MOT SO SAI lAM CUA HOC SINH KHI GIAI TOAN O ThS NGUYEN QUANG THr Trong qud trinh dgy hgc, ed nhung hge sinh (HS) filp thu kiln thirc rd''''t nhanh vd bilt vdn dyng kiln thiic dd hgc vdo gidi cdc bdi todn[.]
MOT SO SAI lAM CUA HOC SINH KHI GIAI TOAN O rong qud trinh dgy hgc, ed nhung hge sinh (HS) filp thu kiln thirc rd't nhanh vd bilt vdn dyng kiln thiic dd hgc vdo gidi cdc bdi todn, ben cgnh dd cd nhimg HS hgc luc ylu se khdng dgt dugc kit qud nhu vdy O cdc frudng phd thdng, hogt ddng gidi todn cuo HS dugc xem Id hinh thirc chu ylu cOa qud frinh dgy hgc mdn Todn Nhiing sai ldm cuo HS frong qud frinh gidi todn tuong ddi dgng vd thudng dugc xud't phdt ta mdt frong so cdc nguyen nhdn co bdn sou ddy: Hieu khdng ddy dii vd ehfnh xdc cdc thudc tfnh cuo khdi niem Trong chuong frinh todn phd thdng cd rdt nhilu khdi niem md HS phdi filp cdn, nhung khdi niem ndy dugcfrinhbdyfrongSGK, nlu ngudi hgc khdng hiiu dung bdn chdt se ddn den viec vdn dyng sai cdc khdi niem dd Chdng hgn frong vf dy sou: Vi dy: Hdy dgc so dd'i cuo sd o Da sd HS trd Idi: Sd dd'i ciio a dgc Id dm a, sai ldm cua HS d chd cii nghT sd ddi mong dd'u «-" ndn ngd nhdn Id so dm, nen dgc dm a Trong (-a) cd t h i duong, hogc dm hoy bdng Ldi gidi dung: Dgc Id frir a Khdng ndm virng cdc phuong phdp gidi mgt so' dgng todn co bdn O l gidi cdc bdi tdp, HS cdn ndm virng If thuylt vd phuong phdp gidi cdc dgng todn co bdn Dd'i vdi HS cd hgc lue dudi h-ung binh, nlu khdng ndm dugc nhung dgng todn tren se ddn din soi ldm nhu cdc vf dy sou: Vidy 1: Cho x S y > 1, chirng minh: T x+y[y>y+yfx Ldi gidi cua sal cua HS: Do x^y>'\, suy ra: d ddy, soi ldm cua HS Id khdng hiiu dung bdn chd't cua bdi todn, dd Id'y hoi v l cuo bd't ddng thiic trCr cho ddn d i n kit qud soi Chdng hgn, nlu: [sli"*^ ^^ ""^ (7 - 5) > (d - 2) hay > (vd If) Id soi Tap ehi Giao due so (M i 9/aoii) ThS NGUYEN QUANG THr Ggi y mdt cdch gidi dung: Xet hdm so y = t-yft, ehiing minh tinh ddng biln cuo hdm sd' de di d i n kit qud Vidu 2: Gidi phuong frinh (x^ - 1) (3x^ + dx + 2) = (x2-1)(2x + 3)(1) ldi gidi eua sai HS: Phuong frinh (1) Q Id «P o Q" khd tay fien, cdc em ehua hiiu dung ndo thi dimg dd'u «=>" vd ndo thi dung ddu « OM = OM tan 30 x = —-— (vd If) hay bdi todn khdng gidi dugc Sai ldm cua HS: HS chi ro BMD Id gdc giiia hoi mgt phdng (SBC) vd (SCD) Id khdng chfnh xdc vi gdc BMD Idn hon 90° That vgy, ta cd OB = oc = ^ ^ , AOCM vudng tgi M, nen OM < OC => OM < OB AAgt khdc,frongtom gidc OBM: tan M = - ^ > ^ ZBMO > 45°, hoy ZBMD > 90° ' OM Ddp sddung eua bdi todn: ZBMD = 120° vd fim dugc x= a Gidi