Essay-Writing in Mathematics

$50,1 +2//(167(,1
(66$< :5,7,1* ,1 0$7+(0$7,&6
6(&21'$5< 6&+22/ 7+ 72 *5$'(
$EVWUDFW
$GHTXDWH PDWKHPDWLVDWLRQ ± WKH WUDQVIRUPDWLRQ RI VXEMHFW PDWWHUV LQWR PDWKHPDWLFDO VWUXFWXUHV
± LV D PDMRU GLIILFXOW\ LQ PDWKHPDWLFV WHDFKLQJ 6WXGHQWV RIWHQ WKLQN RI PDWKHPDWLFV DV D QRQ
VHQVH VFLHQFH RU WKH\ VHH LW DV 0DWKH0DJLF 7KHLU SDUDGLJP IRU GRLQJ DSSOLHG PDWKHPDWLFV LV
WKH HIIRUWOHVV DQG HOHJDQW FHOHEUDWLRQ RI SUHIDEULFDWHG VROXWLRQV 0DWKHPDWLFV HGXFDWLRQ PXVW
DGGUHVV VXFK SKHQRPHQD LQ WKH EURDGHVW VHQVH ,Q RUGHU WR RYHUFRPH VXFK VKRUWFRPLQJV D GL
GDFWLF DSSURDFK LV KHUH SURSRVHG HVVD\ ZULWLQJ LQ PDWKHPDWLFV ,W KDV EHHQ WHVWHG LQ WZR
FODVVHV RI WK JUDGH VWXGHQWV RI KLJK DFKLHYHPHQW OHYHO (PSLULFDO UHVXOWV VKRZ WKDW FRPSDUHG
WR VROYLQJ WUDGLWLRQDO ZRUG EDVHG QXPEHU SUREOHPV HVVD\ ZULWLQJ LQ PDWKHPDWLFV IDFLOLWDWHV D
PRUH VXEMHFW RULHQWHG DQG FRQFHSWXDO DUJXPHQWDWLRQ LQ WKH SURFHVV RI PDWKHPDWLVDWLRQ 7KLV HI
IHFW EHFRPHV PRVW HYLGHQW DPRQJ IHPDOH VWXGHQWV ZKLOH PDOH VWXGHQWV DOVR VKRZ D VLPLODU WHQ
GHQF\ +2//(167(,1
:KDW PDGH PH WLFN"
$ PDMRU GLIILFXOW\ LQ WHDFKLQJ DSSOLHG PDWKHPDWLFV LV WKH PDWKHPDWLVDWLRQ RI SUREOHPV LQ
FRQWH[W &2+256 )5(6(1%25* 0DWKHPDWLFV HGXFDWRUV RIWHQ UHIHU WR WKH VR FDOOHG
FDSWDLQµV V\QGURPH %$58. )5(8'(17+$/ 67(51 ZKLFK GHVFULEHV
VLWXDWLRQV LQ PDWKHPDWLFV FRXUVHV ZKHUHE\ VWXGHQWV WHQG GR VROYH QRQVHQVH SX]]OHV ZLWKRXW
DQ\ KHVLWDWLRQ DV ORQJ DV WKH JLYHQ QXPEHUV FDQ EH PDQLSXODWHG DFFRUGLQJ WR VRPH LQIRUPDO
FRQYHQWLRQV VKHHS DQG JRDWV DUH RQ ERDUG RI D VKLS +RZ ROG LV WKH FDSWDLQ" $ FRQ
VLVWHQW QXPEHU RI VWXGHQWV LQ D FODVV ZLOO DQVZHU 7KH FDSWDLQ LV \HDUV ROG
0DWKHPDWLFV HGXFDWLRQ KDV RIWHQ GLVFXVVHG H[SODQDWLRQV IRU VXFK VWUDQJH EHKDYLRXU
0DQ\ VWXGHQWV WKLQN RI PDWKHPDWLFV DV D QRQ VHQVH VFLHQFH %$58. %850(67(5
%g1,* 6&+2(1)(/' 67(51 &RQWH[W SUREOHPV DUH VHHQ DV
ÄRQH ZD\ ZUDSSLQJV IRU FDOFXODWLRQV³ %\ HPSOR\LQJ LQIRUPDO VWUDWHJLHV WKH KLGGHQ FDO
FXODWLRQ FDQ EH XQSDFNHG WKH ZUDSSLQJ GLVSRVHG RI DQG WKH FDOFXODWLRQ FDQ WKHQ EH H[H
FXWHG
%\ PDWKHPDWLFV WHDFKHUV SUREOHP VROYLQJ LV VHOGRP PRGHOOHG DV DQ DFWLYLW\ GHPDQGLQJ
HQGXUDQFH 0DNLQJ PLVWDNHV RU HYHQ HQGLQJ WKH SURFHVV ZLWKRXW D YDOXDEOH UHVXOW LV XQ
WKLQNDEOH LQ D WUDGLWLRQDO PDWKHPDWLFV FRXUVH ± RU HYHQ ZRUVH LW LV FRQVLGHUHG D IODZ LQ
SHGDJRJ\ 2Q WKH FRQWUDU\ WKH WHDFKHU XVXDOO\ DLPV DW DQ LPPHGLDWH HOHJDQW DQG HIIRUW
OHVV SUREOHP VROYLQJ WHFKQLTXH 7KH\ WHQG WR KLGH WKH DFWXDO SURFHVV RI PDWKHPDWLVDWLRQ
ZLWK DOO LWV LQKHUHQW XQFHUWDLQW\ RU SDLQ 0DWKHPDWLVDWLRQ ORRNV OLNH WKH GHXV H[ PDFKLQD
LQ FODVVLFDO *UHHN GUDPD ZKHUH D JRG DSSHDUV ± RXW RI QRZKHUH ± WUDQVIRUPLQJ FDWDVWUR
SKH LQWR KHDYHQO\ RUGHU 7UDGLWLRQDO PDWKHPDWLFV WHDFKLQJ LV WKXV RULHQWHG WRZDUGV UHVXOWV
DQG DQVZHUV ZKLOH QHJOHFWLQJ WKH XQGHUO\LQJ WKLQNLQJ SURFHVVHV %$58.
6&+2(1)(/'
+LJKO\ VWDQGDUGLVHG SURFHGXUHV LQWHQGHG DV DQ DLG WR WKH VWXGHQWV LQ WKHLU WDFNOLQJ RI
FRQWH[W SUREOHPV LQ IDFW FULSSOHV WKHLU SUREOHP VROYLQJ DELOLWLHV *$//,1 58)
*$03(5 *,16%85* +(1*$571(5 :,770$11
:,770$1 0h//(5 7KH HQVHPEOH RI VWDQGDUGLVHG SUREOHP
VROYLQJ SURFHGXUHV FRQVWLWXWHV D SV\FKRORJLFDO IUDPHZRUN RI WKH ÄPDWKHPDWLFV FODVV³

