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Problem‐solving Processes of Nigerian ChemistryTeachersJ. C. Adigwe aa Institute of Education, University of Calabar , Calabar, NigeriaPublished online: 07 Jul 2006.

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Research in Science & Technological Education, Vol. 10, No. 1, 1992 93

Problem-solving Processes ofNigerian Chemistry Teachers

J . C. A D I G W E , Institute of Education, University of Calabar, Nigeria

ABSTRACT This study investigated the problem-solving difficulties of 240 chemistry teachers inNigeria. The research instruments were three written tests and an interview. The analyses of thewritten responses and problem-solving proposals revealed that: (1) most of the teachers wereincapable of constructing mental representations of the chemical problems and had difficulties inconstructing appropriate solution plans; (2) most of the teachers had inappropriate problem-solvingapproaches and limited problem-solving strategies (they relied mostly on the use of algorithms);(3) most of them exhibited structural errors relating to the generation of wrong information andmisapplication of the given information in solving the problems; (4) most teachers did not evaluatetheir solution processes. The implications of these findings are discussed.

Introduction

A chemistry teacher in a secondary school must be proficient in the intellectualdemands of chemistry at that level and more. The first step in the academicpreparation of chemistry teachers is, therefore, to ensure that they acquire athorough knowledge of the fundamentals of the subject and its process skills.Thus, Bajah (1979) insisted that the mastery of chemical concepts, principles andprocesses must be seen as the first step in the education of secondary levelchemistry teachers, who must be confident and resourceful. The issue of acade-mic competence of chemistry teachers is very crucial: how much knowledge ofchemistry do they possess; how much of this knowledge is functional in the sensethat they can apply it directly and correctly in solving chemical problems; and howeffectively can, they communicate the knowledge they possess to their students?Although problem-solving is regarded as very difficult for secondary schoolstudents because it is a complex intellectual task (Luria, 1976; Larkin, 1980) andone of the principal causes of scholastic failure in school science and mathematics(Gil Periz and Terrogrosa, 1981); it will be highly embarrassing if teachers, whoare supposed to inculcate the skills and processes of problem-solving in students,lack such skills that are basic for developing understanding of the processes aswell as the content of science. Additionally, when one considers that in Nigeriapupils regard their teachers as fountains of knowledge, the teachers' knowledgeand academic achievements invariably affect what the pupils learn and

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94 / . C. Adigwe

assimilate in the classroom (Oberlin and Saunders, 1973; Bajah, 1976; Gil Perez,1982). Any misconceptions or learning difficulties in the acquisition of conceptualknowledge/skills and problem-solving skills the teachers may have will, therefore,be acquired by the students as most classroom teaching, often than not, involvesimparting teachers' knowledge and skills to the students, who have been madepassive receptors in the instructional setting. Any improvement in the quality ofchemical education in the country must, therefore, start from the improvement inthe quality of the teachers of chemistry.

It was in the light of this that this author decided to explore the problem-solving processes of pre-service chemistry teachers in Nigeria (Adigwe, 1991). Thefindings of that study indicated that most of the preservice chemistry teachers inNigeria were not properly prepared in the academic demands of the subject.Their knowledge of chemistry, relevant mathematics and problem-solving capabil-ities were inadequate for die job of chemistry teaching at the secondary schoollevel. On the basis of these findings about the preservice chemistry teachers, thisauthor decided to investigate in-service chemistry teachers. The review of avail-able literature on chemical problem-solving indicated that no attempts had beenmade to explore the problem-solving processes of chemistry teachers with a viewto identifying the difficulties or errors in the processes they employ in solvingquantitative problems in chemistry.

This study, therefore, attempted to identify any persistent problem-solvingdifficulties that chemistry teachers may experience in solving quantitative prob-lems by comparing the problem-solving processes of the successful and theunsuccessful teachers.

Research Questions

The following research questions were advanced.

(1) Are there significant differences between the successful and unsuc-cessful teachers in problem understanding and representation?

(2) Are there significant differences between the successful and unsuc-cessful teachers in construction of problem-solving plans?

