JOURNAL OF SCIENCE OF HNUE Interdisciplinary Sci 2014 VoL 59, No 1, pp 12 18 BAN VE NHUNG NANG LUC TOAN HOC CUA HOC SINH PHO THONG Chu Cam Thd Khoa Todn Tin Trudng Dai hpc Suphgm Hd Npi Tom tat Tren c[.]
JOURNAL OF SCIENCE OF HNUE Interdisciplinary Sci 2014 VoL 59, No 1, pp 12-18 BAN VE NHUNG NANG LUC TOAN HOC CUA HOC SINH PHO THONG Chu Cam Thd Khoa Todn - Tin Trudng Dai hpc Suphgm Hd Npi Tom tat Tren co sd phan tich mot s6 quan diem ve giao due nang luc, bai bao cho thay vai tro cua mdn Toan viec hinh va ren luyen nhflng phan quan Irong cua nang lUc thong Nang luc toan hoc ciia hoc sinh thong dUdc chiing toi hieu la nhilng nang lUc cSn co hoc sinh hpc xong chudng trinh mdn Toan thong Nhflng nang luc dap iJng viec hap thu nhflng tri thflc loan hoc, kha nang hpc tap mdn Toan kha nang van dung kiln ihflc toan vao cupc song, Nhflng nang luc Toan hpc thdng dUdc ban luan bao gom: Nang lite thu nhan ihong im Toan hoc Che bien thong tin loan hoc, Luu irfl ihong tin loan hpc Nang luc van dung Toan hoc vao giai quyet viin dl Tit khda: Nang liic, nang luc phd thong, nang luc toan hoc nang lUc toan hpc phd thong Moi dau Giao due hudng nang Iflc dang la mdt chu de dflpc nhieu nha nghien cflu giao due quan tarn Khuynh hfldng giao due hudng nang luc dupe nhieu quoc gia tren the gidi lua chpn Bai bao xin gidi thieu nhflng ket qua nghien cflu ma chung toi cd dUdc nham trinh bay mdt quan diem xac dinh muc lieu day hpc mdn Toan tren cd sd phan tich mdt sd quan diem vl giao due nang lUc va vai trd cua mdn Toan viec hinh va ren luyen nhflng phan quan cua nang luc thdng Noi dung nghien ciru 2.1 Quan diem ve giao due nang lilc Pham tru nang luc thUdng dUdc hieu theo nhflng each khac va mdi each hieu cd nhflng thuat ngfl tfldng flng - Nang Iflc (Capacity/Ability): hieu theo nghia chung nhat la kha nang (hoac tilm nang) ma ca nhan the hien tham gia mdt boat dpng nao d mdt thdi diem nhat dinh Ngay nhan bai: 13/07/2013 Ngay nhan dang- 15/12/2013 Lien he; Chu Cam Thtt e-mail; canHlio@hnue.edu Bdn ve nhiTng ndng luc Todn hpc ciia hoc sinh pha'thdng - Nang luc (Compentence): thudng goi la nang luc hanh dpng, la kha nang thuc hien hieu qua mot nhiem vu/mdt hanh dpng cu the, lien quan den mot linh vuc nhat dinh dua tren cd sd hieu biet ki nang, ki xao va su san sang hanh dpng - Nang lUe dupe xay dflng tren cd sd tri thflc, thiet lap qua gia tri cau true nhu la cac kha nang, hinh qua trai nghiem/cung co qua kinh nghiem hien thuc hda qua y chi (John Erpenbeck 1998) - Nang luc' la cac kha nang va ki nang nhan thflc vdn cd d ca nhan hay co the hpc dupe, de giai quyet cac van dl dat cupc song Nang luc cung ham chfla nd tinh san sang hanh dpng, ddng cd, y chi va trach nhiem xa hdi de cd the sfl dung mot each cdng va cd trach nhiem cac giai phap, nhflng tinh hudng thay ddi (Weinert, 2001) - Nang Iflc la kha nang ca nhan dap flng cac yeu cau phflc hdp va Ihuc hien cdng nhiem vu mdt boi canh cu the" (OECD, 2002) - Nang Iflc: la "kha nang van dung nhflng kiln thflc, kinh nghiem ki nang, thai dd va hUng thu de hanh ddng mdt each phu hdp va cd hieu qua cac tinh hudng da dang cua cupc song" (Quebec- Ministere de I'Education, 2004) - Nang luc: la kha nang hanh ddng, dat dupe cdng va chflng minh sfl tien bd nhd vao klia nang buy ddng va sfl dung hieu qua nhilu nguon luc lich hdp cua ca nhan giai quyet cac van de cua cudc sdng" (Tremblay 2002) - Nang lUc la kha nang flng phd cdng hay nang luc thflc