The effect of context-based close packing supported with the 3D-virtual model of crystals structure on students’ achievement and attitude

2.1 Description of the background of participants

The nature of this study was a quasi-experiment design which is commonly employed in the evaluation of educational programs when random assignment is not possible or practical. In this study 61 third-year undergraduate chemistry department students and two inorganic chemistry teachers were participated. The assignment of intervention and comparison groups was made based on their academic years to avoid the problem of contamination. Accordingly, all third-year students in the 2020 (N = 37) academic year represented comparison group while all third year students in 2021 (N = 24) academic year represented the intervention group. The participants of the study were deliberately selected from different academic years (comparison group students from 2020 academic year and an intervention group from 2021 academic year) and used for the comparative purpose to reduce the problem of contamination between the groups. Furthermore, if the participants selected from the same academic year and the treatments run parallel, they may share ideas with each other about the newly implemented context based close packing of crystals structure supported with 3D-virtual model on the crystals structure/solid state chemistry.

2.2 Research design

In this study, static group comparison design was used. In other words, two groups are chosen, one of the groups receives the treatment and the other does not receive the treatment. This is an attempt made to isolate the effect of the intervention on those selected research groups and other research groups who did not take the treatment. For this purpose, post-test was used to measure the difference between the two groups after the treatment. Therefore, static-group comparison or comparison group post-test-only design was summarized in the Table 1 below.

where, X is treatment (context based close packing of crystals structure supported with 3D-virtual model), Y is conventional teaching approach/lecture method and Pt₁ is post-test.

2.3 Learning environment for intervention group students

In this study, both (i.e. comparison group and treatment group) group students work with small groups while the context based close packing of crystals structure supported with 3D-virtual model structure was utilized only for the intervention group students on crystals structure topics. Intervention group students were continuously encouraged to meet with their groups two times per week for 2 h each time (for four consecutive weeks). There was no such special treatment provided for the comparison group during the whole treatment period. The same chemistry lesson topics prescribed for the intervention groups were administered for the comparison groups using conventional method. Nevertheless, all necessary precautions were taken for ensuring certain standards and keeping the level of content and scope of coverage to both groups were similar (the teacher who give crystals structure topics; the course contents; post-tests; and the time taken to cover the topic).

2.4 Learning environment for comparison group students

The challenging problems from crystals structure topic were identified during the preliminary study. These problems were considered as triggered problems for both groups. Similar to intervention groups, comparison groups students were continuously encouraged to meet with their groups two times per-week for 2 h each time (for four consecutive weeks) and treated with conventional teaching approach without using context based close packing of crystals structure supported with 3D-virtual model. The instructor gave questions and assignments to assess students’ academic achievement in the crystals structure topics that covered in actual class. Besides, the instructor assisted and encouraged students to work in a group and complete their group assignments during the tutorial session. The students dealt with scenarios involving several problems and tried to find appropriate answers to the problems. Then, the instructor guided and assisted the students in the place where they need explanations and extra help. In such way, all the students were kept active, and they were involved in the learning process. To maintain uniformity, the treatment time for both groups was the same. At the end of this treatment period, the same post-test was administered to both groups.

2.5 Context based close packing of crystals structure and 3D-virtual model

As mentioned in earlier section many students faced challenge with visualizing and mentally manipulating three-dimensional objects (visualizing crystal system of atoms/ions), and therefore, this context based crystal packing supported with 3D-virtual model were employed to help them conceptualize crystals structures. The context based crystal packing was designed by researchers by purchasing uniform multi-colored spherical balls-toys (from kids’ toys supper market). Besides, the researchers installed 3D virtual model (crystal maker) software on physical laboratory computers of chemistry department. So that, students are able to build crystals structure of molecules, and ions/atoms based on the self-developed manual (by researchers) (Table 2). Therefore, IG students were practiced to build, display and manipulate different molecules of a given crystals structure from standard two-dimensional formula of inorganic chemistry books using context based approach and 3D virtual models, visualize the three-dimensional features of some selected crystals structure for a given molecules (Figure 1).

Figure 1:

Close packing model of (a) primitive cubic close packed structure, (b) tetrahedral holes, and, (c) octahedral holes from uniform multi-colored spherical ball-toys, (d) crystals structure of NaCl (Na, green, Cl = golden colour) constructed using crystal maker software (crystal system: cubic; lattice type: face-centered (F); space group symbol: F m −3 m; cell parameters: a = 5.6400 Å; b = 5.6400 Å; c = 5.6400 Å; atomic positions: Cl: 0.5, 0.5, 0.5; Na: 0, 0, 0 …).

