Computers & Education 55 (2010) 1220–1233
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Effects of gender differences and spatial abilities within a digital pentominoes game Jie Chi Yang a, *, Sherry Y. Chen a, b a b
Graduate Institute of Network Learning Technology, National Central University, No. 300, Jungda Road, Jhongli, Taiwan Department of Information Systems and Computing, Brunel University, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 November 2009 Received in revised form 3 May 2010 Accepted 16 May 2010
Spatial ability is a critical skill in geometric learning. Several studies investigate how to use digital games to improve spatial abilities. However, not every learner favors this kind of support. To this end, there is a need to examine how human factors affect learners’ reactions to the use of a digital game to support geometric learning. In this vein, this paper addresses this issue by developing a digital pentominoes game and examining the effects of two essential human factors, especially gender differences and spatial abilities, on students’ performance. The results demonstrate that students’ spatial abilities were significantly improved after they took the digital pentominoes game. The results also demonstrate that the digital game can reasonably reduce the differences between boys and girls. Moreover, the major gender differences lie within mental rotation among the three types of spatial ability and also mainly exist in the low spatial ability group. Finally, the findings are applied to develop a framework that can be used to enhance the understanding of gender differences and spatial abilities within the digital pentominoes game. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Digital game-based learning Gender differences Geometric learning Human factors Pentominoes Spatial ability
1. Introduction Geometry, which is one of the longest-established branches of mathematics, is widely applied in various applications, such as computer aided design (CAD), geometric modeling, robotics, medical imaging, computer animation and visual presentations (Whitely, 1999). Further areas where geometric problems arise are in computer graphics, architecture, chemistry, material physics, biology, Geographic Information Systems (GIS), and most fields of engineering (Jones, 2000). Due to such a widespread use, geometric learning is becoming important in current research. Nevertheless, geometry looks like mathematics, which may be difficult to most of people (Andersson, 2008). Therefore, it is necessary to provide an effective way to learn geometry. To this end, a lot of efforts have been put to help students learn geometry, such as the use of concrete manipulatives (Clements, 1999; Sowell, 1989; Uttal, Scudder, & DeLoache, 1997) as well as computer environment (Chan, Tsai, & Huang, 2006; Chang, Sung, & Lin, 2007; Marrades & Gutierrez, 2000; Ubuz, Ustun, & Erbas, 2009). In addition to the aforementioned approaches, pentomino is another helpful way to improve students’ geometric learning. Pentomino is a kind of polyomino, which is a geometric shape formed by joining five congruent squares connected orthogonally along their edges (Hirschhorn, 2001). In general, a standard pentomino puzzle is designed to tile a rectangular box (game board) using 12 different pieces. More specifically, learners need to select, rotate, translate, flip, mirror and land these pieces onto the game board as well as remove pieces from the board for completing a pentomino puzzle (Corradini, 2008). Manipulating these pieces of pentominoes is an enjoyable exercise to learners and can help them improve geometric learning, such as spatial reasoning, problem solving and visual skills (Cowan, 1977; Jamski, 2003; Tracy & Eckart, 1990; Whitin, 2006). Thus, manipulating pentominoes could be a useful way for geometric learning and is often used to illustrate geometric concepts (Onslow, 1990). On the other hand, pentomino is also generally categorized as a puzzle game or board game (Corradini, 2008; Whitin, 2006) and is proved to be a popular mathematical game (Orman, 1998). Recent research attempted to incorporate computer-based technologies into games (Shaffer, 2006) and indicated that the use of computer-based games is another very popular method to improve geometric learning
* Corresponding author. E-mail addresses:
[email protected] (J.C. Yang),
[email protected] (S.Y. Chen). 0360-1315/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compedu.2010.05.019
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(Ketamo, 2003). Playing computer-based games requires spatial processes, such as rotation of geometric shapes and can be considered as a method for improving geometric learning (De Lisi & Wolford, 2002; Okagaki & Frensch, 1994). As showed in a study by Olkun, Altun, and Smith (2005), students’ geometry scores were improved with a computer-based Tangram puzzles. Other studies, such as Olkun (2003a) and Smith, Olkun, and Middleton (2003), also obtained similar findings, which showed that computer-based puzzles can improve students’ geometric learning. Therefore, developing a digital pentominoes that integrates computer-based technologies into pentominoes may be a useful way to enhance learners’ geometric learning. However, the successful usage of instructional technology depends on the technology itself and the learners’ individual characteristics (Chou & Wang, 2000). Thus, human factors play an important role in student learning (Yang & Chen, in press). Despite of the fact that the use of computer-based games or pentominoes may effectively enhance learners’ geometric learning, however, it is unsure that every learner could get benefits from this type of support. Among various human factors, spatial abilities and gender differences are critical to geometric learning. The former is a potentially important cognitive skill, which involves understanding relations visually, making changes on shapes, rearranging and interpreting them (Tartre, 1990a). Such a skill is essential to geometric learning. The latter plays another influential role in geometric learning because boys and girls show different outcomes in different learning environments when they learn geometry (Casey, Erkut, Ceder, & Young, 2008; Friedman, 1995). In summary, gender differences and spatial abilities are critical to geometric learning. In this vein, the aim of this study is to examine (a) whether boys and girls will get equal benefits from a digital pentominoes game, and (b) whether high spatial ability and low spatial ability students will equally benefit from a digital pentominoes game. To reach this aim, an empirical study was conducted to investigate the effects of gender differences and spatial abilities within a digital pentominoes game. In order to obtain sufficient findings, a digital pentominoes game was specially designed for the empirical study. Thus, the originality of the paper does not only contribute to the knowledge of the influences of gender differences and spatial abilities, but also lies within the development of a digital pentominoes game. This paper is structured as follows. Section 2 describes related works on geometry learning, as well as effects of the two human factors on geometric learning which includes spatial abilities and gender differences. Section 3 describes the design and implementation of the digital pentominoes game. Subsequently, Section 4 describes the methodology design of an empirical study, which examines students’ performance of spatial abilities under the support of the digital pentominoes game. Results and discussions of the empirical study are then presented in Section 5. It subsequently moves on to Section 6, which develops a framework based on the findings of this study. Finally, conclusions are drawn in Section 7. 