Research: Science and Education edited by
Chemical Education Research
Diane M. Bunce The Catholic University of America Washington, D.C. 20064
Using Particulate Drawings to Determine and Improve Students’ Conceptions of Pure Substances and Mixtures Michael J. Sanger Department of Chemistry, University of Northern Iowa, Cedar Falls, IA 50614-0423;
[email protected] ◆ O■ ◆ O■
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The following drawings contain representations of atoms and molecules. Classify each of these drawings (labeled 1–5) according to the three characteristics listed below. You should classify all five drawings for each category.
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Figure 1 shows the particulate drawings that students were asked to consider. Students were asked to classify each picture according to its state of matter (solid, liquid, or gas), its physical composition (pure substance, heterogeneous mixture, or homogeneous mixture), and its chemical composition (containing elements only, compounds only, or both). I constructed the drawings and chose the composition of each drawing to ensure that there was at least one correct response for each of the nine choices in Figure 1. The defining attributes for gas samples are that the particles occupy the entire space of the container and are as far apart from each other as possible. For solid and liquid samples, the particles are much closer to each other and do not occupy the entire space of the container. Particles in solid samples show some kind of organization or a repeating pattern. Particles in liquid samples, on the other hand, are randomly distributed and do not show organized patterns. Pictures 2 and 5 represent gas samples because the particles occupy the entire container, pictures 1 and 3 represent solid samples because the particles do not fill the entire space but have a definite repeating pattern, and picture 4 represents a liquid sample because the particles do not fill the entire space and are randomly spaced. Pure substances contain only one kind of molecule. Pictures 3 and 5 depict pure substances because there are
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Particulate Drawings
only 䉱䉱 molecules in picture 3 and only 䊊䉱䊊 molecules in picture 5. The difference between particulate drawings of heterogeneous and homogeneous mixtures is the extent to which the different types of particles are randomly or thoroughly mixed. Picture 1 represents a heterogeneous mixture because the 䊏 atoms are not randomly mixed with the 䉬䊊 molecules, and pictures 2 and 4 represent homogeneous mixtures because the two types of particles in each picture (䉬 atoms and 䊊䊏 molecules in picture 2, 䉬 and 丢 atoms in picture 4) are randomly mixed together. Elements, substances that contain only one type of atom, are depicted in particulate drawings in one of two ways: as individual atoms or as molecules containing only one kind of atom. Compounds, on the other hand, have a least two types of atoms in them. In particulate drawings that contain mixtures (pictures 1, 2, and 4), each particle must be evaluated separately. Picture 1 contains 䊏 atoms (an element) and 䉬䊊 molecules (a compound) and is classified as having both; picture 2 also contains an element (䉬) and a compound (䊊䊏) and is also classified as having both. Picture 3 contains a diatomic element, picture 4 contains two different elements (䉬 and 丢 atoms), and picture 5 contains a single compound.
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More than a decade ago, Nurrenbern and Pickering alerted chemistry instructors to the fact that students who are successful in solving numerical problems may not understand the concepts underlying these problems (1). Others have used visual conceptual questions based on the particulate nature of matter to corroborate that different student populations exhibit this discrepancy (2–8). Many introductory college chemistry textbooks and American Chemical Society standardized exams have evolved to include particulate drawings, and instructional methods using particulate drawings have been effective in helping students answer visual conceptual questions (9–12). However, few studies have reported how successful and unsuccessful students differ in their thinking as they answer these questions. That is the purpose of this paper. The first part of this paper describes student interviews used to identify the ways students classify particulate drawings as pure substances, heterogeneous mixtures, or homogeneous mixtures. The classification schemes that these interviews found to be successful were incorporated into an instructional lesson that was administered to another set of students. The final portion of this paper reports on the effectiveness of this lesson.
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State of matter __________________ __________________ __________________ solid liquid gas Physical composition of matter __________________ __________________ __________________ pure substance heterogeneous homogeneous mixture mixture Chemical composition of matter __________________ __________________ __________________ elements compounds both
Figure 1. Visual conceptual questions used in this study.
Journal of Chemical Education • Vol. 77 No. 6 June 2000 • JChemEd.chem.wisc.edu
Research: Science and Education Table 1. Classification Methods Identified from Student Interviews Method
Student Responsea
X1
No. (%) of Responses Control Groupb
Experimental Groupc
z
pd
3/1,2,4/5
29.(45)
8.(13)
᎑3.93
.0001
X2
3/1/2,4,5
7.(11)
22.(35)
3.32
.0005
C
3,5/1/2,4
6.(9)
27.(44)
4.41
.0001
aResponses
represent pictures, by number (1–5), listed as pure substance / heterogeneous mixture / homogeneous mixture. bN = 65 students. cN = 62 students. dA p value < .05 is considered significant.
