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