2. Related work 2.1. Geometric learning Geometric conceptions have been considered as a base for learning mathematics so this subject has been studied by many researchers (Hannafin, 2004; Hannafin, Truxaw, Vermillion, & Liu, 2008; Kaufmann & Schmalstieg, 2003). The importance lies within the fact that geometry is not only relating to mathematical courses, but also concerning with the development of students’ cognitive skills, such as investigation, researching, criticizing, creative thinking, illustrating what they have learnt, and self-expression (Erdogan, Akkaya, & Akkaya, 2009; Mistretta, 2000). Furthermore, geometry is necessary to our daily life and various professions (Kerr, 1979) because shapes and objects learnt from geometry are also available in our world (Goos & Spencer, 2003). Due to the importance of geometry, a number of studies attempt to improve geometric learning, e.g., Mistretta (2000). In particular, some studies have put efforts to integrate computer technologies into geometric learning due to the interactive, manageable, dynamic, flexible, replayable, and controllable nature of computer-based environments (Battista, 2002; Clements, 1999, 2000; Olkun, 2003a). For example, a study by Battista (2002) proposed that the teaching activities should be able to encourage students to absorb meaningful geometric concepts and developed a computer program to provide students with shape-making objects that can be manipulated on a screen. The results show that using interactive geometry software can foster students’ understanding and reasoning about two-dimensional shapes. Another study by Olkun (2003a) also investigated the effects of using computer-based Tangram puzzles for learning two-dimensional geometric shapes. The results show that the computer-based Tangram puzzles could effectively enhance students’ geometric learning because the computer-based Tangram puzzles are more interactive and manageable. Recently, Sedig (2008) developed a game-based learning environment to engage children with mathematical representations in an enjoyable and thoughtful fashion. The game took children from almost no knowledge of transformation geometry to some non-trivial knowledge, involving composite reflections and complex rotations. The results of the study show that, despite the explicitness and difficulty of the mathematical concepts involved, children found that learning mathematical representations with games has a lot of fun. Furthermore, children exhibited significant improvements in their understanding of transformation geometry concepts. The aforementioned studies demonstrate that computer-based games have potential to make geometric learning have more fun as well as to improve students’ understanding and reasoning to learn this subject. However, it is still unclear whether applying computer-based games to support geometric learning is suitable to every learner because each learner has different characteristics, skills and background (Calcaterra, Antonietti, & Underwood, 2005; Chen & Macredie, 2004; Ford, Miller, & Moss, 2005a, 2005b). In order to build a learnercentered environment, it is necessary to consider students’ individual differences, of which spatial abilities and gender differences are important. This is due to the fact that the former relates to geometric learning (Battista, 2002) while the latter affects how students use computer-based learning systems (Chou & Tsai, 2007; Imhof, Vollmeyer, & Beierlein, 2007), especially geometric learning (Casey et al., 2008; Friedman, 1995; Tartre, 1990b). Thus, the following two sub-sections discuss how previous studies address these two individual differences elements. 2.2. Spatial abilities Spatial ability, which is an ability to produce a mental picture via individual thinking and solving practical or theoretical problems, is also a potentially essential cognitive skill. Furthermore, it plays an important role in various aspects, including mathematical problem solving
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Table 1 Studies on gender differences in different types of spatial ability. Authors
Types of spatial ability
Results
Linn and Petersen (1985)
Spatial perception, mental rotation, spatial visualization
Kalichman (1988) Robert and Tanguay (1990) Masters and Sanders (1993)
Spatial perception Spatial perception Mental rotation
Voyer, Voyer, and Bryden (1995) Sherman (1996) Collins and Kimura (1997)
Spatial perception
There was a moderate gender difference observed, which males outperform females on spatial perception tasks. Males significantly outperformed females on mental rotation tasks. There was no significant difference between males and females in performing spatial visualization tasks. Men significantly performed better than women on spatial perception task. There was no significant gender difference on spatial perception task. The effect size of the gender difference in mental rotation ability has been found to be stable over time. The finding demonstrates that males scored significantly higher than females in mental rotation. Men outperformed than women on spatial perception tasks such as identifying horizontal lines.
Spatial visualization Mental rotation
Colom, Quiroga, and JuanMental rotation Espinosa (1999) Contreras, Colom, Shih, Alava, Spatial visualization and Santacreu (2001) Roberts and Bell (2003) Mental rotation Rilea et al. (2004) Spatial visualization Rafi, Samsudin, and Said (2008) Spatial visualization
Spatial visualization is a key variable in gender differences in mathematics and geometry. Gender differences were related to the difficulty level of the mental rotation task, but not associated with the number of dimensions. Men were faster and more accurate than women in performing the mental rotation task which contains three-dimensional objects. Males outperformed females with an overall higher dynamic spatial performance. Men performed better than women on the three-dimensional task but there were no differences between men and women on performing the two-dimensional task. Gender differences have not been observed in performance of spatial visualization. Males achieved higher spatial visualization improvement than females.
