Abstract
The authors have developed a computer-based learning module on the unit cell of various types of crystal. The module has two components: the virtual unit cell (VUC) part and the subsequent unit cell hunter part. The VUC is a virtual reality simulation for students to actively arrive at the unit cell from exploring, from a broad view, the crystal lattice of atoms or ions displayed “three dimensionally.” The unit cell hunter (UCH) part, implemented after the VUC, is a board game with students competing in assembling the atomic pieces for two types of unit cell (cubic and hexagonal) framework. The students were evaluated for achievement after having benefited from working with the learning module and participating in the debriefing. Apart from identical pre- and posttests at the beginning and end of the activities, students also responded to a questionnaire. Active participation by the students and the researcher in the debriefing enhanced learning as set out by the objectives, for example, better visualization of the three-dimensional structures of various types of unit cell and crystal lattice.
Keywords
The unit cell of a crystal is conventionally introduced in solid state chemistry and physics as the smallest and most representative unit of crystalline material that, by translation along the three principal orthogonal planes, can generate a whole crystal lattice. We have found the usual two-dimensional (2D) illustrations of the unit cell inadequate in giving students an insight into how the unit cell represents all the essential physical features of the crystal. Foley (1996) reported that many undergraduate students find the unit cell content and symmetry too complicated and highly abstract. One of the reasons is that the use of 2D representations makes it difficult for students to visualize three-dimensional figure (3D) on paper or chalkboards. Without good 3D representations of the crystal lattice and unit cell to learn from, students have a difficult time visualizing them or solving problems related to them. This situation is also true in mineralogy, where some students have initial difficulties with certain visual perceptions of 3D crystal models, their rotation and so on (Ozdemir, 2009). Because learning about this topic involves spatial perception, students’ existing spatial abilities would have a strong influence in facilitating mineralogy learning.
In the past few decades, concrete handheld models have been used for demonstrating mainly the unit cell (Birk & Yezierski, 2003; Cady, 1997; Mattson, 2000; Orlov, Schoeni, & Chapuis, 2006). From our experience, even when handheld unit cell models are made available, students still find it difficult to generate a good 3D crystal lattice because the unit cell pieces are usually opaque and insufficient in number. A computer-drawn model (Gelder, & Jones, 1980) was proposed as an aid for instructing the topic. However the latter was presented only as a short videocassette 3D animation without interactivity.
To address these learning problems, we devised a computer-based interactive learning module, the virtual unit cell (VUC) and the unit cell hunter (UCH), which should challenge students actively, and in which student groups can participate simultaneously. In the VUC, the limitations of two-dimensionality are reduced by the rotability of the unit cell and the crystal lattice. Also the extent of the crystal lattice can be computer generated to imitate the enormous number of unit cells in a real crystal. With proper rendition, the lattice and the unit’s internal structures can be probed. In the VUC simulation, students have to deduce the unit cell from each type of crystal lattice, whereas in the UCH, they have to compete in putting the correct number and type of atomic pieces in the two types of unit cell.
The Virtual Unit Cell
User Interface
The user interface of the VUC consists of two parts as shown in Figure 1. The left panel is the navigator to access the desired models. The right panel is the main screen showing the models selected.
The screen showing the two main panels of the VUC simulation
Structure of the VUC
The simulations in the VUC encompass three parts:
The first part involves models of
The second part,
The last one,
The VUC showing the three main parts and subtopics of the program
Main Advantages of the Simulations
The main advantages of our simulations are the ability to display the lattice and unit cell as virtual 3D models with contrasting-colored atoms and rotability of the models to make them appear “real.” In the process of deducing the unit cell, the color of the atoms and pieces thereof can be changed by a click, as shown in Figure 3. The latter feature helps facilitate the gradual deduction of the unit cell from a crystal lattice as the students gradually narrow the number of unit cells down to the irreducible one eventually. In the simulation of the unit cell translation to generate the lattice, the previous steps are reversed now by expanding of the unit cell along the xy, yz, and zx planes to generate a larger lattice (Figure 4). The instructor should ensure that students do not misconstrue this unit cell translation as the mechanism for crystal growth.