2.6 Data gathering instruments

Relevant data were collected from the participants of the study through the use of multiple instruments (Chemistry achievement tests, questionnaire, interviews and observation).

2.7 Observation

The researchers’ (instructor/subject teacher) conducted observations while intervention group students attended the context based close packing of crystals structure supported with 3D-virtual model in crystals structure topics and evaluated the interactions held between students, the effectiveness of the method in acquiring the major concepts, and overall students’ participation and its drawbacks.

2.8 Methods of data analysis

The collected data were analyzed quantitatively using descriptive statistics such as frequencies; percentage, mean, standard deviation, and inferential statistics (t-test). Furthermore, qualitative analysis method was employed for the data gathered through open-ended questionnaire, semi-structured interviews, and from class room observation.

3.1 Comparison between intervention and comparison group students’ post-test achievement

The t-test was used to decide whether the two groups (IG and CG) posttest achievement is statistically significant or not. The comparative analysis of post-test results showed a significant difference was observed between the two groups (Table 3).

The intervention group students performed better in the post-test exam than the comparison group students. This shows that an experience of using context based develeoped close packing crystals structure models and softwares enhance students’ visualization and reason-out ability in crystals structures, and improve their achivement. A numerous studies have also revealed that there is a significant positive correlation between spatial visualizing ability of students and success in science, technology, engineering, and mathematics courses (Fatemah, Rasool, & Habib, 2020; Hodgkiss, Gilligan, Tolmie, Thomas, & Farran, 2018; Khine, 2017).

3.2 Comparison between intervention and comparison group students’ achievement on the targeted crystals structure questions

The researchers also analyzed the individual student exam scripts on selected targeted crystals structure questions and compared the analysis result between the two groups (Table 4).

Table 4:

Comparison of intervention and comparison group students’ achievement on targeted crystals structure questions.

S. No.	Questions		f (%) CG	% (f) of IG
1.	What is unit cell? Please give brief definition with example (consider NaCl or other if you like)		15(40.54)	21(87.50)
2.	What is a crystal lattice? Please give brief definition		14(37.84)	18(75.00)
3.	What is close packing in an ionic solid? Please give a brief definition with example (i.e. NaCl as an example or other if you like)		9(24.32)	12(50.00)
4.	What is meant by the term coordination number in ionic solids? Please give brief definition		5(13.51)	11(45.83)
5.	What is the coordination number of atoms in a/an
A.	Simple or primitive cubic close packed structure?		6(5.41)	8(33.33)
B.	Body–centered cubic (bcc) structure?		6(16.22)	15(62.50)
C.	Face centered cubic (fcc) close packing structure?		3(8.11)	11(45.83)
D.	Hexagonal closest packed (hcp) structure?		4(10.81)	13(54.17)
6.	How is a coordination number for a given an ionic solid determined? Please give brief explanation by considering NaCl (or other if you like).		8(21.62)	10(41.67)
7.	What is tetrahedral hole? Please give brief definition		14(37.84)	19(79.17)
8.	How many tetrahedral holes are there in the fcc?		4(10.81)	8(33.33)
9.	What are the octahedral and tetrahedral sites in close packed arrangement? Please give brief explanation		4(10.81)	9(37.50)
10.	What is the difference between hexagonal closed packed (hcp) structure and cubic closed packed (ccp) structure? Please give brief explanation on the differences		2(5.41)	13(54.17)
11.	What is the difference between body centered cubic and face centered cubic? Please give brief explanation on the differences		5(13.51)	11(45.83)
12.	Please list the name of all seven crystal lattice systems with their unit cell and their differences		1(2.70)	8(33.33)
13.	Please list the name of all seven crystal lattice systems, their differences and give at least one example for each		1(0.94)	7(29.16)
Match the structures given under B with the type of arrangement given under A (more than 1 answer is possible).
	A.	B.
14.	___ABC,ABC… type structure	A.	9(24.32)	16(66.66)
15.	____A-A-A type arrangement	B.	7(18.9)	18(75)
16.	____Hexagonal close pack	C.	8(21.62)	15(62.5)
17.	____AB-AB type arrangement	D.	11(29.72)	19(79.16)
18.	___Simple or primitive cubic	E.	12(32.43)	17(70.83)
19.	___Body centered cubic	F.	9(24.32)	14(58.33)
20.	___Face centered		10(27.02)	88(62.5)

1. f = frequency, CA = Correct Answer, % = Percentage of respondents, f = frequency of respondents, IG = intervention group, CG = Comparison Group.

