On the Students Creative- Innovative Thinking Skills in...
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Prof. DAFIK, M.Sc, Ph.D THE UNIVERSITY OF JEMBER
On the Students Creative-Innovative Thinking Skills in Solving Two-Dimensional
Arithmetic Sequence Problems Through a Research Based
Learning
Tradition of
Excellence
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MyProfileProf.Drs.Dafik,M.Sc,Ph.D(ProfessorinMathema9cs)
RESEARCHACHIEVEMENTSopus:Documents148/h-index10NaConalSintaRank:34/30.48NaConallyCombinatoricsSintaRank:1NaConallyAppliedMathSintaRank:1NaConallyGraphTheorySintaRank:1NaConallyMathEducaConSintaRank:1
BACHELORDEGREEMathema9csEduc9onUniversitasJember
2020
1992
MASTERDEGREEMathema9calCompu9ngTheUniversityofManchester,UK
DOKTORALCombinatoricsandGraphTheoryTheUniversityofBallarat,Australia
1998
2007
PROFESSORCombinatoricsandGraphTheoryFKIPTheUniversityofJember
2013
DafikUnivJember
hUp://dafik-Yip-unej.org/home
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H-An9magic,Dafik,et.all• ConstrucCons of H-anCmagic graphs using smaller edge-anCmagic graphs (Ars
Combinatoria2017,vol133)• P2�H-superanCmagictotallabelingofcombproductofgraphs(AKCEInterna9onalJournal
ofGraphsandCombinatorics2019,vol16issue2)• On H-supermagic labelings of m-shadow of paths and cycles (Interna9onal Journal of
Mathema9csandMathema9calSciences2019,vol2019)
THE RELEVANT REFERENCES
CryptosystemTechniques,Dafik,et.all• TheConstrucConofEncrypConKeybyUsingaSuperH-anCmagicTotalGraph(Programand
AbstracttheAsianMathema9calConferenceAMC2016,vol408)• ImplementaCon of Super H-anCmagic Total Graph on Establishing Stream Cipher
(IndonesianJournalofCombinatorics2019,vol3issue1)• TheConstrucConofBlockCipherEncrypConKeyByUsingA Local SuperAnCmagic Total
FaceColoring(AdvancesinMathema9cs:Scien9ficJournal2020,vol9issue3)
ResearchBasedLearning,Dafik,et.all• The effecCveness of Research Based Learning in improving students' achievement in
solvingtwo-dimensionalarithmeCcsequenceproblems(Interna9onalJournalofInstruc9on2019,vol12issue1)
• The effecCveness of problem-based learning to improve students’ conjecturing ability insolvingblock-pavingproblems (Interna9onal JournalofScien9ficandTechnologyResearch2019,vol8issue10)
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The Students Creative-Innovative
Thinking Skills
THE 21st CENTURY
SKILLS
CREATIVE-INNOVATIVE: THE 21st CENTURY SKILLS
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The4Cs– Crea9ve-Innova9ve
(Novelty)– Cri9calThinking
(Ques0oning,Reasoning&Analyzing)– Communica9on
(UseofHypermediainCommunica0on)– Collabora9on
(CrossCountryDiversityCollabora0on)
CREATIVE-INNOVATIVE: THE 21st CENTURY SKILLS
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CREATIVE-INNOVATIVE: ON BLOOM DIGITAL TAXONOMY
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TheNumberof
ProductAchievements,Speed,Averagenumbersof
InnovaConandimprovements
PRODUCTIVITYSKILLS
ArCculatethoughtsand
ideasusingoral,wri_enand
nonverbalskillsinavarietyofformsandcontexts
COMMUNICATIONSKILLS
QuesConing,Analysing,Reasoning,Arguments,
InterpreCngandReflecCngeffecCvely
CRITICALTHINKINGSKILLS
Workeffec9velyandrespecbullywithdiverse
teams
COLLABORATIONSKILLS
DemonstrateoriginalityandinvenCveness(NOVELTY)
CREATIVE-INNOVATIVE
THINKINGSKILLS
CREATIVE-INNOVATIVE: THE 21st CENTURY SKILL INDICATORS
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THE TWO-DIMENSIONAL ARITHMETIC SEQUENCE
H-COVERING AND CRYPTOSYSTEM
TWO-DIMENSIONAL ARITHMETIC SEQUENCE: H-COVERING AND CRYPTOSYSTEM
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE SIMPLE CONCEPT
LetabeaniniCalvalue,anddbeadiffrence.TheArithmeCcsequencecanbewri_enasfollows:U1, U2, U3,U4,…,Una, a+d, a+2d,a+3d,…,a+(n-1)d Thei-termofarithmeCcsequenceisUn=a+(n-1)d.ThetwodimensionalArithmeCcsequenceisthesequenceconsistsofm,nelements.
