RJH RHOHG TIT BHY THUAH HGHICH CHR HBG SINH TRRNG RAY HRC KHAI NIlM TOJUI HOC OTRiraNG P H O T H O N G Khdi nifm Id mdt hinh thifc tu duy phdn dnh mdt Idp dd''''i tugng N lu xem tu duy ciio con ngudi nhu[.]
RJH RHOHG TIT BHY THUAH HGHICH CHR HBG SINH TRRNG RAY HRC KHAI NIlM TOJUI HOC OTRiraNG P H O T H O N G Q K hdi nifm Id mdt hinh thifc tu phdn dnh mdt Idp dd'i tugng N l u xem tu ciio ngudi nhu mdt co the sdng fhl khdi niem se Id ede don vj nhd - te bdo d l cd'u thdnh eo t h i hr dd Do dd, hgc td't ede khdi nifm fodn hgc ehinh Id dilu kien eo bdn d l bdo ddm fu fodn hge ehinh xde Trong dgy hge todn d frudng phd thdng, mdt frong nhifng d i l u quon frgng nhd't Id hinh fhdnh eho hge sinh (HS) mdt hf thd'ng khdi niem Khi gdp cdc djnh nghTo dugc phdt bieu fheo hudng: «Ni'u A ihi 6" HS thudng hiiu vd vdn dyng td't chilu «Neu A fhi B", md if suy nghT tdi chilu nguge Igi «Nlu B fhi A" Ben egnh dd, HS thudng khd diln dgt mdt khdi nifm fheo nhilu each khdc cung nhu tim mdt djnh nghTo tuong duong vdi nd; tif dd, cdc em gdp khd khdn frong vife gidi quyet vd'n d l Dudi ddy, chiing fdi d l xud't mdt sd bifn phdp giup HS hieu vd van dyng mgt cdch vung chdc cdc khdi nifm todn hge, ddng fhdi bdi dudng hr thudn nghjch cho cdc em Glijp HS hieu ro tinh cd the ddo nguge cijo mgt khdi niem vd biet vdn dyng djnh nghTa khdi niem theo hoi chieu Djnh nghTa khdi niim Id mat thao tdc logic diing de Ideh sy vdt edn djnh nghTa lu nhung sy vdt tiip can vdi nd, cho Irong phgm vi cua djnh nghTa phdi chi duge nhifng thugc tinh co bdn chung tgo nin ngi hdm eua khdi niim Nhd ede thugc tinh ndy, ed the Ideh dugc tdt cd cdc ddi lugng cd cdc thudc tinh dd vd ehi nhifng ddi tugng dd dugc hgp nhdt vdo mgt the thd'ng nhd't nhd khdi niim dd cho (1; tr 115) To thudng gap ede djnh nghTo, phdt bieu dudi nhilu dgng khdc nhou nhu: « neu (khi) "; « ggi Id (dugc ggi Vi dy: 1) Hoi mdt phdng ggi Id vudng gdc vdi nhou nlu gdc giua chung bdng 90°; 2) Tam gide cd hoi egnh bdng nhou ggi Id torn gide cdn; 3) Gdc gli/a hai mdt phdng Id gdc glifo hoi dudng TtiS THAI THj H C N G L A M * thdng Idn lugt vudng gdc vdi hoi mdt phdng dd D l thyc hifn duge bifn phdp tren, qud trinh dgy hgc khdi nifm, gido vign (GV) edn: Thdng quo cdc vi dy v l khdi nifm, gidi thich cho HS hieu rdng, du dugc phdt b i l u d dgng ndo, djnh nghTa ludn Id mgl dieu kiin edn vd du Neu dgy hge djnh li, GV thudng xuyen phdi luu y eho HS khdng nhdm Idn giua d i l u kifn cdn vdi d i l u kien du fhi dgy hgc khdi nifm, GV cdn giiip HS hiiu dugc cdc edeh phdt b i l u djnh nghTo cd cd'u true logic fheo d i l u kifn cdn vd du Ndi edeh khdc, td'ted cdc djnh nghTa diu cd thi'ddo nguge dugc Vi vdy, GV ed the yeu edu phdt bleu djnh nghTa khdi niim theo cd hai chieu xudi