar, 2005). While Turkey's mean score for geometry was 418 in 1999, it was 411 in 2007 (Şişman, Acat, Aypay, & Karadağ, 2011). Additionally, 42 countries participated in the 2011 TIMSS, in which Turkey came in 21st place this time on the geometry test. Eighth-grade students correctly answered 39% of the questions on the geometry test (Büyüköztürk, Çakan, Tan, & Atar, 2014). While Turkey's mean score for geometry was 411 in the 2007 TIMSS, it increased to 454 in the 2011 TIMSS and 463 in the 2015 TIMSS (Polat, Gönen, Parlak, Yıldırım, & Özgürlük, 2016). This increase could be a result of the new education programs put into effect in 2005 and 2013. However, given that scores of 475 and lower are at the bottom level of math competency, achievement is not being seen at its desired level. When examining the statistics among all the sub-disciplines of mathematics, Turkish students are found to experience the most difficulty in geometry according to the 2007, 2011 and 2015 TIMSS results (Büyüköztürk et al., 2014; Polat et al., 2016; Şişman et al., 2011). The results from the 2003, 2006, 2009, 2012 Programme for International Student Assessment (PISA) resemble the TIMSS results (Anıl, ÖzerÖzkan, & Demir, 2015; PISA, 2003, 2006, 2009). Examining the reasons for this lack of success reveals geometry-related topics being placed at the end of the program, insufficient importance being attached to them, not enough time being given to the program for teachers to cover all these topics, and teachers encouraging rote learning when teaching geometry (Olkun & Aydoğdu, 2003).

One of the reasons for this failure in teaching geometry appears as the negative affective factors students have toward learning geometry (Yenilmez & Uygan, 2010). In consideration of the reasons for the lack of success in geometry instruction, more importance was attached to geometry in the 2005 Middle School 6th-8th Grade Mathematics Education Program, more room was spared for visual units and activities in the program, and many new subjects such as fractals, transformation geometry, and spatial visualization were included in the new program (Ministry of National Education of Turkey [MoNE], 2005). In the Middle School 5th-8th Grade Mathematics Education Program (revised in 2013), Geometry and measurement education were incorporated into the mathematics curriculum for all grades. The mathematics education program includes geometric topics such as basic geometric concepts and shapes, lines and angles, polygons, circles, congruence and similarity, right triangles and the Pythagorean Theorem, different views of geometric objects, transformation geometry, and geometric objects (MoNE, 2013).

Success in geometry has been the subject of much research in recent years. Particularly remarkable is the amount of research focusing on the effect of learning environments using different designs (Altın, 2012; Apaçık, 2009; Arıcı, 2012; Başaran-Şimşek, 2012; Bayram, 2004; Boakes, 2009; Cantürk-Günhan, 2006; Duatepe, 2004; Kaya, 2013; Marangoz, 2010; Öz, 2012; Özdemir, 2006; Sarı, 2010; Terzi, 2010; Yahşi-Sarı, 2012; Zenginobuz, 2005). …

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