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE SIMPLE CONCEPT
Table 2.1.a Base Terms
n = 3 and m = 2 i j
1 2 3
1 1 2 3
2 4 5 6
Jml 5 7 9
d : +2 +2
!! ,!! = !!,!!
Table 2.1.b Local Generalisation
n = 4 and m = 2 i j
1 2 3 4
1 1 2 3 4
2 5 6 7 8
Jml 6 8 10 12
d : +2 +2 +2
!! ,!! = !!,!!
Table 2.1.c Local Generalisation
n = 5 and m = 3
d : +3 +3 +3 +3 !! ,!! = !!,!!
i j
1 2 3 4 5
1 1 2 3 4 5
2 6 7 8 9 10
3 11 12 13 14 15
Jml 18 21 24 27 30
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE SIMPLE CONCEPT
Table 2.2.a Base Terms
n = 3 & m = 2 i j
1 2 3
1 1 3 5
2 2 4 6
Jml 3 7 11
d : +4 +4
!! ,!! = !!,!!
Table 2.2.b Local Generalisation
n = 4 & m = 3 i j
1 2 3 4
1 1 4 7 10
2 2 5 8 11
3 3 6 9 12
Jml 6 15 24 33
d : +9 +9 +9
!! ,!! = !!,!!
Table 2.2.c Local Generalisation
n = 5 & m = 4 i j 1 2 3 4 5
1 1 5 9 13 17
2 2 6 10 14 18 3 3 7 11 15 19 4 4 8 12 16 20
Jml 10 26 42 58 74 d : +16 +16 +16 +16
!! ,!! = !!,!"!
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE SIMPLE CONCEPT
Tabel 2.3.a Base Terms
n = 3 and m = 2
i j 1 2 3
1 1 4 2
2 5 3 6 Jml 6 7 8
d : +1 +1
!! ,!! = !!,!!
Tabel 2.3.b Local Generalisation
n = 5 and m = 4 i j 1 2 3 4 5
1 1 6 2 7 3 2 8 4 9 5 10 3 11 16 12 17 13 4 18 14 19 15 20
Jml 38 40 42 44 46
d : +2 +2 +2 +2
!! ,!! = !!,!!
Tabel 2.3.c Local Generalisation
n = 5 and m = 6 i j 1 2 3 4 5
1 1 6 2 7 3 2 8 4 9 5 10 3 11 16 12 17 13 4 18 14 19 15 20 5 21 26 22 27 23 6 28 24 29 25 30
Jml 87 90 93 96 99
d : +3 +3 +3 +3
!! ,!! = !!,!!
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE GENERALIZATION
Table 2.6.a
Global Generalization of m,n
i j 1 2 3 4 5 6
1 1 2 3 4 5 6 2 7 8 9 10 11 12 3 13 14 15 16 17 18 4 19 20 21 22 23 24 5 … … … … … …
… .!! = ! + ! − 1 ! = 1+ ! − 1 1
… .!! = ! + ! − 1 !
= 1+ ! − 1 !
!!,!! !, ! = ! − 1 ! + !
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE TRANSFORMATIONS
2
26
201
8
14
6
5
4
3
2721
15
2822
1016
2923
1117
30
24
1218
31
25
1319
7
977
71
83
89
95
101
i j
1 2 3 4 5
1 1 2 3 4 5
2 6 7 8 9 10
3 11 12 13 14 15
Jml 18 21 24 27 30
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TheresultofsuperH-an9magictotalgraphonG=Shack(C6,v,4)
DECRYPTION
ENCRYPTION yi=(xi+ki)(mod 26)
xi=(yi-ki)(mod 26)
Affine
Ch
iper
TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE APPLICATIONS
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE CONCEPT OF CRYPTOSYSTEM
The strength of cryptosystem relays on the management ofencryp0onkey.
