Chemical Education and Spatial Ability Hans-Dieter Barke University of Hannover, 3000 Hannover, Germany Modern chemical education provides an introduction to the understanding of the structure of matter as consisting of small particles. Models of the structure of matter are among the most important means. Due to the importance of metals, salts, and other solids a t the beginning of chemistry education, close packing of spheres is introduced first, then crystal lattices or molecular models of other elements and compounds are added later. These structural models can be shown or even can be built by the students during the lessons, but often teachers prefer showing models as illus~rationsin school books or i n transparencies. Figure 1 offers some examples. Teachers exnect the students to recomize the illustrated space models'as three-dimensional &uctures. They expect, for example, that students are able to determine the coordination numbers 12 and 6 of the models (a) and (b) in Figure 1. Are those illustrations of space models actually recognized as being spatial by the learners? At what age is the spatial ability of the students sufEcient to be able to see spatial relations in two-dimensional illustrations? Are there differences between the perceptions of boys and girls? A specific test of spatial ability (called "space test") for empirical research has been developed leading to a n answer to these questions. Firstly, this space test will be presented. Later on the research regarding this test will be described and the results will be discussed. Testing Spatial Ability For the space test, illustrations of polyhedrons and spatial cubes were chosen that require spatial vision and are of central importance in mathematics, chemistry, and physics. The test contains 56 items arranged as multiplechoice questions that have to be answered within 45 min.
For each of the six groups of items there are two example questions that are explained by the teacher before the students have to answer the appropriate test questions. Five of those items are listed as examples in Figure 2. The right answers are bracketed. Initial data conf~rmthe quality of the space test, especially with respect to objectivity, reliability, and validity ( I ) . The space test, answer sheet, and pattern of right answers already have been published (2). A second altered version of the test exists in which the questions concerning only mathematical polyhedrons have been replaced by questions that are more relevant to chemistry (2).This test is just in the process of evaluation and will not be considered in the research described below. SpaceAn Important Parameter of Intelligence In psychology it is certain that intelligence is determined by several parameters, "Space" being a n assured primary parameter of intelligence. This factor, like other parameters of intelligence, appears a t a certain age of developm e n h n l y the minimum age remains controversial. Ausubel(3) claims that "no first-grade student achieves optimal spatial vision, even if he or she is trained." Bloom ( 4 ) states that "at the age of nine only 50% and a t the age of 14 about 80% of the parameter Space have developed." Hofstretter (5)assumes, that "on the average 80% of the IQ-grade is achieved by the age of 16." Trying to assign spatial ability to one of the three Piagetstages of intellectual development of young people, will almost certainly lead to the context of "formal operations of thinking." Figure 1, for example, makes clear that a "concrete" counting of spheres in order to determine coordination numbers isn't possible. It is difficult or impossible for the learner in the stage of "concrete operations" to solve these or related questions.
Figure 1. Structural models: (a) cubic closest packing of spheres (b) structural models of NaCl (packingof spheres and crystal lattice) (c)model of the saccharose-molecule.
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Thus, the question remains, "At what age does the stage of "formal operations" begin? Piaget ( 6 )mentions the range of 11-13 as the beginning ofthis stage. Bruner (7)assumes this to happen "at some time between 10 and 14" and Ausubel(3) points out that "between sixth and ninth grade the use of concrete defmitions decreases while the use of abstract definitions increases correspondingly." In his recent research Grieber (8)states that in 10th grade only 25% of the students achieve the stage of formal operations, 10% are thinking in a wncrete-operational way and 65% are at the transition of both stages of thinking. Finally, there is the problem of differences between the sexes. Ausuhel states: "Most researchers agree that boys are superior with respect to spatial and quantitative ability" To substantiate this result he assumes that "such differences are mainly determined through culture."