vd nguge nhdm ren luyfn ndng luc su dyng chinh xde ngdn ngu todn hgc eho HS, giup cdc em ndm vi/ng ede ddu hifu dgc trung cuo khdi nifm; - Giup HS h i i u tinh cd thi' ddo nguge cuo djnh nghTo Id mdt dde finh ed vol frd rdt quon trgng Thu nhd't Id dung djnh nghTo de ed f h l phdn dodn mdt su vdt ndo dd cd thudc khdi nifm ndy hoy khdng (nhdn dgng khdi nifm) Thu hai Id mfnh d l nguge cuo djnh nghTo cd neu rd tinh chd't eiia mdt danh tif hode thudt ngif ndo dd md nd ed Vi vdy, GV edn quon tdm ddng thdi cdc tinh hudng, cdc bdi todn, hudng dan HS van dyng djnh nghTa, tif dd, cdc em mdi cd the van dyng linh hogt ede djnh nghTa todn hgc vdo qud trinh gidi quyet vd'n d l Vi du 1: Vdi khdi nifm dd thi ciia hdm sd, GV yeu cdu HS gidi quylt hoi vd'n d l , dd Id: - Kiem fro cdc diem cd thudc dd thj cuo hdm sd hoy khdng; Tim cdc dgi lugng hdm sd eua dd thi Vi du 2: Hinh chop Id d l u vd chi hinh chdp ed ddy Id gide d l u vd chdn dudng cao friing vdl tdm cuo gide ddy (Hinh hgc 11) Cd f h l van dyng hoi chieu cuo djnh nghTa de gidl bdi h>dn sou: *IUKMliMii,Mhglfiktc Villi Tap chi Glao due so 9 (ki i - la/aoia) Bdi todn: Cho hinh chdp d l u S.ABC cd egnh ddy bdng a SH Id dudng coo cuo hinh chdp, SH = a-j6 • O Id trung dilm cuo SH Xde djnh tdm vd finh bdn kinh mat edu ngogi Hep hinh chdp O.ABC [hinh 1) Nhdn xet: Tu gid thilt S.ABC Id hinh chdp dlu, fa cd ABC Id tom gide deu vd H Id tdm cuo AABC (djnh nghTo thudn) Khi dd, hinh chdp O.ABC thda mdn mfnh d l nguge, nen O.ABC Id hinh chdp d l u Tt/ dd, HS Hinh de ddng gidi duge bdi todn Tdp luyfn cho HS cdc hogt ddng khdi qudt hdo vd dde b i f t hda qud trinh dgy hgc hinh thdnh khdi n i f m , ti> d d , glup HS linh h$l tri thuc mdt cdch cd he thdng Khdi qudt hda Id chuyen tif mgt tdp hgp dd'i hrgng song mdt top hgp Idn hon cht/o fdp hgp ban ddu bdng cdch nSu bdt mgt so dgc diem chung cuo cdc phdn ft/ fdp xud't phdt (h/c Id di h) cdi rieng d i n cdi chung) Dgc biet hda Id chuyin tu vife nghien ciru mdt fdp hgp ddi fugng sang nghien cuu mdt fdp hgp nhd hon chuo f^p hgp dd eho (tue Id di tif cdi chung den cdi rifng) Thdng thudng, chiing to thye hifn dgc bift hda Ithl chuyen Kf mdt Idp dd'i fugng den mgt ddi h/gng cuo Idp dd Ody Id hai hogt dgng trdi nguge nhung h«3fng ho vdi nhou Khdi nifm v l mdt ddi lugng ndo dd xud't hifn y thire ciia ngirdi thudng theo cdeh sau: Ti> nhifng dd'i fugng rieng If (cdi rieng), bdng cdc hogt dgng phdn tich, so sdnh, tdng hop, trifu tugng hda vd khdi qudt hdo, tinh chd't chung ciio ede dd'i h/gng fdch ro vd dugc xem Id ddu hifu dde trung ciio mdt khdi nifm Cdc khdi nifm dgng ndy dugc ggi Id khdi nifm truu h/gng Vi dy 3: Oe dl d i n djnh nghTa khdi nifm day sd', GV cd the bdt ddu tif khdi nifm addy" vd'n quen thudc frong