hien bieu qua mdt loai/linh vuc hoat ddng nao dd tren cd sd hieu bill (tri thflc), bill each lua chpn va van dung nhflng iri thflc, kinh nghiem ki nang/ki xao de hanh ddng phu hdp vdi nhflng muc tieu va dieu kien thuc le hay hodn canh thay doi Tfl nhflng dinh nghia iren day, cd the thay ngfldi cd nang luc vl mot loai/linh vuc hoat dpng nao dd can cd du cac dau hieu cd ban sau: - Cd kien thflc hay hieu bill he ihong/chuycn sau vl loai/linh vUc hoat ddng dd - Bill each tien hanh hoat ddng dd hieu qua va dat kit qua phii hdp vdi muc dich (bao gdm xac dinh muc lieu cu the each ihflc/hfldng phap thuc hien hanh ddng/ Ifla chon dupe cac giai phap phu hdp va ca cac dieu kicn phUdng lien de dat muc dich) - Hanh ddng cd kit qua, flng phd linh hoat hicu qua nhflng diSu kien mdi khong quen ihupc 2.2 Mot so dac diem va cac nguyen t^c phat trien nang iirc cho hoc sinh thung Nghien cflu cac kit qua tam li hoc giao due hoc cho thay: - Mdi ca nhan dc cdng hoc dudng, dai hanh phuc can sd hflu nhicu loai nang luc khac - Nang luc cua ca nhan the hien qua hoat ddng (cd the quan sat dUdc d cac tinh huong, hoan canh khac nhau) va cd ihe tUdng/ danh gia dUdc - Nang lUc Ihudng ton lai dudi hai hinh thflc: nang lUc chung (key competencies) va Chu Cam Thd nang lUc chuyen biet (domain-specific competencies) Nang luc chung la nhflng nang Iflc can thilt de ca nhan cd the tham gia hieu qua nhilu loai hoat dpng va cac boi canh khac cua ddi song xa hdi Nang Iflc chung can thiet cho moi ngudi Nang lUc chuyen bict (Vi du nang lUc bieu dien kich cam, nang luc nhay danccsport; ) chi can thiet doi vdi mpl sd ngudi hoac can thilt d nhflng boi canh nhat dinh Cac nang Iflc chuyen biet khong the thay the cac nang lUc chung - Nang luc dUdc hinh thanh, phat trien d va ngoai nha trudng Nha trudng dudc coi la mdi trUdng giao due chinh thong giup hpc sinh hinh nhflng nang Iflc chung, can thiet, song khong phai la ndi nhat Nhflng mdi trfldng khac nhU' gia dinh, cdng ddng, cung gdp phan bd sung va hoan thien cac nang Iflc ca nhan - Nang lUc cua mdi ca nhan la mot tfl nang Iflc bac thap nhfl nhan bict/ tim kilm thdng tin (lai tao) tdi nang luc bac cao (khai quat hda/phan anh), Theo nghien cflu ciia OECD (2004) thi cd linh nang Iflc tfl ihap den cao: (I) linh vflc nang lUc 1: Tai tao; (2) Linh vUc nang lUc II: Ket ndi; (3) Linh vuc nang luc III: Khai quat hda/phan anh - Nang luc va cac td cua nd khong bat biln ma dUde hinh va bien doi lien tuc suot cupc sdng cua mdi ca nhan Ddi vdi hpc sinh phd thdng, nang Iflc khong chi la kha nang tai hien tri thflc, thdng hieu tri thflc, ma quan la kha nang hanh dpng, flng dung/van dung tri thflc dc giai quyei nhflng van de cua cupc song Nang luc cua hpc sinh khong chi la von kiln thflc, ki nang, thai dp sdng ma la su kit hdp hai hda cua ca ba yeu to the hien d kha nang hanh ddng (thUc hien) hieu qua, mu6n hanh dpng va san sang hanh ddng (gdm dpng cd y chi, tu tin trach nhiem xa hdi ) Nang lUc nhan thflc cua hpc sinh la mdt phd tfl nang luc bac thap nhu tai hien/bict, thdng hieu kien thflc, cd ki nang (biet lam) den nang Iflc bac cao nhu phan tich, khai quat long hdp, danh gia, sang tao Theo nhdm chuyen gia lU van cho chUdng trinh giao due Viet Nam sau 2015 |2J, thi cac nang Iflc cSn hinh ihanh cho hpc sinh phd thdng bao gdm Nhdm cdc ndng h(c nhan thifc (cot Idi): gdm cac nang lUc thuSn tam than col Idi gan lien vdi cac qua trinh tu (qua trinh nhan thflc): (1) Nang