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Tran Viet Cudng Tap chi KHOA HOC & CONG NGHE 114(11) 199 204 MOT SO BIEN PHAP s y PHAM GOP PHAN B 6 I DUOTNG NANG EUC PHAT HIEN VA GIAI QUVET VAN DE CHO HOC SINH LOP 10 THONG QL A DAY HOC CHL DE HINH[.]
Tran Viet Cudng Tap chi KHOA HOC & CONG NGHE 114(11) 199-204 MOT SO BIEN PHAP s y PHAM GOP PHAN B I DUOTNG NANG EUC PHAT HIEN VA GIAI QUVET VAN DE CHO HOC SINH LOP 10 THONG QL A DAY HOC CHL DE HINH HOC Tran \ iet Cu^ng" Inn'/iig Dai hoc Su pham Dll Thdi \gu-ien roM T A T Neu hpc sinh (HS) co nang luc phat hitin (PH) va giai quyet van dC^ (GQVO) thi se giiip cho qua trinh hoc loan dugc Ihuan loi qua phat uien cac nang luc tri tuc cho ban than Bai biio chiing toi mu6n d^ xuat mot sd bien phap co the bdi duong nang lire PH va GQVD cho HS thong qua da\ hoc hinh hoc Idp 10 Til* khoa, Hinh hoc 10 hoc sinh, phdi luen vd giai c/m it vdn de NANG LUC PH V A G Q V D Bicu hien cua nang luc P! \a G Q V D uong Nang luc PH va G Q V D (irong hgc lap) lii mot liP'^ ff'an duoc the hien o cac mat he thdng cac thuoc tinh ciia ea nhan ngirdi ddng k i d i thuc loan lien quan ldi boat ddng Ihe hien cac kha nang (tu ya hanh ddng) S'^i qu)'^'! mdl ndi dung Toan hoc cu the Cd boat dgng hgc tap iihAin PI y a giai q u y d B i d huy f^' ' " " ^ t'^n himh cac hoat ddng giai bai loan CO hieu qua cac \kn dc nhiem yu irong hoai -^^y dung, niim yfrng khai mem roiui hoc ya ddngdd chimg minh dmh li MI nr • ft^\n^ i ic i i Nang luc PH va G Q V D cua I IS troim il;i\ hoc 'loan bao gom ciic id nhu: ( I ) PI I, nhiin li("'P ^>'I muc dich yCU cau, I lie luen duoe ihiii ' do, linh cam cua minh ydi nhuim Idi s^iai bin loiin Pll sai lam ya sua chiia sai lam, thiiy hiel bieu tiroim true quan lien quan tdi yim dc (2) PI I mau tiriiSii lioiii liiili liuflng lliii> duoc , Dal diioc kel qua phii ' ' " " ^ '"^' '"'•^- ••^" *»'-' """"!^ " " " " ' ' ^ l ' f^''" illiu cju can U O V D Irong linh huong lii ^.Ing luc I'll \a i,i}\ liuS dong, lai hicn nhiing kien lluic ki nang da cac nuic dd hoc CO Iicn quan dc khai Ihiic linh huong licp nllfrng >cu c i u co ban I'll \a ( l y V I ) \i"in can nh.in b i i l linh luiring co v,4n dc- 1.5) Nang dc da duoc ( j \ ' d.il nu'il cach luong doi ro luc I'll nhung Ihiiiic Iinli tliuiig Iian cluil lao \liii D co ihO duoc clii.i l l i c , ilo I IIS da|i ung duoc r.ang -^h'rc dd IIS nhan duoc Mill dc iKn niii hiim cua tim ili) Ihimg iiiia cue Imal '-',\' dila ra: bicl hoan nil MCC I'll Ml ( Q V I ) t e e ằã;ãôô; ^J; N.ing luc hinh llmnh, dicn dai duoi sn d.in dal cua CIV Ciic liin de loan hoc Ihco cac hirong kh.ic (lang PI I \i>" tlc- luan toan hgc dc c h d n g minh hay bac bd 114(14) 199-204 A.\'r = aAB' + (\-a)AC' ha\ a - ]-ar - —c+ b = — {c^b] m n 2V Vi c va h khdng cimg phutmg nen la co Dd la dicu phai ehiing mmh Khai ihac kha lu'mg tinh loan iilianh de giam hot thdi gian I IS linh loan thii cdng danh thdi gian dd cho lim hieu ban ctial loan hgc Hirirng ddn HS hiel ciich tim dt'ic diem ehung vd rieng cua vdn le; biet nhin nhtjn s'tr i'in tlinh, hen virng sir vtin dt'mg cua diii tilting, tir tld giiip viec hoc HS cd clinh huirng Hinh Nhu \iiy di'iiig thirc (1) la tiudiig hop dfie biel cua dfing lluic (2) IT - B C" N Viiy la ed bin Uiiin Clio ilBC dirirng ihdng d bdl ky cdl cite canh 113 IC vd lrung tin en VV! lanttrol lai A' B' M' Ctnnig niinli todn AB I i ttu 2, Cho \ A B C hai lrung tiivi-n AM \ii BNc^l lai (> Ihi AM T.