TRI THUC PHiniNG PHAP TRONG DAY HOC MDN TOAN a TRUQNG TRUNG HOC PHO THONG O PGS, TS O A O THAI LAI '''' ThS LA DUG M I N H " 1 Cdc dgng tri thuc phi/ong phdp (TTPP) Khi cd con ngudi ddng thdi xud''''t hien[.]
TRI THUC PHiniNG PHAP TRONG DAY HOC MDN TOAN a TRUQNG TRUNG HOC PHO THONG O PGS, TS O A O THAI L A I ' - ThS LA DUG M I N H " Cdc d g n g tri thuc phi/ong p h d p (TTPP) Khi cd ngudi ddng thdi xud't hien tri thuc Con ngudi Widng t h i sd'ng dupe n l u khdng cd tri thi/e Tri thuc vCra Id hoqt dqng vi>a td sdn phdm cOo hoqt dpng dd Cd t h i h i l u , tri thuc Id k i t qud cua qud trinh eon ngudi nhpn thuc thye tpi khdch quon dd dupe kiem nghiem quo thyc hen Id phdn dnh Hung Hiue thyc tqi khdch quan y rfiuc ngudi dudi hinh thi/c nhi/ng bieu h/png vd khdi niem, duqe dien dqt ngdn ngu Tri thuc Id k i t qud euo qud Hinh tu tich cue Trong dqy hqe k w n d tn/dng trung hoc phd thdng, tri thire, dqc biet Id Hi thi/c phirang phdp, djnh hudng trye hep cho hoqt dqng (HD) vd dnh hudng trye h i p d i n viec ren tuyen kl nang Day hpc khdng ch? hinh cho hpc sinh (HS) cdc tri thuc su vdt Hi thi/e v l ddi tuqng nghien cuu ciio mdn hoc md cdn hinh thdnh vd phdt trien he thdng TTPP cho HS Cdc TTPP duqe hinh Hidnh Iqi trd nen d i l u kien thudn Ipi de HS h'nh hpi, k i l n too tri thuc mdi Trong mdn Todn, ta ed the gdp mpt so' dqng TTPP nhu sou: - Nhi/ng TTPP thuc hien nhi/ng HD h/ong ung vdi nhi/ng npi dung todn hoc cy the nhu: tfnh dqo hdm, gidi ede bdi v l Hnh ddng bien, nghjch bien, cdc quy tde Hm cue trj, gidl cdc bdi todn khdo sdt hdm sd' ; - Nhi/ng TTPP thyc hien nhi/ng HD todn hqc phi/c hpp nhu dinh nghTa, ehung minh ; - NhUng TTPP thye hien nhi/ng HD tri tue phd b i l n mon Todn nhu HD h/ hdm, phdn chia trudng hpp ; - NhCmg TTPP thye hien nhi/ng HD tri hte ehung nhu so sdnh, khdi qudt hod, truu hrang hod ; - Nhi/ng TTPP thuc hien nhCmg HD ngdn ngU logic nhu thilt lap menh de ddo cua mSnh de cho trudc, lien k i t hoi mgnh de thdnh hdi hoy tuyen cua chiing TTPP frong dqy hqc mdn Todn d h v d n g THPT ddng vai trd Id ca sd dinh hudng trye tiip cho / ^ V i d y : De chung minh bo d i l m A , B, C thdng hdng, gido vien (GV) cd the tdng k i t cho HS su Tap chi Biao due so (ki a • la/aom dyng cdc PP chii y l u sou: su dyng gdc k l bij; chung minh BA; BCcung song song vdi mot dudng thdng; chung minh ABC thudc gloo tuyIn cua hoi mdt phdng phdn biet; ehung minh ABC cd cung hinh c h l l u qua phep ehilu song song cd phuong song song vdi AB; chung minh ABC Id dnh euo ba d i l m thdng hdng qua mot phep ddi hoy mdt phep ddng dpng; chung minh tpa dp cua d i l m C Hiod mdn phuong Hinh euo dudng thdng AB; ehung minh AB =\i AC; TTPP giup HS hinh thdnh cdc tri thdc su vdt mdi ehdng hpn, d l phot hien mot quy ludt; mot djnh If; mdt quy tdc cd t h i cho HS khdo sdt mot trudng hpp rieng lay h/ nql bd todn hope khdo sdt cdc hien h«?ng thye Hen Tu dd nhd HD phdn tich so sdnh, tdng hc^, khdi qudt hod d l phdt hien menh de mdi TTPP gdp phdn quyit djnh viec hinh thdnh boi dudng cdc thao tdc tu eua HS, tren CO so dd ren luyen cho HS khd ndng sdng tqo Todn hgc Cd nhi/ng bdi todn, neu dya vdo logic binh thudng, TTPP thdng dyng thi khdng t h i gidi dupe Chung \a phdi su dyng tu linh hopt, phdi cd khd ndng quan sdt, ddnh g i d , nhdn xet d l tim cdc mdi lien he