ddi sdnq hdng ngdy Mgt ddy gdm nhilu v^f xep thdnh ndng, chdng hgn: ddy nhd, ddy bdn, ddy nui, Trong khdi nifm ddy ed hoi y l u to: mdt Id nhifng vdt ciing logi, hoi Id thu h/ Clio cdc v^t dy Tuong ty, dp dyng vdo ede sd, mdt ddy sd' bao bdm nhieu so sdp fheo thii tif frudc sou Cdeh tdf nhd't de phdn bift cdc phdn h/ ciia day \d ddnh sd' chiing Khi dd, Tap chi Glao due s6 9 (k> i la/aoia) mgt ddy sd, ung vdi mdi so hr nhien fir frd di, to ed mgt so hoy mgt vgf hodn fodn xde djnh Odi chilu vdi djnh nghTa cuo hdm sd cho thdy, mdt ddy so thyc chdf Id mgt hdm sd xde djnh tren top N' hogc fdp hifu hgn M Id tgp cuo N' Tu dd, HS hinh fhdnh khdi nifm ddy sd Khi xdy dung khdi niem ddy sd, to chi giir Igi finh chd't chung dd Id sy tuong ung gii/o mdi so tu nhien fir frd di vdi mgt sd xde djnh, edn dyo vdo cdc tinh chdt khdc nhu: quan he giifa hoi sd lien flip ciJa ddy nhu the ndo hogc cdc phdn hi cuo ddy ed bj chgn hay khdng fa thu dugc khdi nifm v l ddy so tdng, ddy so gidm, day so bj chdn (tren, dudi), cd'p so cdng, cd'p sd nhdn Tif dd, giiip HS ndm vifng mdt edeh ed hf fhdng khdi nifm vd mdi quon hf giifa chiing Tdp luyen cho HS dien dgt djnh nghTo theo ede cdch khdc nhou vd tim djnh nghia h/ong duong Trong mgt khdi nifm todn hgc, chung to thudng chgn mgt hodc mgt nhdm ede finh chd't dgc trung de lay Idm djnh nghTo Vi dy: Mgt hinh binh hdnh ed cdc dgc frung sou: 1) Ld mgt fu gide cd cdc egp egnh dd'i difn song song; 2) Ld mdt tu gide ed ede egp egnh ddi difn bdng nhau; 3) Ld mgt tii gide cd mdt cdp egnh dd'i difn song song vd bdng nhou; 4) Ld mdt tu gide cd hai dudng cheo cdt tgi trung dilm Clio mdi dudng Cdc dgc frung d fren d l u ed t h i trd thdnh djnh nghTa ciio hinh binh hdnh Thdng thudng, dgc frung duge chgn Idm djnh nghTo, dd, ede dgc frung khdc Id djnh li dugc chung minh h/ong duong vdi djnh nghTa dd chgn Cung mdt khdi nifm, fa ed the djnh nghTa theo nhieu edeh tuong duong vdi nhou, mdi trudng hgp edn lyo chgn dgng ndo thich hgp nhd't vdi mye dich md to hudng tdi Chdng hgn, khdi nifm tdp gid trj ciio hdm sd cd f h l dinh nghTo bdi ede cdch sou ddy: Cdch 1: Cho hdm sd / : ,v -> /?;x i-> i = /u), tdp gid frj Clio hdm sd f Id tdp hgp r = [y = /{iiiiiX), hoy ndi each khdc Id fdp tdt ed ede gid fri f(x) vdi VATE.V- Cdch 2: Cho hdm so / : V ^ Rixt-i y = f{x), fdp gid frj ctia hdm so f Id tdp hgp tdf ed cdc so, soo eho, vdi mdi y^ thudc tdp dd thi phuong frinh f(x) = y ed it nhd't mdt nghifm x e ,V Su dyng each ed nhilu thudn Igi hon gidl cdc bdi tdp todn Chdng hgn, vdi bdi todn: «Tim gid trj Idn nhdt, nho nhdt eua hdm sd y=^ ^ ' , ddi vdi HS Idp 10, GV cd f h l su dyng phuong phdp mien gid frj d l gidi bdi todn ndy That vdy, ggi Y Id tdp gid trj ciio hdm sd Theo djnh nghTo, vdi