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Q N6HieNCt)(ULfLUAN HOAT DONG SIEU NHAN THUTC TRONG QUA TRINH KHAM PHA BAI TOAN KET THUC M d NGUnNTH! HUDNG LAN Truimg Bai hpc Tin Trdo Email ngif]renianGiltqeBmall GO Tdm tit Trong nhdng ndm gan ddy[.]
Q N6HieNCt)(ULfLUAN HOAT DONG SIEU NHAN THUTC TRONG QUA TRINH KHAM PHA BAI TOAN KET THUC M d NGUnNTH! HUDNG LAN Truimg Bai hpc Tin Trdo Email: ngif]renianGiltqeBmall.GO Tdm tit: Trong nhdng ndm gan ddy sieu nhdn thdc dd thu hut sa quan tdm eua nhieu nhd gido due todn Mdfmmg nhij-ng vdn di md cdc nhd nghien edu todn hoc theo duoi Id tim hieu vai trd eua sieu nhdn thdc den khd nang gidi quyft vdn de todn hoc eua hoc sinh Bai viit tap trung vdo viec tim hieu hoat ddng sieu nhdn thdc qud trinh khamphibH todn kit thuc mdcua hoc smh cung nha dnh hadng eua sieu nhdn thdc den khd ndng gidi quyet thdnh cdng cdc bdito&i kit thuc md Ben canh dd tde gid cdn chi moi taang tdc gida hoat dong sieu nhdn thde eua hoe sinh vd khd ndnggi^ quyet vdn de eua ede em Tdkhod: Sieu nhdn thdc; khdm phd bai todn ket thuc md (Nhan bai ngdy 07/7/2016; Nhdn ket qud phan bien vd chinh sda ngdy 20/8/2016; Duyet ddng ngdy 27/9/2016) I.DatvSnde V i o khoang nhdng nam 80 cua the ki trude, eae n h i g i i o due t o i n nghien cdu ve g i i i quyet v i n d l b i t dau quan tam den q u i trinh sieu nhan thde (SNT) eOa hoc smh (HS) tim k i l m d d lieu de t r i ldi eho e i u hdi lieu eac h i n h vi SNT co vai tro n h u the nao doi vdi q u i trinh giai quyet van de Nghien cuu cua [Lester, 1982) da chi r i n g h i l u biet cua HS ve hoat dong nhan thdc truoc, va sau g i i i quyet van de eung vdi cac hoat dpng mang tinh d i l u h i n h nhU theo doi va t u d i e u ehinh i n h hudng Idn d i n viee g i i i q u y l t cdng cac van de t o i n eua ngudi hoe, Mdt so nghien edu sau d d tiep tuc tim h i l u i n h hUdng eua SNT den k h i n i n g g i i l quyet bai t o i n cd ldi van (Pennequyn va nhdm t i c g i i , 2010), giai quyet cac van de toan cd tinh x i c thUe (Kramarskivinhdmtiegia, 2002), giai q u y l t van de t o i n mdi trudng eong nghe [Kapa 2001} Trong d d , nhdng nghien cdu ve h i n h vi SNT q u i trinh kham p h i toan cua HS h i u nhu chua dUoc d l c i p d i n Do do, khuon kho b i l vilc nay, ehung tdi trinh bay ket q u i cua mdt nghien edu dmh tinh ve hoat ddng SNT qua tfinh kham pha bai toan ket thue m d eua HS trung hoc thong, Sieu n h i n thdc T h u i t n g d SNT b i t nguon tU Hi Lap Trong tieng H I Lap thuat ngd"meta" cd nghia la "sau" Do do, SNT l i n h i n thdc ve hoat ddng nhan thde eua ea nhan Theo Flavell (1979), SNT la hieu biet cua e i n h i n hen quan den qua trlnh nhan thdc cua moi ngudi bao gom c i eae kl nang mang tlnh dieu hanh nhU theo ddi, dieu chinh va s i p xep cie q u i trlnh n h i n thde d l hudng den muc tieu dat Cu t h l q u i trinh hoe t i p cua HS theo Pennequyn v i nhdm tac gia (2010), SNT bao g6m h i l u biet ve q u i trinh nhan thdc va nhdng hoat ddng mang inh dieu hanh b i c eao n h u phan tieh nhiem vu hoe tap len ke hoach, theo ddi, k i l m tra va danh gia ve sU cong eua viec hpc VI t h l , SNT eo eae d i e trUng sau: N h ^ thde v l q u i trinh t u d u y eiia b i n t h i n ; Theo doi tichcyc va ehu d d n g q u i trinh nhan thdc eiia b i n thSn; Dieu ehinh qua t r i n h nhan thde t r o n g moi quan