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RlN lUYiN Kl NANG KHAI THAC SACH GIAO KHOA MON TOAN 0 PHO THDNG CHO SINH VIEN NGANH SIT PHAIVI TOAN TS NGUYEN C H I ^ N T H A N G " 1 Sach giao khoa (SGK) la Ta i lieu the hien mdt each ey the ndidung[.]
RlN lUYiN Kl NANG KHAI THAC SACH GIAO KHOA MON TOAN PHO THDNG CHO SINH VIEN NGANH SIT PHAIVI TOAN TS N G U Y E N C H I ^ N T H A N G " Sach giao khoa (SGK) la T a i lieu the hien mdt each ey the ndidung, phuang phap giao dye cua tiJmg mdn hpc chuong trinh giao due" Dd'i vdi hau het giao vien (GV) phd'thdng, quatrinh day hpc, kiem tra, danh gia theo SGK cung dong nghla vol viee thuc hien chuong trinh (1) Viee tim hieu, phan tich chuong ttinh, npidung SGK mdn Toandphothdng giup GV:-Hieu dupe eau tmc tong the va dgc diem chuong trinh mdn Toandphottidngi-NSm rdmuc tieu, nadung CO ban, vaittd.vj tri, ynghTa cua tdng mach kien thue, md'iquan hdgiua cac mgch kien thuc; - N^m 3uqc vi tri cua eac npidungvaeaetietdgytrong hettiong chuong trinh va md'i quan hg qua Igi giua ehung; - Hieu dupe mdc dp yeu cau cua Iden ttiuc, kTnang tung chuong, tung phan cuatiethpc;-Cdcosddelua chpn ndidung vaap dyng cae phuong phap day hpe (PPDH) tieh cue (dat eau hdi gpi md van de, bai tap phu hpp vol dd'i tupng hpe sinh (HS), ehpn cac phuong tien hd trpdgy hoc, ) eung nhuthiet kede kiem tra, danh gia ketqua hpc tap eua HS mptcach phu hpp (2) Dgc diem eau true ndi dung chuong trinh mdn Toin a trung hpc thdng (THPT) dupe de cap tuong ddi day dti theo tdng mang kien thdc va dupc ke'tlep npidung chuong trinh mdn Toan dtieu hpc vatrung hpc c o s d Chuong trinh mdn Toan6dqc sip xep theo dudng xo^n d'c, cac kien thdc eu ludn duoc cung cdtrong qua trinh xay dung kien thdc mdl, khdng phai la st/ lap di lap Igi ma ludn dupe phat trien, mdrdng hon Vi vay, GV toan dmdi cap hpc can nam rd khdng chindi dung chuang trinh dgy hpc d e a p hpc minh phy traeh m a c d n p h a i n ^ m dupc npi dung chuong trinh mdn Toan dcae caip hpc kecan (3) Bai viet dua mpt so hudng nhSm ren luyen kTnang khaittiacchuong trinh SGKdphd'ttidng cho sinh vien (SV) cae tmdng su pham nganh toan 2.Mpt5d'hudng phan tich chirong trinh, npi dung SGK mdn Toai 1}Um sing bimach iogic, m^iien hfnhin 52 Tap chi Gido due so 306 qua, moilien heben tmng vimaquan helienmon chuang trinh, SGK mon ToinaUudngpho^ong a) Dam bao kien thdc mon Toan atn/ong phothong Viec dam bao ttiehien ohai khia canh: tinh chlnh xac eua kien thuc khoa hpe (bao gom eae quy t^csuy luan, phuang phap khoa hpc, ), mach kien thue trinh bay ehuong trinh va SGK (nghTa la nSm duae togic mdn hpc) b) Tim cac tinh huong SGK can den khai niem dinh li dang xet Mpt nhdng yeu cau cua viec day hpc khai niem toan hpe dtn/dng phothdng la bietvan dyng khai niem vao nhdng tinh hud'ng cu thd', n^m dupc moiquan he gida cac khai niem.Trong day hoc dinh li, G V can giup HS n^m dupc he thd'ng