(Owens & Clements, 1998), geometrical problem solving (Healy & Hoyles, 2001) and geometric reasoning (Clements & Battista, 1992; Mistretta, 2000). Numerous studies have demonstrated that spatial ability is positively associated with success in geometry, mathematics and science courses (Battista, Wheatley, & Talsma, 1982; Casey, Nuttall, Pezaris, & Benbow, 1995; Delgado & Prieto, 2004). Spatial ability can be defined as various concepts from different points of views by different researchers. However, Linn and Petersen (1985) categorized spatial ability into three types of ability based on cognitive functions: spatial perception, mental rotation and spatial visualization. The first category, spatial perception, means the ability of determining spatial relations with respecting to the orientation of one’s own body or in the context of distracting information. Spatial perception is a critical intelligence, which greatly affects the proficiency of three dimensions, volume and space-time, as well as the training of an engineer (Mohler, 2001). A study by Garcia, Quiros, Santos, Gonzalez, and Fernanz (2005) demonstrates that involving working with the three spatial dimensions, such as geometry, can accelerate the development of students’ spatial perception. More specifically, it has been shown that students with higher capability for spatial perception achieved better results in subjects related to geometric learning. The second category of spatial ability is mental rotation, which means the ability of mentally rotating two- or three-dimensional figures rapidly and accurately in imagination without the assistance of external tools, such as keeping memorizing the correct directions while changing the directions of objects or shapes constantly. A study by Voyer et al. (2006) examined the correlation between the Mental Rotation Test and participants’ high school grades in mathematics, and the result show that participants’ mental rotation ability is significantly correlated with their grades in mathematics. This finding is in line with his previous study that shows a correlation between mental rotation tasks and grades in mathematics (Voyer, 1996). The third category of spatial ability is spatial visualization which means the ability of manipulating spatially presented information, such as image fold and movement, or changing their thinking of a two-dimensional object into three-dimensional one. Spatial visualization is the ability to manipulate complex spatial information involving configurations of shapes (Linn & Petersen, 1985), which is particularly important for individuals who are working in the field of engineering (Leopold, Gorska, & Sorby, 2001). A study by Guven and Kosa (2008) examined the effect of using dynamic geometry software on mathematics teachers’ spatial visualization skills with a spatial visualization
Table 2 Design of the digital pentominoes game. Tasks
Explanations
Standard pentomino puzzle task
To tile the rectangular box using different pieces of pentominoes
Animal pentomino puzzle task
To tile the animal figure using different pieces of pentominoes
Examples
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Fig. 1. Screenshot of the digital pentominoes game.
test. The findings of their study demonstrate that these computer supported activities contributed to the development of mathematics teachers’ spatial visualization skills. One of potential benefits of improving spatial abilities is the enhancement of academic achievement in mathematics and science (Mohler, 2001; Olkun, 2003b; Potter & van der Merwe, 2001; Robichaux, 2003). A number of previous studies show that spatial abilities can be improved through training or learning with appropriate activities (Ben-Chaim, Lappan, & Houang, 1988; Burnet & Lane, 1980; Lord, 1985), in particularly by using computer software or video games. This is due to the fact that undertaking spatial tasks needs to manipulate two- or three-dimensional geometric shapes, which can be found in many computer software or video games (Olkun, 2003b). Thus, the transformational geometry could improve spatial abilities (Clements & Battista, 1992; Smith et al., 2009). For example, Sims and Mayer (2002) show that people could improve their spatial abilities through practicing with a video game environment. A recent study by Do and Lee (2009) also reveals that a 3D computer game is a useful and interesting tool to enhance human’s spatial ability. On the other hand, the use of computer software is not always useful for the improvement of spatial abilities. For example, previous studies show that the use of a computer-based system does not necessarily help all types of students in developing their spatial abilities (Gradinscak & Lewis, 1995; Suzuki et al., 1992; Suzuki, Wakita, & Nagano, 1990). Their findings demonstrate that the less visual type of learners are helped by the computer-based system, but the visual type of learners may lose interests and fail to comprehend the essence of the subject. Therefore, there is a need to examine whether computer-based system is useful to improve spatial abilities for all of learners. 2.3. Gender differences In addition to spatial abilities, which affect geometry learning, gender differences are also an important human factor. As showed in Paraskeva, Mysirlaki, and Papagianni (2010), gender differences affected how online games were used. On the other hand, gender
Fig. 2. Screenshot of an example of the completion of a pentomino puzzle.
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Table 3 Design of the spatial ability test. Dimensions
Explanations
Examples
Spatial perception
To examine whether students can perceive or recognize the assigned piece of pentominoes.
How many piece of pentominoes, box?
Mental rotation
To examine whether students can distinguish the status of the assigned pieces of pentominoes after rotating and flipping them.
Rotate the following two pieces of pentominoes by turning right 90 degrees, and flipping it down simultaneously. What is the result?
a.
Spatial visualization
To examine whether students can find out the combination of different pieces of pentominoes in the assigned geometric shape.
, are included in the following rectangular
, b.
, c.
, d.
Find out possible combination of two pieces of pentominoes in the following geometric shape.
a.
, b.
, c.
