r:
Investigation of Secondary School Students' ' Understanding of the Mole Concept in ltaly R. Cervellati, A. Montuschi, and D. Perugini lstituto Chimico "G.Ciamician." University of Bologna. Via Selmi, 2, 40126 Bologna, ltaly N. Grimellini-Tomasini and B. Pecori Balandi lstituto di Fisica "A. Righi." University of Bologna, Via Irnerio, 46, 40126 Bologna, ltaly The mole and related concepts are essential topics in secondarv school chemistm courses. but to teach and to learn these concepts appear to he remarkably difficult, as pointed out in several studies (1-6). Two of the authors of this paper carried out a small-scale investigation to ascertain the knowledge of chemistry among students entering first-year university courses in science (7).The questions that invoked the largest number of ahstensions and a high number of wrong answers were those involving the mole concept. On the basis of the results just mentioned and those of previous research works (8, 9),we decided to pursue more detailed research on the teaching and learning of this concept (10).This report concerns itself with the followingthree stages of this research: 1) a survey of the chemistry texthwks most used in Italian sec-
ondary schools, 2) devising and administering a multiple-choice test to a large numher of secondary school pu~ils . . in Boloena and the surroundingdistrict,and 3) analysis of the results of the diagnostic exam. Textbooks Analysls
Thirteen of the most commonly used secondary chemistry textbooks were examined, eleven of which were written by Italian authors and two of which were translations of American texts. In analyzing each book, three broad topics were considered: 1) how the mole is defined, 2) Avogadro's number and how it is used, and 3) how the concept of the mole is used.
Each of these topics was then divided into more specific subsets. Table 1summarizes the results of this analysis. How the Mole is Defined In the majority of the texts, the term mole was only a synonym for gram-molecule. A few texts, labelled 0 in Table 1, used an incorrect definition, such as the "molecular weight expressed in grams." In the case of text L, a contradiction was found since both a fairlv correct and an incorrect definition were mentioned. A further difficulty for the pupils resulted from the order
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Journal of Chemical Education
Summary ol lhe Textbooks Analysis
Table 1.
HOWthe
Concept of
.
Haw lhe Male IS Defined
T
A B
C
D E F G
H
e
x
t
1
2
3
L' Ma
N
0
..
Mole Is
9
Used 1 0
. . . .. . . . .. . . . . . . . 0
a 0
0
0
0
a
.
m
e
.
0
.
.
0 0
0
0
I
Avogadro's Number and How It Is Used 4 5 6 7 8
.
0
.
0
0
0
.
.
0
1. gatom, m k u l e . e t c , aredefhedasweights andmeterm moleis used asa syw
onym of gmoleculs. 2. galom. m h k , ,en., we definedas WBW a d m e male h Irmojuosdas a mitying concept but not linked to N. 3. gatm. ~ I B C etc., B weC defined ~ BS . w e i w am me male is I M d as a mitying concern and linked to N. 4. lk mole is linked to Nard me terms gatom. m k u l e . etc.. we abolished 5. The numerical value of N is mentioned.
9. lk mole is
"red aa a 'Y&er
of pani&s:~
la. The mole is wed to explain rtoichiomeby, inclvding urncentrations of oolutimr.