mdi y„ e ) ' , phucmg frinh >•„ = ''* ludn ed nghifm Mgt khdc, phuong tnnh ndy tuong duong vdi y„.j- + (.v„ -2) ? + (i„ - n = o (1) Gidi phuong trinh (1) HS de ddng nhdn thdy, de phuong trinh ed n g h i f m thi yp = hodc I A = l,;,-2)'-4l(,,-l)>0; 9'°' '° *° CO ^^'"^3' Vgy, tdp gid frj cuo hdm sd Id n f - " ^ • Tu ddy, HS tim dugc gid frj Idn nhd't, nhd nhdt ctia hdm so N l u HS gidi bdi todn tren chi cdn eif vdo djnh nghTo tht/ nhdt md khdng edn cu vdo djnh nghTo thu hoi, cdc em se gdp khd khdn Do dd, GV n§n ggi dgng ca kit thue de nhdn mgnh hifu qud cua vife sti dyng miln gid trj, cung nhu Igi ich Clio vife fim them edeh phdt bilu khde ciio khdi nifm Tif dd, frong ehuong frinh Dgi so vd Gidl tieh 11, sou hgc phdn «Phuong trinh bdc nhdt ddi vdi sinx vd casx", HS ed f h l tim gid trj Idn nhdt, gid trj nhd nhd't eiia ede hdm sd r(x) md vife fim dieu kifn eiia y^ de phuong frinh /(jr) = )\, eo nghifm cd the dua ve tim dieu kifn cd nghifm ciio phuong trinh as\nx-t-bcosx = c; vi dy nhu bdi todn sau: tim gid tri Idn nhd't, gid trj nhd nhd't ciia cdc hdm so: a) y = cos r -i- sin x + ; 3cos.x-i-2sin;c-i-3 b) y = : 7-; cosx-sm.v-i-4 c) _y=2sin"x-3cos^x-i-2sin2x-i-2; , _sin"2x-3cof 2x-F2sin2j:cos2x 2cof2x+2 Mdt edeh d l tim ede edeh djnh nghTa khde ctia khdi nifm Id cho HS thiet lap sy tuong ifng da trj giifa khdi niim vdi ede thudc tinh eua khdi niem; h> dd, dyo fren sy phdn tieh ede thudc finh giif nguyin vd thudc h'nh cd f h l thay thi'di thilt ldp thugc tinh khdc hrong duong Vi dy: dgy hgc khdi nifm hinh chop deu d Idp 11, GV nen eho HS thief lap sy h/ong ifng frj sou: «Hinh chop diu" # ifng vdi tdp hgp cdc thudc tinh: «/d hinh chop ed ddy Id da gide diu, nghTa Id ede egnh bang vd cdc gdc bdng nhau" Oe thief ldp them cdc thudc finh h/ong duong, GV yeu cdu IHS phdn tieh d l xde dinh ede thugc tinh: «hinh ehdp'vd «cd ddy Id da gide deu' giif nguyen cdn thugc tinh «cdc egnh bin bdng nhau" co the thay the bdi cdc dde trung khdc h/ong duong nhu: «chdn dudng eao triing vdi tdm Clio ddy" hogc «cdc egnh bin tgo vdi ddy cdc gdc bdng nhau" Tir dd, khdi nifm hinh chdp diu img vdi cdc cdch djnh nghTo h/ong duong sou: «Id hinh chdp cd ddy Id da gide deu vd dudng cao cua hinh chdp di qua tdm eua ddy" hode «/d hinh chdp ed ddy Id da gide deu vd ede egnh bin tgo vdi mat ddy cdc gdc bang nhau"; Vdi cdch thilt ldp tuong ung nhu vdy, HS se van dyng khdi niem hinh chdp dlu vdo gidi quylt vdn de mgt cdch linh hogt, phu hgp vdi dde dilm Clio bdi fodn Chdng hgn, bdi todn: "Cho tii dien deu ABCD cd egnh bdng a Tinh ddi dudng coo h theo a" fhi dde frung eiia hinh chdp dlu nen xet din Id "dudng cao di aua tdm eiia ddy"; edn vdi bdi fodn "Cho tif difn dlu ABCD cd cdc egnh bdng a Tinh khodng cdch giifa