, d.
differences are also related to spatial abilities (Richmond, 1980; Rilea, Roskos-Ewoldsen, & Boles, 2004; Tartre, 1990b). Past research has claimed that there is a significant gender difference in spatial abilities. More specifically, the findings of numerous studies demonstrate that males typically outperformed females on the tests of spatial abilities (Ferrini-Mundy, 1987; Hedges & Nowell, 1995; McGee, 1979, 1982). For example, a study by Richmond (1980) examined the spatial abilities between boys and girls and found that boys were better performing than girls in the ability of distinguishing the position changing of objects. Although most of the previous studies demonstrate that males outperform females in spatial abilities, some studies show that gender differences may not exist or females benefited more than males. For example, Cornell and Heth (1984) found that there were no gender differences in the test of searching the Jigsaw Puzzle. A study by Halat (2006) examined gender differences in the acquisition of geometric learning, and the result show that gender was not a factor in geometric learning. In addition, a recent study by Casey et al. (2008) investigated the effects of a storytelling-context for teaching geometry skills to kindergarten boys and girls, their results demonstrate that girls benefited more from the geometry-content regardless of a story context than boys. The aforementioned studies give an overall picture of the effects of gender differences on spatial abilities. Furthermore, previous research also found that gender differences are also associated with each type of spatial ability, which includes spatial perception, mental rotation and spatial visualization according to the categorization by Linn and Petersen (1985). Table 1 presents a list of those results. As shown in this table, it is still inconclusive whether gender differences affect different types of spatial ability. More specifically, the inconsistent results appeared among the studies on gender differences in the three types of spatial ability. For the spatial perception ability, the magnitude of
Filling out the Spatial Intelligence Scale & the spatial ability test (pretest)
Instruction on operation of the digital pentominoes game
Interacting with the digital pentominoes game
Filling out the spatial ability test (posttest) Fig. 3. Procedures of this study.
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Table 4 The spatial abilities between pretest and posttest. Test
N
Mean
SD
t
p
Pretest Posttest
34 34
5.471 7.897
2.617 1.999
6.968
0.000**
**p < 0.01.
gender differences varied with different studies. Some studies show that males significantly outperform females, whereas other studies show that there was no significant difference between males and females or only a moderate gender difference existed. Similarly, the inconsistent results on gender differences are also found for the spatial visualization ability. Like the results on spatial perception ability, some studies show that gender differences existed but other studies show that gender differences have not been observed. However, the majority of the studies have found a stable gender difference for the mental rotation ability, which demonstrates males significantly outperform females. The aforementioned inconsistent results indicated that gender differences are associated with different types of spatial ability. Consequently, there is a need to examine how these two human factors, of which spatial abilities and gender differences affect students’ performance of spatial abilities. To this end, this study emphasizes on whether spatial abilities and gender differences affect students’ performance by taking a computer-based system (the digital pentominoes game). 3. The digital pentominoes game 3.1. Design of the digital pentominoes game As mentioned earlier, a digital pentominoes game was designed to investigate the effects of gender differences and spatial abilities within this game. Although some digital pentominoes are available on the Internet or can be provided by private companies, the digital pentominoes game was specially designed for this study. This is due to the fact that most available digital pentominoes mainly support one particular task. In order to reduce the bias of our study, the digital pentominoes game designed for this study can provide a variety of pentominoes puzzles. Additionally, the puzzles in our digital pentominoes game are randomly displayed when students play the game so that students are not allowed to memorize the answers. In summary, the digital pentominoes game can help us objectively examine students’ spatial abilities. In this vein, two kinds of tasks are designed in the digital pentominoes game, which include a standard pentomino puzzle task and an animal pentomino puzzle task. The former uses a rectangular shape for learners to tile the shape using all pieces of pentominoes whereas the later uses several animal shapes as the game boards. More specifically, the digital pentominoes game contains two types of pentomino puzzles that represent two kinds of tasks (see Table 2). The goal of each task is to cover the assigned shape (game board) without overlaps and gaps by using different pieces of pentominoes. The two tasks include the following. Standard pentomino puzzle task. To tile a rectangular box using different pieces of pentominoes; and Animal pentomino puzzle task. To tile an animal shape, which comprises different animal shapes, including elephant, crocodile, dog, deer, bird, turtle, camel, chicken, and kangaroo, using different pieces of pentominoes. Based on the aforementioned design rationale of the pentomino puzzles in the digital pentominoes game, the three types of spatial ability mentioned earlier (spatial perception, mental rotation and spatial visualization) were adopted to investigate the effects of gender differences and spatial abilities within this game. The spatial perception is an ability to find out a shape, which is a piece of pentominoes included in the puzzle. The mental rotation is an ability to mentally rotate and flip a piece of pentominoes to be accurately fitted into the puzzle. The spatial visualization is an ability to determine possible combination of different pieces of pentominoes to be a part of the assigned geometric shape. All of the three types of spatial ability are associated with the manipulations of the pentomino puzzles, which are the key elements for examining spatial abilities in the study. More specifically, the study investigates whether students’ spatial abilities will improve through taking the digital pentominoes game. 3.2. System implementation The software tools used to develop the pentomino puzzles implemented in the digital pentominoes game include two categories. The first category includes Adobe Flex Builder and Flash ActionScript object-oriented programming language, which are used to establish the main aspects of the game. The second category includes MXML to design the layout of interface, which employs graphics components to communicate with Flash ActionScript files through transferring internal messages. Under the implementation by these tools, the digital pentominoes game can be executed under any environment that installs Flash Player 9.0 or upper versions due to its characteristic of cross platforms. In other words, the game can be executed under different web browsers with different operating systems, such as Windows, Linux or Mac OS X.