As can be seen in Table 4, questions 1–4 focussed on the basic concept of crystals structure such as: meaning of unit cell, crystal lattice, close packing in an ionic solid. For these questions only few comparison group students were gave correct and scientifically accepted meanings while majority of them didn’t give the correct answers or in another word majority of comparison students failed to give scientifically accepted definitions and even they didn’t distinguish the difference between the above-mentioned concepts compared to intervention group students. Surprisingly majority of comparison group students know the chemical formulas of NaCl, but they have no mental pictures of the close packing structures of this substance. We understood from their exam scripts, students only know the terminology or words than the full meanings of the crystals structures. Compared to intervention groups majority of comparison group students’ answers were incomplete and inconsistent about the definition of the unit cell as a small repeating entity, basic structural unit, and fail to distinguish the difference between a unit cell and crystal lattice. Besides, they failed to give concrete and complete information about the spatial representation of unit cell and crystal lattice.

To answer these questions students should have a concrete understanding of the particulate nature of the matter in the level of the unit cell with spatial structures and their means of representation. However, understanding the spatial crystals structures of a given atom, ions, or molecules require concrete understanding of it at unit cell level which is the smallest repeating unit and shows the full symmetry of the crystals structure. When we describe crystals structures using unit cells, the size and shape of the unit cell and the positions of the atoms inside the cell are needed. For further illustration the researchers assisted intervention group students to construct and use the following context based close packing supported with 3D-virtual model approach (Diagram 1: (a) and (b) to distinguish the difference between a unit cell and crystal lattice).

Diagram 1:

(a) Example of unit cell, and (b) example of crystal lattice.

This gives all the necessary information about the crystals structure, and it is important because a crystal is a solid material that contains atoms or groups of atoms arranged in a highly ordered structure described in three-dimensions and a crystal lattice describes the arrangement of these atoms in a crystal. In this regard, the approach helped IG students to visualize and understand the spatial structures of a given atom, ions, or molecules.

Questions number 5–7 were focused on coordination chemistry. For the above-mentioned questions, only a few CG students gave scientifically correct answers while majority of them do not have the concrete understanding the meaning of coordination number in different ionic solids; fail to determine coordination number of atoms in simple or primitive cubic close-packed structure, Body-centered cubic (bcc) structure, face-centered cubic (fcc) close packing structure, Hexagonal close pack (hcp) structure, and they failed to give example for each question. Before giving the right answers for these questions, students should primarily, be able to understand the unique properties of crystal solids, type of structure, and able to visualize the reasonable and acceptable structural representations of each crystal packing structure. In this regard, the researchers assisted intervention group students to construct crystal structure of atoms/ions or molecules using context based close packing supported with 3D-virtual model. Accordingly, different conceptual representation models of crystals structure systems used during intervention periods were indicated in Figure 2.

Figure 2:

(a) In one dimensional spheres; (b) two dimensional close packing; (c) square close packing from two-dimensional; (d) three-dimensional square close packing from two-dimensional layers (AAA … type); (e) hexagonal close packing in two dimensions; (f) hexagonal close packing from two dimensions (ABAB … type); (g) three-dimensional hexagonal close packing from two dimensions (ABAB … type).

Questions number 8–12 were focused on types of close packing and associated properties (i.e., types of holes formed or octahedral and tetrahedral etc.). For the above-mentioned questions, majority of comparison group students failed to clearly explain the difference between hexagonal closed packed (hcp) and cubic closed packed (ccp) structures, failed to explain the difference between body-centered and face-centered cubic while only few students were successfully explained scientifically correct answers. It is evident from students exam scripts, some of CG students tried to give their answers based on the framework of their pre-instructional understanding of words like hexagonal = six angle, cube = equal size etc. not based on their literal meaning of crystals structure or visual arrangement of atoms/ions and molecules, and its associated properties.