d|nh li va md'i lien he gida ehung de van dung vao hoat dpng giai loan ciJng nhu giai quyet cae van de tht/c tien Vi vay, viec tim eae tinh hud'ng SG K lien quan den khai niem, djnh li dang xet giup cae em n§m dupe mach kien thue ehuang trinh, SGK, hieu duoc dyng y cua tacgia khidua khai niem ddvao SGK Chang han, khainiem gk/ihanmgtben6\Jdcsu dyng cac tinh hudng sau chuang trinh Dal sd'va Gial tich 1 : tinh gidi han cua ham so'cho bdi nhieu cdng thde, tinh gidi han cua ham so dudi can baehai,tinhgicShanvdciffi-daylacdsddekhaosat thj ham phan ttidc, chdng minh khdng ton tgi gkii han, xay diing khai niem ham so lien tuc tren mpt dogn, khao sat hinh dgng dd thj ham phan thdc bae nha't tren bae nha't; xay dung khai niem dao ham mpt ben, dinh nghTa dudng tiem can dting cua ham so, c) Visa lien ket dethay duae moi lien he giira cae yeu toco mattrong bai hgc, b-ongmgtchucmg.QAip HS n ^ dupc mach kien ttiuc bong chuang ttinh SGK Chung tdi da dgt cau hdi cho GV toan dtn/dng ttidng hudng d i n S V su phgm toan ttiuc tap giang dgy: ttieo ttiay (cd), viee veso lien ket cae kiai ttiuc chinh * Khoa Toan, T r t f i j Bai bpc VinIi -(ki 2-3/2013) eua tiet dgy dat dcudi bai soan cdtac dyng tot ddi vdi SV giaidoan thuc tap hay khdng? (khoanh trdn dap an lt/a chpn): a) Cd; b) Khdng Ketqua ttiu dupc la 100% GVlraldi-Cff d)Nkndupcnhuhgti^i)cc6ilacuatoa/)hgce6m$ trc}ngchuangtrinh.SGK.HeuSVcaclnidr\gsispham nam duoc tri thuc cot Idi se giup eae em thich nghl duoc vc< nhung ttiay dacua chuong trinh va SGK Theo (4), nhung tutudng eo ban ttong chuong trinh mdn Toan la:-Dam bao vi tri trung tam cua khai niem ham sd'; - TSng eudng m dt sdye'u to cua giai tieh toan hoc va hinh hpc giai tieh; - Tang eudng va lam rd mgch toan ung dung va ung dyng toan hpc; - Sudung hap li ngdn ngutap hpp va logic toan 2)Limsmgtdtrithuc phuang ph^cdii&tiong chuong tinh, SGK mon Toan atruaig phothdng ajHiiiJdugcvi^'euatungmachki&ithtJcWngSGK Cac npidung kien thuc toan hpc dupc x ^ dcae vittikhac SGK hoae ttong chuong trinh; phan tieh SGK.SV cdhieu dupc vi tri eua kien thuc ttieo dung ytae giadenam sau s§c kien thue han b) Hieu duc/c cic hoat dgng ctia HS duoc thiet ke SGK:- Hogt ddng goi ddng co cd m yc dieh giup HS y thue ve vai trd, y nghTa va tam quan eiia kien thde qua trinh hpe tap, vetinh can thie't nghidn cdu nd; tddd, ed nhu cau va hdng thu hpc tap; - Hoatdpng kham pha kien thue mdi gdm hai dang la hoatdgng kham phi toin phin (nhim m uc dich sau glai quyet xong van de dat ra, HS kham pha gan nhu trpn vgn dd'i tupng kien thdc mdi can Hnh hdi) va hoat dgng khim phi bg phin {nham giup HS kham phachi mptphan kien th dcmdi hay mdt kien thuc ed tinh chat "dja phuong") Nhdng hoatdpng gdp phan rat Idn viee tich cue hda hoatdpng hpe tap eua HS theo dung tinh than doi mdi PPDH hien nay, nhidn, ddi hoi G V phai bd nhieu thdi gian va edng sdc qua trinh bidn sogn