Table 5 The spatial perception ability between pretest and posttest. Test
N
Mean
SD
t
p
Pretest Posttest
34 34
2.150 2.820
1.306 0.968
3.438
0.002**
**p < 0.01.
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Table 6 The mental rotation ability between pretest and posttest. Test
N
Mean
SD
t
p
Pretest Posttest
34 34
1.529 1.956
0.969 0.956
3.361
0.002**
**p < 0.01.
The digital pentominoes game comprises three modules for handling all system functionalities. The three modules are Graphic Module, Puzzle Module and Matching Module, which are described as follows. Graphic module. This module provides functions for drawing graphic components in the game, such as background, grid lines, and shapes. The core components, pentominoes, are drawn dynamically while students operating them. Puzzle module. This module provides functions for dispatching different pentomino puzzles on the screen according to which kind of task is selected. The pentomino puzzles will be randomly displayed. The intention of using such an approach is that students are not able to memorize the answers if the puzzles are displayed in the same order. Matching module. This module provides functions for verifying whether the completion of a pentomino puzzle is identical to the correct answer or not. Fig. 1 shows a screenshot of the digital pentominoes game. The right side of the figure is the menu for selecting different kinds of tasks. The left side of the figure displays some messages, such as selected puzzle and time duration. The bottom side of the figure displays different pieces of pentominoes that can be used to complete the puzzle. The center of the figure is the area for playing the game. Learners should complete the pentomino puzzle with a few steps by selecting an appropriate piece of pentominoe, rotating or flipping it, and then dragging it from the bottom side to tile the assigned shape without overlaps and gaps. Fig. 2 shows a screenshot of an example of the completion of a pentomino puzzle. 4. Methods To reach the aim of this study described in Section 1, an empirical study was conducted with a quantitative approach. Thirty-four students participated in the empirical study, of which results were analyzed with descriptive statistics analysis a paired sample t-test and an independent sample t-test. 4.1. Participants The participants, who volunteered to take part in the study, were fifth-grade students in an elementary school. These participants were selected because the digital pentominoes game was designed based on the unit of mathematics curriculum, geometric shapes and space, for fifth-grade students. Moreover, a balanced sample between boys and girls were also taken into account in the process of selecting the participants because gender differences are an essential human factor to be addressed in this study. As a result, 18 boys and 16 girls participated in this study. Thus, the total number of participants in this study comprises of 34 students. In addition, all participants should operate the digital pentominoes game. Therefore, they are selected under the condition of having the basic computing skills to operate a digital game on the computer. 4.2. Instruments In order to examine students’ spatial abilities, two types of instruments are applied in this study. The first type, a Spatial Intelligence Scale, is used to identify students’ levels of spatial ability. The Spatial Intelligence Scale is adopted because it suits for the sample in this study for two reasons. Firstly, it contains a Chinese version scale. Secondly, it has been tested for large samples in Taiwan and gained high reliabilities (inter-rater reliability is 0.86–0.92, test–retest reliability is 0.77–0.90) (Wu, 2007). The Spatial Intelligence Scale is adopted from a Chinese version of Multiple Intelligence Developmental Assessment Scales (CMIDAS), which was originally developed by Shearer (1999), and was adapted to a Chinese version by Wu (2004, 2007). The CMIDAS is designed to assess nine kinds of intelligences. However, only the Spatial Intelligence Scale is used in this study because this study focuses on students’ spatial abilities. In total, 12 questions were included in the Spatial Intelligence Scale. It is also worth mentioning that the CMIDAS can be used for different ages of samples. More specifically, the CMIDAS have three different forms (Forms A, B and C), of which Form B is applied for our study because it is suitable to assess samples between 9 and 15 years old, i.e. the ages of the sample in this study. The second type, a spatial ability test, is applied to examine students’ performance of spatial abilities. The spatial ability test was built because the tasks in this study involve pentomino puzzles. More specifically, the questions in the spatial ability test are particularly designed based on the pentomino puzzles used in this study. As mentioned in Section 3.1, our study addresses three different types of Table 7 The spatial visualization ability between pretest and posttest. Test
N
Mean
SD
t
p
Pretest Posttest
34 34
1.790 3.120
1.175 0.977
5.398
0.000**
**p < 0.01.
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Table 8 Different levels of spatial ability in the pretest and posttest. Test
Spatial ability
N
Mean
SD
t
p
Pretest
High Low High Low
17 17 17 17
5.882 5.059 8.118 7.676
2.747 2.493 1.833 2.186
0.915
0.367
0.474
0.528
Posttest
spatial ability (spatial perception, mental rotation and spatial visualization), which would be examined in the spatial ability test. In other words, the spatial ability test includes three dimensions to identify the three types of spatial ability. These three dimensions are described as follows. Spatial perception. This dimension is designed to examine whether students can perceive or recognize the assigned piece of pentominoes. Students should correctly recognize the piece of pentominoes in a rectangular box. It contains the ability to perceive the piece of pentominoes and its neighbor shapes. Students should find out all the possible pieces of pentominoses with the same shape of assigned piece of pentominoes in different positions of the rectangular box. Mental rotation. This dimension is designed to examine whether students can distinguish the status of the assigned pieces of pentominoes after rotating and flipping them. Each question contains two pieces of pentominoes that students should rotate and flip simultaneously. The action of rotation means that the two pieces of pentominoes are simultaneously turning right or left to 90, 180, or 270 degrees within a plane surface. The action of flip means that the two pieces of pentominoes are simultaneously rotating to 180 degrees with a horizontal axis or a symmetrical axis. Both of rotation and flip actions can be thought as good means to assess students’ mental rotation abilities (Shepard & Metzler, 1971). Spatial visualization. This dimension is designed to examine whether students can visualize the combination of different pieces of pentominoes in the assigned geometric shape. Students should try to find out possible combination of two pieces of pentominoes in the answers list, and compare the results with the assigned geometric shape to check which combination is the correct answer. The spatial ability test is used to assess the spatial abilities of the aforementioned three dimensions, each of which contains four questions. In other words, 12 questions are included in the test. Table 3 presents the details of the design of the spatial ability test. 4.3. Procedure The procedure of this study consists of four steps, which is illustrated in Fig. 3. At the beginning, each participant was asked to fill out the Spatial Intelligence Scale and the spatial ability test (i.e. a pretest) with approximate 30 min. In the next step, a brief instruction on how to operate the digital pentominoes game was given within 20 min. The instruction contains how to solve pentomino puzzles by using some geometric characteristics, such as rotation, flip, and symmetry. Subsequently, all of the participants were required to interact with the digital pentominoes game with 60 min. When interacting with the digital pentominoes game, they need to complete the tasks of pentomino puzzles in the game. As mentioned in Section 3.1, the two tasks include tiling a rectangular box and tiling an animal shape. Upon the completion of the aforementioned steps, each participant was asked to fill out the spatial ability test (i.e. a posttest) with about 20 min. The questions in the posttest were identical to those in the pretest. 