For question 13, only one student listed the name of the entire seven crystal lattices (Cubic, Tetragonal, Orthorhombic, Trigonal, Hexagonal, Monoclinic, and Triclinic). Majority of CG as well as IG students were failed to clearly articulate the difference between the seven lattice structures and the possible unit cell they have. However, number of IG students who gave correct answer was better than number of CG students. This indicates that still students have difficulty with the topic and it needs further emphasis to minimize students’ difficulty.

Questions 14–20 were focused on the assessment of students’ ability to describe the crystals structures using a close packing approach. The crystals structures of a large number of alloys, metals, and inorganic compounds can be described geometrically in terms of a close-packing arrangement of atoms/ions in equal size spheres, held together by interatomic forces. However, only a few CG students gave correct answers for these questions while the majority of them failed to describe the types of crystal packing; failed to distinguish hexagonal close pack from cubic close packing, face-centered cubic from body-centered cubic, and type of hexagonal arrangement. Conversely, the majority of IG students describe the types of crystal packing and hexagonal arrangement, distinguished the types of hexagonal close pack from cubic close packing, and face-centered cubic from body-centered cubic. It is evident from students’ exam scripts that many IG students are good in recall of facts, knowledge and terminologies while majority of CG students have difficulty in transform and interpret theoretical concept to visual or geometrical aspects of structures and vice versa.

In general, we can conclude from the above observed students’ exam script analysis, many intervention group students have better understanding the scientific meaning of unit cell and crystal lattice, better in visualizing arrangement of atoms/ions and molecules of crystal systems or in three-dimensional forms; have better in transforming the symbolic representation to macroscopic, microscopic/ionic representation to macroscopic and vice-versa; easily distinguished face-centered cubic from body-centered cubic; and type of hexagonal arrangement compared to comparison group student. A number of researchers also reported that the combination of three-dimensional representations and activities with three-dimensional models enhance students’ mental representations and understanding crystals structures futures (Fogarty et al., 2018; Melaku & Dabke, 2021; Rossi et al., 2015; Sunderland, 2014).

3.3 Survey of attitude of intervention group students

The researchers assessed intervention group students’ attitude towards context based close packing of crystals structure supported with 3D-virtual model at the end of the course using close ended, open ended and interview questions. The analysis result of the close ended questions given in Table 5.

Generally, as can be seen from Table 5, majority of intervention group students have positive attitude toward using context based close packing of crystals structure supported with 3D-virtual model which helped them in understanding the concepts. They also appreciated the contribution of the approach in bringing students together which develop the experience of working together in addition to academic achievement.

3.4 Interview with intervention group students

The researchers opened the session by welcoming participants and introduced the objective of the interview, and gave chance to each interviewee to introduce his/her name. Then, the interviewer proceeds to his questions (the following interview was held with one randomly selected intervention group student).

Researcher: I would like to ask you some questions about using context based close packing of crystals structure supported with 3D-virtual model we used during our class or in learning crystals structure topic and the experiences you had during the class. So can you tell me a little bit about your experiences with the approach in your class?

Student 1: Yes, I do.

Researcher: Ok, how do you see learning crystals structure topic (constructing different crystal system) with the approach?

Student 1: Yeah, learning crystals structure topic with such approach is good and I believe that it is useful, because what we learned during the session was like a practical (i.e. learning by doing, construct different structures from simply small plastic balls, draw on the computer and compare with context based constructed crystals structures by rotating, etc), was too memorable. The session was interesting and different from other learning sessions.

Researcher: What do you mean the session was different from other sessions? What made it different from other sessions?

Student 1: Yeah, from my view I got it different because I didn’t learn other chemistry courses in such way (by constructing with local available was well as practicing with software). I don’t have such experience before, also I think, this is everyone’s first-class to learn crystals structure topic with such approach (manipulate things with hands, constructed and rotate the 3D-structure of different ions and molecules on the PC screen and observed their structures etc. I can say a lot of things more.

Researcher: In your opinion, do you think learning crystals structure with such approach would help you in your studying, and to achieve a good result in crystals structure?

Student 1: Definitely!

Researcher: How? Please could you explain about it?

Student 1: Ok, learning crystals structure topic with the approach helped me to understand things in a better way. For example, as I said earlier, I don’t have experience of construct different molecules from locally available materials as well as with such software. But, this class helped me to do so i.e. rotate and simulate the three-dimensional structure of the molecules, identify the difference between molecules, and easily visualize the crystals structure of different molecules. For example, to decide the configuration of any molecules, I always tried to understand the 2D structures drawn on the text book and visualizing the hypothetical structure of the compound. But, now during this session, I realized that it is possible to construct and visualize the hypothetical 2D drawings from a textbook with such approach. Even, we discussed with my colleagues about things we confused on and fixed as soon without any further assistance from teacher or technician.