The color of the atoms can be changed by a click during the narrowing down to an irreducible unit representing the unit cell
The step-by-step 3D simulation of unit cell translation to reproduce the larger lattice
The Unit Cell Hunter
User Interface
At each level of the game, the user interface of the UCH consists of two scenes. For the first scene, the player collects atomic pieces of the unit cell to put them in their proper places on the cubic framework (the second scene) as shown in Figure 5.
In the pilot version, the pieces are picked up (A) and assembled to make up the unit cell (B) while the player overcomes obstacles and red herring
The present game is an improvement on the pilot one trialed earlier. In the early stages of our game design, we challenged the students to make side scrolling moves to eliminate enemies and to jump over floating objects (see Figure 6A). Assessing the game with undergraduate students and looking into their responses to questionnaires and interviews led us to conclude that students with low game skills encountered the problem of controlling the characters, with the consequence that they were unjustly penalized. This problem was discussed at the International Simulation and Gaming Association 2009 conference, and we benefited from suggestions for a change in the genre of the game, such as changing from a side-scrolling game to a board-based (tile-based) game with only up-down and sideways moves as shown in Figure 6B.
The game was transformed from: (A) one demanding more manipulative skills involving side scrolling to (B) the present one based on a board game
Structure of the UCH
The UCH game has four difficulty levels, starting with the easiest to the most difficult unit cell structures: simple cubic, body-centered cubic, face-centered cubic and hexagonal close packed.
Level 1: Primitive cubic
Level 2: Body-centered cubic
Level 3: Face-centered cubic
Level 4: Hexagonal close packed
Each level has two scenes of the same type:
Scene 1 involves collecting correct number and type of the atomic pieces of the unit cell.
Scene 2 involves putting the collected pieces at their proper places in the unit cell to make a quasi-3D display. The game structure and relationship between level and scene are shown in Figure 7.
Illustration of the UCH game structure and relationship between level and scene
Main Advantages of the UCH
The students acquire manipulative skills and visual knowledge in going through the manipulative and cognitive challenges from Levels 1 to 4. Also we have made the unit cell framework for each type rotatable to facilitate the assembly of the pieces as shown in Figure 8.
Because the atomic pieces may visually block each other in the static framework, thus causing perceptual inconvenience to the gamer, we have created a rotatable cubic frame to make the blocked unfilled spaces visible and ensure that correct pieces are put in as shown in Figure 9. This type of realistic interface prevents irrelevant obstacles from diminishing learning possibilities (Pelletier, 2009).
Rotatable cubic framework allowing different viewpoints
A rotatable cubic frame for better visualization and playing of the game
Relationship between the VUC and UCH components
The scheme in Figure 10 shows the relationship and the steps in the learning module. The VUC is a simulation tool for helping students deduce the unit cell and generate the lattice. The UCH is a game for students to collect the correct type and number of pieces and put them in their proper places in the unit cell.
Illustration of the relationship and the steps in the learning module
The improved visualization skills acquired in this VUC help students play the UCH game in which they have to find the missing unit cell pieces and assemble them correctly. The UCH game has three steps:
The UCH games have four levels of difficulty, for both the cubic and hexagonal crystal systems. Figure 11 shows the ways students/players use knowledge from the VUC for the UCH game. Figure 11A shows that, at beginning of each level in the UCH, students can use their knowledge gained from “simulation of the unit cell translation” and “deduction of the unit cell” to find out the unit cell type. In Figure 11B, the students use “3D model of unit cell” for collecting all unit cell parts and constructing a correct and complete unit cell type.
Diagram showing the way the student uses knowledge acquired from the VUC simulation for the UCH game
Research Method
Research Objectives
This pilot study aimed (a) to determine the effectiveness of the learning module on the students’ learning about the unit cell and crystal lattice and (b) to assess their opinions on the module they had actively participated in.