4.4. Data analyses The data collected from the Spatial Intelligence Scale, pretest and posttest of the spatial ability test were coded for quantitative analyses. The students’ responses given on the Spatial Intelligence Scale were coded as follows: 5 ¼ Excellent, 4 ¼ Very good, 3 ¼ Good, 2 ¼ Fairly good, and 1 ¼ Not at all. We classified the participants into two groups based on their average score gained from the Spatial Intelligence Scale. More specifically, those who gained higher scores than the average were assigned to the high spatial ability group, whereas those who gained lower scores than the average were assigned to the low spatial ability group. On the other hand, the students’ answers given on the pretest and posttest of the spatial ability test were coded based on the correctness of the question. In other words, if one question was correctly answered then the student can get one point. Since each dimension contains four questions and three dimensions were included in the spatial ability test, the highest score in one dimension was four points, and the total score for the whole test was 12 points. The pretest and posttest of the spatial ability test are analyzed with descriptive statistics, e.g., mean and standard deviation. In addition to descriptive statistics analysis, a paired samples t-test and an independent samples t-test, which are suitable for identifying significant differences of two independent groups (Kaufhold, 2007), were applied to conduct data analyses.
Table 9 The spatial abilities between boys and girls in the pretest and posttest. Test
Sex
N
Mean
SD
t
p
Pretest
M F M F
18 16 18 16
6.389 4.438 8.333 7.406
2.837 1.948 2.036 1.899
2.308
0.028*
1.367
0.181
Posttest *p < 0.05.
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Table 10 The spatial perception ability between boys and girls in the pretest and posttest. Test
Sex
N
Mean
SD
Pretest
M F M F
18 16 18 16
2.390 1.880 2.720 2.940
1.335 1.258 1.074 0.854
Posttest
t
p 1.151
0.258
0.641
0.526
5. Results and discussions 5.1. Spatial abilities 5.1.1. Overall spatial ability Table 4 shows the results of the spatial ability test, in terms of mean and Standard Deviation (SD), between the pretest and posttest. The result shows that there was a significant difference between the pretest and posttest on students’ performance of spatial abilities (t ¼ 6.968, p ¼ 0.000**). More specifically, students performed better in the posttest than in the pretest. It indicates that students’ spatial abilities were significantly improved after taking the digital pentominoes game. This result echoes the findings by You, Chuang, and Chen (2008), which showed that a digital game may be one of the useful ways to enhance students’ spatial abilities. The explanation for this result may be the fact that the digital pentominoes game provided opportunities for students to practice various kinds of manipulations. For example, when students were involved in the game, they could manipulate different kinds of geometric shapes, such as rotation or flip of pentominoes, for solving pentomino puzzles. As shown in Table 4, it seems obviously that the standard deviation was largely decreased from almost half of the mean in the pretest to one fourth of the mean in the posttest. This result indicates that students’ initial spatial abilities were largely different but the discrepancy was reduced after taking the game. 5.1.2. Different types of spatial ability In order to examine the differences among the three different types of spatial ability, analyses were undertaken between the pretest and posttest for the three types of spatial ability. Tables 5–7 show the results of these analyses. The results show that there were significant differences between the pretest and posttest for all of the three types of spatial ability: spatial perception (t ¼ 3.438, p ¼ 0.002**), mental rotation (t ¼ 3.361, p ¼ 0.002**) and spatial visualization (t ¼ 5.398, p ¼ 0.000**). These results are consistent with those of Cherney (2008), which demonstrated that computer games improved spatial abilities. More specifically, students performed better in the posttest than in the pretest for the three types of spatial ability. In other words, the results indicate that not only students’ overall spatial abilities were improved, but also all the three types of spatial ability were significantly improved after taking the digital pentominoes game. These results may be due to the fact that the process of operating the digital pentominoes game includes a lot of manipulations on geometric shapes. As described previously in Section 3.1, such manipulations are related to three types of spatial ability to complete pentomino puzzles in the digital pentominoes game. For example, to (1) find out a piece of pentominoes to be included in the puzzle is related to the ability of spatial perception; (2) rotate and flip a piece of pentominoes to be correctly fitted into the puzzle is related to the ability of mental rotation; (3) decide a possible combination of different pieces of pentominoes to complete the tasks of pentomino puzzles is related to the ability of spatial visualization. These manipulations in the digital pentominoes game are useful to improve students’ three types of spatial ability, namely, spatial perception, mental rotation and spatial visualization. 5.1.3. Different levels of spatial ability As described in Section 4.4, participants were divided into two levels, high spatial ability group and low spatial ability group, based on the scores gained from the Spatial Intelligence Scale. This instrument is used to identify students’ levels of spatial ability. On the other hand, students’ performance of spatial abilities was obtained from the pretest and posttest of the spatial ability test. Table 8 shows the results of the comparison between different levels of spatial ability groups in the pretest and posttest. The results show that there were no significant differences between the high spatial ability group and the low spatial ability group neither in the pretest nor posttest. However, it is worth mentioning that the high spatial ability group gained higher scores than the low spatial ability group, but such a result did not reach a significant level. This is probably because the values of standard deviation in the pretest were very high. In other words, the initial spatial abilities among students were largely different in both groups so there was no significant difference between the high spatial ability group and the low spatial ability group. 5.2. Gender differences 5.2.1. Gender differences in overall spatial ability Table 9 shows the results of students’ performance of spatial abilities, in terms of mean and Standard Deviation (SD), between boys and girls in the pretest and posttest. The result of the pretest shows that there was a significant difference between boys and girls for their Table 11 The mental rotation ability between boys and girls in the pretest and posttest. Test
Sex
N
Mean
SD
t
p
Pretest
M F M F
18 16 18 16
1.944 1.062 2.222 1.656
0.984 0.727 0.958 0.889
2.941
0.006**
1.778
0.085
Posttest **p < 0.01.