Researcher: Do you think working together is useful in such case?

Student 1: Definitely! We worked in groups or with my colleagues throughout the class and we enjoyed it a lot. I gained a lot of things from working together. I can say working with group is very important in such case to share ideas and tackle problems which might be difficult to understand alone. For example, if I don’t understand something, I need to talk to my friends and observe how they solve that problem. Here in the crystals structure class, sometimes we faced similar challenges in identifying the correct configuration of a given molecules but we discussed together with my colleagues and easily identify the correct structures which represent the designers of molecules. In my opinion, working together is better than working alone. I felt, construct the structure of a given molecule alone, might be misrepresented the correct structure of the molecules and for me better to work together for better understanding. Even, I realized the importance of working together at the end of the class.

Researcher: What skills, if any, do you think you have gained from using context based close packing of crystals structure supported with 3D-virtual model?

Student 1: Well, I would say that I enjoyed and learned many skills such as using 3D-virtual model software which has numerous applications, and visualizing the structure of different molecules.

The analysis of semi-structured interview indicates that all of the interviewed participants gave a positive response or they appreciated the way they learned the topic. The researchers categorized their responses into three main ideas. The first point deals with the importance of context based close packing of crystals structure supported with 3D-virtual model in enhancing student visualization ability, help students to recognise the way atoms arranged in a given crystals structure (pattern), and recognize the unit cell and number of holes (tetrahedral and octahedral holes). The other point which the respondents specifically emphasized is the importance of group work which creates an opportunity for students to discuss with each other. The last point the respondents accentuated was the suitability (good-looking) of the approach. Based on points raised above, it is possible to summarize the importance of context based close packing of crystals structure supported with 3D-virtual model to visualize and understand the nature and structure of crystal molecules/ions explicitly which is basic to understand the properties of materials. The skills and experiences they gained from the approach is in agreement with other researchers’ findings (Bortnik, Stozhko, & Pervukhina, 2021; Chiu, 2021; Wu & Shah, 2004).

3.5 Summary of observation results

The researchers conducted observation while intervention group students practicing their activities using physical and virtual model to evaluate overall students’ activities during the session such as: observing and evaluating the interactions held between students, conduciveness of the method to users, students’ interest and participation, students time usage, and its drawback (Table 6).

During the observation period, the researchers were evaluated intervention group students’ interaction within the group and across the group, and concluded that the approach is effective in creating conducive learning environment or there is a positive interaction between the students (discussed together and helped each other). The researchers also, evaluated the effectiveness of the method in acquiring crystals structure concepts and they found that the approach is better in improving students’ visualizing ability (visualize atoms/ions arrangement orders). It familiarizes students with working with computer (rotate 3D structure of the molecules and create mental representation), help teachers to assess his/her students’ limitation/gap of understanding crystals structures (used as assessment tool to identify students’ visualization ability and properties of crystal solids).

The researchers explored the time students spent on the approach construction and discussion on the constructed model. When we compare the time students spent on constructing context based close packing of crystals structure supported with 3D-virtual model activity with discussion about the constructed model, majority of students spent 60 % of their time on discussion about the structure-property of the constructed model (students touched and moved the constructed structure, occupation sites, identify the coordination number, compare the types of arrangements, etc.) while 40 % of their time on the reading pre-instruction and construction of the model (gluing the balls, arrangement, interchange the positions and modify the arrangements etc.). Therefore, the time students spent on the discussion about the relation between crystals structure and physical or chemical properties is much higher than the time spent on pre-instruction and construction of the models. In all these processes the researchers facilitates and guides students in the process of independent learning and students also shown good participation in constructing the given crystals structures which makes the learning enjoyable.

Based on the result of the study, the researchers concluded that using context based close packing of crystals structure supported with 3D-virtual model would entices learners’ interest, enhance students interaction within the group and across the group, improve students’ visualizing ability and understanding, and enhance their participation which is in agreement with the previously reported findings (Fogarty et al., 2018; Shamsuddin, Adamu, Muhammad, & Oluwatoyin, 2018; Sunderland, 2014).