of topics presented in these texts, since Avonadro's number was introduced some time after the mole concept had been presented and understanding assumed. Furthermore, it must be pointed out that to confine the term of mole to a single
snecific case, Le.. molecular compounds, is incorrect, since the mole has been introduced in th; international System as the unit of amount ot'substance.'l'hedefinitionsri~~en in texts A and H can thus be criticized, because they fa:led to link the concept of mole with that of a standard number of particles. Onlv three texts (C. I. M)eave both a correct definition of the inole and linked it to the ieiinitiun oiAvogadn,'s number; i.e.. '.One mole oianv substance is that amount oithat substance which contains as many particles (molecules, atoms, ions, and so on) as there are atoms of '2C in exactly twelve grams of W." The Avogadro's Number and How It Is Used With a single exception (text O), all books gave the numerical value of Avogadro's number ( N ) ,although if one looks a t item 6 in Table 1,it can be seen that very little importance was given to its experimental determination. Eleven texts put an emphasis on the connection between N and the molar volume of gases. Only four texts define the Faraday as the charge of a mole of electrons, while six do not mention the Faraday a t all. How the Mole Concept k Used Very little attention was given to the use of the mole concept in stoichiometry. Only five texts explained the reaction coefficients in terms of a standard number of particles, and only four of these use the mole in a quantitative sense as a "particle counter." Most texts merely gave rules to be learned by rote to solve simple problems. Diagnostic Exam T o gain more detailed information about the pupils' knowledge of these concepts and their ability to use them, we desimed a diagnostic exam which would also enable us to investigate the pupils' most common mistakes and misconceuticms. Copies uf this 25.aut.stion, 4-oution, multiple.c.hoice exam (in the-original language), details df its &nstruction, and testing procedures are available from the authors upon request. The concept and the levels of understanding ( 1 1 ) which were tested are outlined in Table 2. Test items were placed into these classifications based on our perception of the knowledge required by a pupil of "average experience and training." We were, of course, aware that this "average" pupil does not exist and thus were prepared to deal with deviations that might occur from class to class. Seven different types of secondary school were tested. However, only three gave statistically significant results and are thus included in this discussion. The f i n t one is divided into two subgroups (AV and OB) because pupils came from two different schools of the same type. Table 3 presents the general characteristics and the mean scores of these three erouns of nuoils. The three erouns renresented a total of 78~stuhents:1~houldbepoinied out that s from one croup to another since the aces of the n u ~ i l differ the mile conceit id studied in differentiear; in different types of school. Though the test was given to the pupils toward the end uf theschool vear, the touicon electrwhemistw had not vet heen taught in mostclasses. We decided, therefore, to leave out of the analysis the two items involving these topics. The differences in the mean scores t hat we& observed can be relaced to the age of the pupils, to the teaching methcd, and t o the school curr~culum.A Eomparison between the results of the two Istituto Tecnico Industriale subgroups shows that the OB pupils performance was higher than that of the A V pupils. This difference can be attributed to the teaching method; chemistry is taught essentially with a traditional method in AV, while the OB is largely based on the American Chem-study project.
Table 2.
Scheme of the Concepts and Levels of Understanding in Diagnostic Exam
Levels of Understanding A1 A2 A 3 Total Concepts C1. General features of the male concept 5 5 1 11 C2. Avogadro's number: meaning of 2 3 1 6 numerical value and its determination 2 3 1 6 C3. Use of the moie concept to interpret chemical equations and to solve stoichiometric calculations including solutions concentrations 1 1 2 C4. Use of the mole concept to interpret Faraday's Laws 9 12 4 25 Total Levels of understanding: Al. Knowledge A2. Comprehension A3. Application and higher processes
Table 3.
Characterlstlcsol the Groups Tested, Mean Scores, and Reliability Coefficients
Hours1 week
Mean
No. of Devoted Scored Pupils Pupils' to 8 Standard Reliability Examined Aaes Chemistw Deviation Coefficient'
Type ol
Scbi
1stituto Tecnico lndustriaie
314
15
5
21
*1
0.77
(a = 17)
AVa
istituto Tecnico industdale
306
15
87
16
76
17
5
OBb
Liceo Classicob Lice0 ScientifKb
4 O
3
30i1 (a = 171 17 i 2 (0 = 17) 29 & 2 (a= 14)
0.78 0.78 0.69
a Technical Sawndsry Education [as defined in "Clssificatlon of Educational Sy, terns--Summary volume," oECD. paris. 1975). b GBnerai Semndary ducati ion (as defined in "Claosification of Educational SystemSummary volume," OECD. Paris, 1975). ~ ~ o haws u r devoted both to cheminry and biofw. dMinimum scare = -23, maximum score = 69. 'Reliability cosfficiem as given by K-R formula 20 (72).
Students in the Liceo Scientifico are typically one to two vears older than those in the other schools. We susnect that this a t least partially accounts for the high mean scores achieved. althoueh chemistrv a t the Liceo Scientifico is taueht with a tradition2 approach: ~t the Liceo Classico, chemi& and the sciences in general have little importance in the curriculum as a whole. (See note (a) in Table 3.) The results reflect this fact. I t is worth noting that all teachers were chemistry graduates; therefore, preservice training was assumed to be roughly the same and has not been included in the analysis. I t must be pointed out that the results from the two Istituto Tecnico Industriale subgroups are statistically more significant and even more representative than those of the two Liceo groups. because thi, test was giwm to all the pupils of all 1stituto Tecnico industriale schwls of Bnlornn, while it was riven only to afew of the classes in the other s~hools.The reliability coefficients were taken to be acceptable due to the nonhomogeneous structure of the test. The analysis of the results, therefore, can be carried out only by grouping together those questions which were intended to be homogeneous. Volume 59 Number 10 October 1982
853
Table 4. Inter-Item Correlation Coefllcients 02 02
1.00
03
0.93
03
06
Table 5. Percentage of Correct Answers to 0 2 , (13, and Q2-3 08
100
Student Mistakes and Misconceptions The Mole as a Standard Number of Particles Four questions on the exam concerned the mole as a standard number of particles. Two of them (62, Q3) were meant to test simple knowledge, whereas the other two (66, Q8) were aimed at testing comprehension. This group of questions proved to be homogeneous, as can he seen from the inter-item correlation coefficients, shown in Tahle 4. As a n example of item analysis, the results of these four questions will he discussed in detail. The texts of questions Q2 and Q3 are shown below (An asterisk denotes the correct answers throughout.) The term gram-molecule was used in these questions, because the textbooks analysis showed this to be most commonly used and thus most likely to be understood by the students.