Thekeyshouldbemanagedsuchthat it ishard forany intruder toanalyzethekey.
The main issue is how to develop a secure modern cryptosystemsuchthatthekeybetweenplaintextandciphertextishidden.
Cryptosystemisasystemwhichconvertsplaintexttociphertextorcipher text to plain text by the applica9on of encryp9on ordecryp9onalgorithm.
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE ENCRYPTION AND DECRYPTION
Encryp9on• theprocessoftransforminginforma9onsoitisunintelligibletoanyonebuttheintendedrecipient
Decryp9on• theprocessoftransformingencryptedinforma9onsothatitisintelligibleagain
Plaintext Keysystem Chipertext Key
system Plaintext
EncrypCon DecrypCon
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TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE APPLICATIONS
Theresultofencryp9onprocesswhichsuperH-an9magictotalgraphonG=Shack(C6,v,4)askeystream Plaintext xi ki xi+ki yi Chipertext
F 5 1 6 6 G
K 10 2 12 12 M
I 8 9 17 17 R
P 15 12 27 1 B
U 20 14 34 8 I
N 13 15 28 2 C
E 4 3 7 7 H
J 9 8 17 17 R
Theresultofdecryp9onprocesswhichsuperH-an9magictotalgraphonG=Shack(C6,v,4)askeystreamChipertext yi ki yi-ki xi Plaintext
G 6 1 5 5 F
M 12 2 10 10 K
R 17 9 8 8 I
B 1 12 15 15 P
I 8 14 20 20 U
C 2 15 13 13 N
H 7 3 4 4 E
R 17 8 9 9 J
FKIPUNEJ GMRBICHREncryp9on
Decryp9on
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The well-known founding fathers of combinatorial problems were Pascal (1623-1662), Jacob Bernoulli (1654-1705)
and Leonhard Euler (1707-1783)
Combinatorics
DoesthesoluConexist?
Howuniquearethey?
HowopCmumarethey?
Combinatorial Problems
Canwegeneralizeit?
TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE COMBINATORIAL PROBLEMS
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and
characterizing a property of finite structures
Canweproveit?
21st Century Skills
Innovative Thinking Skills
Creative Thinking Skills
Critical Thinking Skills
Communication Skills
Collaboration Skills
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LEVEL4
CREATIVEANDINNOVATIVETHINKINGLEVELStudentscanfindotherpa_erns,candolocalgeneralisaCon,globalgeneralisaCom
CREATIVEANDINNOVATIVETHINKINGLEVELStudentscanfindnewpa_erns,candolocalgeneralisaCon,cannotdoglobalgeneralisaCom
TWO-DIMENSIONAL ARITHMETIC SEQUENCE: THE CREATIVE-INNOVATIVE INDICATORS
LEVEL2 LEVEL1 LEVEL0LEVEL3
CREATIVEANDINNOVATIVETHINKINGLEVELStudentscannotfindnewpa_erns,dolocalgeneralisaCon,doglobalgeneralisaCom
CREATIVEANDINNOVATIVETHINKINGLEVELStudentscannotfindnewpa_erns,dolocalgeneralisaCon,cannotdoglobalgeneralisaCom
CREATIVEANDINNOVATIVETHINKINGLEVELStudentscannotfindnewpa_erns,cannotdolocalgeneralisaCon,cannotdoglobalgeneralisaCom
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RESEARCH-BASED LEARNING: FOR LEARNING AND RESEARCH DEVELOPMENT
RESEACRHBASED
LEARNING
FORLEARNING
INNOVATION
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RESEARCH BASED LEARNING: THE TRIPLE HELIX RELATION
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STUDENTSRESEARCH
ALECTURERRESEARCH
IS
RESEARCH BASED LEARNING: THE PRINCIPLES ON RESEARCH PROCESS
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RESEARCHGROUPisagroupofresearcherswhoworkonteaching,researchingandsupervisingonspecificresearchofinteresttosolveafundamentalproblemfromasimpleto
complex,frominven9on,innova9onanddiffusiontopursueareal-lifeapplica9ons,journalpublica9ons,books,patents,
prototypefor,andcopyrightscontainingahighnoveltyresults.