thieu trudng hgp dd'i vdi cdc bdi todn bien ludn hoy tim thom so Nhieu HS cdn lungtangkhi gap dgng todn ndy, nguyen nhdn chfnh cd t h i Id cdc em khdng Vidy 2:Tfnh tfch phdn: l^^x ndm vtfrig phdn If thuyet nen ddn tdi Idi gidi sai hogc xet thieu cdc frudng hop cuo tham so Vi dy 1: Tim m de bilu thiic f(x) = (m + 2) 3 x^ + 2(m + 2)x -I- m + ludn duong (bdi 50, Ldi gidi sai eua HS: \^dx = ^x^dx = -VJC' 0 ' fr 140 - Dgi so' 10 ndng coo) Sai ldm eua HS xud't phdt ta viee dp dyng Ldi gidi cua HS: cdng thiie luy thira vdi so mu huu fr a" =Va" , {a = m + 2>0 f(x)>0,VxeR'^\ «>m>-2 vdi a > 0, m eR, n e R* HS sii dyng cdng thiic [A=(m + 2)'-(m + 2)(m+3)BDlSC { Ke SCI MB SC1 MD Mdt khdc: (SBC) n (SCD) = SC, MB c (SBC), MD c (SCD) Vdy gdc BMD Id gdc giua hai mdt phdng (SBC) vd (SCD), hoy ZBMD = dO° To cd: A S A C ddng dan g # VOI &OMC=> 14 = r =>OM = OC.SA SC 2^x' + 2a' "TTT = theo thom so' m (bdi 25, tr 85 SGK Dgi so' 10 ndng coo) Ldi gidi cua HS: Dilu kien x * - , suy (m-1)x = m + Xet trudng hgp m = thi phuong trinh vd nghiem, nlu m ^ 1, phuong trinh cd mgt nghiem nhd't ;c = ^ m-l Vgy: m = 1, ta cd S = ; m^1,tacd5 = { ^ } Sai lam cua HS: HS chua kilm tra dilu ki§n nghiem fim dugc cd khdc -1 hay khdng Tap ehi Giao due so (ki i 9/aoii) Cdch khdc phye sai lam cua HS: Trinh bdy nhu tren vd k i l m tro them d i l u kien nghiei nqhiem m+4 5^-1 X = m-\ Tim thieu d i l u kien ciio b d i todn g i d i cdc b d i todn phiic t g p Moi bdi todn khd vd phirc tgp thudng khdng ed mdt phuong phdp gidi ey t h i G d p nhirng bdi todn nhu vdy, kinh nghiem eho thdy HS thudng xet thiiu d i l u kien ddn d i n Idi gidi khdng chgt che hogc soi Mgt so vf dy minh hga sou: Vi dy 1: Tim gid trj nhd nhdt eiia b i l u thirc: f(x)=y]x-2^f^ Qua mdt sd sai ldm duge phdn tich d tren, theo chung tdi, mdi sai ldm cua HS edn theo ddi qua hoi giai dogn: sai ldm ehua xudt hien vd soi ldm xudt hien Chung tdi d l xudt bien phdp nhdm khde phye thdng qua so dd sou: r Sai lam Xuat hien ChUa xuat hien Phan tich sii^a chufa Cung c6 kien thurc + ,Jx+2sim Ldi gidi eua HS: z Phan tich rasailam Phong tranh Kpt th''"" Ketthuc^ Tai lieu tham khao \J7^-i\+\JI^+\\>2,p7^-]\\4^+\\ = 2,l\^ ( t h e o Nguyin Ba Kim Phuung phap day hoc mon Toan bd't ddng thiic Cdsi) Vdy, f(x) dgt gid tri nhd nhdt NXB Dai hpc supham, H 2006 Dao Tam - Le Hien Duong Tiep can cac phuung bdng ^ | x - | phap day hoc khdng truyen thd'ng day hoc Sai lam eua HS: Thieu d i l u kien x > vd v l Toan NXB Dai hpc supham, H 2008 Doan Quynh (tdng chii biSn) Dai so 10 nang cao phdi ^ - | ehua phdi Id hdng so