NGHIEN O/U & UNG DUNG CHUYEN HOA TRI THITC TOAN HOC VAO CHlfONG TRINH MON TOAN O TIEU HOC TS Tr^n Trung, TYu^ng Du bi 0gi hgc Dan tgc Sam San ThS Le Thi T^y^t Trinh, Trudng Dgi hgc Dong Thdp 1 Sy chuy[.]
NGHIEN O/U & UNG DUNG CHUYEN HOA TRI THITC TOAN HOC VAO CHlfONG TRINH MON TOAN O TIEU HOC TS Tr^n Trung, TYu^ng Du bi 0gi hgc Dan tgc Sam San ThS Le Thi T^y^t Trinh, Trudng Dgi hgc Dong Thdp Sy chuyen h6a tri thih; todn hoc vA tri thih: day h^c Trong d9.y hge todn d tnidng thong can c6 sy chuyen hoa su pb^un gi&a ba cap dO tri thuc: - Tri thuc todn hgc: d cl.p dg cdc nhd khoa hgc, ngudi ta ndi tdi hi thuc toan hgc, Id doi tugng cua nhdn thiic Nhd todn hgc nghiSn c&u vd edng b6 tri thiic todn hgc dat dugc dudi mdt dang tdng quat nhdt CO the dugc theo nh&ng quy tic dien dat hi?n hdnh cgng dong khoa hgc - Tri thuc chuang trinh: De lya chgn dua nh&ng tri th&c toan hgc vdo ehuong trinh mon Toan d trudng phd thdng, cdc tri thiic todn hgc cdn dugc sang Igc, dinh miic dd yeu cdu vd cdch thuc di€n d^t cho phii hgp vdi myc tieu va dieu ki8n xd hdi de dam bao sy phii hgp ciia h$ thdng day hgc voi mdi trudng cua no thi tri thiic todn hgc trd tri thuc chuang trinh Day la ddi tugng day hgc Id myc tieu dgy cua GV vd myc tieu hgc ciia HS - Tri thuc day hgc: D8 dat dugc myc tieu day hge, GV phai to chiic Igi tri thuc quy dinh chuang trinh, sach gido khoa va bien tri th&c day hgc theo khd ndng su phgm cua minh, phu hgp vdi trhih dd HS vd nh&ng dieu ki?n hgc t|ip cy thi Sy ehuyen h6a su pham bao g6m hai khau: ehuyen tri thiic khoa hgc tri thiic chuang trinh va chuyin tri thirc ehuong trinh tri thijrc d^y hgc GV can e6 khd ndng thdm thdy vi$e vdn dyng kien th&c todn cao cap de soi sang toan thdng vd tu to chue cho HS dudng kham phd tlm kiem cdc ngi dung kien th&c Quy trinh hinh sy ehuyen hoa su pham nhu sau: Bu&c 1: Nghidn cuu mdi quan h$ giua phdn kiln thiic Todn phd thdng vdi co sd ly thuylt todn hgc cao cap va toan so cap ma GV da dugc trang bi d trudng Dai hgc Su pham Buac 2: Six dung gde nhin vd ngon ngfi ciia Todn cao cdp de phan tich kiln th&c Todn thdng, nhdm thay rQ bdn chit sdu sac vl khoa hgc todn hgc Buac 3: Thdng qua boat dgng chuyen ddi ngdn ng& dl hen hdnh chuy6n hoa su pham tri thuc khoa hgc - tri thftc chuang trinh - tri thuc day hge Minh hpa nhung thi hifn cfia dnh x^ chiromg trinh mdn Toan & tieu hgc 2.1 Tri thuc todn hoc ve dnhxg Anh xa Id mdt khdi niem CO t& rdt sdm Ijch s& vd Id khdi ni$m khong the thieu todn hgc ngdy Hau hit cdc ITnh vyc tri th^c todn hgc hi^n d^i deu sir dung khdi ni$m dnh x? Ve m^t lich sOr, tii 1000 ndm trudc Cong nguy^n, ngudi Babylon dd l|p dugc nh&ng bdng ghi ch^p cdc hien tugng thi6n vdn dudi d^g bang ciia dnh xa nhu ngdy Trong cdc edng trinh ciia Dl-cdc (1596 - 1660); d^i lugng biln thi€n vd bilu ^ i sy bi€n thien phy thugc gi&a dai lugng ndy vdi d^i lugng khdc da dugc dl cdp den Dl-cdc da su dyng he tog dO dl nghiSn cuu bilu diln hmh hgc cua sy phy thudc Dilu da ddn den phuang phap mdi nghien c&u hinh hgc vd sy ddi Hinh hgc gidi tich Di-rich-Ie, 0-le, Id nhihig ngudi nghien cuu cac hdm sd d dang tdng quat Tuy nhi6n, khdi niem dnh xa chi mdi dugc nghien cuu gdn day li thuyet tap hgp dd ddi Sau day la