\G (I) Ta nhin lrung luyen BN la truinig hgp diic bict eiia d u d n g ihiing d bai ky ciit AB B", AC a C va AM a M' Vim de dat la cac ti sd AB A B ' AC AC" A M : A M ' cd quan he nhu the mio'' ho dudng ihang d o' mgl vin y i tri d i e bici la , , dir doan IB IC , n / ,.^ _ -i = — — (2) 1.1/' AB' «' a; K "1, 'W -"- II .-IC - iiC •IC' Nhu yiiy tu mdt bai loiin quen ihudc neu chiu khd dao sail suy nghT biel nhin mdl khiii m d n ihco nlncu gdc khae la se duoc ciic bill loim ldng quat khac ma bai loiiii ban diiu cln lii mot irudng h a p n e n g T a | ) luyen H S su' d u n g ngiin ngii' ki hieu Toiin hoc dc dien d a l cac noi d u n g Toan nhiil tao I h u a n Igi c h o y itc PH ya ( I Q V I ) \ e l quan he cua hai dicm Ua, bi ya lUa -b/ d u i y cite ciieh dien dat ye mill ndi dung nhu 1.1/' -^h.AXr i\r ye mat p h u o n g phap kin da\ yiin de luiy cin ci 1- VU - n h a u til' dd clign each dien d a l ldi u'u v'.AB^ c.7K' = b Ta AB' h o c : dien d a t yiin de t h e o nhieu each khac Ta se chi rng 1luiiili dieu du doan la dinii iLil viiv d,il: AB '' \gdn ngu loa eld "A B lii iuu didii co hoiinii nhu ya tung dd doi nliau" JA^i.- -Uc+k \gdn ngii Hinh lioc long hop " friic lioiuih hi duiuig u u n g iruc cua doan ihiuig IB" Do ba diem A', B' M' thang hang nen 211 .\g6n ngir phep ![4(]4)- ! 9 - Tap chi KHOA HOC & CONG NGHE Tran Viet Cudng hien timh: "A \k B ddi \ung qua true h o a n h " GV cd the dua ddi vdi HS kha gidi cac cua hai doan thang PA = PB ina HS thirdng dimg sir d u n g tinh chat trung diem cua doan t h a n s dang: Flai diem ddi x u n g qua d u d n g phan giac thir nhSt (Aia b) va A'ib: aj) thii hai (A(a: h) ya A'l-b -a)) hoac qua mpl diem bat ky HS giai quyet tdt cac van de tiiv thugc yao kha nang chuyen ddi ngdn ngii' ngi lai mgl noi dung Toan hoc va chu>en ddi lii ngon ngir na) sang ngdn ngU khac dc dien dal - Ta cd the md rgng bai toiin tren de ed bai Cling mot ndi dung Toan hgc Khi xac dinh toan tdng quat hon va d i m g ngdn ngu dien nang luc huy ddng kien thiic chung tdi cho dal de bien ddi bai toan theo cac h u d n g khac rang kha nang bien doi van de bien ddi cac nhau: bill loan ddng vai tro quan trgng Nhd qua trinh bien ddi van de bien ddi cac bai toan HS CO the qu> cac van de tinh huong moi cac biii loan la ve cac van de quen thuoc Cluing la cd the xem \et vi dii sau day de lam tai B cho diem P chia doan AB theo ty so I) c h o t r u d c Gat i' ciich gioi: T r u d c het ta chuyen ngon ngu hinh hgc tdng h g p •"Dicm P chia doan AB sang to dieu noi tren Tren mat phang 0,\y cho d u d n g Ihiing (d|): \ - > + = (d.) \ + y - - yii dicin P(2: I) F a p p h u o n g trinh dudng thang A qua P cho A cat (di) tai A, cat ((/_-) k (k^ cac bai loan t u o n g lu da giai Vi du Hir&ng ihir nhdi: Viel p h u o n g trinji d u d n g theo ti sd k (A: ?^ I ) " ve ngon ngii vecta P.4 - kPB (k t 1) sau dd sir d u n g cdng thiic linh toa diem chia doan thang theo li %okt Ihiing qua P yii ck\ (d,) (d^) luong irng tai A B s;io cho P la lrung diem cua AB Lot gun [dA nen B(b - b ) T a c d : Ki = (a-2.ci):~PB ^ (b -2'.