Student Interviews To better understand how students classify particulate drawings as pure substances, heterogeneous mixtures, or homogeneous mixtures, 65 students (mostly physical and life science majors) enrolled in a first-semester introductory college chemistry course were asked to classify the five pictures in Figure 1 according to their states of matter, their physical composition of matter, and their chemical composition of matter. These students had received traditional instruction regarding these topics and served as the control group for this study. The 44 students who agreed to be interviewed were asked to explain how they classified the five pictures according to the physical composition of matter. These interviews were recorded and transcribed verbatim. Student responses were analyzed to identify the classification methods used by successful and unsuccessful students. These methods are listed in Table 1 and are discussed below. X1 and X2 represent unsuccessful methods; C represents a method that resulted in the correct responses (discussed in the previous section). The percentage of students using X1, X2, and C do not add up to 100% because some students used other (often unidentified) classification schemes. Responses for 29 of the 65 students were consistent with X1. Students using this method identified picture 3 as a pure substance, pictures 1, 2, and 4 as heterogeneous mixtures, and picture 5 as a homogeneous mixture. The following student quote (which is representative of other student quotes) demonstrates that these students classified elements as pure substances, pure compounds (with two or more elements) as homogeneous mixtures, and all mixtures as heterogeneous mixtures:1 STUDENT A: For the pure substance [3], there are no other symbols in it that are unlike it, they’re all the same … they’re all triangles. For the heterogeneous mixture, I thought it was these three [1, 2, and 4] because they all had different things in them that weren’t all bonded together … different things are inside the mixture. They’re not all the same. For the homogeneous [mixtures], they’re all the same and they’re all bonded together. … They’re all the same molecule, so the mixture is all the same.
The majority of these students defined heterogeneous and homogeneous mixtures using macroscopic characteristics. Some students used a simple description based on “visual” cues (e.g., Student B), while others used a “sampling” definition
(e.g., Student C). STUDENT B: [A] heterogeneous [mixture] is different particles, you can actually see a difference and [in] homogeneous [mixtures] you really can’t see any difference in it. STUDENT C: If a mixture is not homogeneous, then you can take one sample from one area and it wouldn’t be the same as a sample from another, different area. [For a homogeneous mixture], if you take a sample in one area, it would be the same as a sample in another area.
Student D’s definitions of heterogeneous and homogeneous mixtures, as well as the real-world analogies evoked by the student, are consistent with this macroscopic view. STUDENT D: In a heterogeneous mixture you can see all of them, right? If there’s three different things mixed together, you can see all three. I think of Raisin Bran— you’ve got the bran and then you have the raisins. For homogeneous [mixtures] if you mix something up, you can see only one thing. Like if you mix Kool-Aid and lemonade, you just get one, colored thing.
While these definitions may be effective when visually inspecting a mixture (a macroscopic observation), they do not work when describing microscopic representations. Students using the visual definition classified pure compounds (like picture 5) as mixtures because they contain two or more atom types, but as homogeneous because they look the same throughout the picture, and classified all mixtures (pictures 1, 2, and 4) as heterogeneous because there are two different chemicals in the picture, and therefore they can “see” two different kinds of things in the mixture. The sampling definition works when looking at samples of a physical mixture because this sampling includes an enormous number of atoms and molecules among which slight variations in composition would go undetected. However, when taking different samples from a picture containing fewer than 20 atoms or molecules (pictures 2 and 4), these slight variations in composition can be very misleading. For example, although picture 2 depicts a homogeneous mixture (i.e., randomly mixed), it is possible to split the picture in half so that the left half has two 䊊䊏 molecules for every two 䉬 atoms, while the right half has three 䊊䊏 molecules for every two 䉬 atoms. While this may seem like a fine distinction, students using the sampling definition may use these slight differences as evidence that all mixtures are heterogeneous mixtures. For X2, which was used by 7 of the 65 control students, students identified picture 3 as a pure substance, picture 1 as a heterogeneous mixture, and pictures 2, 4, and 5 as homogeneous mixtures. Although these students were able to correctly assign the pictures of heterogeneous and homogeneous mixtures, they classified pure compounds (like picture 5) as homogeneous mixtures. The most striking difference between these students and those using X1 is their definitions of heterogeneous and homogeneous mixtures. Students who successfully identified heterogeneous and homogeneous mixtures were more likely to use definitions based on how thoroughly mixed (or randomized) the sample was. As an example, Student E correctly classified pictures 1 and 2 on the basis of how evenly mixed the two types of atoms and molecules were.
