ERG SES D 04, Mathematics and Education
Spatial ability can be defined as the ability to perceive, imagine, arrange and re-construct objects or forms that are present in the space (Carroll, 1993). Spatial ability helps individuals recognize the objects surrounding them, make sense of the positions and dimensions of the objects and notice any changes in these positions and dimensions; thus, spatial ability facilitates individuals’ daily lives and is critical for achieving success in many areas (Smith, 1998; Miller, 1992, as cited in Takahashi, 2011).
It was pointed in previous studies that spatial ability is a significant factor in mathematics education (Battista, 1990; Clements&Battista, 1992). In the Principles and Standards of School Mathematics (2000) determined by The National Council of Teachers of Mathematics (NCTM) and in the Middle School Mathematics Curriculum (5th-8th Grades) designed by the Turkish Ministry of National Education (MoNE) (2013), there is an emphasis on spatial ability. It is underlined that students should be able to achieve the following learning outcomes which are associated with spatial ability such as making rotation and translation, drawing the visualization of a 3D object from different viewpoints. Furthermore, NCTM (2003) indicates that mathematics teachers should be able to achieve these learning outcomes.
Spatial ability has many sub-ability, one of them is spatial visualization ability (McGee, 1979; Tartre, 1990; Maier, 1996; Clements, 1998). In the literature, Maier (1996, p.: 64) defines spatial visualization as ‘the ability to imagine the visualization of a shape or the replacement among different parts of an object’. Moreover, it was stated that spatial visualization ability is significant and necessary to develop the ability (Clements, 1998; Ben-Chaim, Lappan&Houang, 1985; Smith, 1998). In this respect, we focused on the spatial visualization ability of pre-service middle school mathematics teachers who arrange learning environments for their students. In more detail the spatial visualization ability will be investigated via mental games.
Mental games can be used as an effective tool for improving intellectual capabilities and skills of students (MoNE, 2013). The Mental Games Course has been offered in middle schools across Turkey since 2012-2013 education year as an elective course. Furthermore, the Mental Games Course can also be taken as an elective course in undergraduate level. Sudoku, Skyscrapers Game, Memory Games, Puzzles, Go and Intelligence Questions are some examples of games which are included in Mental Games Course.
The study will be carried out based on the Skyscrapers Game among mental games; this game can be played with tables of 3x3, 4x4,…,nxn. The numbers in the game played with a table of ‘nxn’ are 1,2,3,…,n. These numbers should be used only once in each row and column as in Sudoku. In the game, there are numbers inside and outside the table. The numbers written outside the table show how many buildings will be seen from that viewpoint. The numbers written inside of a cell show the number of floors that building has. For example, in 3x3 Skyscrapers Game: the numbers 1, 2 and 3 are used. In the case that 2 is written outside of the table, 2 buildings must be seen from that viewpoint. Similarly, if 2 is written inside of a cell, the building on that cell has 2 floors. Skyscrapers Game is originally a paper-and-pencil game. Since in literature, it was stated that using concrete materials has positive effect on spatial visualization ability (Ben Chaim et al., 1985; Clements, 1998; Yıldız&Tüzün, 2011; Yurt&Sünbül, 2011), participants will play the game with unit cubes.
Considering these points, the purpose of the present study is to investigate whether playing Skyscrapers Game with unit cubes have an effect on the spatial visualization ability of pre-service middle school mathematics teachers.
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