h?viS( e i c nhiem vu hoe t i p ; Tu t i m k i l m phuong phipgiJI q u y l t vi'n d e ; D a n h gia ve q u i trinh g i i i q u y l t vSn d^vi ket q u i dat duoe Vdl n h d n g d i e trUng d d , SNT dUoe p h i n bl§t mffl e i c h ro rang vdi nhan thde, Ve npi dung, SNT bao g&n kien thde, ki nang va t h d n g tin cua n h i n thdc, t h u ^ m o t phan cua the gidi t r i tue, t m h than, Trong 66, nhan thdc bao g o m hieu b i l t c i c ddi tuong, eon ngi/ii, su kien, hi&n t u o n g t i m li va e i e ki n i n g d l xd II eicvSn de n i y Do do, SNT k h d n g eo n g u o n goe t d thUe t l bfei ngoai chil the m i g i n vdi hoat d o n g tn tue v i tinh ihJn cua ehu t h l , no cd t h l bao g o m n h d n g gi m i c i nhSn b l l t v l q u i trinh h u d n g ndi, c i c h thde thUc hien v i cSdi ngudi ta c i m nhan v l no, Ve chde nang, n h i n thu'c ciS ehdc nang g i i i quyet van d l v i mang lai k i t q u i giii quyet van de Trong do, SNT d u n g d l d i l u chlnh V* dmh h u d n g nhan thdc cua ea n h i n qua trinh giil q u y l t van de, M d hinh sieu nhan thdc ciia Tobias v^ Evn«n C6 n h i l u m o hinh ve SNT da duoc nghien eiilivi ap d u n g v i o hoat d d n g t a m If hoe va day hoc, Trong dft / L J P ke boach / / / Lira chpu chiin hr^c E>inh ga Mfc b ^ Tbto ddi hieu brfl \ \ \/^S ^^\ \ Hlnh 1: ft/Id hlnh phdn cdp vequd trinh SNT • KHOA Hpc GUtO DUC NBHIEN CtUU UIAN I mo hlnh SNT theo kieu phan cap cua Tobias va Everson glupcho ngudi hoc ed dinh hddng rd rang viec tim (2002) da dddc sd dung trdng cie nghien edu vi qui klim phddng i n giai quyft van de dit bai toin tnnh day hoe Tlieo cic dng, SNT la sd ket hop gida cic ban dau Cu the hoat ddng SNT se dinh hddng qui trlnh yeu to nhd ki ning, kien thdc (hieu biet «e nhin thdc) khim phi bai toin kft thuc md bing cic hoat ddng theo doi qua trinh nhin thdc cua ngudi hoc cung nhu thinh phan cuthe sau: dieu khien qui trinhdd theo md hinh ! - Lap ke hoach: Cdng viic dau tiin cua HS - Ldp klhoach: Cong viec dau tien cua HS hoat ddng SNT la len ke hoach di' fim hieu tinh hudng • hoat dong SNT li lip ke hoaeh, bao gom xac dinh mue toan hoe dit bai toin kft thuc md Viec lin ke tieu hoe tip thdi gian hoc tap, ddklen ket qui dat duoc hoach dUde bit dau bang eie edng viic cu the la dit -/('"^''oncWerr/i/crcr Sau lip ke hoach, ngudi eac eiu hdl, dm kiem cie muc dich de khim phi xiy ftl hoc cin lua chon ehien Idoc, phddng phap phil hdp de ddng cic gii thuyft de khim phi tlnh huong ban diu % thuc hien nhiem vu hoc tap dd -lu-ocftonc/iienJi/ocrSaukhidatraeacciuhdI.gii iff -Odn* gid vlec hpc: Khi thuc hien xong ehien Iddc V! hoc tap, ngddi hoc can dinh gii ve viec hoe cua minh thuyft v i mue dich di' khim phi tlnh hudng ban dad ' " " ' ' " * " * ' " *?' IKdng ti le thuan vien bi Nhdng kien thde niy nim mien hieu bift toin cua - Bdnh gid vlec hpc: Dd lieu thu thap dude td viic •' cic em td eap Trung hoc eosd quan sit Idp hdc eho tha'y HS thao luin can than ve cic '"'""•'""••Vdlbiitoinl.hSuhftHSdeutriiqua hoat dong kham phi toin vdi ba cho trlnh khep kin phdong i n ehia sd bl ban dau Mdt so nhdm HS d i de xua't duoc phUdng i n toi du de chia so bi ban diu Dd "bdng tang dan yeu cau v i mdc dd nhan thdc nhSm tim la chia theo xie suat thing eudc eua tdng nguft neu tro '• phUdng i n tdl uu de' giii quyft va'n de ma bii toin ehoi van tiep