-2b) Hiiuiig Do P la lrung diem ciia AB nen ta cd PA = 3^ Lap phirong trinh (d:) lai B cho PA dudng - k PB (k > 0), De giai quyet bai toan la can chia hai Do dd phuong trinll d u d n g thang AB la: A B : \ - y - - /)' bdl lodn trill la cd nhdn xii sau - Biu loan Ircn giai quyet duoc la nhd tham sd hoa toa diem ,\ e (d|) va B & (d:) day la yeu td quyel dnih eho bai toan Viec ehuyen "P lii lrung diem cua doan thang AB" sang ngdn ngd yecto theo each qii>' ye sir bang eiia hai yecln PA = -BB 6a lam cho bai loan don gian hon so ydi viec quv ye su bang 202 thir hai thang \ dl qua P c h o A cat (di) tai A, cat -PBc:>i \b = A/3 Suy \-k , -, , la se lim duoc yA - ^'B \:'^'" ]-k p h u o n g trinh ciia dirdng thang A B , eho trudc Vi A e ( d | ) n e n A(a a + I), vi B e trudng hgp PA = kPB hoac PA = -k7'B lam tuo'ng tir n h u h u d n g thu nhat rfii To chiic cho HS P H , Ihuc hanh cac qui tac thuat ^iai, tua thuat ^iai de boi dudng niing luc finh toan, suy luar) va chiing minh Vi clu Cho gdc Kt)y va hai diem M N lan luot di chuyen tren hai canh Ox Oy cho OM = N C h i m g minh trung dicm I ciia MN luon thugc mdl dirdng thang co dinh Birdc Lay diem A e O x B e > cho OA - O B Chgn hai vecta OA.OB lam hai v e c t o CO sa Moi v e c t a bai loan deu Tran Viei Cirdng Tap chi KHOA HOC & CONG NGHH phan tich d u g c qua hai v e c t a Burk Tir gia thi§t ta cd OM = N nen neu (~)\=kOB thi T)\1^2kOA mu phai chimg minh la I thugc mgt dudng thSng eo dinh (de lha>' dudng thang qua O) tuong duang 114(14) 199-204 dang loan cd nhieu c a hdi dc lam rd y^ii de Tuy' nhicn khdng phai hie nao cung lam theo budc nhu tren khdng phai hie nao cung phan tieh eac vecta theo hai vecta eo sd cho tru'dc ma cd the giai quyet bai loan mot each linh boat vdi Ol - pv ( V la vecto cd dinh nao dd) Bu'dc 3, Do I la trung diem cua MN nen la co Ngoai GV cd the van dung mdl sd bien phap sau nham gdp phan ren lii>en nang lire PH va 7)i^-\(}M + 7)N\^~k[2C)A Dal -k^ pwAlOA^'OB^v G Q V D eho HS dav hgc hinh hoc 10 + m\ la dugc didu phai chiing minh Hirdng clan cho HS thdng cpia cdc hoai dimg tri tue de id chirc tri thirc vdc clinh ban chdt cua vdn de tim ciich GQVD vd khdi cfiidt hod vdn cle eld, - Vdn clung cpian diem elen hoc lich hcrp giiip HS hieu tluirc mdi cjitcin lie giira loan lioc vin lliitc tiim, qua dd vein dung kien thdc loc'ui lioc vdt) gun i/iiyel mdt sd imh huimg ihuc le - Tdng cuirng den hcic phdn hda iheo cite mirc do, cdp khdc nlian Irong cdc nhdm ddi Iirong khdc nhan vii Irong cimg mdl ldp etc tern ret mdt Iruimg pint hop vdi trinli eld t net Birii-c Nhan \ c t : Neu lay (hV - 2()A ihi V OA' + OB d u d n g thang cd dinh dd di qua lirng lis nhdm giiip HS cd ntnin dimg, cldc ldp Pllvd Chimg ldi dii budc dim lien hanh llu'r nghiem trung diem ciia A ' B Trong qua trinh h u d n g dan IIS giai hiii loiin su phiim cac bien phap Iren liii truinig 11 IPI bang phirong phap vecta GV can d u i y di:n riiiii Hda tmh Tu_yc-n Quang nhung tn thiic p h u o n g phiip' nghiem cho ihay budc I: Nen eac vecto Irong dirge thuan lgi dugc viec chgn co hdi ctm GQVD chon cac yecto e a so cho bai loiin phan tich Ihco cluing Q u a mdi bai loan, I IS se lluiy