%$8(56)(/' 5$'$7= 6(/7(5 LQ ZKLFK VXEMHFW RULHQWHG
PDWKHPDWLFDO DUJXPHQWDWLRQ EDVHG RQ LQVLJKW DQG FRPPRQ VHQVH LV XQXVXDO 7KHUH LV
ÄSUREOHP VROYLQJ EH\RQG WKH ORJLF RI WKLQJV³ 5(866(5 (YHU\ IDFHW RI D JLYHQ
SUREOHP RXJKW WR KDYH LWV KLGGHQ VWDQGDUG SURFHGXUH %\ DQDO\VLQJ WKH VXUIDFH VWUXFWXUH
RI WKH SUREOHP WH[W VWXGHQWV DUH PHUHO\ WU\LQJ WR ILJXUH RXW ZKLFK FRQYHQWLRQDO IRUPXOD
WR FKRRVH
5HVHDUFK TXHVWLRQV DQG K\SRWKHVHV
,Q WKH ILHOG RI DSSOLHG PDWKHPDWLFV DOO WKH WUDGLWLRQDO SDWWHUQV PHQWLRQHG DERYH FRQFHQWUDWH
RQ WKH VROYLQJ RI ZRUG QXPEHU SX]]OHV ,Q H[WUHPH FDVHV WKH WHDFKHU DQG VWXGHQW PD\ ZRUN
ZLWK WH[W EDVHG SUREOHPV ZLWKRXW HYHU JHWWLQJ LQYROYHG LQ VXEMHFW RULHQWHG SUREOHP VROYLQJ
7KH\ DUH JXLGHG E\ VWDQGDUGLVHG IRUPXODWLRQV DQG FRPSDWLEOH SURFHGXUHV 7KHUHIRUH VROYLQJ
WKH ÄZRUG QXPEHU SX]]OHV³ VRPHWLPHV WDNHV RQ WKH TXDOLW\ RI ULWXDO EHKDYLRXU DQG GRHV QRW
FRQVLVW RI DQ\ NLQG RI FRQFHSWXDO DVVLPLODWLRQ RI ÄUHDOLW\³ :LWK WKLV LQ PLQG , KDYH GHYHO
RSHG D PHWKRG RI WHDFKLQJ DSSOLHG PDWKHPDWLFV WKDW RI HVVD\ ZULWLQJ LQ PDWKHPDWLFV
7KHRUHWLFDO %DFNJURXQG
D 0DWKHPDWLFV WHDFKLQJ FDQ EH VHHQ LQ WKH FRQWH[W RI ODQJXDJH DQG FRPPXQLFDWLRQ 7ZR
SHGDJRJLFDOO\ LPSRUWDQW LGHDV EOHQG LQ P\ ZRUN
*$//,1 58)µV LGHDV DERXW PDWKHPDWLFV DQG ODQJXDJH ± RULHQWHG
WRZDUGV WKH SUDFWLFH RI WHDFKLQJ LQ ZKLFK WKH PDLQ LGHD LV WKDW RI MRXUQDO ZULWLQJ LQ
PDWKHPDWLFV 6HWWLQJ RXW IURP FDUHIXOO\ FKRVHQ SUREOHPV WKH VWXGHQWV ILUVW GHYHORS
WKHLU RZQ LQGLYLGXDO PDWKHPDWLFDO ZRUOG 7KH\ VHDUFK RQ WKHLU RZQ IRU DSSURDFKHV WR
DQG ZD\V RI VROYLQJ WKH JLYHQ SUREOHP 7KHVH LQGLYLGXDO OLQHV RI WKRXJKW DUH UHJLVWHUHG
LQ WKH MRXUQDOV HQWLWOHG ÄGLDU\ RI D MRXUQH\³ ,Q D VHFRQG SKDVH WKH GLYHUJHQW LGHDV
DSSURDFKHV DQG PHWKRGV ZKLFK UHVXOW DUH GLVFXVVHG LQ WKH JURXS 7KH JURXS WULHV WR
XQGHUVWDQG WKH GLIIHUHQW DSSURDFKHV LQ WKLV GLYHUJHQW ZRUOG RI WKRXJKW ,W LV LQ WKH WKLUG
SKDVH WKDW WKH WHDFKHU SODFHV WKHVH LGHDV LQ WKH UHJXODU ZRUOG RI VFKRRO PDWKHPDWLFV
6LQFH WKH HDUO\ VHYHQWLHV FRJQLWLYH FRQVWUXFWLRQLVP KDV EHFRPH WKH WKHRUHWLFDO EDFNERQH
RI HGXFDWLRQ LQ PDWKHPDWLFV 0HDQZKLOH VRFLDO FRQVWUXFWLRQLVP KDV DOVR JDLQHG
LPSRUWDQFH (VVHQWLDO WR P\ ZRUN DUH WKH FRQFHSWV RI VKDUHG FRJQLWLRQ RU FR RSHUDWLYH
OHDUQLQJ '8,7 +8%(5 HW DO 5(61,&. /(9,1( 7($6/(< 7KH
FRQFHSW RI VRFLDOO\ PHGLDWHG OHDUQLQJ LV DOVR YHU\ KHOSIXO LQ WKH DQDO\VLV RI WKH SURFHVVHV
LQYROYHG LQ PHDQLQJIXO DUJXPHQWDWLRQ GXULQJ SUREOHP VROYLQJ :(576&+
E 6KRUWFRPLQJV LQ WHDFKLQJ DSSO\LQJ PDWKHPDWLFV DV RXWOLQHG DERYH FDQQRW EH UHVROYHG E\
WKH LQILQLWH UHILQHPHQW RI WKH WUDGLWLRQDO ÄVWHS E\ VWHS³ LQVWUXFWLRQ %\ PDNLQJ WKH VWHSV
HYHQ VPDOOHU WKH VWXGHQWV ZLOO RQO\ LQFUHDVH WKHLU DOLHQDWLRQ IURP WKH JHQXLQH
PDWKHPDWLFDO WKLQNLQJ DQG SUREOHP VROYLQJ +(1*$571(5 5g7+/,6%(5*(5
.5$87+$86(1 :,(/$1' :,770$11 HW DO ,W LV QRW WKH LQVWUXFWLRQ
WKURXJK VPDOO ULJLG VWHSV WKDW ZLOO HQULFK WKH PDWKHPDWLFDO WKLQNLQJ EXW UDWKHU WKH OHDUQLQJ
WKURXJK DFWLYH GLVFRYHU\ LQ ZHOO GHVLJQHG OHDUQLQJ HQYLURQPHQWV OLNH RSHQ VLWXDWLRQV
(**(1%(5* +2//(167(,1 7KLV NLQG RI OHDUQLQJ HQYLURQPHQW KDV WR EH
VXEVWDQWLDO UHSUHVHQWLQJ LPSRUWDQW REMHFWLYHV FRQWHQWV DQG SULQFLSOHV RI PDWKHPDWLFV
7KHLU SRWHQWLDO IRU PDWKHPDWLFDO DFWLYLW\ PXVW EH H[WHQVLYH WKH\ PXVW EH IOH[LEOH DQG
DGDSWDEOH LQ WKH KDQGV RI WKH WHDFKHUV DQG WKH\ VKRXOG LQWHJUDWH PDWKHPDWLFDO
SV\FKRORJLFDO DQG SHGDJRJLFDO DVSHFWV RI OHDUQLQJ DQG WHDFKLQJ .5$87+$86(1

6XEVWDQWLDO SUREOHPV IRVWHU WKH SRWHQWLDO IRU QDWXUDO LQQHU GLIIHUHQWLDWLRQ :,770$11 HW DO
LQ D FODVV RU D JURXS RI OHDUQHUV ± WKH VWXGHQWV GHILQH WKH OHYHO RI GLIILFXOW\ E\ WKHLU
VXEMHFW RULHQWHG FKRLFHV DQG GHFLVLRQV
F :LWK %$8(56)(/' DQG :,770$11 WKH GLVFLSOLQH RI PDWKHPDWLFDO HGXFDWLRQ
LV VHHQ DV D GHVLJQ VFLHQFH ,Q WKLV YLHZ LW LV QRW SRVVLEOH WR JDLQ LQVLJKWV LQWR PHWKRGV RU
WHDFKLQJ VWUDWHJLHV PHUHO\ E\ GHGXFWLRQ IURP UHODWHG GLVFLSOLQHV VXFK DV PDWKHPDWLFV
SHGDJRJ\ DQG SV\FKRORJ\ 7KH IXQGDPHQWDO TXHVWLRQ LV KRZ PDWKHPDWLFV WHDFKLQJ FDQ EH
GHVLJQHG WR DFKLHYH WKHLU REMHFWLYHV 'XULQJ WKH GHVLJQ SURFHVVHV RI FRXUVH FRQFHSWV IURP
UHODWHG VFLHQWLILF ILHOGV DUH FUXFLDO %XW Ä> @ WKH TXDOLW\ RI WKHVH FRQVWUXFWV GHSHQGV RQ WKH
WKHRU\ EDVHG FRQVWUXFWLYH IDQWDV\ WKH ÄLQJHQLXP³ RI WKH GHVLJQHUV DQG RQ V\VWHPDWLF
HYDOXDWLRQ ERWK W\SLFDO RI GHVLJQ VFLHQFHV³ :,770$11 S &/$5. DQG

