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TANG ClfONG CAC BAI TOAN CO NO! DUNG THITG TIEN TRONG OAY HOG GHO SINH VIEN NGANH TOAN 6 CAC TRL/ONG CAO DANG SU PHAM O ThS, PHAN VAN LY'''' T odn hqc cd vai trd quan trqng trong ddi sdng Dudi ddy, chung[.]
TANG ClfONG CAC BAI TOAN CO NO! DUNG THITG TIEN TRONG OAY HOG GHO SINH VIEN NGANH TOAN CAC TRL/ONG CAO DANG SU PHAM O odn hqc cd vai trd quan trqng ddi sdng T xd hdi khd ndng ung dyng vd tdn cua nd Ndng cao ndng lye vdn dyng todn hqc vdo thue Hen eho hqc sinh (HS) Id mdt frong nhi?ng myc Heu eo bdn dqy hqe todn d THCS Trong nhi?ng ndm ddu t h l ki , cdc nudc td chuc OECD (td chuc hqp tde vd Phdt triln kinh tl) dd dua chuong trinh ddnh gid qudc te PISA eho HS phd thdng d lua hrdi 15 Phqm vi ddnh gid ndng luc HS cua PISA cd lien quan d i n khd nang phdn tfch, suy ludn eua ngudi hqe ldp cdng thuc, gidi quylt vd'n d l ede Hnh hudng dqy hqe Theo (1), cdc chuong trinh ddnh gid HS qudc te phdn Idn khong ehi don thudn Id su xep hgng md nd cdn neu dugc nhdng diem mgnh, diem yeu cua he thdng giao dye cua cdc qudc gia tham gia khdo sdt de khong ngung edi thien chdt lugng giao dye Theo (2), cdc tde gid dd de xudt ve mye Heu ehuong trinh SGK mdn Todn phd thdng sou ndm 2015 Id: Khdng ehi frong bj cho HS cdc kiln thue dd bilt md edn phdi bj cho HS kiln thee d l ldm; ren luyen eho ngudi hqe ndng Iyc gidi quylt vd'n 6e vd ung dyng todn hqe vdo thue tiSn Cdc hqe phdn todn eo bdn ehuong trinh ddo tqo gido vien THCS d cdc trudng cao ddng su phqm hien cd Hnh truu hrqng cao, cdc khdi niem duqc djnh nghio vd chung minh chdt ehe, vf dy dua mong tfnh chd't todn hqe thudn D l ddp ung yeu cdu dqy hqc todn d THCS Id ddo tqo t h l he tr6 ed trinh do, ed khd ndng ung dyng todn hqe vdo thyc tiln, thom gia cdc ehuong trinh ddnh gid PISA dd'i vdl HS d tudi 15 D l ddnh gid khd ndng ung dyng kiln thuc vd kl nang cua ngudi hqe vdo cdc Hnh hud'ng thue t l (THTT) cuo HS, d ede trudng eao ddng su phqm (CDSP) edn phdi trang bj kiln thue v l viec vdn dyng todn hqe vdo thue Hen eho sinh vien (SV) todn todn bd chuong frinh ddo tqo ^ ThS, PHAN VAN LY' Dudi ddy, chung tdi xin de xud't mdt sd THTT phdt triln thdnh cdc bdi todn cd ndi dung thyc tien (hoy bdi todn thuc tl) dqy hqc todn cho SV a ede trudng CDSP nhu sou: 1) Bdi todn thuc te(BTTT) dugc xdy dung nhdm ggi dgng co (GDC) hgc tap Cd t h l hiiu, GDC qud trinh dqy hqe Id ldm eho HS hiiu duqc y nghia cuo nhi?ng hoqt ddng hqc tdp vd biet chuyin h> myc Heu su phqm thdnh myc tieu cuo ngudi hqe Viee GDC hqe tdp xud't phdt h> thyc t l , giup ngudi hqe y thuc duqc viee edi tqo the gidi vd gidi quylt cdc vd'n de todn hqe, tuc la ndm duqc todn hqc bdt ngudn Kr nhu edu cua thyc t l Vi vdy, viec xdy dung BTTT thdng qua GDC dqy hqe rdt cd y nghio viec phdt triln ndng luc vdn dyng todn hqc vdo thyc Hen cho ngudi hqc Vf dy: Khi dqy djnh nghia hdm so mqt bien so, nhieu biln so cdc hqc phdn Phep finh vi phan, tich