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Table 12 The spatial visualization ability between boys and girls in the pretest and posttest. Test
Sex
N
Mean
SD
t
p
Pretest
M F M F
18 16 18 16
2.060 1.500 3.390 2.810
1.259 1.033 0.698 1.167
1.396
0.172
1.771
0.086
Posttest
performance of spatial abilities (t ¼ 2.308, p ¼ 0.028*). More specifically, boys’ spatial abilities were higher than girls in the pretest. This result echoes previous studies on gender differences in spatial abilities, which showed that males outperformed females (Monahan, Harke, & Shelley, 2008; Terlecki & Newcombe, 2005). However, the result of the posttest shows that there was no significant difference between boys and girls for their spatial abilities. In other words, spatial abilities between boys and girls were not different in the posttest. These results indicate that boys’ initial spatial abilities were better than girls, but the differences between boys and girls were reduced. More specifically, the results reveal that girls’ spatial abilities were significantly improved after taking the digital pentominoes game. The results are consistent with those of Saccuzzo, Craig, Johnson, and Larson (1996), which showed that gender differences existed in the beginning but women improved at a faster rate and were not statistically different from the men in the end of the computer tasks. 5.2.2. Gender differences in different types of spatial ability In order to examine the gender differences for the three different types of spatial ability, analyses were undertaken between boys and girls in the pretest and posttest for the three types of spatial ability. Tables 10–12 show the results of these analyses. The results show that there was a significant difference between boys and girls for their spatial abilities on mental rotation in the pretest (t ¼ 2.941, p ¼ 0.006**), which reveals that boys performed better than girls. These findings are in line with those of past studies, which showed that males performed better than females in mental rotation ability (Kozaki & Yasukouchi, 2009; Masters & Sanders, 1993). However, there was no significant difference between boys and girls for their spatial abilities on mental rotation in the posttest (see Table 11). This result echoes those of the study by McClurg and Chaille (1987), which found that computer games enhanced the spatial ability measured by a mental rotation test. When girls play computer games that facilitate to their spatial abilities, they are as great as the boys. On the contrary, there were no significant differences between boys and girls for the results of spatial abilities on spatial perception and spatial visualization neither in the pretest nor posttest. More specifically, the performance of boys and girls was not different on these two types of spatial ability (see Tables 10 and 12). The abovementioned results indicate that the results for the mental rotation ability were consistent with those of the overall comparison between boys and girls, which showed that gender differences exist in the pretest, but not in the posttest for the mental rotation ability. These findings reveal that the major difference between boys and girls’ spatial abilities lies within mental rotation. Moreover, among the three types of spatial ability, the results show that students’ mental rotation ability was relatively lower than the other two types of spatial ability. Especially in the pretest, girls’ performance on the mental rotation ability was almost twice lower than boys. It indicates that the mental rotation was the most difficult spatial ability and it is particularly difficult to girls. This was why gender differences only existed in the mental rotation in the pretest. 5.2.3. Gender differences in different levels of spatial ability To examine the gender differences for the high and low spatial ability groups, analyses were undertaken between boys and girls in the pretest and posttest for the two groups in different levels of spatial ability. Tables 13 and 14 show the results of these analyses. The results show that there was a significant difference between boys and girls in the pretest of the low spatial ability group (t ¼ 2.288, p ¼ 0.039*), which means that boys performed better than girls, but there was no significant difference in the posttest (see Table 14). This result is consistent with the findings by Terlecki, Newcombe, and Little (2008), which found that low spatial experience group women improved their spatial abilities so gender differences are also reduced. On the contrary, there were no significant differences between boys and girls neither in the pretest nor posttest of the high spatial ability group. More specifically, the performance of boys and girls was not different for the high spatial ability group (see Table 13). The abovementioned results indicate that the results for the low spatial ability group were consistent with those of the overall comparison between boys and girls, which showed that gender differences existed in the pretest, but not in the posttest for the low spatial ability group. These findings reveal that the major difference between boys and girls mainly lie within the low spatial ability group. Boys who were in the low spatial ability group outperformed girls on spatial abilities prior to take the digital pentominoes game, but the differences between boys and girls were reduced after taking the game. In other words, this game enabled the low spatial ability girls to make significant improvement. 6. Development of a framework Based on the key findings presented in the aforementioned section, Fig. 4 presents a conceptual framework that illustrates the effects of gender differences and spatial abilities within the digital pentominoes game. More specifically, it illustrates how the two human factors Table 13 Performance of the high spatial ability group between boys and girls in the pretest and posttest. Test
Sex
N
Mean
SD
t
p
Pretest
M F M F
8 9 8 9
6.875 5.000 8.563 7.722
3.068 2.236 1.522 2.078
1.452
0.167
0.940
0.362
Posttest
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Table 14 Performance of the low spatial ability group between boys and girls in the pretest and posttest. Test
Sex
N
Mean
SD
t
p
Pretest
M F M F
10 7 10 7
6.000 3.714 8.150 7.000
2.739 1.318 2.439 1.708
2.288
0.039*
1.072
0.300
Post-test *p < 0.05.