luc ngdn ngfl; (2) Nang Iflc tinh loan va suy luan logic/tu trflu tUcfng, (3) Nang luc giai quyet van dl; (4) Nang life sang lao; (5) Nang lUc cam xuc; (6) Nang luc tUdng tac xa hot; (7) Niing luc tu hpc/ hpc suot ddi; (8) Nang luc sieu nhan thflc (nghi vl each suy nghi) Mdi nang luc nhan thflc lai gdm mdt nhdm cac nang Iflc cu the/ nang luc phan Mdi nang luc chung va cac niing luc ihanh phan cua chung dUdc hinh ihanh chu yeu qua cac mdn hoc/ tren Idp hpc/ nha trudng., treji nin cua mdt mdi trudng hoc lap than Ihicn lich cue hda ngudi hoc vdi cac li thuyet day hoc hien dai nhU day hoc kiln Bdn ve nhiing ndng luc Todn hoc cua hoc sinh phd ihdng tao; day hoc trai nghiem; day hpc tfldng tac; day hpc bang trd chdi Nhdm cdc ndng luc phi nhan thiic (cdt Idi): gom cac nang luc khdng thuan tam than, ma cd su pha Iron cac net/pham chat nhan each rSt can thilt cho su cdng hoc dudng, cdng cudc song: (1) Nang luc vupt khd; (2) Nang lUc thich flng, nang Iflc flng phd stress; (3) Nang luc thay doi suy nghi /tao nilm dn tich cue: (4) Nang luc quan sat; nang lUc tap trung chu y; (5) Nang luc quan li/lanh dao/phat trien ban than) Moi nang lUc phi nhan thflc cot Idi lai gdm mdt nhdm cac nang luc cu they nang lUe Ihanh phan Mdi nang lUc chung va cac nang lUc phan cua chung cflng dupe hinh qua mdn hoc, nhung chu ylu qua cac boat ddng giao due ngoai mdn hpc/ ngoai Idp hpc tren nen cua mdt mdi trudng tUdng tac van hoa xa hdi tich cflc (giau tinh tfldng tac, lien tuc dUdc trai nghiem khdng ap dat tfl giao vien/phu huynh hpc sinh dfldc tu bay td y kien, ludn ton trpng y kiln hpc smh, giao vien ludn khuyen khich, nudi dudng cam xuc tich cue), vdi cac li thuyet giao due hien dai nhU: trai nghiem; lUdng lac; trd chdi 2.3 Vai tro cua mon Toan hinh nang IiJc thong cho hoc sinh Phan tich cac nhdm nang lUc va dac dic'm cua mdn Toan, cho Ihay, mdn Toan cd vai trd rat quan gdp phSn hinh ca nhflng nang life cdt Idi va phi cdt Idi Thdng qua hpc tap mdn Toan ngUdi hpc cd the true lilp hinh cac nang Iflc: Nang Iflc tinh loan va suy luan logic/tfl triu tfldng Nang lUc giai quylt van dl; Nang lUc sang tao; Nang lUc tu hpc/ hpc sudt ddi; Nang luc sieu nhan thflc (nghi vl each suy nghi); Nang luc vudt khd; Nang lUc quan sat; nang luc tap trung chfl y Nghien cflu mdt sd chfldng irinh giao due cua mdt so quoc gia vung lanh thci cho thay nhflng nang Iflc sau dfldc chfl thdng qua mdn Toan (Bang I) Bang 1.1iang phan tich mot so chtfdng trinh gido due Todn hpc CliUimg trinh Mi Uc Phap Quebec Singapore New Zealand Kien thflc va ki nang loan Cac thao tac tfl duv Tfldng tfldng khdng gian X X X X X X Lap luan X X X X X X Giai quyet van de X X X X Md hinh hda TH Nang I^c de cap >^ IB X X X Chu Cam Tha Giao tiep, ngdn ngfl toan hpc Sit dung cdng cu phUdng tien hpc toan (IB: He Ihdng tu tai qudc te) - Trich dan Dao Thai Lai (2012) 2.4 Ban ve nhu'ng nang l^c toan hoc thong va chitdng trinh giao due Chuan nang luc Toan hpc ciia hpc sinh phd thdng dfldc chung toi hieu la nhung nang Iflc can cd hpc sinh hpc xong chUdng trinh mdn Toan phd thdng Nhflng nang luc dap flng viec hap thu nhflng tri thflc toan hpc, kha nang hpc tap mdn Toan, kha nang van dung kien thflc toan vao cudc sdng Chung toi quan tam den y kiln cho rang nang Iflc la tdng hda cac mdi quan he bien chflng ciia nhilu ylu to, dd ba yeu td ddng vai trd trpng tam dd la: di truyen gia dinh, xa hdi Xin dan sd dd ve ba tang tri tue cua Eyseck (2001) de