JChemEd.chem.wisc.edu • Vol. 77 No. 6 June 2000 • Journal of Chemical Education
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Research: Science and Education STUDENT E: I put number 1 as a heterogeneous mixture because they’re not equally distributed, it looks like the outsides are different than the inside. For homogeneous mixture, I put number 2 as homogeneous because the O and the boxes are bonded [together] and are evenly mixed with the [diamonds].
Only 6 of the 65 control students were able to correctly classify all five pictures and each of these students used the randomly mixed definition to classify the pictures. Before the interviews were conducted, there was no indication that successful and unsuccessful students were using different definitions of how to distinguish pure substances and heterogeneous and homogeneous mixtures. However, on the basis of these interviews, it appears that definitions based on how thoroughly mixed or randomized a sample is can be successfully used to identify heterogeneous and homogeneous mixtures, at both the macroscopic and the microscopic level. To test this hypothesis, I created a lesson on pure substances and heterogeneous and homogeneous mixtures that focused on the randomly mixed definition. Instructional Lesson The 50-minute lesson focused on how to classify substances at the macroscopic and microscopic level according to four categories: (i) solids, liquids, and gases; (ii) pure substances, heterogeneous mixtures, and homogeneous mixtures; (iii) elements and compounds; and (iv) atoms and molecules. The students were informed that these categories represent different ways of classifying the same samples and they are related. For example, elements and compounds can be viewed as a subcategory of pure substances, and atoms and molecules can be viewed as a subcategory of elements (i.e., all compounds are made of molecules, but elements can exist as atoms or molecules). The students who viewed this lesson serve as the experimental group for this study. To help students classify macroscopic samples, the instructor passed around test tubes containing samples of pure elements, Cu(s) and Br2(g); pure compounds, H2O(ᐉ) and NaCl(s); homogeneous mixtures, air(g) and I2 in H2O(ᐉ); and heterogeneous mixtures, pentane/water(ᐉ) and Al/Pb(s). To help students classify microscopic samples, the instructor used computer-generated visuals of the samples listed above. Each animation started out with a macroscopic drawing of the sample with three highlighted regions surrounded by a box. When the instructor clicked on each of the highlighted regions, the screen changed to a microscopic view of the atoms and molecules. When discussing the physical composition of the macroscopic samples and the microscopic computer images, the instructor focused on the randomly mixed definition. For example, when looking at the macroscopic sample of the aluminum–lead mixture, the instructor pointed out how the visual, sampling, and randomly mixed definitions were successful in identifying this mixture as heterogeneous. The instructor also used the microscopic drawings to discuss how the atoms were not completely randomized because chunks of each metal (which represent huge numbers of similar atoms bound together) can be seen. The students were cautioned that although the aluminum chunks and the lead shot were
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homogeneously mixed inside the test tube, the aluminum and lead atoms were not. Although the visual, sampling, and randomly mixed definitions are successful in identifying macroscopic samples of homogeneous mixtures, the visual and sampling definitions are not generally successful in identifying homogeneous mixtures at the microscopic level. For example, when discussing the microscopic view of the homogeneous I2-in-H 2O(ᐉ) sample, the students were told that this sample is a mixture because it contains two types of molecules. They were also told that at the molecular level, the visual definition of being able to see two or more different things is useful only for distinguishing pure substances from mixtures and not for distinguishing what kind of mixture (heterogeneous or homogeneous) the sample is. The students were also cautioned that when dealing with small numbers of atoms and molecules (in the case of these pictures, fewer than 50), the sampling definition may not be helpful because slight variations in the composition of individual samples can be very misleading. Effectiveness of the Instructional Lesson The questions in Figure 1 were administered as a quiz at the beginning of the next lecture period. Table 2 contains the number of students in the control (interviewed) and experimental (instructional lesson) groups who classified each of the pictures as solid, liquid, or gas. A χ2 test of independence was performed for each picture and the χ2 values and probability values (p) are also listed in Table 2.2 Tables 3 and 4 contain similar data for the physical and chemical composition of matter classifications, respectively. For the states of matter classification, 88% of the control students’ responses and 97% of the experimental students’ responses were correct. This is not unexpected, since many instructors and textbooks, including the one used in these classes (13, p 17), teach this topic using molecular pictures. However, the experimental students were more likely than the control students to correctly identify picture 4, the only liquid substance ( p = .008). Instruction using the computergenerated visuals appears to have reinforced the concepts that solid substances have distinct, repeating patterns and that gas molecules occupy the entire container (1). The percentage of correct responses for the physical composition of matter classifications was much lower for the control group (46%) than for the experimental group (80%). Neither set of students appeared to have difficulty assigning Table 2. Students’ Classifications of Microscopic Pictures: States of Matter Response, as No. (%) Responding a Picture
Control Group
Experimental Group
solid
liquid
gas
1
59.(91)
5.(7)
1.(2)
2
0.(0)
3
59.(91)
5.(7)
1.(2)
4
5.(8)
54.(83)
6.(9)
5
0.(0)
9.(14) 56.(86)
8.(12) 57.(88)
solid
pb
liquid
gas
61.(98) 1.(2)
0.(0)
2.22 .13
59.(95)
2.05 .15
0.(0)
2.22 .13
0.(0)
3.(5)
61.(98) 1.(2) 0.(0)
61.(98)
1.(2)
0.(0)
4.(6)
58.(94)
aThe bA
χ2
7.00 .008 0.68 .41
correct response for each picture is indicated in boldface. p value < .05 is considered significant.