School lstituto Tecnico lndustriale AV istituto Tecnico lndushiale OB Liceo Classico Liceo Scientific0
02
03
02-3
62
61
43
71 44
73 56 74
58 29
79
64
$2-Among the following definitions of the gram-molecule, chwse the correct one. The gram-molecule is: *A. the amount of substance containing N (Avogadro's number) molecules. B. the number of molecules contained in 1 g of the substance. C. the number of molecules contained in 22.4 liters of the substance, at STP. D. the volume of substance containing N molecules. $3-Gram-molecules of different substances: *A. always contain the same number of molecules. B. always occupy the same volume. C. always have the same weight. D. always contain the same number of atoms.
In both items, the wrong answers intentionally contained the pupil's most common misconcentions. ~. I he response distribution is shown in Figure I, where the facility ( f )and disrriminntion ( d l aoffirients are also shown (13).I t can he seen that the overall picture of these results is good enough for Liceo Scientifico and Istituto Tecnico Industriale but not for Liceo Classico. In Q2 the incorrect answer. B. was i referred t o all other wrong answers by all g r o u p s . ~ h ereason for this incorrect choice can he found in the misleading definition used by most teachers and some textbooks where the gram-molecule is identified with a weight in grams. Some pupils answered C to this question, showing their misconception that the molar volume of 22.4 liters is useful reaardless of the state of the substance. The choice of B in Q3, which was the most frequent wrong answer in almost all groups, confirms our impression about pupils' misunderstandings of molar volume. Similar results were obtained also in other research studies (6). The percentage of pupils who gave the correct answer t o both questions are shown in Table 5. I t can be seen that in Liceo Scientifico and OB Istituto Tecnico Industriale, the percentage decreases only slightly when both questions are considered; however, the decrease becomes more significant in AV Istituto Tecnico Industriale and even dramatic in Liceo Classico. These results also proved to be correlated to the mean scores of the whole test.
Figure 1. Distribution on Me alternatives tor 0 2 and 03. The f and dvalues represent the facilityand discrimination coefficients(-0.33 5 f 5 1: -1.33 5 d _ < 1.33).In this figureandthe followingthetwo IstitutoTecnico lndustriale subgroups are mentioned as OB and AV, the Liceo Classico group as LC, the Liceo Scientifico group as LS.
Figure 2. Distribution on the alternatives for 06 and 08 (for fand dvalues see Fig. 1).
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Journal of Chemical Education
..
~
~
Table 6. Percentage of Correct Answers From a Combined Analysls ofthe Four Items Q2,03, Q6,Q8 School lstituto Tecnico induslriale A V lstituto Tecnico lndustriale OB Lice0 Classic0 Lice0 Scientific0
Q2-3
Q5
(18
(16-8
(12-3-6-8
43
41
36
25
18
58 29 64
54 33 45
41 29 38
35 23 33
26
13 29
The texts of questions Q6 and Q8 are the following: quantity in grams equal to the number expressing the relative molecular weight of a suhstance represents: A. the weight in grams of one molecule of the substance. B. the weight of one molecule of the suhstance in gas phase. *C. the weight of N molecules of the suhstance. D. the weight of the amount of suhstance that reacts with 32 g of oxygen. $&--A quantity in grams equal to the number expressing the relative atomic weight of an element represents: A. the weight in grams of one atom of the element. *B. the weight of N atoms of the element. C. the weight in grams of the element. D. the weight of the protons in one atom of the element.