bdi todn Ta se su dyng edeh ddnh gid cdc b i l u thirc de Hm Idi gidl TTPP giup HS ung xu vd gidi quyit nhOng tinh hudng tuong tu hgc tap cung nhu cudc sd'ng: HS di/qc truyen thy nhimg TTPP Hm tdi Idi gidl cdc bdi todn thong qua li/pc dd budc euo G.Polya (Hm h i l u ndi dung bdi todn dpc biet lien tt/dng tdi cdc bdi todn lien quan, ede menh de lien he vdl bdi todn, xdy dung chuong Hinh gidi, thyc hien chuong trinh dqy, k i l m tra k i t qud vd nghien cuu Idi gidi) se giup hp khd ndng phdt hiSn vd'n de, gidi q u y l t ede vdn d l H/ong ung Hong thye t l * Vien Khoa hoc gias due Viet Nam " Tnrong Dir IH dai boc dan tqc San Son Cdc cd'p d p cOo TTPP / Dqy hgc tudng minh TTPP mdn Todn d trudng phd thdng Vlee dqy hqc tudng minh, TTPP Id dd'i h/qng trung tdm euo mdt Hnh hud'ng dqy hpc cy the, k i t qud Id tri thuc ndv dupe trinh bdy mpt cdch tdng qudt vd tudng minh dudi dqng mdt quy tde, mdt thudt todn hay mdt danh sdch cdc Idi khuySn, chi dSn, Chfnh vi vdy, GV phdt rdn luy^n cho HS nhung HD dya tren TTPP dupe phdt b l l u mdt cdch td'ng qudt, khdng chi di>ng Ipi d muc d d thyc hdnh theo mdu dn khdp vdi TTPP ndy TOng budc hdnh ddng, phdl Idm cho HS h i l u dupe ngdn ngu dien td btnSrc dd vd tdp cho hp b l l f hdnh ddng duo trSn phuong Hen ngdn ngi/ dd Day hpc h/dng minh TTPP dupe phdt b l l u mot cdch tdng qudt Id mot nhung cdch 1dm dd'i vdl nhi/ng tri thuc dupe quy djnh ehi/emg trinh, Muc d d hodn chinh euo TTPP cdn dpy vd muc dp chdt che euo qud trinh hinh thdnh nhi/ng TTPP d d duoc quy djnh chuong trinh vd SGK hope cung cd dupe gido vien q u y l t dinh cdn cu vdo d i l u kl#n ey t h i euo Idp hpc Vi dy: to thudng d p dyng cdp dp day hpc tudng minh dd'i vdi nhCrng TTPP ed Hnh chd't thudt todn duqe quy dinh ehuemg trinh, SGK, nhu: PP gidi phuemg trinh bdc h o i ; quy tdc Hnh dqo hdm Clio hdm sd f(x) tqi d i l m XQ(bdng djnh nghla); day hqe gidi bdi todn bdng edeh Idp phuang trinh Muc chdt che cua qud trinh dan tdi ede cdng thuc nghiem ciJa phuong trinh bdc hai dupe yeu cdu Id phdi chung minh chu khdng chi thua nhdn Muc dp hodn chinh cua quy trinh gidl bdi todn bdng edeh Idp phuang trinh thi ehi cdn dung loi d budc Idn (Chpn dn sd -> lap phuong trinh -> gidi phtrang Hinh -> k i t ludn v l Idi gidl bdi todn) hoy cdn cd H i l ehi tilt hem cho mdi budc cdn thudc vdo npi dung hien tpi cua chuong Hinh, SGK hoy ddc d l l m thyc t l euo Idp hpc 2.2 Thdng tydo TTPP qud trinh HD Khde vdi cd'p dp tren, d ddy TTPP khdng phdl Id dd'i h/png ehij y l u cua mpt Hnh hud'ng day hpc cy t h i md chf cdn dupe thdng bdo Hong qud trinh day hpc Thdng bdo ndy cd t h i dupe lap Iqi n h i l u CO hpi khde nhau, d n h i l u thdi d i l m khde Ddy Id nhi/ng Hirang hpp thudng dp dyng cho cdc TTPP chua duqe quy djnh Hong ehuemg trinh nhung phdi thod mdn ede yeu adu: - Nhi/ng TTPP ndy giup HS de ddng thuc hien mot sd HD quan trpng ndo d d dupe quy dinh chuong trinh; - Vi$c thdng bdo nhCrng tri thuc ndy de hilu vd ton ft thdi gian e h d n g hqn, «quy Iq v l quen" Id mot TTPP khong dupe quy djnh chuong trinh nhung thod mdn cd hai dieu kidn trSn Tri thuc ndy c6 t h i dupe thdng bdo cho HS qud trinii hp HD d rdt n h l l u co hdi khde nhau, nhu: gidi phuong trinh bde coo dua bdng edeh chpn dn phy thieh hpp d l duo v l phuong trinh bdc hoi; chung minh dinh ll sin