GLVFXVV WKH WRSLFV DQG WKH EDFNJURXQG LQ D EURDGHU VHQVH WHQGLQJ WR DYRLG PDWKHPDWLFDO
IRUPDOLVDWLRQV DV ORQJ DV SRVVLEOH
%DVLF 7KHVLV
0\ EDVLF WKHVLV WKHUHIRUH LV WKDW WUDGLWLRQDO HVVD\ ZULWLQJ LQ VFKRRO JHQHUDWHV D PHWD
FRJQLWLYH DQG KHXULVWLF ZD\ RI WKLQNLQJ DV ZHOO DV SUREOHP VROYLQJ VWUDWHJLHV DQG DWWLWXGHV
WRZDUGV WKH WLPH FRQVXPLQJ FRPSRVLWLRQ RI D WH[W 7KLV IUDPHZRUN RI FRQYHQWLRQV
)5(8'(17+$/ ZKLFK LV IXQGDPHQWDOO\ GLIIHUHQW IURP WKH WUDGLWLRQDO IUDPHZRUN RI
ÄGRLQJ YHUEDO SX]]OHV³ LV WUDQVIHUDEOH WR WKH PDWKHPDWLFV FRXUVHV 7KLV DOUHDG\ H[LVWLQJ
NQRZOHGJH PD\ DQG VKRXOG EH XVHG WR VROYH DSSOLHG PDWKHPDWLFV SUREOHPV
(VVD\ ZULWLQJ LQ PDWKHPDWLFV ± D GLGDFWLFDO DSSURDFK
(VVD\ ZULWLQJ LQ PDWKHPDWLFV PHDQV HVVHQWLDOO\ WKH VROYLQJ RI WH[W EDVHG SUREOHPV LQ WKH
ILHOG RI DSSOLHG PDWKHPDWLFV 7KH JLYHQ SUREOHP ± WKH WRSLF RI WKH HVVD\ WR EH ZULWWHQ ± LV
FDOOHG D WRUVR ZKLFK VKRZV DQ XQILQLVKHG JHVWDOW :(57+(,0(5 :ULWLQJ WKH HVVD\
PHDQV FKRRVLQJ DQ LQWHUHVWLQJ DVSHFW RI WKH JLYHQ VHPDQWLF VWUXFWXUH DQG VWULYLQJ IRU D JRRG
JHVWDOW FRPSOHWLQJ WKH WRUVRµV VWUXFWXUH LQ WKLV YHU\ DVSHFW $(%/, $OO WKH HVVD\V
HPHUJLQJ IURP WKLV SURFHVV KDYH D FRPPRQ FRUH HOHPHQW WKH WRUVR %XW WKH\ PD\ EH YHU\
GLIIHUHQW LQ WKHLU REMHFWLYHV ZD\V RI GHDOLQJ ZLWK WKH SUREOHPV DQG PHWKRGV RI WDFNOLQJ WKH
SUREOHP
7KH OHDUQLQJ HQYLURQPHQW RI HVVD\ ZULWLQJ LQ PDWKHPDWLFV VKRZV WKH IROORZLQJ SURSHUWLHV
7KH WHDFKHU LQWURGXFHV WKH QHZ NLQG RI WH[W WR EH ZULWWHQ E\ WKH VWXGHQWV WKH ÄPDWKH
PDWLFDO HVVD\³ 0DWKHPDWLFDO HVVD\V PD\ EH FRPSRVHG RI ZULWWHQ ODQJXDJH FDOFXODWLRQV
VNHWFKHV GLDJUDPV V\PEROV RU SLFWXUHV ,W LV LPSRUWDQW WR VWUHVV WKH IUDPHZRUN RI HVVD\
ZULWLQJ DV LW LV NQRZQ IURP ODQJXDJH RULHQWHG FRXUVHV 7KH VWXGHQWV RXJKW WR NQRZ WKH
RXWOLQHV RI WKH DFWXDO SURFHGXUH WLPH IUDPH ZRUNLQJ FRQGLWLRQV RUJDQLVDWLRQ DQG VR RQ
7KH SUREOHP WH[W LV SUHVHQWHG DQG GLVFXVVHG 7KLV LV WR EH WKH WKHPH IRU WKH PDWKHPDWLFDO
HVVD\
6WXGHQWV ORRN IRU LQWHUHVWLQJ TXHVWLRQV WKDW PD\ EH ± DW OHDVW SDUWO\ ± DQVZHUHG E\ WKH
FDOFXODWLRQV 7KH\ PD\ DOVR IRUPXODWH VWDWHPHQWV WR EH VXSSRUWHG RU GHQLHG E\ PHDQLQJ
IXO FDOFXODWLRQV 7KH VWXGHQWV FKRRVH WKHLU UHVSHFWLYH WRSLFV DQG VWDUW WR ZULWH WKH HVVD\
$IWHU ILQLVKLQJ WKH ZULWLQJ SURFHVV HVVD\V DUH SUHVHQWHG DQG GLVFXVVHG LQ FODVV
7KH FULWHULD RI DVVHVVPHQW DQG FRQWHQW RI WKH GLVFXVVLRQ VKRXOG QRW VLPSO\ EH ÄFRUUHFW RU
QRW³ :KDW LV HVVHQWLDO LV WKH W\SH RI WRSLFV UDLVHG E\ WKH VWXGHQW V WKH RULJLQDOLW\ DQG
OLQH RI DUJXPHQWDWLRQ WKH DGHTXDF\ DQG VXLWDELOLW\ RI WKH FDOFXODWLRQV HOHJDQFH DQG
HFRQRP\ RI VW\OH WKH TXDOLW\ RI WKH HVVD\
%HFN 0DLHU LQWURGXFH WKH FRQFHSW RI WH[W LQWR PDWKHPDWLFV HGXFDWLRQ *RLQJ EDFN WR 5LFRHXU
WKH WH[W LV GHILQHG LQ D EURDG VHQVH DV DQ\ UHSUHVHQWHG DQG ÄUHDGDEOH³ LQIRUPDWLRQ $ VLPLODU FRQFHSW LV XVHG E\
:HLGHQPDQQ .UDSS DQG 'RHONHU :ULWWHQ ODQJXDJH LNRQV SLFWXUHV VNHWFKHV GLDJUDPV
V\PEROV DUH DOO WH[W
,Q D SLORW VWXG\ ZH DVNHG VRPH VWXGHQWV WR LQYHQW ZRUG SUREOHPV UHODWHG WR D JLYHQ WRUVR 7KH RXWFRPH ZDV
VWXQQLQJ 7KH\ VKRZHG D VWURQJ WHQGHQF\ WR ORRN RXW ILUVW IRU QXPEHU FRPELQDWLRQV WKH\ NQHZ KRZ WR FDOFXODWH
LQ VRPH ZD\ 6HFRQGO\ WKH\ LQYHQWHG ÄVWRULHV³ WR ZUDS XS DQG KLGH WKH HQYLVDJHG FDOFXODWLRQV 7KH\ SURGXFHG
FDULFDWXUHV RI WKH ZRUG QXPEHU SX]]OHV ZULWWHQ E\ WHDFKHUV DQG DXWKRUV RI WH[WERRNV 3HUFHSWXDO VXEMHFW RULHQWHG
DUJXPHQWDWLRQ ZDV DOPRVW HQWLUHO\ DEVHQW