(3) Are there significant differences between the successful and unsuc-cessful teachers in execution of problem-solving operations?

(4) Are there significant differences between the successful and unsuc-cessful students in exhibition of structural errors?

(5) Are die successful teachers more likely to evaluate dieir problem-solving processes dian the unsuccessful teachers?

Research Methodology

The Sample

The subjects consisted of 240 chemistry teachers in five Nigerian states (Anam-bra, Imo, Cross River, Akwa Ibom and Bendel) who were willing to participate inthe study. They were all non-graduate teachers holding Nigerian Certificate inEducation with chemistry as one of their specialisation areas.

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Problem-solving Processes 95

Design

A repeated-measures design with three written tests (constructed to assess eachteacher's problem solving capability, knowledge of chemistry and mathematics)was employed. In a repeated measures design each subject in the sample is givenall the treatments (Pedhuzer, 1973).

Instrumentation

The three types of tests developed were the free-response, structured-responseand mathematics skills tests. The free-response test (FRA) consisted of fourquantitative chemical problems based on senior secondary school chemistrysyllabus. The teachers were instructed to list their computational steps beforesolving each of the problems. This instruction was intended to make the teacherthink about the problems and write down their procedures for each problem theysolve. This was used in the analyses of the teachers' problem solving procedures.

The free-response problems were solved and the conceptual knowledge/skillsinherent in them were constructed into sub-problems. These constituted thestructured-response test (STA). It was meant to assess the conceptual knowl-edge/skills possessed by the teachers. Since problem solving in chemistry demandsmathematical operations, it was necessary to isolate the difficulties that mightarise from the lack of mathematics skills from those arising from lack of problem-solving skills. In developing the mathematics skills test (MTA) the free-responseproblems were solved and the mathematical operations inherent in them wereisolated. From these mathematical operations, problems (without chemical infor-mation) were then constructed. The three tests were found to have facility indicesbetween 0-32 and 0-40, using the percentage mean mark for a test (Morrison,1978). For a diagnostic purpose this was judged adequate.

Procedure

The tests were administered separately on three different occasions. The FRA wasadministered first, followed after 1 week by the STA and then the MTA afteranother week. Since these tests were not identical, and were administered atintervals of some weeks, an order effect among them was not expected (cf. Fox etal., 1982).

TABLE I. Means and standard deviations ofteachers' performances in FRA, STA andMTA

Tests FRA STA MTA

X 42-92 69-34 60-28SD 24-00 21-68 22-43

N=240.

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96 J. C. Adigwe

Treatment of Data

The statistical properties of the teachers' scores were determined and collated.Tables I, II and III present the statistical properties of the three tests. The meansof the teachers' scores in these tests appeared to be different.

TABLE II. One-way

Source

TreatmentError

Total

ANOVA for teachers' performance in tests

SS

113,546233,400

346,946

DF

2714716

MS

56,773326-89

57,099-89

FRA, STA and

F

173-68

MTA

Sign

P<0-05

In order to test for significant differences among the three means a one-wayANOVA was done. Table II presents the ANOVA results. This indicated thatthere were significant differences in the means of the scores. Further analysisusing Scheffs method (Ferguson, 1976) revealed significant differences betweenany pair of the means.

TABLE III. Multiple compartments of i1

values for FRA, STA and MTA

FRASTA 256-62 —MTA 110-79 30-18 —

FRA STA MTA

(K-1)F=2F.Note: dfs=2, 714 at 0-05 level

(F=2-996; 2^=5-98). These values weretested against the quantity (K— l)F, whereK is the number of groups being com-pared, and F the value from table with dfs2 and 714.

Categorisation of Teachers' Performances

In order to investigate the difficulties in problem-solving processes of theteachers it was necessary to categorise them into higher and low achievers inchemical knowledge (STA), mathematics (MTA) and problem solving (FRA), andidentify those who were successful and those who were unsuccessful in solvingproblems. The problem-solving processes of these groups were, therefore, ana-lysed. Such an analysis revealed the unsuccessful teachers' areas of difficulties. Acut-off point of 70% was used for the categorisation (see Fig. 1). The result of thiscategorisation is presented in Table IV.

