ERG SES B 03, Parallel Session B 03
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.
Battista, M. T. (1982). The importance of spatial visualization and cognitive development for geometry learning in preservice elementary teachers. Journal for Research in Mathematics Education, 13, 332–340. Battista, M. T., & Clements, D. H. (1996). Students’ understanding of three- dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27 (3), 258- 292. Ben-Chaim, D., Lappan, G., & Houang, R. T. (1988). The effect of instruction on spatial visualization skills of middle school boys and girls. American Educational Research Journal, 25(1), 51-71. Bishop, A. J. (1980). Spatial abilities and mathematics education - a review. Educational Studies in Mathematics, 11, 257-269. Clements, D. H. (1998). Geometric and spatial thinking in young children. (Report No. PS027722). Arlington: National science foundation. (ERIC Document Reproduction Service No. ED436232). Fennema, E., & Sherman, J. (1977). Sex related differences in mathematics achievement, spatial visualization and affective factors. American Educational Journal, 14, 51–71. Hodgson, T. (1996). Students’ Ability to Visualize Set Expressions: An Initial Investigation. Educational Studies in Mathematics, 30, 159- 178. National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Ng, G. L. (1998). Exploring children’s geometrical thinking. Unpublished doctoral dissertation, University of Oklahoma, Norman. (UMI No: 9828779) Olkun, S. (2003b). Making connections: Improving spatial abilities with engineering drawing activities. International Journal of Mathematics Teaching and Learning, 1-10. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. (E. Lunzer, Trans.) New York: W. W. Norton. Sedgwick, L. K. (1961). The Effect of Spatial Perception of lnstruction in Descriptive Geometry. (Unpublished master’s thesis). Southern Illinois University. Van Hiele, P. M. (1986). Structure and insight. New York: Academic Press.
- Search for keywords and phrases in "Text Search"
- Restrict in which part of the abstracts to search in "Where to search"
- Search for authors and in the respective field.
- For planning your conference attendance you may want to use the conference app, which will be issued some weeks before the conference
- If you are a session chair, best look up your chairing duties in the conference system (Conftool) or the app.