torn gidc bdt ki dupe duo v l trudng hpp tarn gidc vudng 2.3 Tdp luydn nhung hoqt ddng dn khdp vdl nhOng TTPP Trong trudng hop ndy TTPP khdng d u q e trinh b d y mdt edeh tdng qudt, tudng minh dudi d p n g mdt quy tde, mdt thudt todn; nd cung khdng dupe thdng b d o mot cdch rd rdng qud trinh HD HS tinh hql no mot cdch ngdm d n n h d vdo viSc dupe thye hiSn n h i l u HD tuong thich vdl mdt e h l l n lupc, mot djnh hudng gidl quyet ehung N d i cdch khde, d d Id nhi/ng HD dn khdp vdl TTPP dong duoc ndi den Muc d d hodn chinh euo TTPP ndy rdt khde d moi HS vi n d hien dien d HS nhu mpt kinh nghifim md hp tu rut dupe tu nhllu HD khde N h u vdy, cdch thuc ndy ed the dp dyng ddi vdl cdc TTPP dupe quy djnh rd hoy chi ngdm an Hong chi/ong Hinh, SGK De HS Itnh hpi tdt hon TTPP ta dang xet, GV thudng phdi td chi>c coc HD theo mpt mye dich xdc djnh trudc ehu khdng the hjy Hen N h i m g TTPP ndy cdn dupe GV van dyng mpt cdch ed y thuc Hong viec ro bdi tap, viec hudng dan vd nhpn xet hoy binh luqn cdc HD eua HS N h d nhCmg viec Idm d d , HS dupe Idm quen vd cd t h i vdn dyng Hong qud trinh HO Cdc d u d n g t r u y i n thy TTPP 3.1 Truyin thy nhung TTPP c6 tinh chit thudt loan Thudt todn Hi cd t h i h i l u Id mpl ddy thu HJ cdc thoo tdc dupe thyc hien Hen mot so huu hqn cdc so' lieu vd ddm bdo sou mdt sd huu hqn bt/dc se dqt mot k i t qud ndo d d ; hoqe Thudt todn Id mot ddy hi/u hqn ede budc duoc thuc hlSn theo mpt thu h/ nhd't djnh de gidi quylt mfit nhiem vy ndo Trong qud trinh truyen thy tri thi/c ndy, GV cho HS b i l t n h i l u hinh thuc the hien mot quy tac, d l \u d d hq ndm vung ndi dung tt/ng budc vd Hinh h j thyc ede bt/dc ciia quy tdc d d Trinh b d / rd cdc budc theo mdt so dd nhd't q u d n ; tap luySn Tap chi Giao due so (ki a - la/aoiH I i I cho HS thye hien tdt nhCrng chi dan thudt todn; Idm cho HS y thi/c dt/pc vd b i l t st/ dyng cdc cd'u true d i l u k h i l n eo bdn de q u y l t dinh trinh tu cdc budc Thdng quo viec truyen thy tri thuc ndy ehu trpng viec phdt trien tu thudt Hjdn cho HS Bdi le, tu thupt todn gop phdn phdt trien ndng lye Hi tue chung nhu: phdn tfch, tdng hpp, khdi qudt hda.,., ddng thdi hinh thdnh nhCmg phdm chd't nhu: tfnh khoa hpc, ki ludt, tinh phe phdn vd thdi quen k i l m tra 3.2 Truyin thy nhung TTPP ed tinh ehd't tim dodn TTPP cd tinh ehd't tim dodn boo gdm cdc HD: quy Iq ve quen, khdi qudt hda, tuong ty hda, Hm \6\ Idi gidi, Nhi/ng quy tdc, PP Hm dodn chi td nht/ng gpi y d l gidi q u y l t vd'n d l ehu khdng phdi Id thuqt todn ddm bdo chdc chdn ddn hii su thdnh cdng Cho nen cdn ren Iuy6n cho HS tinh mem deo, linh hopt, b i l t dieu chinh phuong hudng cdn thilt d l ddn tdi sy rfidnh cdng Truyin Hiy TTPP mang Hnh chdt tim dodn thifdng dtrpc thyc hien theo hai cd'p dp: thdng bdo TTPP Hong qud trinh HD; tap luy&n cho HS nhung HD dn khdp vdi TTPP md ta mong mud'n ho b i l t thuc hien G Tiii lifu tham khdo Nguyin Ba Kim Phinmg phap day hoc mdn T o i n NXB Daihocsupiigm H 2006 La Diic Minh - Nguyen Thi Quy nh Nga "B6i duOng tri thiic phuong phap cho hpc sinh day hoc mOn t o i n a t r u a n g ph6 thOng" Tgp chi Gido due s6' 244/2010 BiJi Van Nghj V&n d u n g li loan vao thyc tien day hpc mOn Toan a trudng ph6 thong NXB Dgi hoc sir phgm R2009 Dao Tam - Tran Trung T6' chirc hoat ddng nhan thiir day hpc mon