Participants
The participants in this study were 23 undergraduate students, from the Faculty of Science of a competitive university, who were interested in computer graphics and animations and volunteered to participate in the study. All of them had no previous exposure to the unit cell concepts.
Research Design
We employed a single-group pretest–posttest research design. The group took the pretest, participated in learning with the module, underwent the debriefing, and finally took the identical posttest. The pretest and posttest scores were used to evaluate the effects the learning module had on the students’ learning achievements about the unit cell. The test comprised six questions designed to examine exactly what the students learned from the module.
The rating scale questionnaire was then given to the students after the posttest to evaluate their opinions of the module. All eight questions in the questionnaire were graded as strongly agree = 5, agree = 4, undecided = 3, disagree = 2, and strongly disagree = 1.
The research design is shown in the Figure 12.
Research design
Data collection
The data collection steps are as follows:
The students took the pretest.
The lecturer went through the VUC followed by the UCH activities.
The researcher and the participants performed the debriefing via group discussion.
The students took the posttest
The students responded to the questions in the questionnaire about their opinions on the learning module.
Data Analysis
The pretest and the posttest scores were paired and analyzed with the paired-samples t test statistic using SPSS. The effect size was calculated to examine the magnitude of a treatment effect using the equation and the general guide proposed by Cohen (as cited in Becker, 2000). Each question in the questionnaire was analyzed individually for the frequency of students’ opinions as rated on the graduated response scale.
Research Hypotheses
We expected the VUC to help students visualize the unit cell and the crystal structure more easily. In the same way, the UCH should help students construct knowledge by themselves, while enjoying the learning environment. Pre-exposure to the VUC followed by the UCH should improve learning and students’ attitude toward these difficult and highly abstract topics.
We proposed the null (H0) and alternative (H1) hypotheses for a more rigorous statistical evaluation of the module for any learning improvement as follows:
H0: The pretest mean score (
H1: The posttest mean score (
Results and Discussion
Debriefing
At the end of the learning unit, students participated in the debriefing, a group discussion guided by the researcher, to ensure that they achieved the learning objectives as much as possible. After playing the UCH game, all participants adjourned to a room with a round table and began the three phases of debriefing (Steinwachs, 1992) as follows:
What happened during game playing? Which task was the most difficult? How did you feel? How many participants managed to assemble all the pieces? How did you do it? Which aspects of the game were most challenging? How did you overcome the problems?
We collected some interesting observations from this phase:
Students who succeeded in assembling the pieces without any mistakes agreed that the 3-D models of the unit cells in each VUC helped in their playing of the game.
The most difficult task in the game was to figure out the unit cell from the lattice. They agreed that different colored atoms helped them visualize the unit cell, which was being deduced, more easily.
It was very challenging, especially, in the case of the hexagonal close packing because of the large number of types and pieces of atoms involved.
2. Which activity(ies) could you have used for learning more about the unit cell? Were there any simulated situations that you normally do not find in your classroom? Were there aspects of normal classroom learning about the unit cell not addressed in the game simulation?
Toward the end of this phase, the researcher made a summary of what the participants had contributed to ensure common understanding so they could apply what they had learned together.
Results from phase 2 showed that all participants could very well relate task performance in the game to learning the contents of the unit cell. They also concurred that all tasks had relevance to all the unit cells. On the contrary, they found that some unit cells had not been simulated in the game.
3. Has your experience in playing game helped you in any special way? Please elaborate. Can you imagine any future situation that you can bring your experience to bear on? How?
We found that the participants were confident that they could apply the knowledge gained from game in authentic learning situations:
The participants indicated that they understood the arrangement of atoms in the unit cell and crystal lattice.
One third of the participants also believed they could visualize other unit cells (not yet simulated) better so much so that they thought they could apply their newly acquired skills in solving future visuospatial problems.