+\SRWKHVHV
• (VVD\ ZULWLQJ LQ PDWKHPDWLFV IRVWHUV QDWXUDO LQQHU GLIIHUHQWLDWLRQ 7KH SUREOHPV JHQHUDWHG
E\ WKH VWXGHQWV DUH GLIIHUHQW LQ WHUPV RI FRQWHQW DQG OHYHO RI FRPSOH[LW\
• &RPSDUHG WR WKH SURFHVVHV LQYROYHG LQ VROYLQJ WUDGLWLRQDO ZRUG QXPEHU SX]]OHV HVVD\
ZULWLQJ LQ PDWKHPDWLFV IDFLOLWDWHV PDWKHPDWLVDWLRQ DQG SUREOHP VROYLQJ EDVHG RQ VXEMHFW
RULHQWHG FRQFHSWXDO DUJXPHQWDWLRQ 0DWKHPDWLVDWLRQ EDVHG RQ V\QWDFWLFDO SURSHUWLHV RI WKH
JLYHQ SUREOHP WH[W DUH OHVV IUHTXHQW LQ DQ H[SHULPHQWDO JURXS ZULWLQJ PDWKHPDWLFDO HVVD\V
WKDQ LQ D FRQWURO JURXS GRLQJ WUDGLWLRQDO ZRUG QXPEHU SX]]OHV
• )RVWHULQJ VXEMHFW RULHQWHG DUJXPHQWDWLRQ E\ HVVD\ ZULWLQJ LQ PDWKHPDWLFV LV PRUH LPSRU
WDQW DPRQJ IHPDOH WKDQ PDOH VWXGHQWV
(PSLULFDO GHVLJQ
7ZR FODVVHV RI KLJK DFKLHYLQJ VWXGHQWV LQ DOO WK JUDGH DJHV IURP WR FROODER
UDWHG RQ WKLV SURMHFW 7R EH DFFHSWHG DV D VWXGHQW E\ WKHLU KLJK VFKRRO DOO RI WKHP SDVVHG UH
FHQWO\ D WHVW LQ 0DWKHPDWLFV *HUPDQ DQG )UHQFK DV D IRUHLJQ ODQJXDJH 7KH H[SHULPHQWDO
GDWD ZDV JDWKHUHG WZR DQG WKUHH ZHHNV DIWHU WKH\ VWDUWHG DW WKHLU QHZ VFKRRO
$ ZHHN EHIRUH WKH JDWKHULQJ RI GDWD WKH WZR FR RSHUDWLQJ FODVVHV ZHUH FRQWDFWHG 6WDUWLQJ RXW
IURP D WRUVR Ä'LQRVDXUV³ (5,&+621 WKH VWXGHQWV ORRNHG IRU IHDVLEOH WRSLFV WR ZULWH
DERXW 7KH\ ZHUH WROG WR ÄDVN GLIIHUHQW TXHVWLRQV WKDW PD\ EH DQVZHUHG E\ FDOFXODWLRQV RU WR
IRUPXODWH VWDWHPHQWV WKDW FRXOG EH XSKHOG RU GHQLHG E\ QXPEHUV DQG FDOFXODWLRQV³ 7KH LGHDV
UDLVHG ZHUH GLVFXVVHG LQ WKH FODVV DOWKRXJK QR HVVD\V ZHUH ZULWWHQ DW WKDW VWDJH RQH OHVVRQ
,Q D VHFRQG OHVVRQ WKH VWXGHQWV GLYLGHG LQWR SDLUV IRU WKH VXEVHTXHQW FR RSHUDWLYH ZRUN 7KH
VWXGHQWV ZHUH IUHH WR FKRRVH WKHLU SDUWQHUV DQG JHQHUDOO\ WKH\ SDLUHG XS ZLWK WKH VDPH VH[
7KHUH ZDV RQO\ RQH PL[HG SDLU LQ HDFK FODVV WKH ÄOHIWRYHUV³ IURP WKH JURXSLQJ SURFHVV
7KHVH G\DGHV ZHUH SODFHG HLWKHU LQ D H[SHULPHQWDO JURXS RU D FRQWURO JURXS 7KHVH JURXSV
ZHUH EDODQFHG DFFRUGLQJ WR WKH IROORZLQJ FULWHULD VH[ LQWHUHVW LQ ZULWLQJ HVVD\V LQWHUHVW LQ
GRLQJ ZRUG QXPEHU SX]]OHV DQG IDFWRUV RI PRWLYDWLRQ +(50$16
7KH H[SHULPHQWDO ZRUN
7KH H[SHULPHQWDO JURXS FDUULHG RXW WKH ZRUN LQ WKH OHDUQLQJ HQYLURQPHQW RI WKH HVVD\ ZULWLQJ
LQ PDWKHPDWLFV (DFK G\DGH LV FRQIURQWHG ZLWK D VKHHW RI SDSHU FRQWDLQLQJ WKH WRUVR Ä7KH (D
JOH³ (5,&+621
7RJHWKHU \RX ZLOO ZULWH D VKRUW PDWKHPDWLFDO HVVD\
• 5HDG WKH WH[W Ä7KH (DJOH³ ,W LV WKH WKHPH RI \RXU SURMHFW
• 6HDUFK WRJHWKHU IRU VRPH IHDVLEOH WRSLFV IRU \RXU PDWKHPDWLFDO HVVD\ $VN GLIIHUHQW TXHV
WLRQV WKDW FDQ EH DQVZHUHG E\ FDOFXODWLRQV RU IRUPXODWH VWDWHPHQWV WKDW PD\ EH XSKHOG RU
GHQLHG E\ QXPEHUV DQG FDOFXODWLRQV
• &KRRVH RQH RI WKHVH WRSLFV IRU \RXU PDWKHPDWLFDO HVVD\
• 6WDUW ZULWLQJ DQ RXWOLQH IRU WKH HVVD\ ,W VKRXOG LQ WKH HQG FRQWDLQ VHQWHQFHV DQG FDOFXOD
WLRQV DQG SHUKDSV VRPH GUDZLQJ VNHWFKHV DQG GLDJUDPV
7KH (DJOH +LVWRULF GUDZLQJ ,QDXJXUDWLRQ RI WKH 5DLOZD\ /LQH IURP 1 UQEHUJ WR ) UWK
2Q 'HFHPEHU WK WKH ILUVW UDLOZD\ OLQH LQ *HUPDQ\ ZDV LQDXJXUDWHG ,W FRQQHFWHG
1 UQEHUJ ZLWK ) UWK DQG ZDV D PHUH NP ORQJ 7KH HQJLQH WRZLQJ WKH WUDLQ ZDV ERXJKW IURP