$6-A
Because these questions were meant to test the comprehension of the mole as a standard number of particles, the pupils were required to use this concept in a context where simple recall might lead to the choice of a wrong answer. All the wrong answers, particularly A, are grammatically very similar to that widely used in textbook definitions. The results are shown in Fieure 2. proved to be more difficult and, in general, These more discriminating than those discussed previously. Among the wrong answers most pupils chose were those connecting g-atom and g-molecule to the weight of a single atom or molecule. Table 6 gives the results of acombined analysis of answers to Q2,Q3, Q6, and 68. The percentage of right answers decreases remarkablv from Q(2-3) to Q(6-8). If this set of questions is a measure of complete comprehension, then it is obvious that only a few students have achieved the goal. The Mole as an SI Unit
Students generally were not familiar with the use of the mole concept as a unit of the amount of suhstance; most of them identified the term mole only with that of gram-molecule. This seems to he the result of the way most textbooks introduce this topic.
concept for solving swichiometric problems (including those about solutionsl. This is not sur~risinebecause the teachina method of most chemistry teachers i A t a l y does not includi laboratory activities. A Summary of the Results
Figures 3 and 4 show the results of the analysis carried out by grouping the items according to the concepts and the levels of understanding involved; the groups are those already reported in Table 2. Figure 3 shows the distribution of the mean percentage of right answers given by the pupils of each type of school to each mouu - - of questions concerning the same concepts. Figure 4 shows the distribution of the mean percentage of right answers given by the pupils of each type of school to each group of questions concerning the same level. The questions of category A3 have not been considered, being too few to be representative. I t can be seen from Figure 4 that there is a
Figure 3. Distribution of the mean pwcenlage of right answers corresponding to concepts C1. C2.C3. as defined in Table 2. X lstituto Tecnico Industriaie AV: Istit~toTecnIco lndustriaie OB; 0 Liceo Sciemifico; 0 Liceo Ciassico
The Mole and the Molar Volume
Both textbooks and teachers generally emphasize the concept of molar volume and the fact that equal volumes of gases represent equal numbers of molecules, which is based on the Avogadro's hypothesis. The value of 22.4 liters is well known by the students, hut most of them link i t to the grammolecule without taking into account pressure, temperature, or condition of state. Avogadro's Number
The students from the three different types of school were
all somewhat familiar with the magnitude of Avogadro's number. However, very poor results were obtained in the question concerning its experimental determination. Thii can be attrihuted to the superficiality with which this topic is generally dealt both by textbooks and teachers. Stoichiometry
With the exception of the OB Istituto Tecnico Industriale, most students showed several difficulties in the use of the mole
Figure 4, Dislribution of the mean percentage of right answers correswndlng to Ieveis of understanding A l , A2 as defined in Table 2. Volume 59 Number 10 October 1982
855
systematic decrease of t h e percentage going from t h e A1 questions to t h e A2 questions.
Some Final Remarks and Proposals Having obtained t h e evidence t h a t t h e mole concept is n o t mastered h v most ~ u ~ i lwe s ,shall t r v t o retrace t h e possible W e think t h a t t h e main causes causes of s&h a r e found in t h e chemistry curriculum which is taught in secondary schools i n Italy a n d i n teacher training. Curriculum Content. The approach to the study of chemistry is in most eases hased on the introduction of atomic and molecular structures. Such an approach is suitable to higher level courses, when both general and specific information necessary to handle quantum concepts is already known to the students, hut we do not think it is likely to give good results in an introductory course on chemistry. Other authors also are of the same opinion (14-15). Methodology. Both the Italian school structure (the last reform dates hack to 1923) and the unwillingness of the teachers to use laboratories. even where thev exist. are the causes of the almost complete ahsence of experimental activities in the scwnce courses. m u thi+olnim~sly allectr the quality of the reaching. Srhdrnl L'ruluolton. The evaluatim instrumenrs used are almost all of a very traditional kind (in Italy this means that oral examinations are mainly used), which encourages the students to learn by rote. Teacher Training. In Italy the statement that "he who knows something knows also how to teach it" is still accepted.
.