bai giang c) Dieu ehinh eie viductja bii hgc eho phu hap vai cic tinh hu6ng dien hinh day hgc toin a tn/ang phothong vi die diem ctia HS • Ting, giam dgkhocua vidij Trong mdt top hpc ed nhieudd'itupngHS nhu: ye'u, tnjngbinh (dai tra},kha gidLDoivditdngdoitupngHS, vigc cung cdmdt don vi kien thuccandeacmde dp khac Dodo, dephat ttien cho nhung HS cd hpc luc khagidi, GV can tang dp khdcua cac vi dy b ^ g each bdsung ttidm cac cau hdi Ching hgn, xet Wtfi/4(Hinh hpc 11, tr.51):'C/T0)'am (ki2-3/2023)- giic BCD va diem A khong thuoc matphing (BCD) GgiK ta trung diem ciJa doan AD va G li trgng tam ciJa^ tam giae ABC Tim giao diem cua dudng thing GK va matphing (BCD)' Sau khldin d§t HS giai bai toan va nJt quy trinh tim giao diem cua dudng thing va mat phing, G V cd the bosung them yeu cau:tmng diem J eua canh BC chiadoanLDtheotisd'nao?Detraldicauhdinay,GV cdthe'xet rieng mat phang (AJD) cung vdi cae ydu to hinh vahudng d i n HS tt; die'm K ke dudng thing song song vdi canh AJ Sau dd HS cd hpc lue kha va gidi cd the" sd dung djnh li Talet hoae • mini I Q dinh ll Menelauytde'giai b a i t o a n {hinh 1) Ddi GV cung can thay dd'i each phat bieu eae vi dy de' lam giam dp khd cua bai toan Chang han, xet baitoan I (tr 7, Hinh h p c 11 nang cao): "Cho hai diem B, C co djnh tren dudng Iron (O; R) va m gt diem A thay doi tren dudng trdn Chiing minh rang tn/c tam tam giic ABC nim t/en mgtdudngtron co'dinh" G V edttiephat bie'u ttieo cachkhacnhusa[i:"ChotamgiacABCngitiep dudng trdn (0; R) va H la true tim eija tam giic do: a) Hiy xac dinh anh cua (0; R) qua phep tjnh tien theo vecta: b) Cho A thay doi tren (0:R) HoiH chay tren dudng nao?".Cach phat bieu dupc sudyng HS ehua giai dupc bal toan ban dau Hon nua, each phat bieu mdi cdn ren luydn cho HS kTnang veanh eua mdt hinh qua mdtphep tjnh tien •Bosung vagiam bdtvidu S V cae frudng su pham can ren luyen kTnang bd'sung vi dy, nhgn dang vattid' hidn dgy hpc toan DTnhien, khibdsung vidy ean bdt vi du khac SGK de dam bao thdi lupng cho phep Vidy dupc bdt cdthe'la mpt bai toan dng dyng nang cao hoacvi dijcdcung muc dich vdl vidy bdsung nhung SV nhan thay ehua phu hop vdi tinh hudng C h i n g han, day hpc cae phep bien hinh, kT nang co ban dau tien can hinh la kTnang xac dinh anh eua mdt hinh qua phep bidn hinh dd KT nang khdng chi xac djnh b i n g anh can dt/ng ma Tap chi Gido due so 306 ! edn bao ham thao tae eua HS tren hinh ve Vi nim mgt mat phing, diem cung thuoc vay, vdi bai hoc: Phep tjnh tien va phep ddi mgt matphing: - Xae dinh goc gida hai vecta, hinh (Hinh hpc 11 nang cao), SV cd the bo goc giua hai dudng thing; - Chiing minh hai sung them vidu veviec xac dinh anh eua mpt dudng thing vudng gde: • Xac dinh gdc giiia hinh qua mot phep tjnh tien cho trudc: Cho dudng thing va matphing, goc gliia hai mat tam giac ABC eo trgng tam G Hay xac dinh phing: - Xac dinh khoang cieh giiia