tuc i dat - Theo ddl hiiu biit: Mdt nhdng kien thdc ; Sau lim quen vdl viee kham phi bil toin diu tien, HS tiep tuc tien hanh hoat ddng SNT tim kie'm ma HS can sd dung di" giai quyft van de dat bii phUdng i n tdi uu de giii quyft vin de bai toin thd toan l i dai luong ti l i thuan Tuy nhien, cie kien thde Cung gidng nhu kham phi bii toin 1, hau hft HS ve dai luong B le thuin lai khdng du de mang den cho - deu cho ring cd thS ehia sd bi d i eUdc theo tl le 1 hoic cac em phUdng i n tdi du de giii quyft van de Do dd, HS • chia theo tl l i so van thing eua hai ngddi chdL Cac pha IJhii buy ddng kien thdc d cip eao hon la xie suft hoat ddng SNT eua HS kham phi bai toin niy tim kiemjjhuong i n tdi uu de giii quyft van de _ - Kiim sodu Khi lam viee vft bai toin 2, ehi ed mot augc md t i cu the nhu sau - Ldp kihodch: HS phan tich gii thift eua bil toin so HS trai qua hoat dong kham pha toin vft ba chu trlnh dit mdt sd hudng khic de khim phi tlnh hudng khep km nhung ting din yiu eau ve mdc nhan thdc ban dad Do inh hddng td each giii quyft va'n de de tim phUdng i n tdi du de giil quyft van d i ma bil khim pha bai toin mdt nen ta't ea cie nhdm HS diu lin toan dat Cie em bift van dung mdt cich hop II hieu ke hoach chia deu sd bi d i dat cuoc eho hai ngudi hoac biet ve xie suft de khim phi bai toin ban diu Hau hft cae HS cdn lal deu ddng lai d viee sd dung kien thdc ve chia theo ti i i thing code cua hai ngudi dai Iddng tl le thuan de giai quyft van de nen chda dip - Laa chgn chiin luac: HauhftHSdeusddungklen thde ve eae dai Iddng d le thuin de dua phUdng an dng dddc yeu ciu ma bil toin ban dau dda Nhdng hoat ddng SNT mi HS d i tien hanh de khim chia so bl dat cudc luc diu khim phi bai toan hai Tat ci cie HS dda phuong i n thd nhft l i chia sd bi dat phi ba, toin thd hai d i giup cho cic em nhanh chdng cuoc theo ti le -1 luc dd mdl ngudi chdi se nhan dudc bm kiem eho minh phuong i n Idi uu de giii quyft van li_12 yien bi Tiep tuc vin dung phddng i n giii quyft de ban dau Nhdng kien thdc ve xic suft d i duoc van van de d bai toan 1, tft ci cie HS deu eho ring chia sd dung de dua phuang i n chia bin thddng mdt each bl theo tl le thing cude cua mdl ngudi l i phUdng an chia toi uu nhat Tddng tu nhd bai toin thd hai, hau hft HS bl toi uu nha't Chi cd 20% HS Idp nhin ring cd deu gii su trd ehoi van tiep tuc de tim co hdl thing thi tiep can bai toin theo hudng khac gia sd trd cuoc cua moi nguft Sau dd cae em Ida chon phuong i n Choi van tiep tuc de tim kiem cd hoi thing cude cua mdi ehia tien thUdng theo ti le xic sua't thing cudc cua mol ngudi VI neu trd choi vin tiip toc thl ehi can tdl da ngddc Cac em chi ring ne'u trO choi vin hip tuc thl van nua tro Choi se kft thdc Hai van ehdl tao nin ngiu can toi da van nda mdi xic dinh dudc ddl chie'n Ihing nhien mi chi cd mdt ngau nhiin Hii thing ei W ba van ehd, tao ngau nhien, dd chi eo van moi thuan loi cho Hil nghla li loc dd Hii l i ngdft mot ngau nhien lam eho ddl thd hai trd thinh dni ehie'n thang ehung cudc nen xie sua't de' ddi thd hai ehie'n I ^ —^ — •-"^ ="•" uc uui tnu nai chiin Ch,.n thing Nhdviy Hi, ehi cd i cd hdi chie'n thing thing trudng hop l i I Xic suft d ddl thd cdn Nam cd den — ^ CO hdi ehiln thing nen chia sdbi theo tl le lue Nam duoc 16 n bl cdn Hil ddde nhatthingcupetrong trdehoi nayla : W vay