T o overcome t h e difficulties which arise from t h e situation described, we believe t h a t i t is necessary: 1) To increase the importance of chemistry in the secondary school
curriculum. The revision should include increasing the number of periods of chemistry and distributing them over more than one year. Scientific education at this level should follow without interruptions that of the previous level, and the chemistry curriculum should be linked both to nrevious knowledee and to the traching uf phviim in a parallel ccnrrae. A hill oireform of the Italian secondary school is being discussed, which xhwld aim at revising the present etmcture ofour schud system and eitaldishing a comprehensive type of school. This opportunity must he taken in order to introduce changes in the contents and methods of chemistry teaching. 2) To rearrange the chemistry contents in the curriculum. If chemistry in the new secondary school has the position we hope, it will be possible to make the study more effective and attractive by dividing chemistry teaching into two stages, as suggested by L. Paoloni (14). Chemistry should be based on the postulates and procedures of "classical chemistry" in the first stage, whereas the theory of electronic structure of the atom and chemical bond should be introduced in the second staee in order to rationalize the chenlical concepts prerlouzly learned. As far as the mole concept is r~mrrnrd,iui learning requwes that both same "empirical" concepts uuat~er,operational d r t ~ n ~ t i uufn mass, phyairal state, chemical and physical change, compound, element, model) and
856
Journal of Chemical Education
some "theoretical" concents molecule. formula. relative . (atom. . atomic and molecular mass, etc.! should h~ mastered hg the students. Empirkalomwprs should beacquired dur~ngrhe fimt stage. whereas theoretical ones should find their place halfway hetween the first and the second. An example of analysis of hierarchies among the concepts which underlie the mole is given in Reference (5). Such an approach to chemistry teaching, of course, requires that concepts should be taught only when pupils have reached the level of cognitive development necessary to gain full understanding; it should therefore be carefully checked that they have reached such level. Some authors (16-17) suggest that learning the mole concept involves formal thinking (as defined by Piaget) while others (18) maintain that an adequate training a t the canmete operational level is all that is required. 3) To revme the teaching methods. Chemistry teaching should he hased on laboratory activities, especially in the first stage. The laboratory is not simply a "teaching a i d but rather the best place where mental abilities linked to experimental methods can he developed. Finally, we are aware t h a t n o reform could give a n y positive result unless those who actually have to p u t i t i n practice a r e really convinced t h a t t h e changes a r e necessary a n d have received a n adequate preparation. Therefore, teacher p r e s e ~ c e and in-service training m u s t include t h e necessary activities to make these changes possible.
Acknowledgment T h e authors wish to t h a n k t h e teachers and t h e students of t h e schools who took Dart i n this investieation. W e also thank Dr. F. Viaggi. Mr. i'errari,and Mr. Gi&nnnnrdi u f t h e C u m ~ u t a t i o nCentre of the lstiruto di Fisica-Boloma for their a s s i s k e in t h e calculations, and Miss G. Roffi f& typing the manuscript. Literature Cited (1) Kolh,D..J. C~~~,E~u~.,55,728(1978). 12) Dierks, W., Eur J Sei.Educ., 3, I45 (19811. (3) Duncan, 1. M.,and Johnston,A. H.,Edue.Cham., 10,213 (1973). (0 Gower, D.M.,Dsnieh,D.J.,andLloyd,G.,Seh. Sci. Re~..58,658(1977). (51 Gouer,D. M., Daniels, D. J., and Lloyd, G., Seh. Sei. Re". 59,285 (1977). (6) Novih, S., and Menis, J.,J. CHEM. EDUC.,53.720 (19761. (71 Cervellati, R., Manfrin, M. F., and Perulini. D., Lo Chimico ndlo Scuola, 114-5.74 (1979). R i d . M.,"IIm"eettodi massan.ll'inwgnam.ntoxmndariariari"pepeiiii.~~PhvsicnTheis, University ofBologns, Italy, 1977. Bettoli, D., "11 mncetto di form nell'insegnsmentoaemndario superiom."Phyaica Thesis. Universityof Bologna, Italy, 1978. Monkusehi,A.,"IIeoncettodimolenell'inse~mento-ndariosuperiore," Chemistry Thesis, Univ~rsityof Bologna, Italy, 1980. Bloom, 8.S.,"Taronomy ofEducationa1Ohjwtive Handbook 1: Cognitive Domain: LongmanGroupLtd.. London. 1956, p. 18. Kuder, G. F..and Richardson, M. W.. Psyrhometriko.2.151(1937). Nedelsky. L.. "Science T~schingandTestin~:Harcourt, Brsceand World Ine.,New
York,1965. (14) Paoloni, L., Eur J. Sei. Edue., 1,365(1979).
(15) Mirone, P., La Chimico nailo Scuola, 1112.8 (1980). (161 Shayer,M..Edue. Chom..7,182 (19701. (17) Ingle.R.B..and Shsver.M.,Edue.Chem.8.182(19711. (181 Rawell, J. A., and D a w n , C. J., Sci. Educ., 64,693(1980).