Interviews

A post-problem-solving technique was employed in exploring the teachers' rea-soning processes when they solved problems. The interview focused on and

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Problem-solving Processes 97

Total sample

( I ) '

Unsatisfactory chemistryand mathematics

( a ) Poor chemistry only(b ) Poor mathematics only( c ) Poor mathematics and

chemistry(scores < 7 0 % on eachof ( a ) , ( b ) a n d ( c ) )

( 2 )Satisfactorymathematics andchemistry ^

(scores ^ 70%)

Successful problem-solvers(scores 5 70% onfree-response problems)

(E )

Unsuccessfulproblem-solvers(scores < 70% onfree-response problems)

FIG. 1.

TABLE IV. Categories of teachers' performances

Testcategories FRA STA MTA No. of teachers Diagnosis

H H H 48 Good in problem-solving,(20%) chemical knowledge and

mathematics skills

H L L Nil Good in problem-solvingonly

L H H 91 Good in chemical knowledge(37-92%) and mathematics skills only

L L H 19 Good in mathematics skills(7-92%) only

L H L 39 Good in chemical knowledge(16-25%) only

H L H Nil Good in problem-solvingand mathematics only

H H L Nil Good in problem-solvingand chemical knowledge only

L L L 43 Not good in the three skills(17-92%)

B

C

D

E

F

G

H

H=high scores (>70%); L=low scores (<70%).

probed their problem-solving skills as exhibited in their written responses for allthe free-response problems. A random subsample of 20 successful and 40unsuccessful teachers from categories A and C in Table IV were interviewed.These numbers were taken on the basis of successful/unsuccessful teachers' ratioof approximately 1:2. These represented 42 and 44% of the successful andunsuccessful teachers.

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98 J. C. Adigwe

Protocol Analysis

The teachers' verbal responses were tape-recorded and later translated intoprotocols. The analysis of the protocols involved careful examination of ateacher's •written responses together with the computational steps he (or she) hadwritten down. The protocols were hand-coded using a modified version of thecoding scheme used by Gabel et al. (1984) in the analysis of students' problem-solving behaviour, and a problem-solving checklist. For a research question thediscrete data for each subcategory (in the appropriate main category for thatquestion) for all the problem solutions were summed up and the percentagefrequency was determined for both the successful and unsuccessful teachers. Thiswas done because the relation was obscured in frequency tables owing to anunequal number of problem solutions (80) of the successful teachers and 160solutions for the unsuccessful teachers. The percentage calculation transformsboth rows to a common base and makes the comparison and the relationshipbetween the two groups clearer. A 2 X 2 Chi square test with Yate's Correction(Ferguson, 1976, p. 201) was done on the frequencies to determine the signifi-cance of any differences between the two groups of solvers in their performancesof the problem-solving skills.

Results

Problem Understanding/Representation

Table V indicates that a significant difference exists between the successful andunsuccessful teachers in their capabilities to identify, understand and work withinthe problem conditions/restrictions. In other words, the successful teachersrestricted their problem-solving operations within the scope specified or deter-mined by the problem conditions. In other subcategories there were statisticallyinsignificant differences.

Table VI indicates that:

(1) the successful teachers significantly differed from the unsuccessfulteachers in their capabilities to state the useful relationships betweenthe knowns and unknowns of the problems;

(2) the successful teachers were found to check the validity of therelationships between the known and unknown they stated forsolving the problems than the unsuccessful teachers;

(3) the successful teachers significantly differed from the unsuccessfulteachers in their capabilities to translate physical principles/relation-ships into correct mathematical relationships/formulae;

(4) the successful teachers significantly differed in their capabilities tocorrectly transform rules/formulae in order to solve the problems;

(5) there was no significant difference between both groups in theirlikelihood to make estimations of the possible solutions to theproblems at the planning phase.

The successful teachers, therefore, differed from the unsuccessful teachers intheir capabilities to construct problem-solving plans.