mmh hoa; ="•'; - ' • Siillils i Tmliiiaiii: ki^Ji KJIIII iic:iiiem| D o n g co Gel iia dinl; \ j l i i llu« u« \^ _ T l i e d i S i • TII tiif 1,1111 h Veu cf- • :ui hoS HoKi caiili Tiiih trails k : \ h CaL-li^uliiaiiHliJii Tren cd sd tan ddng thuyet da tri tue (do Gardner (1993) de xfldng) va Li thuyet tfldng tac van hda - xa hdi (Social-cultural Theory) cua VUgdtsky, cac nghien cflu cua Kdrutecxki chung tdi nhan thay cd the cd the coi nhflng nang Iflc sau day la nhflng nang lUc ma giao due Toan hoc thdng can hUdng tdi: (1) Nang luc thu nhan Ihdng tin Toan hpc Nang luc in giac hinh thflc hoa tai lieu toan hoe, nang Iflc nam cau true hinh thflc cua bai loan (2) Che biln thdng tin toan hoc: - Nang Iflc tu logic linh vuc cac quan he so lUdng va khdng gian he thdng ki hieu so va dau Nang luc tU bang cac ki hieu toan hpe - Nang lUc khai qual hoa nhanh va rdng cac doi tfldng, quan he toan hoc va cac phep - Nang luc rut gon qua trinh suy luan toan hoc va he thong cac phep loan tUdng flng Nang luc lU bang cac cau true rut gon Bdn ve nhiing ndng luc Todn hoc cua hoc smh phd thdng - Tinh linh hoat cua cac qua trinh tfl hoat dpng loan hpc - Khuynh hudng vudn tdi tinh ro rang, ddn gian, tilt kiem, hdp li cua Idi giai - Nang luc nhanh chdng va dl dang sfla lai phUdng hudng cua qua trinh tfl duy, nang lUc chuyen tfl tien trinh tu thuan sang tien trinh tu dao (3) LUu trfl thong tin toan hpc: - Tri nhd toan hpc (Tri nhd khai quat ve cac: quan he toan hpc, dac diem vl loai sd suy luan va chflng minh, phUdng phap giai toan, nguyen tac, dudng Idi giai toan) (4) Nang lUc van dung Toan hoc vao giai quyet van dl: - Nang lUc van dung cac tri thflc Toan (chu ylu la tri thflc chuan) nhu cdng cu hpc tap - Nang luc giai mot so bai toan cd tinh thUc tiln dien hinh - Nang luc van dung tri thflc Toan, phfldng phap tfl Toan vao thflc tien - Khuynh hudng, kha nang Toan hoc hda cac tinh huong Ve mat thuc tiln, "chuan" ndi chung hay chu& nang luc ndi rieng can dupc the hien qua chfldng trinh, npi dung, phfldng phap va kiem tra danh gia Tren cd sd nghien cflu chUdng trinh cua mdt so quoc gia tien tien (Han Quoc, Anh, Singapore My, ) chflng tdi nhan thay chUdng trinh mdn 'tban cua cac quoc gia cd may dac diem dang chu y: - Dua sdm cac van de toan hpc cd tinh he thong, hien dai vao giai doan tieu hpe (he thong so: het tap so nguyen, hflu ti; hinh hpc: cac van dl cd ban cua hinh hpc 0-clit (Euclid), tu tfldng ve hudng; ve dai so: cae yeu to ve phUdng trinh, quan he tUdng flng, vl toan flng dung: cac ylu to ed ban vl xac suat thong ke, - Dac biet quan tam din tinh flng dung cua cac iri thflc Toan Van de dat la can cu the hda nhflng muc tieu dd xay dung chuan nhu the nao, thuc hien xay dung chUdng trinh, ndi dung day hpe, hien thuc hda d thflc tiln, danh gia euoi cung Bdi thdi quen da hinh nep suy nghi cfla ngfldi Viet chung ta la "thi gi hpc nay" rat khd thay ddi Theo chung toi, can xay dflng chuan theo can cfl sau day: (1) Xac djnh chuan dau (nhflng yeu cau can dat) d6i vdi giao due mon Toan phd thdng (tot nghiep phd thdng thi ngfldi hpc cln dat nhu^g chuan nao) (2) Xac dmh chuan dSu ra/dau vao cho iflng cap, tflng Idp Chuan dau cua cap/'^ip dfldi la can cfl de xac dinh chuan dlu vao cua cap/ldp tren (3) Ndi dung day hpc cd the rdng, sau, cao hdn so vdi chuan (4) Chuan can cu the hda d mflc cd the danh gia dUde (IhUdng thi nang lUc sc dfldc the hien qua cac ki nang d cac mflc dd nhan thflc