phan hdm sdmgt bien sd; Phep tinh vi phan, tich phan hdm sd nhieu bien sd, xet THTf sau: Trong hogt dgng sdn xudt kinh doanh, cdc nhd qudn Ki quan tam den doanh thu Gid sir sdn phdm duge bdn vdi gid P vd khdi lugng bdn thdng Id Q thi tdng doanh thu (Total Revenue): TR - P.Q, dd TR, P, Q deu Id ki hieu cho cac bien kinh te Nghia Id, chungtotinh doanh thu phy thudc vdo gid vd sd lugng, bated mgt su thay ddi eua gid hoac sd lugng cung ldm thay ddi doanh thu Nhu vgy, tinh mgt bien kinh te ndy phy thudc vao mgt hay nhieu bien kinh te khac, nghia Id chung ta da xdc lap mot quan he ham gida cdc bien kinh te Xudt phdt h> Hnh hudng fren, ed t h l phdt triln thdnh Hnh hudng tdng qudt hon gqi Q Id son phdm qud'c gia, N Id y l u td hr nhien, K Id T bdn, L Id nhdn cdng, S Id khoa hqe kl thuqt, E Id moi * Tnrcing Cao dang sir pham Binh PhiAlc Tap ehi Giao due so (ki i • 10/2011) trudng xd hdi thi hdm sd sdn xudt Id Q = f(K, L, N , S, E) N h u vdy, trudng hqp ndy, hdm sd sdn xudt Q phy thudc vdo bien so (hdm nhieu b i l n so) 2) BTTT dugc hinh thdnh giai dogn xay dung li thuyet cua bdi hgc Mqt nhi?ng ddng lye thuc ddy su phdt trien cua cdc li thuyit todn hqe vd hodn thien qud trinh xdy dyng he thdng todn hqe Id Ilnh vuc ung dyng nd Vi vdy, giai doqn xdy dung li thuyit eua bdi hqe, edn thilt ldp nhi?ng bdi todn vdi yeu cdu mdi tCr mqt Hnh hud'ng ndo d d , giup HS he thdng k i l n thuc If thuyit cua bdi hqc Vf dy: Khi d q y hqe k i l n thuc trung binh mdu hqe phdn Xdc sudt thdng ke, g i d n g vien (GV) yeu edu SV thdng ke d i l m thi mdn Dgi sd tuyen tfnh ciia Idp Sau d d , tfnh d i l m trung binh cua Idp b d n g cdch ldy tdng d i l m chia cho tdng sd SV Tu d d , phdt b i l u thdnh bdi todn tdng qudt: Gid su cho (X^, X., , Xn) Id mdu ngdu nhien, trung binh mdu dugc tfnh bdi cong thuc: X= Y,^"i=l • Mdc khde, GV yeu cdu SV thd'ng ke sd Idn xudt hien diem sd, Kr do, hinh thdnh bdng phdn bdtdn sd Khi d d , SV Hnh d i l m trung binh bdng cdch nhdn h/ng d i l m so vdi tdn sd, sau dd cdng chung Iqi Tdng ndy chio eho tdng ede tdn so se duqc diem frung binh Ta duqc cdng thue tfnh tdng qudt sau: c h o mdu ngdu nhien dudi dqng tdn so: X X, n, "i X, n, XK n» b i l t khdi qudt Hnh hudng dd xet mdt cdch ddy du, phong phu vd tdng quan hon Vf dy: Sou SV hqe xong bdi He phuong trinh tuyen tfnh Cramer cua hqe phdn Dgi sd tuyen tfnh, ngodi vf dy ve mqt he phuong trinh tuyen tfnh Cramer thudn tCiy todn hqe ed gido trinh, chung tdi eung cdp mdt Hnh hudng v l viec vdn dyng k i l n thue bdi hqe vua duqc h'nh hdi, dd Id Mo hinh cdn bdng thl trudng cd logi sdn phdm nhu sou: Bdi todn: Cd sdn phdm, luqng cung (Q3) vd luqng cdu (Q^) duqc eho cy t h l : Sdn phdm Qs : = 8p,+P2 + P3 40 vd Qp = -1 l p , + p , +2p3 + 133 Sdn phdm Qs : = p, + 15?