Age and Spatial Ability What is the minimum age for being able to rewgnize spatial relations in two-dimensional illustrations of structural models ? The age limits mentioned by the psychologists range from 12-16 years of age. Chemistry lessons at many German schools start in seventh grade (13-year-old students), a t others in eighth grade (14 years) or even in ninth grade (15-16 years). In which grade do students have sufficient spatial ability to interpret structural models in a three-dimensional way? One possible way of answering this question can he based on the consideration that the parameter "Space" is a primary parameter of intelligence. If a group of persons is tested by a normal intelligence test and the space test and afterwards a correlation between both results is calculated, the quality of this correlation permits the following statements. If there is a good correlation, the spatial ability of all students, compared with general intelligence, is developed equally stongly;
If there is only a weak correlation or even no correlation, considerable differences in the development of spatial ability can he realized.
A group of students (male and female) in the seventh, eighth, and ninth grade was selected for an intelligence test and the space test. The quality of the spot check was judged by compaling the evaluated Q Is' and the averages described in the intelligence test manual for all age groups (1).Table 1shows the spot check. The evaluation of averages achieved in the space test leads to the expected results. With the increasing age the averages rise. Boys achieve higher averages than girls a t the same age. Table 2 shows the relevant averages and deviations. Testing the correlation between performance in intelligence and spatial ability, Tables 3 and 4 make clear that a sufficient correlation does not exist for seventh graders. The judgement of the correlation coefficients of Table 3 shows that in seventh grade, except for two results, no correlation differs significantly from zero; i. e., correlations do Table 1. Spot Check of the Students' Group
all boys girls
7th grade
8th grade
9th grade
125 63 62
71 45 26
59 27 32
Table 2. Space Test Averages and Deviations (in brackets)
x all x boys x airls
7th grade 27.3 (6.1) 28.5 (5.7) 25.5 16.71
8th grade 30.0 (7.5) 31.3 (7.9) 27.4 (6.9)
9th grade 36.9 (9.1) 39.8 (8.6) 34.5 (9.31
How many cubes are i n t h e i l l u s t r a t e d packing of cubes ?
How many cubes are placed completely i n s i d e of t h e packing ? (1) 4 6 12 15 19 27
How many spheres are in t h e i l l u s t r a t e d packing of spheres ? 30 37 50 (55) 64 72 80
How many cubes are t o be seen only by two l a t e r a l f a c e s ? 1 4 6 (12) 15 19 27
How many spheres are placed completely i n s i d e of t h e packing 7 3 4 (5) 6 7 8 10
Figure 2. Five examples of the space test, correct answers in brackets. Volume 70 Number 12 December 1993
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Table 3. Correlation Coefficients between IQ's and Space Averages (italicized coefficients are significantly different from zero)
Grade 7a all boys girls
7b
7c
7d
7e
8a
8b
8c
9a
9b
.28 30 .28 .36 .62 .50 .72 .70 .78 .69 -.12 .59 .38 .61 .69 .78 .80 .85 .78 39 .47 .40 .27 .I5 .65 .70 .56 .96 .80 .60
of chemical reactions). I n wntrol proups, formulas were introduced by means of compariso~o f masses or the mole concept. These groups did not use structural models in their iessons (9).Without reproduc~ngthe relevant graphics or tables, the following findmgs wrrr obta~ned(70,. .The experimental gmup using structural models achieved signif~cantly(5%-level)better results in spatial ability than mouos. all control . . .The improvement of all groups can be rxplaincd through knoning and repeating ihe spa1.e itat. The b ~ improvement a ofthcrxprrimental group isdue toan increase in spatial ability.