chia tiln thdfttg cho hai ddi theo ti le l i 7:1 nen ddl thd nha't 0132-I1IIDISIKI11I.63 "-^J Q NGNIEN COUU LUAN Do ehuyen td viec khim p h i b i l toan mdt sam bai toan hai, chl eo hai tong s6 mUcri nhdmHS dua duoe phuong an tdi Uu di giii quyet van dl^Tuy nhien, so luong nhom HS dUa dupe phUemg an toi d l giil quyet van d i c i n g t i n g cic em quen dan vfi hoatddng sleu thdc no lue kham p h i eac bil toin kit thuc md, Cu t h l , da eo nam so mudi nhdm HS d i d l xuat duoe phuang i n tdi Uude kham p h i bil toin bai toin thdba Ket luan Ket q u i thu dUoe tCf nghien cdu niy eho thiy, rf^ ti'eh hop eic bii toin k i t thue mdvao eae thue hinh dm hpe toan da mang d i n eo hoi de HS tien hanh hoat Sfyn SNT va phit trien ning glii quylt van d l Ben canh do, viee tiln hanh eie hoat dgng SNT trude, vi sau khim p h i cic b i i t o i n k i t thue md nhu lap klhojdi Hinb 4- Bdi Idm cua nhdm v i lUa chon ehiln luoe eiing cic hoat ddng mang tfi* Thdng ke sd lieu ve cie phuong an khim phi ba bai dilu hanh nhU dinh g i i viee hoe, theo doi hieu biltvS toin ma cac nhdm HS dua daac trinh biy d bang sau: kiem soit i n h hudng d i n k h i nang giii quylt thSnh Bdng Phaang dn gidi quyet vdn de cua cdc nhdm HS cdng bai toan k i t thuc md ban diu, Chlnh hoat ding SNT d i dmh hudng eho HS tim kilm nhilu phucnig it\ Bii toin Phuong an SonhdmHS khic d l glii quyet van de va d l xuat duoe phudng Phuong in 10 i n giil quylt vin de tdi Uu nhat eho cie b i i toin Itlt thdc md Do do, cd the thay vide tich hop eic b i l toin kit thik Bai toin Phuong an md v i o cie thue hinh day hoe t o i n la ean thilt nhim Phuang an ren luyen v i phit triln ki nang SNT eho HS Phuang in 10 duoe 875.000 dong v i ddi thU duoc 125.000 dong nhU eaeh tiep can van de cua eae HS d nhom 7: Bil toan Phuong an 10 TAILI$UTHAMKHAO [1], Nguyen Thl Duyln, ^20^ 4), Nghiin cdu bdi hgc eua gido viin tdp trung vao khdm phd todn cua hoc siiA Phuong an 10 day hgc mdn todn d tradng trung hoc phS thdng, Bil toan Phuong an 10 Luin an Tien si, Trudng Dai hpc Supham HaNdi, [2], Kapa, E., [2001], A metacognltive suppat Phuong an during the process of problem solving in a computerisd So lieu thu duoc td nghien cdu eho thay, kiln thde environment Educational Studies In Mathematics,47(3), da cd eua HS v l cac dai luong ti le thuin d i anh hudng 317-336 den each giii quylt van de cua HS eae em lam viee [3j, Schneider, W/,, & Artelt, C, (2010), fvletacognltlon vdl eie bii toan thd hai v i thu ba Nhdng kien thde and mathematics education, ZDM, 42(2), 149-161 trd thfinh ehudng ngai ein trd HS tim phuong an tdi E4] Tobias, S & Everson, H T, (2002), Knowing uu d l giil quyet van de, Oiy la chudng ngai sinh what you know and what you don't Further research « qua trinh phit tnen kiln thdc td cap thap d i n metacognltiveknov/ledgemonitoring.Technical Reports, cap cao hon, la ehudng ngai mang tinh tn thdc iuin The College Board Research Report Phuong an METACOGNITIVE ACTIVITY IN PROCESS TO EXPLORE OPEN-ENDED MATHS EXERCISE NguyenThiHuong LM Tan Trao OnivtriUf Email: nguyenlancdtq@gmaU.OM was "h'^'r'o'le"olm'J^r""T' ' " " " " S " ' " " " ""' "fueled the attention of Maths educators One afihe interesllnglm oc2„'heoZesToZ7 '° '""' "'"'"-'""I -''"Ity- The paper focuses on understanding metacogiiHK Z eZdeZ^s\L7°y ""r'"""'"""'' " ""'"