diem den anh eua cae diem A, B, C, G qua phep tjnh matphing, diem den dudng thing, khoang tien ^'^^) hoae su dyng bii loan (Hinh each giiia dudng thing den mat phang song hoc 11 nang cao, tr 7) da duoc phat bieu lai song, hai mat phang song song, khoang each theo each ma ehung tdi de xuat nhu tren Vi giua hai dudng thing cheo du dua sau djnh nghTa khai niem 4) Hinh kha ning doc co phe phin phep tjnh tien nham giup HS hieu hon ve" phep SGK toin phothong Dole, Duffy, Roehler & tinh tien vi khai niem phep tjnh tien hoan toan mdi dd'Person i (1991) da dua mpt sdphUOng phap vdi HS (khdng gidng nhucae khai niem phep ddi xdngdd' cd thd' dpc SGK hieu qua (dan theo (6)) taic va phep dd'i xung tam la nhung khai niem ma HSNgudi bidt each dpc thudng se nhan bidt y ehinh va tach ehung td nhtJng vi du va ddn chdng; da duae tiep can dTHCS) tdm tit thdng tin bing each xem lai tatca nhung 3) Nim viphin tich duqc chuan kien thue, kf tudng mpt doan van hoae mot ehuong, nangmon Toan otutmg phothdng Chuan kienythuc, kTnang cua chuang trinh mon hge la cac yeu eautim co y tudng quan trpng, sau dua bai ban,tcSthid'uvekien thtjfc, kTnang cua mdn hpc maHS td'ng kd't kidn thde da dpe; dua cae cau hdi cdthe'dat dupe sau mdi don vj kien thdc (mdi bai, chu nhu ngy y eua tac gia lagi vaed ging tra Idi eae die'm, module) Moi yeu cau ve kienttiuc,kTnang cdttiecau hdi doc Ngudi bid't each dpc khdng tung budc dgttdimdcdplupng hda; minh ehung bang chi nim dupc mdc dp hid'u eua minh ma cdn nhung vi dy thd'hien duoc ca ndl dung, kien thuc, kTbiet nen lam gi va tai hp chua hieu tai Heu DcSvc^viecdpcSGKmdn Toandttudngphottidng, nangvamdcddvan dung cho cac dang toan De'nim dupc ehuan kien thdc, kTnang mdn Toan.eae bidn phap trdn rat hdu ich Ben cgnh dd, S V nganh GV nen tdchuc cho HS hinh eac nhdm, mdl su phgm toan hpc can dpc saeh vdi tuduy phe phan, nhdm nghien cdu chua'n kien thdc, kTnang cua mdt dd la tu cd suy xet, can nhic dd'dua quyet djnh ndi dung va de xuat cac dgng toan tuong ung de renhpp li hid'u hoaettiiA;hien mptvan de (7) Mdt khai luyen Chang hgn chuong trinh Hinh hpc 11, niem toan hpc cdthe cdnhieu each tiep can, mdt van HS bit dau dupc tiep can vdl hinh hpe khdng gian, de toan hpc cd the cd nhieu each giai quyet Thdng ehuy^ tukhdng gian ehieu sang khdng gian chieuttiudng, SGK chpn mpt each tiep can nao dd ca va tiep can vdi nhieu khai nidm mdi; vi vay, G V caneach tren va trinh bay mptcach chinh thdng Vide tiep hid'u dung ndi dung cung nhu dyng y, yeu eau eua can dT nhien se cd nhdng uu va nhupc die'm Vi SGK Do dd, viec bam sat ehuan kien thde, kTnang lavay, dpe eac tai lieu SG K mdn Toin, SV can tim rat can thiet Trong (5) da lam rd chua'n kien thuc, kThieu va dua chinh kien eua minh, tddd edeach dgy nang ddi vdi cae khai niem eua hinh hpe khdng gian;hoc hieuquachoHStrongquatrinh cdng tae sau ddng thdi, phan rd muc can dat dupc cua tdng