Table VII shows the following.(1) Successful teachers significantly differed from the unsuccessful

teachers in logical analyses and organising skills as shown by the

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Problem-solving Processes

TABLE V. Protocol category I: problem understanding

99

Protocolsubcategories

1. Correct interpretationof data provided inthe problem statement

2. Correct descriptionsof the nature ofthe unknown

3. Correct descriptionsof the basic concepts,principles, laws, rulesinvolved in theproblems

4. Correct descriptionsof the conditions/restrictions in theproblems

NSt

NU

X2

NS

NU

£NS

NU

X2

NS

NU

X2

fNS=number of successful teachers.NU=number of unsuccessful

1

20(100%)

40(100%)

—

19(95%)

40(100%)2-2019

(95%)39

(97-50%)0-60

18(90%)

14(35%)16-31*

Problems

2

20(100%)

37(92-50%)

2-4516

(80%)28

(70%)0-8517

(85%)25

(62-50%)3-45

17(85%)

11(27-50%)17-75*

*P<0-05;df=l; criticalteachers.

3

20(100%)

39(97-50%)

2-1518

(90%)33

(82-25%)0-87

19(95%)

33(82-25%)

2-24

18(90%)

10(25%)

22-66*

value of X2

4

18(90%)

30(75%)2-1819

(95%)31

(77-50%)3-3513

(65%)36

(90%)5-33*

13(65%)

8(20%)3-08

=3-84.

percentage of non-systematic approaches of the unsuccessful teach-ers.

(2) While all the successful solvers were able to initiate some approachesto tackle the problems and had solutions most of the unsuccessfulteachers could not initiate appropriate problem-solving approachesand or had no solutions.

(3) The unsuccessful teachers significantly differed from successfulteachers in having more incomplete solutions.

(4) The unsuccessful teachers significantly differed from the successfulteachers in having more non-systematic productions. The successfulteachers, therefore, significantly differed from the unsuccessfulteachers in the execution of problem-solving operations.

Table VIII indicates that the successful teachers differed from the unsuccessfulteachers in correct application of information, and/or data and generation of thenecessary correct information for solving the problems.

Table IX indicates that both groups only differed in checking the structuralerrors in their problem solving processes.

Discussion

Both the successful and unsuccessful teachers were capable of interpreting thechemical data and principles, and of describing the unknowns involved in the

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100 J. C. Adigwe

TABLE VI. Construction of problem-solving plans

PT-J

r n atocolsubcategories

1.

2.

3.

4.

5.

Stated possibleuseful relationshipsbetween the knownsand unknowns

Checked the validityof the relationships

Translated physicalprinciples/relationshipsinto correct mathe-matical relationships(where appropriate)

Carried out correcttransformations ofrules/equations/formulae(where appropriate)

Estimated possibleanswers to theproblems

Groupsof

teachers

NS

NU

tNS

NU

tNS

NU

X2

NS

NU

X2

NS

NU

X2

1

19(95%)

15(37-50%)18-15*

15(75%)

9(22-50%)15-25*

20(100%)

10(25%)

30-08*

20(100%)

9(22-50%)32-08*

2(10%)

7(17-50%)

0-87 .

Problems

2

15(75%)

13(32-50%)

9-72*

10(50%)

7(17-50%)

6-79*

+

+

—+

+

—6

(30%)10

(25%)1-83

3

17(85%)

14(35%)13-47*

14(70%)

10(25%)11-20*

18(90%)

13(32-50%)17-77*

18(90%)

10(25%)

22-66*

3(15%)

6(15%)0-15

4

13(65%)

10(25%)9-03*

11(55%)

8(20%)7-46*

14(70%)

7(17-50%)

5-32*

14(70%)

6(15%)6-87*

5(25%)

10(25%)0-10

*P<0-05; d f= l ; +not applicable in these problems.

problems correctly. However, the unsuccessful teachers could not identify and/orunderstand the conditions of the problems in spite of their adequate knowledgeof the principles and data in the problems. In some instances this gave rise to'illegal' applications of the principles and manipulation of data. The reason forthis was not obvious. Since both groups had adequate knowledge of the subjectmatter one would have expected them not to differ significantly in their capabili-ties to identify and define the conditions in the problems.