DEFINITIO
NOFRESEARCHGRO
UP
THEEXISTENCEO
FRG
1. ResearchGroupcabeindepartmentallevel2. ResearchGroupcabeinfacultylevel3. ResearchGroupcabeinuniversitylevelForNaConalorinternaConallevel,wenameasaresearchsociety
RESEARCH BASED LEARNING: THE RESEARCH GROUP CONCEPT
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2010 2011 2012 2013 2014-Now
GTA(GraphTheoryand
AplicaCon)WORLDWIDE
CGANT(CombinatoricsGraphTheoryandNetwork
Topology)UNEJ
INACOMBS(IndonesianCombinatoric
Society)INDONESIA
RESEARCH-BASED LEARNING: THE RESEARCH GROUP DEVELOPMENT
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LEVELOFRESEARCH
GRO
UP
CEREBEL(POSTGRADUATELEVEL)
COMBINATORIALEDUCATIONANDRESEARCHBASEDLEARNING
COMPUSTABEL(UNDERGRADUATELEVEL)
COMBINATORIC,COMPUTATION,STATISTICANDLEARNING
CGANT(UNIVERSITYLEVEL)
COMBINATORICS,GRAPHTHEORYANDNETWORKTOPOLOGY
INACOMBS(NATIONALLEVEL)
INDONESIANCOMBINATORICSSOCIETY
RESEARCH-BASED LEARNING: THE RESEARCH GROUP DEVELOPMENT
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1 2 43 5 6 7
EXPERIENCESOneoftheRGmembershouldhavearesearch
experienceandpublicaConinreputablejournal
SOMERESEARCHERSwhohaveacommonresearchofinterest
RESEARCHACTIVITYTheacrCvityofresearchshouldbecarriedout
InfullCmejobandconCnuetimetoCmeforthespecific
researchofinterest
NATIONAL/INTERNATIONALSOCIETY
TheRGshouldmeetanaConalorinternaConalSocietyofresearchofinterest
RESEACRHOFINTERESTTheinterestofstudyshouldbe
afundamentalissue
INTEGRATEDINTHEDEPARTMENTALCURRICULUMAllresearchroadmapshouldbeintegratedindepartmentalcurriculumofsubjectcourse
THEACADEMICLEVELOFTHELEADERAtleastadoctorate
ResearcherleadtheRG
8
INSTITUTIONALLYRECOCNISEDShouldbein
Department/facultyorUniversityLevel
RESEARCH BASED LEARNING: THE SYNTAX OF LEARNING PROCESS IMPLEMENTATION
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RESEARCH BASED LEARNING IS A TYPE OF SCL MODELS THAT BRINGS THE RESEARCH ELEMENTS INTO THE LEARNING PROCESS (BLACKMORE, P. AND FRASER, M. 2010) Research based learning is a constructivism based learning involving four aspects: Problem posing regarding on the research open problems, conceptual orientation respecting to the problems, collaboration in collecting and and analyzing data regarding to the problem solving, communicating the research result both oral or writing. Luanganggoon, Nuchwana, 2012 stated that RBL can improve 5 students skills, namely: 1) Cognitive, 2) Knowledge, 3) Ethics Skill, 4) Social skill and 5) Communication, Arithmetic, Information and Technology skill.