khai Vidir.Wmh hoc 11 nang caottinhbay tinh cha nidm.Caedang toan dua phaidupc nghien edu kT tti ua nhgn cua hinh hpc khdng gian,k^ luan cuatinh cha tdcac vi dy va bal tap toan phu hpp vdi ehuan da xaethLanhan4chuapha djnh Chang han, dd'i vdi chuan kien thdc, kTnang cualatcittileu machi can khai niem hinh hpc khdng gian, GV ed the'cho HS giaiphat bieu nhu sau: "Neu hai m^ phing eae dang toan sau day: -Xacdinh vi tri tuang doi giOa hai duang thing, giQa duang than^ vi matphing: -phinbietcomctdiem Xac dinh giao diem eua duang thing vi matphing,Chung ^i ehung eon xic dinh giao tuyen eQa matphing va mat()hing; CO - mgl diem ehung • A/iacnt^.k^hppvd Chung minh vecta dong phing, during thing cting 54 Tap chi Gido due so 306 -(ki2-3/2023) cac dnh chatttiua nhan cdn lai ta cdthe chiJrig minh dupc f^g.'Noj haimMph^gphin b^cdmgtdi&n t^ung ffiichungcomgtdudngthangchungduynhiicht^ts^ca cac di&n ehung cua hai matphing dS That vay, ga suhai m a phing (P), (Q) cd mot diem Chung la A ttii ehung edn edmpt dian ehung khac la B; ttieotinh cheBttiua nhgnSttiittong matphing (P)cdmpt ducng ttiang a dl qua A va B va mat phang (Q) cd met dudng thang a- dl qua A va B; ttieo tinh chat ttiua nhgn ttii qua A va B chi cd nhat mot dudng thing nena'ttunga,doddaladudngthinp Chung cua haimat phang (P) va (Q) Neu hai mat phang cdn cd met diem Chung C nim ngoai a thi ttieo tinh cheittiuanhgn qua ba di«n khdng ttiing hang A, B, C chi cdduy nhat m?t mat phing nen (P) se ttung vdi (Q), dieu mau tfiuin vc* giattiiet(P) va (Q) phSn biet Vgy, naj hai mat phang phSn bigt ed mgt diem ehung thi ehung cd mot ducng thang ehung nh£& ehua tat cacao dian Chung cija hai mSt phing {hinh 2) Trong quatrinh giang dgy deae trudng su phgm, giang vien cdttiesddung hai hinh ttiue ren kjygn kTnang khaittiac SG K mdn roar? eho SV sau day: • Cai dat mdl sdhudng khaittiaevao bai giang tren Idp dgy hpc cae mdn Phuang phap dgy hpe toan dbac dgi hpc; • Tdchuc seminar ttieo hudng van dyng hogtdpng nhdm de'eae nhdm ttiao lugn each thuc khai thac mpt sdehuda Trong hai hinhttiuctrdn, ttieo ehung tdi, hinh thuc thu hai can dugc sddyng vdi tan suait nhieu hon denang cao kha ndng hpc tap hpp tae, tim hieu SGK eua SV Vigc phan tieh chuong trinh,SGK mdn ToandtR/dng phdttidngcdvaltrdrE^quan trgng ddi vdiGVviquadd,hp cdthenim dupcmach kien ttitjccua chuong trinh, diffig ycuaSGK, tdddhiaj sau sic hon vemdn hpe maminh giang dgy, giup cho vigc soan giao an dupc tdt vaphuhpp hon; hon nua, G V se ttiugn Ipi hon ttong viee van dyng cac k i ^ ttiuc cua toan hpc cao cap vao giaittiichkien ttiuc ttong SG K Vi vay, tdkhi cdn hpc tap ogling dudng dgi hgc, S V can dugc ren luyen kTnang phan tieh ehuong ttinh, SGK.Q (1) BO GD-DT Tdi li$u Bdi d t i ^ g gido vifin t h u c hi^n chuong t r i n h , sdch gido khoa Idp 10 t n i n g hoc phd thfing mfin Todn NXB Gido d^c, H 2006 (2) T r ^ NgQC Lan Gido trinh