Most of the unsuccessful teachers were incapable of stating the correct rela-tionships between the knowns and unknowns of the problems, checking validity ofsuch relationships, translating mathematical relations, transforming rules/formu-lae in order to solve problems and making estimates of the possible solutions ofthe problems at the planning phase. These difficulties may be attributed to theirinabilities to reason with data, apply the necessary knowledge, recall or recogniseitems of correct knowledge and incapable of generalising or integrating conceptsand principles to related conditions or perceptual set.

Most of the unsuccessful teachers exhibited structural errors relating to theirincapability to generate the necessary and correct information for solving theproblems and misapplication or disregard- of information. The occurrence of

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Problem-solving Processes 101

TABLE VII. Executive operations in problem-solving

Protocolsubcategories

1. Lacked approach/no solution tothe problems

2. Systematic approachto the problems

3. + Incompletesolutions

4. Systematicproductions

Groupsof

teachers

NSNU

X1

NS

NU

X2

NS

NU

X2

NS

NU

X2

1

Nil13

(32-50%)8-02*

18(90%)

12(30%)19-28

Nil

5(12-50%)10-11*

18(90%)

11(27-50%)20-89*

Problems

2

Nil12

(30%)7-99*

14(70%)

10(25%)11-20*

2(10%)

9(22-50%)

1-69

13(65%)

10(25%)9-03*

3

Nil8

(20%)10-29*

17(85%)

18(45%)8-52*

Nil

6(15%)3-99*

17(85%)

15(37-50%)12-19*

4

Nil13

(32-50%)8-02*

16(80%)

11(27-50%)14-85*

3(15%)

10(25%)5-84*

15(75%)

10(25%)13-69*

*P<0-05; d f= l ; critical value of *2=3.84.

TABLE VIII. Structural errors in problem-solving

Protocol •subcategories

1. Disregarded providedinformation/data

2. Misappliedinformation/data

3. Disregarded generationof information(where necessary)

4. Generated wronginformation

Groupsof

teachers

NSNUX2

NSNUX2

X2

NS

NU

X2

NS

NU

X2

1

NilNil

NilNil

Nil

Nil

Nil

Nil

Problems

2

NilNil

Nil10

(25%)6-53*

2(10%)

19(47-50%)30-87*

Nil

13(32-50%)

8-03*

3

NilNil

Nil10

(25%)6-53*

Nil

15(37-50%)24-89*

2(10%)

11(27-50%)

2-70

4

NilNil

Nil10

(25%)6-53*

2(10%)

10(25%)2-18

5(25%)

17(42-50%)11-42*

*P<0-05;df=l .

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102 J. C. Adigwe

TABLE IX. Evaluation of problem-solving process

Protocolsubcategories

1. Checked forcorrectness ofproblem-solving plans

2. Checked forstructural errors

3. Checked forexecutive errors

Groupsof

teachers

NS

NU

X2

NS

NU

X2

NS

NU(5%)X2

1

2(10%)

2(5%)0-60

5(25%)

3(7-50%)

3-31

2(10%)

2(10%)0-60

Problems

2

4(20%)

3(7-50%)

2-26

8(40%)

5(12-50%)

5-76*

3(15%)

4(7-50%)

2-26

3

2(10%)

4(10%)0-21

3(15%)

4(10%)2-26

2(10%)

3

0-03

4

3(15%)

3(7-50%)

0-81

7(35%)

6(15%)3-04

4(20%)

5(12-50%)

0-60

*P<0-05; df=l . Critical value of ^=3-84.