THECONCEPTO
FRESEARCHBASEDLEARNING(RBL)
RESEARCH-BASED LEARNING: THE DEFINITION
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THE INTEGRATION OF RESEARCH INTO LEARNING PROCESS ( HEALEY, 2013)
Learningprocessareenrichedbyresearchresults,journalpaperreview,journalproceeding,orbookchapterfromRG.Studentsareencouragedto
reviewthem
LearningprocessacCvelyinvolvesstudentstodoresearchinsolvingaproblemarisingfromRGopen
problems
LearningprocessareenrichedbylecturerandtheotherscienCst
researchresults,journalpaperreview,journalpaperbasedFGD,orbook
chapter
CurriculumandlearningprocessareenrichedbymodernresearchmethodeitheracCon
research,casestudy,qualitaCveandquanCtaCveaswellasresearchand
development
FOURQUADRANTOFRESEARCHBASED
LEARNING
MoreStudentsInvolvements
LessStudentsInvolvements
Research-Tutored Research-Based
Research-Lead Research-Oriented
III
II
IV
I
70% 80%
60% 40%
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1 PROBLEM POSING ARISING FROM RG OPEN PROBLEMS
2 STUDENTS ARE
ENCOURAGED TO DEVELOP A
PROBLEM SOLVING STRATEGY
3 ORIENTATION,
DATA COLLECTION, TABULATING, HYPOTHESIS
4 DATA ANALYSIS,
PREDICTING PROCESS,
VALIDATION
5 LOCAL
CONJECTURING, CORROLLARING,
HYPOTHESIS/LEMMA/THEOREM, LOCAL GENERALIZATION
6 FGD BY INVOLVING RESEARCH GROUP
MEMBERS
RGMEMBERSDEVELOPAJOINTSEMESTERLEARNINGPLAN
ENDORSINGTHEUSEOFAUTHENTICASSESSMENTSBYINVOLVINGRESEARCHGROUPMEMBERS
YES
NO
7RBL
REPORT
RESEARCH BASED LEARNING: THE SYNTAX OF LEARNING PROCESS IMPLEMENTATION
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7 SELECTING WHICH RBL CAN BE POTENTIALLY TO BE A PAPER
OR STUDENTS THESIS
8 PAPER:
JOINT PAPER THESIS:
SUPERVISOR
9 FGD, WORKSHOP,
SEMINAR, CONFERNECE
10 GLOBAL
CONJECTURING, GLOBAL
GENERALISATION
11 INTERPRETATION,
TESTING HIPOTESIS, LEMMA, THEOREM
12 PAPER AND
THESIS WRITING
RGMEMBERSASSESSTHERBLREPORTFORPOTENTIALPUBLICATION/THESIS
RGMEMBERSACTIVELYDOAJOINTRESEARCHTOFINISHSTUDENTSRBLREPORT
YES
NO
13PUBLICATIONS
RESEARCH BASED LEARNING: THE SYNTAX OF LEARNING PROCESS IMPLEMENTATION
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THE PUBLICATION ACHIEVEMENTS GAINED BY CGANT RESEARCH GROUP
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THE COUNTRY COMPARISON OF SCOPUS JOURNAL PUBLICATIONS
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ResearchTopics
IdenCficaCon
Hypermedia-Based
ResearchWorksheet
ResearchProcess
RESEARCHGROUPBRAINSTORMING,
FGDANDWORKSHOPFORPAPER
PUBLICATION
RESEARCH BASED LEARNING: HOW DO WE INTERACT EACH OTHERS
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DEVELOPINGAGREENSCREENPODCASTINGBYUSINGTHESOFTWAREAPPLICATIONFILMORA
DEVELOPINGASTUDENTSRESEARCHWORKSHEETBYINSERTINGQR-CODEWITHAUDIO,VIDEOANDWEBPAGELINK
UTILIZINGAZOOMCLOUDMEETINGTODOABRAINSTORMING,FGDANDWORKSHOPONTHESEARCH-BASEDLEARNINGACTIVITIES
DEVELOPINGALEARNINGMATERIALSBYUSINGA
SIMPLETUTORIALAZ-SCREENRECORDER
DEVELOPINGASLIDEPRESENTATIONBYUSINGCANVA,CAMTASIA,ORSCREECAST-O-MATIC
DEVELOPINGASLIDEPOWERPOINT
PRESENTATIONBYINSERTINGAUDIOAND
VIDEOFEATURES
RESEARCH BASED LEARNING: HOW DO WE INTERACT EACH OTHERS
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EXAMINERCRITICISES/ATTACKS
SUPERVISORALSOCRITICISES/ATTACKS
RESEARCH BASED LEARNING: THE POTENTIAL MISGUIDANCE MINDSET
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EXAMINERSCRITICISES/ATTACKS
SUPERVISORHELPSTHESTUDENTSTOCLARIFY
RESEARCH BASED LEARNING: THE POTENTIAL MISGUIDANCE MINDSET
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SUPERVISINGSTUDENTSOFRESULTSX
PAPERPUBLICATIONALSOABOUTX
AUTHORSHIP:Students,Principlesupervisor,Co-Supervisor,AssociateSupervisors
RESEARCH BASED LEARNING: THE ETHIC CODE OF AUTHORSHIP
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SUPERVISINGSTUDENTSOFRESULTSX
SUPERVISORSADDARESULTY,ANDPUBLISHABOUTX+Y
AUTHORSHIP:Principlesupervisor,Co-Supervisor,AssociateSupervisors,Students,
RESEARCH BASED LEARNING: THE ETHIC CODE OF AUTHORSHIP