Todn a trirong Trung hpc phd thdng NXB Dgi hoc suphgm H 2010 Nguyen V3n Thuiln Gdp phdn phdt trien ndng luc tu logic vd siJe dung chinh xdc ngdn nga todn hgc cho hgc sinh ddu cdp trung hpc phS thdng dgy hgc Dgi sd' LuSn kn ti^n si Giao due hpc, Trucrng Dai h p c Vinh, 2004 Edgarmorin- Tri thuc ve tri thirc (Le Difin dich) NXB Dgi hoc qudc gia Hd Noi, 2006 Thiet ke cau hoi trac nghiem (Tiip theo trang 24) chua chdc dd cd dp gid tri (cd diem so dn djnh, nhung khdng dupe edi edn do); nhung ngupc Iql, mdt bdi TN ed gid tri thi chdc chdn cd dp tin cdy Dd gid trj lien quan d i n mOc dp md bdi TN dd phye vy duoc cho mye dich cOa su ludng vdi nhdm ngudi ta mudn khdo sdt, Thdng thudng, ed mpt sd lopi «gid Hj" nhu; ddng thdi Hen dodn, npi dung, khdi niem tqo Idp Trong Ht/dng hqp soqn thdo cdc bdi thi TN, khdng cd thdi gian de thi thu vd phdn tich cdc cdu hdi cung nhu todn bdi thi, GV cd the st) dyng sy phdn dodn de xdc djnh gid Hj cua bdi thi, Cd t h i ndi kiem tra, DG KQHT eua HS chi ed tde dyng nd dupe t i l n hdnh cd muc dich, cd ke hoqch, gdn vdl ede chuan D G Viec ddi mdi kiem tro, DG tren co sd chudn k i l n tht/c kl ndng eua mon hqc se gdp phdn ndng coo chd't lupng gido dye cdc nhd trudng phd thdng, khde phye sy phdt trien khdng ddng deu v l kinh t l xd hpi vd dieu kien gido dye khde gii/a cdc VLing, mien; ddng rtndi se tpo su binh ddng v l CO hpl hpc tdp cd chdt luong cho mqi HS, khde phye hien tupng «qud tdi" day hpc, qua dd hinh thdnh edeh DG thdn thien, tqo sy ty Hn vd thu hpc tdp dd'i vdi cdc em Q Tai lieu tham khao Le Due Ngpc V3n tat ve lirung vii d a n h gia qua hpc tap giao due dai hpc NXB Dgi hoc qu&c gia Hd N^i 2001 Nguyen Thi Lan Phuemg - Phan Thj LuyfEn "Dinh gia kft qua hpc tap mdn Toan phd thdng theo chuin kit?n thirc, kl nSng", Tgp chi Gido d^c, &6 237/2010 D^o Tam - Tr^n Trung Td chuc boat ddng nhSn thuc day hoc mdn Toan o trinmg trung hpc phd thdng NXB Dgi hgc suphgm H.2010 SUMMARY Ministry of Education and Training has issued standards of knowledge, skills for high school programs Currently there have been some documentation done SUMMARY preparing and teaching standard So It is necessary To improve the quality ot teaching mathematics to inspect, evaluate standard to ensure the teachers should always aim to equip the intellectual implem&->tafion of objective secondary program This methods for students This article refers the types, levels article presents the process of designing objective test and ways of imparting the Intellectual methods In questions to assess learning outcomes of students teaching mathematics at high Schools according to the standard of knowledge, skills Tap chi Giao due so (ki a • la/aoii) # ... 1dm dd''i vdl nhi/ng tri thuc dupe quy djnh ehi/emg trinh, Muc d d hodn chinh euo TTPP cdn dpy vd muc dp chdt che euo qud trinh hinh thdnh nhi/ng TTPP d d duoc quy djnh chuong trinh vd SGK hope cung... trinh, SGK, nhu: PP gidi phuemg trinh bdc h o i ; quy tdc Hnh dqo hdm Clio hdm sd f(x) tqi d i l m XQ(bdng djnh nghla); day hqe gidi bdi todn bdng edeh Idp phuang trinh Muc chdt che cua qud trinh... dupe quy djnh chuong trinh nhung thod mdn cd hai dieu kidn trSn Tri thuc ndy c6 t h i dupe thdng bdo cho HS qud trinii hp HD d rdt n h l l u co hdi khde nhau, nhu: gidi phuong trinh bde coo dua bdng