nen Idi gidi NXB Gido due Viet Nam, H 2010 ndy khdng dung SUI\/IIVIARY Ldi giai dung: D i l u kien cuo bdi todn Id x S f(x) =Wx^-\\ + l/I^ + l\>-^I7^ + X + yfI^+l = The author points out mistakes frequently made by students in solving mafhematic problems Vdy, f(x) dgt gid trj nhd nhd't bdng , dd'u with specific examples; as well as proposing bdng xdy ro < x < overcoming measures Mot SO bien phap (Tiip theo trang 40) Tai lieu tham khao NguySn Thi C6i "Nang cao hieu qua viec day hoc Ljch sir dja phuang d truong ph6 thftng" Tgp chi Khoa hpc trucmg Dai hpc supham Hd Ndi, s6' 6/2002 Phan Ngoc Lien (chii bien) Phuung phap day hoc Lich su, tap NXB Dai hpc supham, H 2009 Nguyen Canh Minh (chu bien) Giao trinh Lich siir dia phuung NXB Dai hpc supham, H 2(K)7 W B Stephen Teaching local history Manchester University Press 1977 Mftt s6' trang Web: http://en.wilcipedia.org/wilci/ Local history: http://curruculum.qcda.gov.ulc: http:/ /www.schoolhistory.co.uk tgo td ehiie DH eiia G V eho phu hgp dgc diem HS, d i l u kien kinh t l d tirng OP - Phdi chu y tdi viec phdt huy tfnh tich eye, chii dgng ciio HS DHLSDP Dii sii dyng bien phdp ndo, GV eung phdi phdt huy tfnh tfch eye, chu ddng ciia HS, b i l n qud trinh gido due thdnh qud trinh h; gido dye - Cdc sd GD-OT xdy dung nhirng d i i n ddn d l GV ed t h i trao ddi kinh nghiem gidng dgy ndi ehung vd gidng dgy LSOP ndi rieng GV ed t h i dua len cdc tu lieu md minh cd dugc, hodc tdi v l nhirng tu lieu khde, d i l u ndy giup cho GV vd HS hit kiem thdi gian, cdng sire fim k i l m tu lieu Cde SUIVIMARY Sd GD-DT vung, m i i n ed mdi quan he LS, The article introduces some measures of chfnh trj, kinh t l , vdn hod Idu ddi cd t h i lien k i t teaching Local History In teaching History subject qua Internet d l tgo ro nhirng kho tu lieu Idn, giup in the United Kingdom and experience lessons for ndng cao hieu qud DHLSDP vimg • teaching this content in Viet Nam ap ehi Giao due so (ki i »/2oii) IF # ... nhdt eiia b i l u thirc: f(x)=y]x-2^f^ Qua mdt sd sai ldm duge phdn tich d tren, theo chung tdi, mdi sai ldm cua HS edn theo ddi qua hoi giai dogn: sai ldm ehua xudt hien vd soi ldm xudt hien Chung... ta cd S = ; m^1,tacd5 = { ^ } Sai lam cua HS: HS chua kilm tra dilu ki§n nghiem fim dugc cd khdc -1 hay khdng Tap ehi Giao due so (ki i 9/aoii) Cdch khdc phye sai lam cua HS: Trinh bdy nhu tren... thuyet nen ddn tdi Idi gidi sai hogc xet thieu cdc frudng hop cuo tham so Vi dy 1: Tim m de bilu thiic f(x) = (m + 2) 3 x^ + 2(m + 2)x -I- m + ludn duong (bdi 50, Ldi gidi sai eua HS: \^dx = ^x^dx