The Effectiveness of the Learning Module
The paired-samples t test results from SPSS show significant differences between the pretest and posttest mean scores as can be seen from the column “Significance” in Table 1. Therefore the alternative hypothesis (H1) is accepted and it can be concluded that the posttest mean score is greater than the pretest mean score. The statistical results are shown in Table 1.
The Results of Paired-Samples t Test
Effect Size (ES)
The formula used for determining the effect size is as follows:
where M1 = posttest mean score, M2 = pretest mean score, σpooled = pooled standard deviation, σ1 = standard deviation of M1, σ2 = standard deviation of M2.
For this work
According to the general guide developed by Cohen, the effect size at 7.3 of this work indicates a large treatment effect, implying that treatment with the learning module had a large effect on the aimed learning achievements.
Students’ Opinions on the Module
The results obtained are presented separately, statement by statement, as in Figure 13. For most statements, the highest frequency of the students’ opinions falls in the range of strongly agree to agree, except for Question Number 2, which falls in the category of strongly agree. The results revealed that most of the students showed high satisfaction with the module in terms of understanding, knowledge gained, and visualization skills.
Frequency of responses to the eight questions in the questionnaire
Compared with learning from paper 2D illustrations, 3D handheld models made from ping-pong balls or folded paper boxes with atomic pieces drawn on them, our VUC module helped the students understand better the relationship between the unit cell and the crystal lattice. The students found it fun to learn the fundamentals of the unit cell from the UCH game. For playing the latter game, they also benefited from the VUC simulation. There was a consensus among the students that studying the VUC beforehand helped improve skills in playing the UCH game by sharpening their visualization abilities.
Conclusion
A major effort in this study was spent in making the VUC simulation and the UCH game. We designed the programs for the simulation and game including the atomic pieces and frameworks for all crystal types reported here.
We conducted a pilot study to assess learning improvement of 23 undergraduates participating in our learning module on the unit cell and the crystal lattice. The students were expected not only to explore the computer graphic models of crystal lattices and unit cells in a 3D environment but also practice a method of deducing the unit cell from a lattice. Statistical analysis showed that posttest scores were significantly higher than those of the pretest with a large effect size. From the above, we can safely conclude that the learning module aided in the visualization and learning of contents presented as on-screen 3D simulations. From their responses to our questionnaire, most students were satisfied with the module up to the level of agree to strongly agree.
The main advantage of a computer game for education is that students are personally engaged, especially when game activities are challenging and lead to more analysis and problem solving (see, e.g., Whitton, forthcoming). However, the challenge should not be based too heavily on manipulative skills. The emphasis of hand-to-eye skills may incur extraneous variables that are difficult to interpret in terms of learning. The fun generated by the game should also not lead to the sacrifice of authentic learning. Thus one pilot study should at least be conducted to eliminate effects that do not help student learning.
Finally, we would like to propose some improvements for a follow-up study:
Change the research design to a two-group experimental one to increase the validity of the study.
Perform validity and reliability tests for the research instruments and/or use available standard tests.
Footnotes
Acknowledgements
We thank David Crookall for valuable suggestions and guidance during the preparation of the article. Ethan Kennerly’s helpful comments led to a change in the genre of our game. The editorial assistance of Jonnie Hill and Mercedes T. Rodrigo and the anonymous reviewers have greatly improved this article.
This article is a substantially augmented rewrite of a paper presented at the 40th conference of the International Simulation and Gaming Association (ISAGA), organized by the Society of Simulation and Gaming of Singapore, Yeo Gee Kin (National University of Singapore), and Cai Yiyu (Nanyang Technological University, Singapore), from 29 June to 3 July, 2009, and published as Panjipan, B., & Sutha Luealamai, S. (2009, July). A game and simulation multimedia to teach atomic packing in crystal unit cells. Paper presented at the 40th Conference of ISAGA, Singapore.
The author(s) declared no conflicts of interest with respect to the authorship and/or publication of this article.
This research was supported by a Mahidol University research grant.