tfldng flng (ghi nhd, hieu van dung ) (5) Muc tieu day toan phd thdng nen hfldng tdi la: "hpc de bilt van dung va khang dinh gia tri ban than", cu the day hpc toan phd thdng phai dat nhflng nang luc: - Lap luan logic giai toan - Giao tilp, sfl dung ngdn ngfl toan - van dung kiln thflc Toan de giai quylt tinh huong cd van de 3 Ket luan Chuyen manh qua trinh giao due tfl chu yeu trang bi kiln thflc sang phat trien toan dien nang Iflc va pham chit ngfldi hoc la mot dinh hudng tat ylu cua cong cupc ddi mdi ed ban, toan dien giao due Viet Nam lit viec xac dinh khung nang Iflc chung va nang l\ic chuyen biet lien quan din mdn Toan din xay dflng chfldng trinh, noi dung, phUdng phap, danh gia moi mdn hoc la mot chudi cac nghien cflu va thUc nghiem Trong dd can thong nhit each hieu cau true, bieu hien thuc tiln day va hoc, each va dac biet la each hinh va phat trien tflng nang Iflc hoac nhdm nang Iflc TAI LIEU THAM KIIAO [1] [2] [3] [4] [5] Nguyin Cdng Khanh, 2012 Ndng luc vd danh gia ket qua gido diic theo ndng lixc chuong trinh gido due phd thong sau nam 2015 Ixki Kieu va nhdm nghien cflu, 2012 Mot sd nhan xet vS qud trinh phat trien chUdiig trinh gido due phd thong ciia Viet Nam ti( nam 1945 den Hpi thao tdng kit giao due phd thdng cua Viet Nam va mdt sd nUdc tren thi gidi de xuit nghien cflu tiep theo vl ddi mdi giao due phd thdng sau nam 2015 cua Viet Nam Dao Thai Lai va nhdm nghien cflu, 2012 Tdng quan kinh nghiem qudc te ve phat trien chitdng trinh gido due thong Hdi thao tdng kit giao diic phd thdng cfla Viet Nam va mot so nfldc tren the gidi de xuat nghien cflu tiep theo ve ddi mdi giao due phd thdng sau nam 2015 cua Viet Nam Chfldng trinh giao due mdn Toan cac nfldc: Han Quoc, Anh, Canada, Singapore, My (BCD Qudc gia ddi mdi chfldng trinh, sach giao khoa giao due thdng sau 2015 cung cap) Mdt so chUdng trinh giao due: Australian Curriculum, ANCARA 2011; CCl standards mathematics America, 2010; Chudng trinh Tieu hpc, ChUdng trinh Trung hoc, ChUdng trinh Du bj Dai hpc IB 2012 (ban dich Tilng Viet); Math standards New Zealand curriculum, 2010; Madison Metropolitan School District, Canada, 2011; Mathematic curriculum Quebec, Canada, 2010; Maththematics curriculum, Singapore, 2011 ABSTRACT About high school students' mathematics capacity Based on analyzing some theories of capacity educating, articles, it was shown that Mathematics is absolutely important in forming and practicing high school capacities High school students' Mathematics capacities are understood as necessary ones that students can have after high school Mathematics program These capacities satisfied absorbing Mathematics knowledge, learning capacity, applying theories into the real life These capacities include Mathematics information collecting, processing, storing and applying, and problem solving 18 ... thong va chitdng trinh giao due Chuan nang luc Toan hpc ciia hpc sinh phd thdng dfldc chung toi hieu la nhung nang Iflc can cd hpc sinh hpc xong chUdng trinh mdn Toan phd thdng Nhflng nang luc dap... diSu kien mdi khong quen ihupc 2.2 Mot so dac diem va cac nguyen t^c phat trien nang iirc cho hoc sinh thung Nghien cflu cac kit qua tam li hoc giao due hoc cho thay: - Mdi ca nhan dc cdng hoc dudng,... phat trien d va ngoai nha trudng Nha trudng dudc coi la mdi trUdng giao due chinh thong giup hpc sinh hinh nhflng nang Iflc chung, can thiet, song khong phai la ndi nhat Nhflng mdi trfldng khac