Table 4. Averages of the Correlation Coefficients of Table 3
all boys girls
7th grade 0.41 0.46 0.39
8th grade 0.64 0.81 0.74
9th grade 0.74 0.74 0.70
not exist. Conversely, all wrrelation coefficients in grades eight and nine appear to be significantly different from zero, pointing to a correlation between intelligence and spatial ability. I t is striking that on the average the girls' correlation coefficients show a weaker correlati& than the boys'. These results can be interpreted in the following way. I n the case of a great number of seventh-grade students, spatial ability has not developed sufficiently compared with. general intelligence, so that teachers should avoid those problems that require the application of spatial ability. Particularly, students cannot be expected to rewgnize twodimensional drawings or illustrations of spatial structures as being three-dimensional. In grades eight and nine, spatial ability has improved so far, compared with general intelligence, that this ability can be presupposed in the malority of students. Due to the fact t h a t many students at-the-age of 14 or 15 are in Piaget's stage of "concrete operations of thinking", real spatial models of the structure of solids such a s close packingof spheres and crystal lattices should be employed first. Later on the teacher can beein usina two-dimensional illustrations of structural models. Now the students are able to recognize spatial relations that they have seen with real models. Because girls show some deficiencies in spatial abilitv. the teacher has to be es~eciallvsure that all girls are actively handling spatial models during chemistry lessons.
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Training of Spatial Ability Further researrh shows the connection between the use of structural models and the training- ofspatial abilitv. Is it possible to train and evidently improve students' spatial ability by using structural models in chemistry lessons? In some eighth grades, chemical symbols have been introduced in different ways and the success of the introduction has been researched.-of three methods, one was based on the use ofstructural models and the derivation of formulas from these models. This method proved to be the most successful (9). Parallel to this research, the space test was employed. As the design in Figure 3 shows, the test was taken before and after all lessons involving the introduction of chemical symbols. During this period of about four months the experimental group worked with structural models such a s packings of spheres, crystal lattices, and 3D-stereo-pictures. They built structural models of substances before and after chemical reactions, and derived chemical symbols from these models (formulas of substances, equations A
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Journal of Chemical Education
Interpreting the results with regard to the sexes, the presumption is confirmed that boys have greater success than girls with respect to spatial ability. While the increase of the boys' spatial ability was highly significant (1%-level),the girls'increase (as well a s that of the control groups) can be attributed to the effect of knowing and repeating the space test. The hypothesis that spatial vision can be improved by training could thus be verified only with regard to boys Girls and Spatial Ability The results of the previous research did not indicate a significant improvement in the spatial ability of girls. There could be several reasons. On the one hand, the possibility of training is limited for eighth-graders a t the ap.propriate . age. - Spatial . abilitv ~robablvcanbe trained more successfully in earlier grades. Because chemistry is not yet on the schedule in these grades, the training would have to be based on other subjects like mathematics, biology, or geography. On the other hand, it often is observed that when using structural models during the lessons the boys take the initiative and prevent eirls from handling the models or building them. I n order to observe the eirls in chemistrv lessons and to find out if it is possible to Gain spatial ability by using spatial models. some proups of eirls from an eighth made were taught sep&atelF he lessons were part o f th;! scientific proiect "Girls in science and technoloer" (11).German: ~ ~ d c h ien nNaturwissenschaften und yechnik, "MiNT". The girls, enrolled by their parents for the lessons of the MiNT-project, came together once a week in the afternoon and were taught in chemistry with the use of structural models for about six months (2). The space test was taken a t the beginning and a t the end of this teaching period. Besides the MiNT-experimental group two control groups were tested (Fig. 3). A group of girls of the same age and boys of the same age joined only the regular lessons in the morning. Without going into details, the results of the test are a s follows (2, 12). Comparing boys and girls the first test proved the result discussed above. The boys achieved the highest score; they have better spatial abilities than girls of the same age. In the sewnd test after the lessons with structural models all three test groups improved as the test was familiar to them. I t is striking that the increase in
-.
Yv Yv
X -X
Yn Yn Yn
experimental group control group A control group B X: lessons "structural chemistry" -X: not X (different lessons) Yv: pretest (spacetest) Yn: retest (space test)
Figure 3. Research design for using the space test
each of the control moups, who did not make use of struc.~ tural models i n their lessons, amounted to 14%. The increase seems to correspond to t h e knowledge . of the test, to the effect of practice. The results of the experimental group have increased by 20% hinting at t h e fact t h a t besides mere practice t h e training h a s affected the spatial abilities of the girls. By training this ability with t h e use of structural models, the girls who joined the MiNT-project achieved equal abilities to the boys of the same age. The girls' control group, however, achieved lower results i n the second test than the boys' control group. Thus, girls also improve their spatial ability when they get a n opportunity to work actively with the model material offered to them.