^ 23 vd Qs = 2p, 7p2 + p + ' Sdn phdm Q5 : = -p, + ZPj 20 vd Q Q = 2p2 -IOP3 + 79 ' ^ ' Trong d d , p, Id gid bdn sdn phdm 1, pj Id gid bdn sdn phdm 2, Pj Id gid bdn sdn phdm Tim diem cdn bdng tren thj trudng? N h u chung ta dd b i l t , thj trudng cdn bdng cung vd edu bdng nhau, tuc Id: n p j - p - P3 = 173 -Pj+22p2- P3=93 Qc =Qn ^2 \%=\ - - P j - p + 17p3=99 He phuong trinh (1) Id he Cramer vi ed sd phuang trinh bdng sd dn so vd bdng 3, cd ma 19 - -l^ , det (A) = -398 ^ 0, trdn he so A = -1 22 -1 - 17 nen he phuong trinh (1) ed nhdt nghiem: (p,, P2/ P3) = { , , 7) Vdy, diem cdn bdng thj trudng -^"i^i Khi d d , trung binh mdu duqc tfnh: X=>=L dqt duqc tqi p, = 10, P2 = 5, P3 = Nhu vdy, Inthdng qua viee gidi bdi todn tren, SV dd dp dyng i=l ' Tu Hnh hud'ng ey t h l d tren, SV dd hinh thdnh k i l n thuc vua hqc vdo mqt THTT 4) BTTT dugc xay dung quan diem thuc duqc cdng thue Hnh tdng qudt vd b i l t duqc d i l m hien vdn de lien mdn Thue hien quan d i l m lien trung binh mdn Dgi sd tuyen tinh cua Idp Id cao mdn xdy dyng BTTT se ddn d i n viee xem hay thdp xet mdt THTT dya vdo k i l n thue eua cdc mdn hqc 3) BTTT duge xdy dung giai dogn cung khde, duqc eung cdp them cdc gid thilt, cdng ey cd bdi hgc Trong todn hqe, qud trinh eung cd khde d l xdy dung ede BTTT kiln thuc dien dudi ede hinh thue luyen tqp, Vidy: Khi dqy djnh nghia hdm sd nhilu b i l n ddo sdu, ung d y n g , he thd'ng hda vd dn tdp Sou hodn chinh mdt phdn If thuyit cua bdi hqe, so hqe phdn Phep tinh vi phan, tich phdn SV Hip thu them k i l n thue mdi nhdm Hm ede hdm sd nhieu bien sd, chOng ta xet THTT sou: Qud hudng de phdt friln bdi todn ban ddu Phdt friln bom nguyen tu nd dd tqo thdnh ddm mdy hinh cae THTT eung ed k i l n thue giup ngudi hqc ndm (hinh 1) Tap chi Giao due so (kii -10/2011) # Quci trinh dion rci ddnh gid PISA ddi vdi HS a tudi 15 d cdc cua c|ud boni ncjuycn ti> trudng CDSP edn trang bj cho SV todn nhung no giay fJau lion kiln thue, kl ndng ve viec vdn dyng todn hqc xem hinh vdo thuc tien • Qua tiinh quci bom nguyen tu no dicn co the ducrc don gicin hoo la riK)t dong nhic^u nang luong duoc phc'it tai mot thoi diom Cho ban Hmh / kmh dam may hinh nam Hinh qud bom nguyen tu nd tqo thdnh Id R, bdn kfnh tang theo thdi gian Nhu chung ta biet, R cd lien quan d i n thdi gian t, ndng luqng phdt E, ddy khdng khf xung quanh p, vd dp sudt Pg Vdy: R = < (t E, p^, P^) Trong trudng hqp ndy, R Id mqt hdm sd bdn biln so Vf dy tren eho thdy mdi lien he gii?a todn hqe vd vdt If Id (1) I riin Vui Danh gia hied biet toan hyc cho hpc sinh 15 turfi, chmmg trinh danh gi^ hyc sinh qu6c te (PISA) NXB Gido due H 2008 (2) Trdn Luan Mdt so suy nghi vk chuemg trinh sdeh gido khoei mdn Todn phd thdng trung hge d nudc ta lie ldi (dch din ddi mdi vd nhang di xudt eho ehuong trinh sail ndm 2015 Ki y^u HOi thao quO'c gia vi giao due Toan hpc d trudng phd thOng Tai liiu tham khao R Courant - H Robbins Toan hpc \k gi tap (Hin LiCn Hai djch) NXB Khoa hx kUhudt, H 1984 Nguyfin Ba Kim Phuvng phap day hpc mdn Toan NXB Dgi hge suphgm H 2006 Biii Huy Ngpc Tdng eu&ng khai thdc ndi