WKH IDFWRU\ RZQHG E\ WKH IDPRXV *HRUJH 6WHSKHQVRQ ,W ZDV QDPHG Ä7KH (DJOH³ $W SUHFLVHO\
RµFORFN D FDQQRQ VKRW JDYH WKH VLJQDO IRU WKH VWDUW 7HQ PLQXWHV ODWHU WKH WUDLQ KDG DOUHDG\
UHDFKHG LWV GHVWLQDWLRQ :LOOLDP :LOVRQ WKH HQJLQHHU GULYLQJ Ä7KH (DJOH³ FDPH IURP %ULW
DLQ WRR IRU VDIHW\ UHDVRQV +H ZDV SDLG OLNH D VWDU PDUNV ZDV KLV \HDUO\ VDODU\ WKH
GLUHFWRU RI WKH UDLOZD\ FRPSDQ\ HDUQHG RQO\ PDUNV Ä7KH (DJOH³ ZDV D KXJH VXFFHVV
,Q WKH ILUVW \HDU WLFNHWV ZHUH VROG DW FHQWV SHU WLFNHW 7KH YDOXH RI WKH PDUN ZDV
GLIIHUHQW IURP WRGD\µV '0 'HXWVFKH 0DUN
$W WKDW WLPH 7RGD\
7LFNHW 1 UQEHUJ ± ) UWK FHQWV '0
NJ RI EUHG FHQWV '0
OLWHU RI PLON FHQWV '0
NJ RI PHDW YHDO 0DUN '0
NJ RI VXJDU FHQWV '0
HJJ FHQWV FHQWV
E 7KH G\DGHV LQ WKH FRQWURO JURXS VROYHG WUDGLWLRQDO ORRNLQJ ZRUG SX]]OHV ZKLFK ZHUH FRQ
VWUXFWHG E\ GLYLGLQJ WKH H[SHULPHQWDO WH[W LQWR QXPEHUHG VHFWLRQV DQG FRQYHUJHQW TXHV
WLRQV ZHUH DGGHG
7RJHWKHU \RX ZLOO VROYH WKH IROORZLQJ SUREOHPV
7KH (DJOH +LVWRULF GUDZLQJ ,QDXJXUDWLRQ RI WKH 5DLOZD\ /LQH IURP 1 UQEHUJ WR ) UWK
2Q 'HFHPEHU WK WKH ILUVW UDLOZD\ OLQH LQ *HUPDQ\ ZDV LQDXJXUDWHG ,W FRQQHFWHG
1 UQEHUJ ZLWK ) UWK DQG ZDV D PHUH NP ORQJ 7KH HQJLQH WRZLQJ WKH WUDLQ ZDV ERXJKW
IURP WKH IDFWRU\ RZQHG E\ WKH IDPRXV *HRUJH 6WHSKHQVRQ ,W ZDV QDPHG Ä7KH (DJOH³ $W
SUHFLVHO\ RµFORFN D FDQQRQ VKRW JDYH WKH VLJQDO IRU WKH ILUVW VWDUW 7HQ PLQXWHV ODWHU WKH
WUDLQ KDG DOUHDG\ UHDFKHG LWV GHVWLQDWLRQ
:KDW ZDV Ä7KH (DJOHµV³ DYHUDJH VSHHG GXULQJ LWV PDLGHQ YR\DJH"
:LOOLDP :LOVRQ WKH HQJLQHHU GULYLQJ Ä7KH (DJOH³ FDPH IURP %ULWDLQ WRR IRU VDIHW\ UHD
VRQV +H ZDV SDLG OLNH D VWDU PDUNV ZDV KLV \HDUO\ VDODU\
+RZ PXFK GLG 0U :LOVRQ HDUQ LQ D PRQWK"
7KH GLUHFWRU RI WKH UDLOZD\ FRPSDQ\ HDUQHG RQO\ PDUNV
+RZ PXFK PRUH GLG 0U :LOVRQ HDUQ LQ D \HDU WKDQ WKH GLUHFWRU GLG"
Ä7KH (DJOH³ ZDV D KXJH VXFFHVV ,Q WKH ILUVW \HDU WLFNHWV ZHUH VROG DW FHQWV
SHU WLFNHW
+RZ PXFK ZDV WKH LQWDNH IRU WKH ILUVW \HDU"
7KH YDOXH RI WKH PDUN ZDV GLIIHUHQW IURP WRGD\µV '0 'HXWVFKH 0DUN

$W WKDW WLPH 7RGD\ +RZ PDQ\
WLPHV"
7LFNHW 1 UQEHUJ±) UWK FHQWV '0 DSSUR[
WLPHV
NJ RI EUHG FHQWV '0
OLWHU RI PLON FHQWV '0
NJ RI PHDW YHDO 0DUN '0
NJ RI VXJDU FHQWV '0
HJJ FHQWV FHQWV
+RZ PXFK ZRXOG 0U :LOVRQµV VDODU\ EH ZRUWK WRGD\ LQ 6ZLVV )UDQFV" H[FKDQJH UDWH
%HIRUH WKH GDWD JDWKHULQJ VHVVLRQ WKH VWXGHQWV JRW XVHG WR ZDWFKLQJ DQG KHDULQJ WKHPVHOYHV
RQ YLGHR 'XULQJ WKH FR RSHUDWLYH SDLU ZRUN VWDJH HDFK G\DGH ZRUNHG DORQH LQ D URRP ZLWK
WKH YLGHR FDPHUD LQ IURQW RI WKHP $IWHU PLQXWHV WKH\ ZHUH LQWHUUXSWHG DQG WKH WZR FOLQLFDO
LQWHUYLHZV EDVHG RQ VHOI FRQIURQWDWLRQ ZHUH FDUULHG RXW LQ WZR VHSDUDWH URRPV 7KLV VHFRQG
VWDJH RI GDWD JDWKHULQJ ZDV EDVHG RQ WKH 5H ,QWHUYLHZ 7HFKQLTXH :,/' D IRUP RI VHOI
FRQIURQWDWLRQ 9LHZLQJ WKHLU RZQ SHUIRUPDQFH RQ YLGHR WKH VWXGHQWV ZHUH LQWHUYLHZHG VHSD
UDWHO\ DQG HDFK VWXGHQW ZDV DVNHG WR FRPPHQW DQG LQWHUSUHW WKH G\DGHµV SURFHVV RI GHILQLQJ
DQG VROYLQJ SUREOHPV
7KHUH DUH WKHUHIRUH WKUHH GLIIHUHQW UHFRUGLQJV IRU HDFK G\DGH )LUVW WKH YLGHR GRFXPHQWDU\ RI
WKH FR RSHUDWLYH SDLU ZRUN VHVVLRQ 6HFRQG WKH WZR UHFRUGLQJV RI WKH FOLQLFDO LQWHUYLHZV HDFK
VWXGHQW H[SODLQLQJ WKH G\DGHµV EHKDYLRXU ZKLFK ZHUH WUDQVFULEHG DQG GLUHFWO\ DGGHG DV
FRPPHQWDU\ WR WKH SDLU ZRUN WUDQVFULSWV 7KLV ZDV E\ QR PHDQV HDV\ DV WKH WZR LQWHUYLHZHUV
ZHUH IUHH WR VWRS WKH WDSH WR UHSHDW LQWHUHVWLQJ VFHQHV RU WR ZLQG EDFNZDUGV DQG RU IRUZDUGV
7KH UHVXOWLQJ ÄSDUWLWXU³ WUDQVFULSW IROORZHG WKH FKURQRORJ\ RI WKH SDLU ZRUN EXW EURNH XS
WKH FKURQRORJ\ RI WKH FOLQLFDO LQWHUYLHZV
(PSLULFDO GHVLJQ
Cooperative problem solving
¼ Two identical video tapes «1»
Immediately
afterwards
Self-confrontation and
Self-confrontation and
clinical interview «A»
clinical interview «B»
¼ Tape «2A»
¼
Tape «2B»
«2A» «1» «2B»
(Integration of transcripts)
¼ Partitur-Transcript