affect learners’ performance on the types and levels of spatial ability within the digital pentominoes game. This framework can help designers to develop a proper digital game that provide a proper type of spatial ability task to learners with a proper level of spatial ability, which, in turn, can reduce gender differences and improve spatial abilities. Spatial abilities can be improved with the support of the digital pentominoes game. The results of the study reveal that students’ spatial abilities were significantly improved after taking the digital pentominoes game. Moreover, the results reveal that not only students’ overall spatial abilities were enhanced, but also all the three types of spatial ability were improved. All of the abovementioned results suggest that the digital pentominoes game is an effective training mechanism to improve students’ spatial abilities (Kyllonen, Lohmans, & Snow, 1984). This may be due to the fact that the digital pentominoes game provides an interactive, interesting and joyful environment where students can manipulate various kinds of geometric shapes. Through playing the game, students can practice many kinds of spatial related skills, such as figuring out correct geometric shapes, rotating and flipping appropriate direction on geometric shapes, and determining possible combination of geometric shapes. Therefore, spatial abilities can be improved through training if appropriate materials are provided, for example playing computer-based games (Subrahmanyam & Greenfield, 1994). Gender differences in spatial abilities can be reduced with the support of the digital pentominoes game. The results of the study show that boys outperformed girls in the pretest but not in the posttest. These results suggest that girls’ initial spatial abilities may not be as good as boys, but girls’ spatial abilities could be significantly improved after taking the digital pentominoes game. This echoes the views proposed by Tkacz and LaForce (1998), which indicated that game practice was most effective for students who started out with relatively poor spatial skills though playing digital games improved spatial abilities for both boys and girls. Most of the girls in this study initially showed lower spatial abilities than boys. In other words, they are those who have relatively poor spatial skills so the digital pentominoes game is particularly useful to improve their spatial abilities. Therefore, we can conclude that training with a properly designed computer-based game plays an important role for improving girls’ spatial abilities, and thus helps reduce gender differences in spatial abilities (Quaiser-Pohl & Lehmann, 2002; Quaiser-Pohl, Geiser, & Lehmann, 2006). Mental rotation is a major element that affects gender differences in spatial abilities. As described earlier, the initial spatial abilities of boys and girls are different. Such differences mainly exist in mental rotation because we found that such differences can significantly be reduced after taking the digital pentominoes game. Thus, reducing the gender differences of spatial abilities mainly lies within the improvement of students’ mental rotation abilities. One possible reason for such a gender difference in mental rotation may be due to the task difficulty. In other words, increasing the task difficulty resulted in a greater gender difference (Prinzel & Freeman, 1995). The design of the pentomino puzzles in the digital pentominoes game provides an environment where the tasks were relatively easy with only a few steps for solving puzzles. Thus, this environment is a possible approach to reduce gender differences in mental rotation ability (Feng, Spence, & Pratt, 2007). Gender differences mainly exist in the low spatial ability group. As described earlier, the gender differences in spatial abilities could be reduced after taking the digital pentominoes game. However, we found that such a reduction mainly existed in the low spatial ability group. The result suggests that girls of the low spatial ability group initially showed lower spatial abilities than boys but girls’ spatial abilities could be considerably improved. In general, low spatial ability individuals have difficulties in constructing a mental model of the space. However, additional support is useful to improve the effectiveness of low spatial ability group so the differences between the high and low spatial groups can significantly be reduced. For example, we can provide appropriate design interface, use visual mediators to compensate for the inability of low spatial ability individuals to readily construct visual mental models (Stanney & Salvendy, 1995). Another reason could be accounted for spatial cognitive skills may be most improvable in participants who have not much practiced these skills previously (Lohman & Nichols, 1990). The digital pentominoes game is such a potential mechanism to train the low spatial ability girls, which, in turn, could reduce gender differences in their spatial abilities.
Gender differences
Types of spatial ability
Spatial perception
-
-
Girls
+
Low
+ Boys
High
Spatial Intelligence Scale
Digital pentominoes game
Mental rotation
Levels of spatial ability
Spatial visualization
Fig. 4. A framework of gender differences on spatial abilities with a digital game.
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7. Conclusion This study developed a digital pentominoes game and examined the effects of two essential human factors, spatial abilities and gender differences, within this game. The main findings of the empirical study include four parts: (a) spatial abilities can be improved with the support of the digital pentominoes game; (b) gender differences in spatial abilities can be reduced with the support of the digital pentominoes game; (c) mental rotation is a major element that affects gender differences in spatial abilities; and (d) gender differences mainly exist in the low spatial ability group. These findings reveal that an appropriately designed digital pentominoes game can improve students’ spatial abilities and reduce gender differences in spatial abilities. Such improvement is, especially obvious for mental rotation and for the low level of spatial ability group. The abovementioned findings demonstrate the values of providing support of digital pentominoes game and the importance of investigating spatial abilities and gender differences. However, it was only a small-scale study. Therefore, further empirical studies have to be undertaken with a larger sample to provide additional evidence and verify the results described in this study. There is also a need to conduct further research to examine how other human factors, such as cognitive styles or prior knowledge, influence learners’ spatial abilities in geometric learning. On the other hand, this study emphasized on two-dimensional digital pentominoes but pentominoes can be presented with multiple ways, e.g. three-dimensional digital pentominoes or non-digital pentominoes. 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