Thvc hdnh Phuong phdp d^y hpc todn d^ti& hpc NXB D^ hpcsuphpm H 2009 (3) BQi Thi Hudng Gido trinh P h m m g phdp day hpc mfin Todn o* t r u n g hpc phd thdng theo dinh h u o n g Kch CMC NXB Gido due Vi?l Nam, H 2010 (ki2-3/2013)- (4) Nguygn Ba Kim Phuong phap day hpc mon Todn NXB Bai hoc suphgm, H 2009 (5) Nguygn Th£Th£ich (chu bien) H u o n g ddn thuc hien chu^n kig^n thirc, kl ndng mon Toan Idp I I NXB Gido due Viel Nam, H 2006 (6) Nguyen Thanh Long (chu bifin) - Ly Thj Minh Chau - Nguygn Khanh Trung Ki ndng hpc dai hoc va Phuong phap nghidn cuu NXB Gido due, H 2008 (7) Du an Vifit - Bi Day cdc kl ndng t u (trich dich) H, 2000 SUMMARY In this article, we analyze the role, characteristic of mathematics textbooks at school and the necessary of training the skill at exploiting textbooks for mathemaUcal pedagogic students On that base, we propose some main orientaUons of exploiting and how to carry out training for students lfng dung phirong phap (Ti^ Iheo bang 57} giai Si/oc bSng phirong phap nao khac nen doi hoi HS phai 00 IK linh hoat, sang tao GV can giiip HS nhan d^ng toan colhegiaibjng phuang phap gia thiel tam SiJdgng phi/ong phuong phap gia thiet tam giai loan, GV cothe ren luyen dupc tuduy va boi duong kien thiic cho HS, dae biet la nhUng HS gioi toan dtieu hpc; vi vay, GV can thuang xuyen cho HS thirc hanh van dung cac BT co the giai b i n g phuong phap • Tai lieu t h a m khao Dd Trung Hi$u - VQ Duong Thuy Cdc phuong phdp giai toan 6- tieu hpc NXB Gido duc H 1999 TrSn Dien Hi^n Ren kl ndng giai todn li^u hpc NXB Dai hgc supham, H 2008 D6 Trung Hieu - Nguyen Hung Quang - Ki^u Due Th^nh Phuong phdp day hpc todn tdp hai (phSn thuc h^nh giai toan) - Giao trinh d a o tao gido vi£n ti^u hoc he cao d^ng s u p h a m NXB Gido due H 2000 Nguyfin Ang - Duong Qu6'c An - Hoang Thj Phuoc Hao - Phan Thj NghTa T o a n boi du&ng hoc sinh Idp N X B / / d W(5( H 1998 SUMMARY This article pointed out the importance and necessity of 'method assumes temporary' in training and development ofthinking for students In general, elementary school students in particular To prove the uniqueness of this method, after each example the authors analyzed to compare the soluUon of the problem with this method with other methods Tap chl Gido due so 306 5! ... gdc giiia hinh qua mot phep tjnh tien cho trudc: Cho dudng thing va matphing, goc gliia hai mat tam giac ABC eo trgng tam G Hay xac dinh phing: - Xac dinh khoang cieh giiia diem den anh eua cae... minh, tddd edeach dgy nang ddi vdi cae khai niem eua hinh hpe khdng gian;hoc hieuquachoHStrongquatrinh cdng tae sau ddng thdi, phan rd muc can dat dupc cua tdng khai Vidir.Wmh hoc 11 nang caottinhbay... dudng thing, khoang tien ^''^^) hoae su dyng bii loan (Hinh each giiia dudng thing den mat phang song hoc 11 nang cao, tr 7) da duoc phat bieu lai song, hai mat phang song song, khoang each theo