Journal of Chemical Education • Vol. 77 No. 6 June 2000 • JChemEd.chem.wisc.edu
Research: Science and Education Table 3. Students’ Classifications of Microscopic Pictures: Physical Composition Response, as No. (%) Responding a Picture
Control Group pure hetero. substance mixture
Experimental Group
homo. mixture
pure substance
hetero. mixture
χ
2
homo. mixture
b
p
1
5.(7)
38.(58)
22.(34)
1.(2)
55.(90)
5.(8)
14.76
.0001
2
1.(2)
47.(72)
17.(26)
1.(2)
14.(23)
46.(75)
28.60
.0001
3
64.(98)
0.(0)
1.(2)
0.(0)
0.(0)
4
1.(1)
50.(77)
14.(22)
0.(0)
10.(16)
51.(84)
46.09
5
18.(28)
8.(12)
39.(60)
28.(46)
2.(3)
31.(51)
6.57
61.(100)
0.00
.97 .0001 .04
aThe
correct response for each picture is indicated in boldface. bA p value < .05 is considered significant.
picture 3 as a pure substance. Comparison of the responses for pictures 1, 2, and 4, however, demonstrates that students who viewed the instructional lesson were better able to correctly identify heterogeneous and homogeneous mixtures than those who did not (all p’s < .0001). Although the students in the experimental group were more likely than students in the control group to correctly identify picture 5 as a pure substance (p = .04), more than half of these students still categorized it as a homogeneous mixture. Therefore, it appears that instruction focused on the randomly mixed definition was successful in helping students distinguish heterogeneous and homogeneous mixtures, but was only moderately successful in preventing students from identifying pure compounds as homogenous mixtures. The responses of individual students in the experimental group were also analyzed to confirm that they were using the same classification methods as students in the control group. The common responses from students in both groups are listed in Table 1. The proportion of students from the experimental and control groups using X1, X2, and C were compared and the z values and p values are listed in Table 1. In particular, fewer students in the experimental group used X1 (p < .0001) and more used X2 ( p < .0005) and C ( p < .0001) than in the control group. The three classification schemes identified here appear to be developmental in nature: students start out using X1, assuming that all mixtures are heterogeneous and pure compounds are homogeneous mixtures; they then move on to X2, where they learn to correctly classify mixtures but still view pure compounds as homogeneous mixtures; and finally they reach C, where they can correctly classify mixtures and pure compounds. Therefore, instruction based on the randomly mixed definition that used computer-generated visuals appears to have helped the students in the experimental group progress from X1 through X2 to C more readily than students in the control group. For the classification according to chemical composition of matter, the percentage of correct responses was also lower for the control group (69%) than for the experimental group (84%). Comparison of the responses for pictures 1, 2, 3, and 5 demonstrates that students who viewed the instructional lesson were more likely to correctly classify the pictures as containing elements only, compounds only, or both (all p < .05, see Table 4). For picture 4, half of the students in each group correctly classified the picture; however, students in the control group were more likely to suggest that it contains both elements and compounds than students in the experimental
group ( p = .014). Owing to the low proportion of students in each group who answered this question correctly, it is likely that the students were having difficulty interpreting the picture in a way consistent with my intention. In general, however, it appears that this instructional lesson was also successful in helping students correctly identify microscopic pictures of elements and compounds. Although the lesson was not explicitly designed to address student classification schemes for distinguishing between elements and compounds (because they were not identified), it is not surprising that a lesson focused on microscopic representations of atoms and molecules would help students classify microscopic pictures as containing elements, compounds, or both (14 ). Implications for the Classroom For the past decade or so, chemical education researchers have stressed the importance of asking students to think about chemistry concepts at the particulate level (1–8). Although the inclusion of particulate drawings in traditional college chemistry textbooks and lectures has been slow, the evidence suggests that when students receive instruction including particulate drawings they are better able to answer conceptual questions that are particulate in nature (9–12), and this study is no exception. Both groups of students received instruction that stressed the particulate characteristics of solids, liquids, and gases, and both groups were successful at identifying particulate drawings on the basis of their states of matter. However, students who received instruction that focused on the characteristics of pure substances and mixtures at the microscopic level were more likely than students who received traditional
Table 4. Students’ Classifications of Microscopic Pictures: Chemical Composition Response, as No. (%) Responding Control Group
Picture
comelements pounds
a
Experimental Group both
comelements pounds
χ2
pb
both
1
2.(4)
19.(33) 36.(63)
2.(3)
6.(10) 53.(87) 7.72 .006
2
1.(2)
14.(24) 42.(74)
0.(0)
5.(8)
3
45.(79)
11.(19)
59.(96)
1.(2)
4
28.(49)
15.(26) 14.(25)
5
2.(3)
46.(81)
1.(2) 9.(16)
56.(92) 5.65 .018 1.(2)
7.28 .007
31.(51) 26.(43)
4.(6)
8.54 .014
58.(95)
1.(2)
4.53 .033
2.(3)
aThe
correct response for each picture is indicated in boldface. bA p value < .05 is considered significant.