these difficulties appears to be related to the previous ones and their causes arealso related. They failed to include the knowns, unknowns and the conditions of aproblem in a clear-cut fashion and employed inappropriate proportional reason-ing skills in solving the problems. They showed a tendency to disregard anyinformation/data that could not be easily fitted in somewhere in their solutionplans. This could be attributed to the manner in which they perceived, categor-ised and chunked the information in their working memory and their incapabilityto discriminate between concepts and principles. It appears that an individual'scapacity to distinguish between concepts and identify/recognise the principlerelating them affects, to a great extent, his capability to apply both the conceptsand principles relating them in the problem-solving process. The teachers failedto generate information where it was appropriate because of their incapability toidentify the stages in the solution process where information generation wasnecessary and what could be the appropriate information. This indicated inade-quacies in their planning and organising skills. If they had made adequatesolution plans they would have been able to identify or recognise where thegeneration of information or partial solutions were necessary. The structuralerrors exhibited by the unsuccessful solvers appeared to be unrelated to theirproblem representations since the successful and unsuccessful teachers did notsignificantly differ in problem representation. This implies that there were someinhibiting factors between mental representations of the problems and construc-tion of solution plans out of the representations. If this is so, then the assertionsof Harootinam et al. (1960) that "a problem well-stated (represented) is "aproblem half-solved" is not totally correct.

The unsuccessful teachers lacked perspective as they approached the problems.As a result, they could not initiate some appropriate approaches to tackle theproblems. The lack of appropriate approach could have arisen from inhibition,

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Problem-solving Processes 103

inability to apply knowledge, difficulties in reasoning with data, recognition orrecall of correct items of knowledge, integration and generation of appropriateideas.

Most of the unsuccessful teachers had non-systematic approaches to theproblems characterised by illogical analyses and organising skills. Most instancesof incomplete solutions were due to the use of insufficient numerical informationand errors in numerical calculations which lead to dead-ends.

More of the successful teachers than the unsuccessful ones checked theirsolution processes for structural errors. However, there were no statisticaldifferences between them in checking executive errors and the correctness of thesolutions they obtained. Krammers-Pals et al. (1982) attributed the failure toevaluate solution plans to the fact that the students in their study sample did notmake estimates of the solutions at the planning phase against which to check thecorrectness of their solutions. In this study this appears to have arisen from over-confidence in solutions obtained, ignorance of this stage in the problem solvingor negligence of the importance of this stage of the process.

Since the effectiveness of an educational system depends largely on the qualityof the teachers (Platt, 1970) such lack of problem-solving skills by the chemistryteachers would effect their competence to teach, and what their students learnand assimiliate in the classrooms. In the light of this, the findings of this studyhave immense pedagogical and psychological implications for chemistry teachereducation in Nigeria.

The pedagogical implications of this is that these chemistry teachers (who donot possess an adequate level of understanding of the chemical knowledge/skillsand relevant mathematics, and lacked appropriate problem-solving skills) mayturn out poor quality products. Since the secondary school is where the basicfoundation in chemical education is laid, their products may acquire a weak andmisconceived foundation in chemical education, which may be difficult to restruc-ture and improve upon. If these products happen to embark on a teachingcareer, they may produce students of like quality: a vicious circle may thus becreated.

The psychological implications may lie in the area of intellectual functioning.Problem solving is said to be complex intellectual task. Processes like mentalrepresentation and understanding of problems, constructing solution plans out ofmental representations of the problems, execution of the mental plans andevaluation of the mental process all involve some sort of intellectual operation ormental creation. The failure of most chemistry teachers to solve successfully thechemical problems may be attributed to ineffective or inadequate mental oper-ations. They may, therefore, be lacking appropriate mental or cognitive skills forsuch intellectual operations as are required in solving such quantitative chemicalproblems. Since the problems were based on the secondary school syllabus,does it imply in any way that their mental functioning may not be above themental operations required in the chemistry content which they are expected toteach?

However, on the other hand, it is equally surprising that these teachers havegone through advanced chemistry courses (either at the College of Education orUniversity level), but still most of them have inadequate understanding of thefundamentals, which is what they seem to have been teaching at the secondaryschools.

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104 J. C. Adigwe

Correspondence: Dr J. C. Adigwe, Institute of Education, University of Calabar,Calabar, Nigeria.

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BAJAH, S.T. (1979) How should we educate chemistry teachers for a changing world?,Proceedings of the 3rd International Conference on Chemical Education, Department ofChemistry, University College, Dublin.

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