Conclusions I n trvine . to answer t h e auestions. at which age students' spatial abilities a r e sufficibnt to see and to intekpret structural models and their illustrations a s spatial, and to what extent spatial ability can be trained by lessons based on the use of structural models, t h e research h a s revealed:
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1. Spatial ability with respect to
S ~ N C ~ Uchemistry T ~ has not developed sufiiciently until eighth grade a t the age of 14. Before this time, spatial relations cannot be recognized by the majority . . of students. 2. I3y usmg structural mud& and appropriate illustrations. the spatial abilities 01'hoth h o p and girls can hr improved. 3. The effect of training spatial ability is particularly distinct when students work with snatial models in class. In o~ducatlonalgruups the teachrr has to make sure that rhc erl- nlw use th? mndd materrsl amvrlv and do not leave it just to the boys. Therefore, chemistry lessons where structural models a r e used more frequently have the following advantages:
1. nesidss knowledge in chemistry, the learners get an idea about the stucture of matter consisting of smnll particles. They hnvc in mind nn nrrnngcmmt of stoms and 3 change of t h ~ arrangement by chemical reactions. By the means of illustrative material, students understand chemistry and do not just learn some facts in order to pass the next exam.
In particular, students are able to differentiate between cryatal lattices and molecules. By deriving formulas from packing~ of spheres or lattices and using these models to illustrate formulas, they later will be able tolmagine crystal structures corresponding to given formulas of solids. Without lessons including the use of these models, students would not be able to get an idea about structures at all. Formulas would remain incomprehensible knowledge. 2. Chemistry lessons including the use of structural models support spatial ability. This ability is not only for the benetit of chemistry, but also of many other subjects like mathematics, physics, geography, ete. Studies show that spatial ability for success in school (13). seems eenerallv . ~. , imoartant . >loreover, puvmve prerequiitres fnr mans professions are nchievrd hy spatinl abilities. Currespunding to an estimntion of rxpens there sre mure than RU profesrinnr "which require a h~ghamount of spatial nhility tbr a sntiafanory practm" tj3,. Thcrcforc "items in a rrsr refrmna to watlal abdits haw n higher prognostic status", in indust& "space tests ba;e shown highest correlation to performance in profession; intelligence tests often rank second place" (14). Chemistry lessons based on spatial models of the struct u r e of m a t t e r show many advantages with respect to chemistry, to psychology of learning a n d even to aspects of sociology. Therefore, do not hesitate to employ packings of spheres, crystal lattices, o r molecular models i n your chemistry lessons.
Literature Cited 1. Barke, H.-D. PhD thesis, University ofHannouer,G e m y , 1978. 2. Bsrko, H.-D.; Kuhrk~,R. Einfuhrung in die Chem* Lung: Frsnkhrf New York, 1992. 3. Ausubel, D. P.Psycholo& dm Untemichts; Beltz Weinheim, 1974. 4. Bloom, B. S. Stability and Change in H u m o n Chametwistics;Mffiraw-Hill: New York. 1964. 5. ~ofstretter,P D J T J T J T J T ~ ~ ~ ~ Gner: ~~P~S ~ t~u~t aJrTt , I1971. I&; 6. &get, J.Psychol*&r I n f e N i g ~Rascher: ~; Stuttgert, 1967. 7. B m e r J. S.DsrPmeO&rEnkhune: Schwann: Berlin. 1972.
H n g : Frankfurt, New York, 1992. 12. Barke. H.-D.Chemieuwstdndnls udRoumuorstellung; MNU l s s P , 4 5 , 4 3 7 4 9 . 13. Rost, 0. H. Raurnvorstellung. Psychologiache und padag~gisckaAspkte; Beltx We"heim, 1977. 14. Krech. D.: Crutchfield,D. Grundlogen der Psychdogie: Belts: Weinheim, 1973.
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