mgt s6 tri th&e co ban vl dnh xg todn hgc nhdm 1dm ca sd de nhin nhan sy hi$n di?n chuang trinh mdn Todn d heu hgc dudi nhihig dang khac - Dfnh nghia dnh xg: Cho cdc tdp hgp X, Y khdc rdng MOt quy tac cho mdi phdn hi x thugc X tuong ung vdi mdt phdn td nhdt y thudc Y dugc ggi Id mdt dnh xg (don tri) tu X din Y va dugc ki hidu Ngay nhan bai 25/12/2012: Ngay duyfl dang 25/01/2013 TAP CHI THIET BI GIAO DUG-SO - / • NGHIEN CUU & UNG DUNG * Todn : Phep nhan hai si + Cho dnh xg thdng qua Id f : X -» Y Khi dd ta ggi ty nhien dugc trinh bdy X Id tap ngudn, Y Id t$p dich bilu do thj + Cdc dnh xg Id hdm so cd SGK Idanhxa cua dnh xg f Phan hi y tuang x:NxN^N ung vdi ph4n tii x qua dnh xg thi cho bdi thj ciia nd f dugc ggi Id dnh ciia x vd ki 2.2 Nhitng thi hi$n cua (a,b) a a b hi?u la x •-* y hay x >— y = f(x) tri thUc vi dnh x^ mdn - Trong SGK todn 2: Viec Anh vd tgo dnh cua tap Todn&tiiuhpc tim dnh etia mgt tap qua mot harp qua dnh xg: Neu f: X -> * Todn 1: Sy thilt Idp tuang dnh xa cgng (+) dugc neu dudi Y Id mgt dnh xg thi ta ggi tgp umg bdi "bdng nhau, dau dgng bdi tap: hgpfl:X)= {fl;x)|x e X} Id ^" SGK toan dugc coi Dien sd thich hgp'' vao dnh cua dnh xg f Tdng quat, id ph^p dnh xg mgt ddi mgt d trong: (Toan 2, trang 17) vdi mdi tgp hgp A ciia X, gi&a t$p cdc vgt can dem vdi (Bdng 1) ta ggi {f(x) IX e A} Id dnh ciia mgt t^p thich hgp cua tgp - Vi^c tim dnh cua dnh xa tgp hgp A qua f vd ki hi$u Id s6 ty nhign, ddy Id nhihig dnh nhdn ciing dugc thdng qua cdc f(A) Khi cho trudc mgt tgp xg song dnh, dugc trinh bay bdi tgp dgng: hgp B ciia Y, ta ggi tap hgp thdng qua cac hinh anh sinh Viet sd thich hgp vdo {x e XJ f(x) e B} \k tgo dnh dgng trong: (Toan 2, trang 106) toan phdn ciia t^p hgp B qua (Bdng 2) anh xg f vd ki hi?u Id f"'(B) - Tim tgo dnh todn phdn Khi B = {b} chi gom nhdt cua mgt tap bdi dnh xg cgng mdt phan tu thi ta diing ki hieu (+) qua bai tap dgng: f-'(b) thay cho f'({b}) Viet sd thich hgp vao Ngodi cdc dnh xg dan tri h-dng: (Todn 2, trang 45) dinh nghia tren ddy, todn (Bang 3) hgc ngudi ta cdn dinh nghia * Todn : Viet so thich hgp loai anh xa da tri hay dnh xa vdo d trong: ( Toan 3, trang - Phep cgng hai sd ty nhien 26) (Bdng 4) gid tri tgp Dd la quy tdc cho moi phan t& x thugc tap hgp dugc trinh bay SGK todn Ddy Cling Id mgt vi du ve X tuang ling vdi mgt tgp hgp Id mgt dnh xg tim mih cua mdt tap hgp qua + :NxN->N ndo dd ciia tap hgp Y cdc anh xa don dnh - Cdc cdch cho dnh xg: D I (a,b) a a + b f : N X N -^ N Phep dim la don dnh cho mgt dnh xg ngudi ta co a •— a + Cling la song dnh hi tap hgp nh&ng cdch khdc Sau g: N X N ^ N day Id mgt sd cdch thong dung cac vgt can dem den tap a — ax hgp thich hgp cua tap s6 nhdt de cho dnh xa f: X -> Y: - Anh xa sau day Id mgt ty nhien + Cho dnh xg bdng bdng Sy thiet lap tuang ung toan dnh vi vdi mgi sd ty nhien tuong ung gi&a cdc gid tri ciia bdi be ban Ddu < dugc bat ky, ta deu phan tich dugc tap hgp X vd Y coi la nh&ng don dnh hj tap hgp tdng cua hai sd ty nhien, + Khi X va Y la cdc tap hgp mdt vudng din tap hgp hai d dieu cd nghia la: CO trang bi phep todn thi cd thi vudng, vd hj tap hgp hai tam Ve G N, (a,b) e N x N cho anh xg thong qua mdt hay giac din tap hgp ba tam gidc cho c ^ a + b nhieu bieu th&e cho bilt quy Dieu ndy dugc thd hiSn luat tuong ling gi&a cdc phdn dudi dgng bdi tap; hi cua cdc tap hgp X vd Y Viet sd thich hgp vdo + Cho dnh xg thong qua md trong: (Bdng 5) ta bdng Idi quy lugt hjong ling - Khdi niem tich hai dnh xa gi&a cdc phdn tu cua X vd Y dugc thi hien SGK qua ffl A-4 • TAP CHI THIFT 81 GIAO DgC - SO 90 - 02/2013 NGHIEN cuu & UNG DUNG cdc bdi tap dang: rTlgklikj I them ,1 I * Todn : Phep cgng hai phan so, phep nhan hai phdn sd dugc trinh bdy SGK la nhihig anh xa : +: 9+ x 8^ -> e+ fa c"\ ad + bc \b'~dr bd d thdng tren quan diem Todn cao cdp de qud trinh dgy hgc td chiic h u ( ^ g ddn HS eon dudng khdm phd tim kilm nh&ng ngi dung kien th&c thifit thyc thdng qua cac budc chuyen h6a su pham gifta cdc tri thuc Summary Mathematics program at the elementary school was built on the basis of modem mathematical knowledge, which requires that teachers must have certain knowledge about the metabolism of mathematical knowledge in Mathematics program to recognize internal teaching content in a uniform way This paper presents the transformation of teachers' mathematical knowledge Tdi li^u tham Ichdo Nguyen Bd Kim, Phuang phdp dgy hgc mdn Todn, NXB Dai hgc su phgm (2004) Chu Trgng Thanh, Tran from the program knowledge Kb d) bd teaching knowledge, - Tim tao anh cua mdt t|ip Trung, Ca sd todn hoc hien and dgi cua kiin thuc mdn Todn demonstrated by the expression bdi anh xg nhan qua bai tgp of knowledge mapping in math phd thdng, NXB Gido due Viet dgng: in elementary school Viet so thich hgp vao Nam (2011) trdng: (Toan 4, trang 84) (Bdng 6) 49 59 29 So hang 29 * Todn : Phep egng va 18 34 27 S6 h^ng Tong IS phep nhdn hai sd thdp phdn dugc trinh bdy SGK Bang todn Id nhung anh xg: Thias6 + : 0+10 ** 6+10 ~^ 6+!o Thuaso 8 (a;^aa+;S Tich x : 0+10 X 0+jo—> 0+10 my (a^^aax^ De dgy tot mdn Todn d Tilu hge, GV cdn hieu dugc sy chuyen hoa t& tri thiic khoa hgc (toan hgc hien dgi) vdo tri thiic chuang trinh mdn Todn md minh gidng day thi mdi e6 the tich eye h6a boat dgng hgc tap cua hgc sinh GV cdn ndm vihig cdc ca sd Todn hgc hien dgi cua kien thuc mdn Todn chuang trinh phd thdng nhu: Tap hgp, dnh xa, cdc phep todn dgi sd, cdu tnic dgi so GV cd kha nang van dyng cdc kien th&c cua Toan cao cdp d€ soi xudng Todn so cap ehuong trinh phd thdng, nhin nhan cac maeh ki6n th&c Todn S6hang S6 h^g T6ng 12 [ 18 S6 da cho Them dem vi Gap I^n So hang So hang Tong Thira so Thiraso Tich 12 18 15 10 113 119 678 24 34 15 1015 10 39 1107 1009 15 24 34 Bang 15 17 21 42 39 2/9 2/3 8/21 17 21 42 1/3 8/9 Bang 6/11 TAP CHI THIET BI GIAO DUC-SO 90-02/2013 • II ... De dgy tot mdn Todn d Tilu hge, GV cdn hieu dugc sy chuyen hoa t& tri thiic khoa hgc (toan hgc hien dgi) vdo tri thiic chuang trinh mdn Todn md minh gidng day thi mdi e6 the tich eye h6a boat... trong: ( Toan 3, trang - Phep cgng hai sd ty nhien 26) (Bdng 4) gid tri tgp Dd la quy tdc cho moi phan t& x thugc tap hgp dugc trinh bay SGK todn Ddy Cling Id mgt vi du ve X tuang ling vdi mgt... phan so, phep nhan hai phdn sd dugc trinh bdy SGK la nhihig anh xa : +: 9+ x 8^ -> e+ fa c"\ ad + bc \b''~dr bd d thdng tren quan diem Todn cao cdp de qud trinh dgy hgc td chiic h u ( ^ g ddn