JChemEd.chem.wisc.edu • Vol. 77 No. 6 June 2000 • Journal of Chemical Education
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Research: Science and Education
instruction at the macroscopic level to correctly identify particulate drawings of liquids, pure compounds, heterogeneous mixtures, homogeneous mixtures, elements, and compounds. These results suggest that the best way to help students develop the ability to think about chemical processes at the microscopic level is to instruct them using particulate drawings (including computer animations) in ways that are consistent with the methods typically used by these students. Although the use of particulate drawings is being promoted by researchers, chemistry instructors who choose to use them in instruction and assessment may encounter several difficulties. For example, it can be very difficult to create particulate drawings that faithfully represent chemical phenomena and test the concepts of interest (15). Another problem is that because many students are unfamiliar with particulate drawings, it is possible that they may misinterpret them.1 Since the whole purpose of introducing these drawings is to help students develop their ability to think about the interactions of particles, it is not surprising that students may initially have difficulty interpreting the drawings; however, these difficulties should disappear with additional exposure and practice. The results of this study suggest that, with proper instruction, students will become more adept at correctly interpreting these drawings. For example, using the data in Note 1 we can see that while 12% of the control group misinterpreted picture 1, only 6% of the experimental group misinterpreted it. Further, while only 58% of the control group correctly identified picture 1 as a heterogeneous mixture, 90% of the experimental group correctly identified it. As a result of student interviews, I identified three methods (visual, sampling, and randomly mixed) used by students to identify pure substances and heterogeneous and homogeneous mixtures. Although all these methods are successful for identifying macroscopic samples of heterogeneous and homogeneous mixtures, only the randomly mixed definition is effective at identifying particulate drawings of pure substances and heterogeneous and homogeneous mixtures. Therefore, if instructors are going to include both macroscopic samples and microscopic drawings of pure samples and mixtures in their instruction, they should focus on the randomly mixed definition for identifying these samples. I was also able to document three progressive stages that students use to classify particulate drawings of pure substances and mixtures. They start out using a method by which they assume that all mixtures are heterogeneous and pure compounds are homogeneous mixtures, then move on to a method by which they learn to correctly classify mixtures but still view pure compounds as homogeneous mixtures, and finally reach a method that allows them to correctly classify mixtures and pure compounds.
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Acknowledgments This work was funded by the University of Northern Iowa through its Multimedia Courseware Minigrant (Office of the Provost) and Summer Fellowship (Graduate College) programs. Notes 1. Eight of the 29 students in the control group and 4 of the 8 students in the experimental group classified picture 1 as a homogeneous mixture. Analysis of the student interviews revealed that these students viewed picture 1 as consisting of three 䊏䊏䉬䊊䉬䊊䊏䊏 molecules stacked on top of each other. Therefore, these students actually used X1, but misinterpreted the intended composition of picture 1. 2. Owing to the low number of student responses in many of the incorrect categories, most of the χ2 values calculated were for 2 × 2 contingency tables (correct vs incorrect, control vs experimental) and the degrees of freedom for these χ2 values are 1. For picture 5 in Table 3 and picture 4 in Table 4, a 3 × 2 contingency table was used and the degrees of freedom for these χ2 values are 2.
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Journal of Chemical Education • Vol. 77 No. 6 June 2000 • JChemEd.chem.wisc.edu