,QWHUSUHWDWLRQ RI GDWD
UDFNLQJ GRZQ WKH XQGHUO\LQJ SURFHVVHV PHDQW LQWHUSUHWLQJ WKHVH SDUWLWXU WUDQVFULSWV DV ZHOO DV
WKH FRUUHVSRQGLQJ PDWKHPDWLFDO HVVD\V ZULWWHQ E\ HDFK G\DGH $QDO\WLFDO HQWLWLHV ZHUH WR EH
LVRODWHG LQ WKH IORZ RI WKH GHVFULSWLRQ DQG FRPPHQWLQJ SURFHVVHV $YRLGLQJ D PLFUR OHYHO RI
DQDO\VLV WKH ZRUN FRQFHQWUDWHG RQ WRSLFV ZRUNHG RQ E\ WKH SDLUV RI VWXGHQWV (DFK RI WKHVH
XQLWV RI DQDO\VLV ± HDFK RQH D SUREOHP WDFNOHG E\ D G\DGH ± KDG WR EH LQWHUSUHWHG DQG DVVHVVHG
7ZR LQGHSHQGHQW SHRSOH FDUULHG RXW WKH LQWHUSUHWDWLRQ RI WKH GDWD RQH DQ H[SHULHQFHG PDWKH
PDWLFV WHDFKHU WKH RWKHU D UHVHDUFKHU 7KHUHIRUH WZR VWDJHV ZHUH LQYROYHG XQLWV RI DQDO\
VLV ZHUH GHILQHG LQ D FR RSHUDWLRQ SURFHVV ± VLQJOH SUREOHPV HODERUDWHG E\ WKH G\DGHV ZHUH
LVRODWHG WKHVH XQLWV ZHUH DVVHVVHG E\ WKH WZR UHVHDUFKHUV VHSDUDWHO\ DFFRUGLQJ WR HVWDE
OLVKHG FDWHJRULHV 'LIIHUHQFHV LQ DVVHVVLQJ D XQLW ZHUH GLVFXVVHG DIWHUZDUGV ,Q FDVHV ZKHUH QR
FRQVHQW ZDV UHDFKHG QR DVVHVVPHQW ZDV JLYHQ +2//(167(,1 SS ±
7KH HVVD\V DQG WKHLU FRUUHVSRQGLQJ SDUWLWXU WUDQVFULSWV ZHUH LQWHUSUHWHG IURP WKHVH SHUVSHF
WLYHV
D :KDW LV WKH TXDOLW\ RI WKH ÄFRUSXV³ RI HODERUDWHG SUREOHPV UDLVHG E\ WKH ZULWLQJ RI WKH
PDWKHPDWLFDO HVVD\" 2I VSHFLDO LQWHUHVW DUH WKH ULFKQHVV DQG WKH OHYHO RI GLIIHUHQWLDWLRQ
E 7R ZKDW H[WHQW LV D VXEMHFW RULHQWHG DQG FRQFHSWXDO DUJXPHQWDWLRQ XVHG WR WUHDW WKH FKRVHQ
WRSLF" 2U KRZ IUHTXHQWO\ GR VRPH V\QWDFWLFDO SURSHUWLHV RI WKH JLYHQ WH[W WULJJHU DULWKPHWL
FDO RSHUDWLRQV SURSHUWLHV OLNH WKH NLQG RI JLYHQ QXPEHUV NH\ZRUGV XVHG DV FOXHV IRU
FHUWDLQ FDOFXODWLRQV WKH TXDOLW\ RI UHVXOWV HPHUJLQJ IURP WULDO DQG HUURU XVH RI WKH FDOFXOD
WRU "
7KHVH DVVHVVPHQWV RI VWUDWHJ\ DUH EDVHG RQ WKH IROORZLQJ FDWHJRULVDWLRQ
‡ 7KH G\DGH VKRZV SXUHO\ PHFKDQLFDO DVVRFLDWLYH EHKDYLRXU 3UREOHP VROYLQJ LV FRPSOHWHO\
EDVHG RQ V\QWDFWLFDO SURSHUWLHV RI WKH JLYHQ SUREOHP WH[W WRUVR
PHWLFDO DFWLYLWLHV
ZKLFKWULJJHUVWKHDULWK ‡ 6RPH ORJLFDO VWHSV WDNHQ LQ WKH SUREOHP VROYLQJ SURFHVV DUH EDVHG RQ VXEMHFW RULHQWHG FRQ
FHSWXDO DUJXPHQWDWLRQ VRPH VWHSV LQ WKH SURFHVV VKRZ PHUHO\ PHFKDQLFDO DVVRFLDWLYH EH
KDYLRXU
‡ (YHU\ ORJLFDO LPSRUWDQW VWHS WDNHQ LQ WKH SURFHVV LV EDFNHG E\ D VXEMHFW RULHQWHG DQG FRQ
FHSWXDO DUJXPHQWDWLRQ 7KHUH PD\ EH SKDVHV RI PHFKDQLFDO DVVRFLDWLYH EHKDYLRXU EXW WKH
ORJLFDO VWHSV FRQFHUQHG DUH GLVFXVVHG HOVHZKHUH RU WKH\ DUH RI QR ORJLFDO LPSRUWDQFH LQ WKH
OLQH RI WKLQNLQJ VRPHZKDW OLNH VLGH DFWLRQV ÄSOD\LQJ³ ZLWK WKH FDOFXODWRU WHDVLQJ HWF
5HVXOWV ± GLVFXVVLRQ
7KH TXDOLW\ RI HODERUDWHG SUREOHPV ± ULFKQHVV DQG OHYHO RI GLIIHUHQWLDWLRQ
7KH W\SHV RI SUREOHPV JHQHUDWHG DQG WDFNOHG E\ WKH VWXGHQWV ZULWLQJ DQ HVVD\ DUH VKRZQ LQ WKH
IROORZLQJ WDEOH

7\SH RI SUREOHP H[SHULPHQWDO JURXS 0DOH
G\DGHV
6SHHG 7KH (DJOH 7KH (DJOH FRPSDUHG WR WRGD\µV KLJK VSHHG WUDLQV WR D JRRG
PLGGOH UDQJH VSULQWHU HWF
)LQDQFLDO DVSHFWV RI WKH UDLOZD\ FRPSDQ\ ,QFRPH LQ VHYHUDO \HDUV G\QDPLF
V\VWHPV EDVHG RQ DQQXDO ULVHV LQ EXVLQHVV YROXPH LQFRPH YV VXSSRVHG FRVWV
2UJDQLVDWLRQDO DVSHFWV VFKHGXOLQJ PDQSRZHU WUDLQV HWF
3XUFKDVLQJ SRZHU WKHQ DQG WRGD\
0LVF
6XP
)HPDOH
G\DGHV
7KH FRQWHQW DQDO\VLV VXSSRUWV WKH ILUVW K\SRWKHVLV HVVD\ ZULWLQJ LQ PDWKHPDWLFV VHHPV WR
IRVWHU QDWXUDO LQWHUQDO GLIIHUHQWLDWLRQ .5$87+$86(1 :,770$11 HW DO 7KH
SUREOHPV ZRUNHG RQ LQ WKH H[SHULPHQWDO JURXSV DUH GLIIHUHQW LQ WHUPV RI FRQWHQW DQG OHYHO RI
FRPSOH[LW\ IURP HDFK RWKHU 7KH YDULHW\ LV HYHQ DVWRQLVKLQJ 7KH FRUSXV RI LVVXHV UDLVHG E\
WKH H[SHULPHQWDO G\DGHV LQ ZULWLQJ HVVD\V FRQWDLQV DOVR RSHQO\ IRUPXODWHG DQG GLYHUJHQW
SUREOHPV L H VLPLODU WRSLFV DUH PDWKHPDWLVHG GLIIHUHQWO\
0HDQZKLOH WKH FRQWURO JURXS RI FRXUVH ZRUNHG MXVW DW WKH JLYHQ TXHVWLRQV
([WHQW RI VXEMHFW RULHQWHG FRQFHSWXDO DUJXPHQWDWLRQ
7KH QXPEHUV LQ WKH IROORZLQJ WDEOH UHVXOW IURP WKH LQWHUSUHWDWLRQ DQG DVVHVVPHQW SURFHVV
VNHWFKHG DERYH +2//(167(,1 SS ±
6ROYLQJ WUDGLWLRQDO
ZRUG SUREOHPV
:ULWLQJ HVVD\V
H[SHULPHQWDO JURXS
&DWHJRULHV RI VWUDWHJ\ PDOH IHPDOH PDOH IHPDOH
0HFKDQLFDO DVVRFLDWLYH EDVHG RQ V\QWDFWLFDO SURS
HUWLHV
3DUWO\ PHFKDQLFDO SDUWO\ EDVHG RQ VXEMHFW RULHQWHG
FRQFHSWXDO DUJXPHQWDWLRQ
%DVHG RQ VXEMHFW RULHQWHG FRQFHSWXDO DUJXPHQWD
WLRQ
1RW DVVHVVHG
7RWDO
PDOH IHPDOH PDOH IHPDOH
7DEOH 6WUDWHJ\ RI SUREOHP VROYLQJ ± GLIIHUHQWLDWHG DFFRUGLQJ WR VH[ DQG GLGDFWLF VHWWLQJ

