For many years, researchers have believed that spatial ability is a powerful tool for understanding and solving mathematics and geometry problems (Bishop, 1980; Hodgson, 1996).  Also, NCTM (1989) stated that “spatial understandings are necessary for interpreting, understanding, and appreciating our inherently geometric world.” (p. 48). On account of the importance of spatial ability for learning mathematics and geometry, researchers investigated the factors affecting the development of spatial ability.

Sedgwick (1961) asserted that spatial ability can be a genetic trait and it can not be learned in any way. However, some researchers addressed the effect of instruction on spatial ability.  For instance, Ben- Chaim, Lappan and Houang (1988) claimed that spatial ability can be improved with appropriate activities and Bishop (1980) accepted that spatial ability is a teachable skill. In other words, it was stated that it is possible to improve spatial ability if appropriate materials are provided in mathematics classrooms (Battista, 1982; Ben-Chaim, Lappan & Houang, 1988). This idea was supported by Clements (1998) and he claimed that students can explore the characteristics, the parts and transformations by manipulatives. Also, he added that using manipulatives  provide the opportunity to look at the impact of 2D and 3D representations on the development of spatial ability.

Battista and Clements (1996) and Olkun (2003b) claimed that teaching a formula or a set of procedures for determining the number of cubes in rectangular prism is unnecessary. Since the formula directs students to memorization and they do not try to conceptualize the structure of rectangular prism. Ng (1998) agreed with Battista and Clements (1996) and Olkun (2003b) and criticized teachers in this respect. They stated that teaching concepts of area and volume with brief introduction and then giving formula is a common practice for teachers. Area formula or volume formula are meaningless to students unless the idea of area and volume have made sense for them. Since formula is meaningless, they memorized it without understanding. As a result of this, they fail to see the relationship among length, width, and height.

Lastly, Piaget, Inhelder and Szeminska (1960) claimed that another factor affecting the development of spatial ability is age. They expressed that spatial ability develops with increasing age. This is consistent with the study of Ben-Chaim et al. (1988) and Olkun (2003b). They suggested that there is an increase in performance on the items such as “How many unit cubes are in this rectangular prism?” with an increase in grade level. On the contrary, van Hiele (1986) defended that spatial ability depends on instruction more than physical maturation.

Due to the importance of age, instruction and using manipulative on developing students’ spatial ability, one of the aims of this study was to investigate whether elementary students’ problem solving performance related to volume of three dimensional figures differs regarding their grade level. Moreover, formula and manipulative usage were explored in terms of grade level.  

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