cac vecto eo so nhu the luio, Kel qu;i Ihu N'icc day hoc Ihco hirdng bin dudng nang lue PH ya G Q V D nhu dii dc \uiil la kha lln Day hoc iheo hirdng HS hirng thu hoe tap ban Cac em lu Im han Irong hoc Iiip, manh dan Irinh hiiy >' kien cii nhan hang hai tham gia ihao luiin, lim tin, d budc Can ren hiy'en cho FIS ehuyen ddi ngon ngiT mdt each thao Ciich chiiycn ddi nhu the nao ta cd the thiiy' qua v i du da neu, O budc 3: Can nam y u n g ciic phep toim Pll vil G Q V D giiip HS ren luyen kha nang tu hoe sudt ddi, KFT M I A N \'icc bill duiing cho HS luiiig lue Pll vii \eclo, CiQVD irong hoc loiin sc guip cho vice hoe Dong thdi, Ihdng qua cac biii liip cu llie CiV can Iiun cho HS hieu rd dugc linh uu y i d cua phuong phap yeclo Dac bicl ciic bai Uip ye quy tich, bai tap chirng minh diem liuuig hiing chirng mmh hai duinig Ihiing song song, hai d u d n g thang yudng gde., la nhirng lap mdn loiiii tro nen hieu qua giup IS sc nhm yung cae in thue, phat m e n ur duv hinh e:ic kT nang, kT vao can ihiel cho ban lluin No gdp phiin hinh ihiinh i-ac pluim cluil Iri lue cua e^-^n nguoi noi chung, cuii IIS phd Tran Viet Cuong 114(14): 199-204 Tap chi KHOA HOC & CONG NGHE thdng ndi rieng, Bdi dirdng nang Igc PH ya TAI LIEU THAM KHAO G Q V D la gdp phan phat huy tinh tich c u e cua Tu Due Thao (2012), Bdi duirng niing lire PH va GQVD cho HS lrung hoc phd ihdng day hoc Hinh hoc, Luan an Tien sv giao due hoc Doan Quynh (long chu bien) Van Nhu Cuong (chu bien) Pham Vu Khue Biii Van Nghj (2006)^! Hinh hoc ndng cao 10 Nxb Giao due Nguyen Mong Hv (chu bien) Nguyen ViSn Doanh Tran Due Huy^n (2006) Bin tdp Hinh hoc 10 Nxb Giao due HS hgc lap lao cho HS cd nhirng nhan to nhiTng dieu kien pham chat nhan each de tham gia vao cugc sdng vdi n h u n g yen cau cua ngudi mdi nen kinh te mo' cira hdi nhap so pliat tnen da dang cua ddi sdng xa hdi SUMMARY SOME EDUCATION iMRASCRES CONTRIBUTE TO FOSTERING CAPABILITY DETECTION AND SOL\ ING PROBLEMS FOR 10 GRADE STUDENT THROUGH TEACHING GEO.\IETR\ COURSE Tran Viel Cuong {'ollcic ol liiliicaliou I \l If students have a capacity to detect and solve problems vvill h d p the process of learning mathematics is favorable, thereb> developing ihe intellectual capacity tor them, in ihis article, vvc'd like to buggesl some possible measuies to build the capacity to delect and solve problems for sludenls through leaching 10-grade geometry Key words: lO-gi ade geometry, student, detecl and solve problems nhim bdi 30 2013 \giiy plum bidm 15 2013, Ngiiy duyi'l dcing 25 12 2013 Phu ' hien khoa hoc: TS Dd Thi Trinh - Truimg Dai hoc Su pham - DH Thai \gu\ en Icl 09": 201 ... riiiii Hda tmh Tu_yc-n Quang nhung tn thiic p h u o n g phiip'' nghiem cho ihay budc I: Nen eac vecto Irong dirge thuan lgi dugc viec chgn co hdi ctm GQVD chon cac yecto e a so cho bai loiin phan... KFT M I A N ''icc bill duiing cho HS luiiig lue Pll vii \eclo, CiQVD irong hoc loiin sc guip cho vice hoe Dong thdi, Ihdng qua cac biii liip cu llie CiV can Iiun cho HS hieu rd dugc linh uu y... Ta sir dung phan mem de lao cac md hinh toan hgc, cho HS luong lac vdi md hinh hkng each thay doi mdt sd yeu td nao dd tir y iec quan sat true quan khuven khich H S d u a d u doan Sau diing su>