&RXQW RI SUREOHPV 6WUDWHJLHV RI SUREOHP VROYLQJ ± GLIIHUHQWLDWHG DFFRUGLQJ WR VH[ DQG GLGDFWLF VHWWLQJ
6WDQGDUG GHYLDWLRQ IRU 6WUDWHJ\ RI SUREOHP VROYLQJ GLIIHUHQWLDO DFFRUGLQJ WR VH[ DQG GLGDFWLF VHWWLQJ
7KH VLJQLILFDQFH RI WKH JHQGHU UHODWHG GLIIHUHQFHV LV DVWRQLVKLQJ $OWKRXJK , ZDV IXOO\ DZDUH
RI WKH UHVHDUFK OLWHUDWXUH FRQFHUQLQJ WKLV WRSLF GXULQJ WKH SUHSDUDWLRQ VWDJH RI WKLV H[SHULPHQW

, ZDV WDNHQ E\ VXUSULVH 7KH PDLQ TXDQWLWDWLYH K\SRWKHVLV ZKLFK DVVXPHG D VWURQJ JHQHUDO
HIIHFW EHFDPH VXERUGLQDWH WR WKH JHQGHU UHODWHG RQH 7KH FRQVHTXHQW VXSSRVLWLRQ ZDV WKH
LPSRUWDQW RQH $OO TXDQWLWDWLYH HIIHFWV VHHQ LQ WKLV H[SHULPHQW DUH YHU\ FOHDU DV UHJDUGV IHPDOH
VWXGHQWV ZKHUHDV WKH HIIHFWV IRU PDOH VWXGHQWV DUH PLQRU
&RPSDUHG WR WKH WUDGLWLRQDO ZRUG QXPEHU SX]]OHV WKH OHDUQLQJ HQYLURQPHQW RI HVVD\ ZULWLQJ
LQ PDWKHPDWLFV VHHPV TXLWH FOHDUO\ WR IDFLOLWDWH PDWKHPDWLVDWLRQ DQG SUREOHP VROYLQJ EDVHG
RQ VXEMHFW RULHQWHG FRQFHSWXDO DUJXPHQWDWLRQ 6ROXWLRQV EDVHG RQ SXUHO\ V\QWDFWLF SURSHUWLHV
RI WKH JLYHQ SUREOHP WH[W DUH OHVV IUHTXHQW LQ WKH ZRUN RI WKH H[SHULPHQWDO JURXS WKDQ LQ WKH
FRQWURO JURXS GRLQJ WUDGLWLRQDO ZRUG QXPEHU SX]]OHV
7KHUH LV DOVR LQGLUHFW HYLGHQFH 7KH FRXQW RI DGHTXDWH PDWKHPDWLVDWLRQ DV ZHOO DV WKH QXPEHU
RI FRPSOHWHO\ LQDGHTXDWH DSSURDFKHV WR WKH SUREOHPV FRQFHUQHG DUH VLJQLILFDQWO\ KLJKHU LQ WKH
G\DGHV GRLQJ WUDGLWLRQDO SUREOHP VROYLQJ WKDQ LQ WKH H[SHULPHQWDO JURXS 2Q WKH FRQWUDU\
SDUWO\ DGHTXDWH PDWKHPDWLVDWLRQ LV PRUH LPSRUWDQW DPRQJ WKH HVVD\ ZULWLQJ G\DGHV 7KLV HI
IHFW DOORZV IRU D FRQFOXVLRQ UHJDUGLQJ WKH XQGHUO\LQJ SURFHVVHV RI SUREOHP VROYLQJ $PRQJ
WKH SDLUV GRLQJ WUDGLWLRQ ZRUG QXPEHU SX]]OHV PHFKDQLFDO DVVRFLDWLYH SUREOHP VROYLQJ LV
ZLGHVSUHDG ZKLFK PHDQV WKDW WKH FRXQW RI ÄKLWV³ RU ÄPLVV KLWV³ LV VWDWLVWLFDOO\ KLJKHU WKDQ
H[SHFWHG %XW D VXEMHFW RULHQWHG DUJXPHQWDWLRQ LV OLNHO\ WR UHVXOW LQ SDUWO\ DGHTXDWH PDWKHPD
WLVDWLRQV
/DVW EXW QRW OHDVW $ VXUSULVH UHVXOW RI WKH H[SHULPHQW LV WKH PDVVLYH HIIHFW RI PHFKDQLVHG
WKLQNLQJ /8&+,16 LQ WKH FRQWURO JURXS 3DUDOOHO WR WKH H[SHULPHQW WKH PDWKHPDWLFV
FODVV LQ VFKRRO KDG EHHQ GHDOLQJ ZLWK SURSRUWLRQV :KHQ WKH VWXGHQWV FDPH WR FDOFXODWLQJ WKH
ÄDYHUDJH VSHHG RI 7KH (DJOH³ DOPRVW DOO RI WKHP WULHG WR XVH WKH TXLWH FRPSOLFDWHG ÄRIILFLDO
V\VWHP³ RI FDOFXODWLQJ SURSRUWLRQV 7KH\ WULHG WR FDOFXODWH WKH ZRXOG EH GLVWDQFH RI DQ KRXUµV
FUXLVLQJ EXW PRVW RI WKHP IDLOHG 7KH (DJOH WDNHV PLQXWHV WR FRYHU NP DQG WKHVH DUH
KLJK DFKLHYLQJ VWXGHQWV 2Q WKH RWKHU KDQG VRPH G\DGHV ZKR ZHUH GRLQJ WKHLU HVVD\ HQGHG
XS VROYLQJ WKH VDPH SUREOHP 1RQH RI WKHP XVHG WKH RIILFLDOO\ WDXJKW V\VWHP DQG QRQH RI
WKHP IDLOHG +2//(167(,1 SS ±
:KDW FRXOG WKLV SURMHFW PHDQ IRU HYHU\GD\ VFKRRO OLIH DQG PDWKHPDWLFV
HGXFDWLRQ LQ SDUWLFXODU"
7KH SURSRVHG OHDUQLQJ HQYLURQPHQW RI HVVD\ ZULWLQJ LQ PDWKHPDWLFV LV VLPSOH DQG HIILFLHQW
HQRXJK WR EH DSSOLHG LQ HYHU\GD\ WHDFKLQJ 7KLV LV QRW WR OD\ FODLP WR VRPH NLQG RI ÄIXQGD
PHQWDO UHYROXWLRQ³ EXW VLPSO\ WR UHSUHVHQW D VWHS IRUZDUG LQ SURIHVVLRQDO GHYHORSPHQW
7KH UHTXLUHG ZRUN ORDG RQ WKH SDUW RI WKH WHDFKHU LQ VHWWLQJ XS WKH OHDUQLQJ HQYLURQPHQW IRU
HVVD\ ZULWLQJ LQ PDWKHPDWLFV LV PRGHUDWH DQG LW FDQ EH KDQGOHG ZLWKRXW DQ\ ULVN\ RU IDU
UHDFKLQJ GHFLVLRQV IRU RU DJDLQVW D QHZ PHWKRGRORJLFDO DSSURDFK ,I WKH LGHD ZRUNV WKH SUDF
WLFH RI HVVD\ ZULWLQJ FRXOG EH H[WHQGHG HYHQ WR RWKHU WUDGLWLRQDO GLGDFWLF VHWWLQJV
(VVD\ ZULWLQJ LQ PDWKHPDWLFV FOHDUO\ XQGHUOLQHV WKH UHFHQW WUHQGV LQ LQWHUGLVFLSOLQDU\ HGXFD
WLRQ EULQJLQJ WRJHWKHU IRU LQVWDQFH WKH PDVWHU\ RI ODQJXDJH FRPSHWHQFH LQ IRUPXODWLQJ FRQ
FHSWV DQG DELOLW\ WR DUWLFXODWH LGHDV V\VWHPDWLFDOO\ LQ DOPRVW DQ\ VXEMHFW )XUWKHUPRUH WKLV
NLQG RI PDWKHPDWLFDO DFWLYLW\ VWUHVVHV RQH RI WKH PRVW LPSRUWDQW IRUPDWLYH YDOXHV LQ PDWKH
PDWLFV
,Q DGGLWLRQ IHPDOH VWXGHQWV VHHP WR EHQHILW HQRUPRXVO\ IURP WKLV NLQG RI DSSURDFK ZKLOH
PDOH VWXGHQWV VKRZ QR QHJDWLYH UHDFWLRQV DQG WKLV PD\ ZHOO EH D ZD\ LQ IXWXUH RI HQFRXUDJLQJ
IHPDOH VWXGHQWV WR EHDW WKH SDWKZD\ WR PDWKHPDWLFV DQG WKH VFLHQFHV LQ JHQHUDO