dung thuc ti dgy hgc sdhgc vd dgi sdnhdm ndng eao ndng luc vdn dung Todn hge vdo thue tiin cho hgc sinh trung hge (lems in teaching mathematics at Pedagogk:c3l College Bo GD4T Phgm Vo Lufln; dgi diOn Iflnh dgo cdc • H\\m Ngay khuyen hpc Vietnam2/10,im&i\ bo, ngdnh thom gic BCD xdy dyng XHHT; BCD dgo qudc gio Xfly di/ng xO xdy di/ng XHHT, HOi khuydn hpc cdc cdp; dgi Di hpc lOp (XHHT) pWi hgp didn mOt sd sd GM)T; dgi bidu qudc td; v v Nhdn dip ndy, dfl didn ro nhidu hogt dOng v6i BO G M T , BO Vfln hoO The thoo - Du ljch, HOi Khuyfn hpc ViOt Nom, hudng dng HTSO tpi qufln Odng Oo; tpi cdc thu UBNDTP Ho NOi vO Lifin h(?p quOc tgi ViJI Nom vidn, bdo tdng, nhd vfln hod trdn djo bdn Hd 15 chijc tufin lg H I A J N G IJNG HQC TAP SUffT NOi; td chdc hOi thdo vd HTSO vd tridn Iflm 'Hd Odi ( - / / 1 ) nhflm luygn truyfin nflng ChlMinhvd HTSO'; v.v Ody Id ldn ddu lidn Vidt Nom td chiic tudn coo nhOn Ihix cuo mpi tdng Idp nhdn ddn v§ ang HTSD', vdi thdng didp: hpc top sudi ddi (HTSO) vd xfly dyng XHHT Doy li'Hirdng HTSO-chio khod cuo mpi thdnh cdng P.V Id dip de cdc bO, ngdnh, don v|, td chut Irong vfl ngooi chia se nhQng kinh nghiem ve HTSO vu • Ngdy / / MRUONG 1/8 DA xdy dirng XHHT, de coc co so gido due vd cdc lO CHIJC L^ KHAI GIANG NAM HOC MOI 2011thi^t che gioo dye ngoai nhd tiixmg ndng cao 2012 Ihom dule co iQiih dqo Uy ban don toe, dgi dien kho nOng cung irng gido dye Bo GD-OI, doi dion Ooi suquan loo, v.v Le khai mgc tudn le "Hmng irng HJSD" Ld mot truong chuyen biet ddo too HS ddn diroc td chirc Irong the tqi Vdn Mieu Qudc lir toe ndi tru vd linj hpc sinh num: bgn Ldo, nflm Gidm ngdy / / 1 , vdi' sir thorn gio cua hoc 200-2011, Trirong 178 dfi hodn thdnh tdt Phd Chil tich nuoc Nguyen Thi Doan, Bd truong nhiem vy day hpe vd qudn li, nudi duong HS npi tnj Cdng tdc xdy dyng dOi ngO dupe chd trpng, nhidu GV cd titaih dd thpc ^; Id chuc tdt cdc sinh hogt chuydn mdn, ddi mdi PPDH, rdn kinOngsdng cho HSSV; td chuc nhidu hoot dCng ngodi ( ^ len ldp, hogt dOng ngogi khod dgng, phong phu Nom hpc vin quo, H M //5 D M a a tnidng c6 8S,S% dpt hpnh kidm kigi tdt, 12,8% dgt logi khd; 100% HS ldp 12 tdt nghidp (xdp thiJ 52 sd 207 tnidng THPT cuo Hd Ndi cd II Id HS dd tdt nghidp 100%); cd HS dot gidi Ba thi HS gidi (mdn ljch si;) vd HS dgt gidi Khuyen khidi Kb6i IHS: 85,99% dgo due xdp logi tdt; 23,7% hpc top dgt k)Qi gidi; 99,4% dii ddu kien tieng Viet de hoe tiep d cdc co so ddo too cuo Viet Nom Budc VDO nom hoc mdi 2011-2012, nhd trijmg nhanh chdng on dinh to chuc de HSSV mdi hoc nhdp; tnen khoi mqnh me ede PPDH tich cue; doy tri hieu qud cdc hoot dpng chuyen mdn vo quon li HSSV, thuc hien tdt phong trdo thi duo huong ve ngdy nhd gido Viet Nom 20/11 vd ki niem Quoc khdnh Loo / H'NAU Tap chi Giao due so (n i 10/2011) ... H 2006 Biii Huy Ngpc Tdng eu&ng khai thdc ndi dung thuc ti dgy hgc sdhgc vd dgi sdnhdm ndng eao ndng luc vdn dung Todn hge vdo thue tiin cho hgc sinh trung hge (