7KH VWXGHQWV WDNLQJ SDUW LQ WKLV SURMHFW ZHUH E\ QR PHDQV H[SHULHQFHG ZULWHUV DQG \HW WKH\
VKRZHG VLJQLILFDQW VWLPXODWLRQ , FDQ LPDJLQH WKDW IXUWKHU H[SHULHQFH ZRXOG GHHSHQ WKH SHU
VRQDO EHQHILWV WR EH JDLQHG QRW RQO\ LQ DSSOLHG PDWKHPDWLFV EXW DOVR LQ WKH PDVWHU\ RI ODQ
JXDJH
5()(5(1&(6
$(%/, + 'HQNHQ GDV 2UGQHQ GHV 7XQV 'HQNSUR]HVVH 6WXWWJDUW .OHWW
$(%/, + 67$8% ) 587+(0$11 8 7H[WUHFKQXQJHQ LP 0DWKHPDWLNXQWHUULFKW
0DWKHPDWLN OHKUHQ ±
%$(5 0 5(%(5 :

*$//,1 3 58) 8 6SUDFKH XQG 0DWKHPDWLN = ULFK 9HUODJ /HKUHULQQHQ XQG /HK
UHU 6FKZHL] /&+
*$//,1 3 58) 8 /HUQHQ GXUFK 6FKUHLEHQ ± DXFK LQ GHU 0DWKHPDWLN ,Q
%XQGHVWDJXQJ I U 'LGDNWLN GHU 0DWKHPDWLN SS )ULERXUJ )UDQ]EHFNHU
*$//,1 3 58) 8 6FK OHU VFKUHLEHQ 7H[WDXIJDEHQ ± /HVHQ GXUFK 6FKUHLEHQ PD
WKHPDWLN OHKUHQ
*$03(5 - * /|VXQJVVWUDWHJLHQ XQG )HKOHU YRQ UHFKHQVFKZDFKHQ .LQGHUQ EHLP
/|VHQ YRQ $ULWKPHWLNDXIJDEHQ 'LVVHUWDWLRQ 3V\FKRORJLVFKHV ,QVWLWXW 8QLYHUVLWlW %HUQ
*,16%85* + &KLOGUHQµV $ULWKPHWLF WKH OHDUQLQJ SURFHVV 1HZ

0$,(5 + $QDO\VH YRQ 6FK OHUYHUVWHKHQ LP 8QWHUULFKWVJHVFKHKHQ )UDJHVWHOOXQJHQ
9HUIDKUHQ XQG %HLVSLHOH ,Q + 0$,(5 - 92,*7 (GV 8QWHUVXFKXQJHQ ]XP 0DWKH
PDWLNXQWHUULFKW SS .|OQ 'HXEQHU
1(7+ $ 92,*7 - /HEHQVZHOWOLFKH ,QV]HQLHUXQJ 'LH $XVKDQGOXQJ VFKXOPDWKH
PDWLVFKHU %HGHXWXQJ DQ 6DFKDXIJDEHQ ,Q + 0DLHU - 9RJW (GV 8QWHUVXFKXQJHQ
]XP 08 .|OQ 'HXEQHU
5$'$7= + 8QWHUVXFKXQJHQ ]XP /|VHQ HLQJHNOHLGHWHU $XIJDEHQ -RXUQDO I U 0D
WKHPDWLNGLGDNWLN
5$'$7= + $QVFKDXXQJ XQG 6DFKYHUVWHKHQ LP 0DWKHPDWLNXQWHUULFKW GHU *UXQG
VFKXOH ,Q %HLWUlJH ]XP 0DWKHPDWLNXQWHUULFKW ± )UDQ]EHFNHU
5(61,&. / % /(9,1( - 0 7($6/(< 6 ' 3HUVSHFWLYH RQ VRFLDOO\ VKDUHG FRJ
QLWLRQ :DVKLQJWRQ '& $PHULFDQ 3V\FKRORJLFDO $VV FRS
5(866(5 . 3UREOHP 6ROYLQJ %H\RQG WKH /RJLF RI 7KLQJV 7H[WXDO DQG &RQWH[WXDO
(IIHFWV RQ 8QGHUVWDQGLQJ DQG 6ROYLQJ :RUG 3UREOHPV UHVHDUFK UHSRUW
$EWHLOXQJ 3lGDJRJLVFKH 3V\FKRORJLH
8QLYHUVLWlW %HUQ
5,&+7(5 6 %5h*(/0$11 + 0lGFKHQ OHUQHQ DQGHUV OHUQHQ -XQJHQ *HVFK
OHFKWVVSH]LILVFKH 8QWHUVFKLHGH EHLP 6FKULIWVSUDFKHUZHUE /HQJZLO /LEHOOH
5,&¯85 3 'X WH[WH j OµDFWLRQ (VVDLV GµKHUPpQHXWLTXH 3DULV (GLWLRQV GX VHXLO
6&+2(1)(/' $ + :KHQ *RRG 7HDFKLQJ /HDGV WR %DG 5HVXOWV 7KH 'LVDVWHU RI
Ä:HOO 7KDXJKW³ 0DWKHPDWLFV &RXUVHV (GXFDWLRQDO 3V\FKRORJLVW ±
6(/7(5 & Ä-HGH $XIJDEH KDW µQH /|VXQJ ³ 9RP UDWLRQDOHQ .HUQ LUUDWLRQDOHQ 9RUJH
KHQV *UXQGVFKXOH
67(51 ( :DUXP ZHUGHQ .DSLWlQVDXIJDEHQ ÄJHO|VW³" 08 'HU 0DWKHPDWLNXQ
WHUUULFKW
67(51 ( :LH YLHOH .LQGHU EHNRPPHQ HLQHQ 0RKUHQNRSI" =XU %HGHXWXQJ GHU .RQ
WH[WHLQEHWWXQJ EHLP 9HUVWHKHQ GHV TXDQWLWDWLYHQ 9HUJOHLFKV
OXQJVSV\FKRORJLH XQG 3lG 3V\FKRORJLH
=HLWVFKULIW I U (QWZLFN
:(,'(10$11 % .5$33 $ 3lGDJRJLVFKH 3V\FKRORJLH 0 QFKHQ 3V\FKRORJLH
9HUODJV 8QLRQ
:(57+(,0(5 0 3URGXFWLYH WKLQNLQJ 1HZ

$UPLQ +ROOHQVWHLQ
8QLYHUVLWlW %HUQ )RUVFKXQJVVWHOOH I U 6FKXOSlGDJRJLN XQG )DFKGLGDNWLN
0XHVPDWWVWUDVVH
&+± %HUQ 6ZLW]HUODQG
KROOHQ#VLV XQLEH FK )D[ 7HO