hoi dudng fhdng AB vd CD" thi dgc trung cuo hinh chdp dlu phii hgp nhdt Id "cdc egnh ben bdng nhau" Vife khuyen khich HS tim them cdc djnh nghTa khde fuemg duong vdi djnh nghTa ban ddu glup cdc em khdng chi phdt trien mdt so ndng lye nhu: phdn tich, tdng hgp, suy ludn, md cdn ed fhl khde phye duge nhifng khd khdn qud tnnh gidi quyet vd'n d l Bdi vdy, trude mgt khdi nifm ey the, GV edn khuyen khich HS fim them cdc djnh nghTo tuong duong Khi HS dd tim dugc ede edeh phdt bilu mdi (tuong duong vdi djnh nghTa ban ddu), cdc em se bief vdn dyng vdo qud trinh gidi cdc bdi todn thich hgp ã ô* Trong dgy hge khdi nifm todn hge d phd thdng, neu GV quon tdm fdp luyfn eho HS khal thdc hai chilu ciio djnh nghTo, edeh fim vd phdt bieu djnh nghTo fheo cdc edeh khde nhou, ede dgc diem cd finh chdf nguge nhou se giiip cdc em phdt trien fu duv thudn nghjch, hieu sdu sdc, ddy dli vd ed hf thd'ng cdc khdi nifm Ti/ dd, HS biet vdn dyng vi/ng ehde khdrnif m todn hge frong hgc tdp mdn Todn • (1) Nguyen Difc Ddng - NguySn Van Vlnh Logic Toan NXB Tlianh Hda, 2001 (Xem liip trang 55) Tap chi Glao due so 299 (h i la/aoiai sinh d l fhi eho thi sinh (TS); - Ldm bdi thi: Sou ddng nhdp, HS se Idm bdi fhi fren hf fhdng thi fy ddng true hjyIn HS se duo lya chgn (mdt hodc nhieu) ctja minh qud frinh Idm bdi frong mdt khodng thdi gion djnh frudc; - Kit thue thi: Khi HS mud'n kit thue fhi hodc hit gid Idm bdi, hf fhdng se tien hdnh ket thuc bdi fhi cua TS dd vd duo kef qud chi tilt den tifng phdn fhi cuo TS; - Nhdn kit qud thi: Vife phdn logi phy thudc vdo kit qud fhi cuo TS Cd mifc phdn loai: Trung binh (50%-d0%), Khd tot (dl%-70%), Td't (71%80%),Xud'f sdc(81%-90%), Ndi bdt (91%-100%) Quy trinh truy cap: Ddng nhdp/Vdo thi/Chgn hinh thifc thi Tren hf fhdng fhi true tuyen ed hai hinh thuc tham gio thi d l kilm tra, OG kit qud hge tgp mdn Todn eua HS Idp 12 THPT: - HS ly thi: Di thorn gia Idm bdi fhi ty fren hf fhdng, TS ehi cdn kich chgn vdo ten bdi fhi cd sdn tren hf fhdng Id ed the Idm bdi fhi Vdi bdi fhi that ty do, TS ed the fhom gio thi vdo bd't eu fhdi gion ndo Hinh thuc thi ndy rd't phii hgp eho HS h/hge Sou kef thuc bdi thi, TS ed the xem Igi ehi tilt bdi thi Clio minh bdng cdch chgn chirc ndng «Bdo cdo chl tilt" d gdc trdi phio fren gioo difn Trong bdo cdo ehi tilt ndy hiln thj nhifng cdu trd Idi TS, gidi thich cuo ddp dn dung - GV id chuc thi: Bdi thi ed td cht/c ngudi qudn trj tgo vd cd hgn che v l fhdi gion tdn tgi bdi fhi, sou fhdi gion dd bdi fhi se frd v l frgng fhdi kit thuc vd TS khdng duge phep Idm bdi thi mde dii dd ddng ki O l fhom gio Idm bdi fhi ed fd chuc, TS phdi ddng ki fhi frudc fhdi gian bdi thi bdt ddu Trong khodng thdi gion bdi fhi tdn tgi (fheo quy djnh cuo ngudi tgo), TS cd the vdo thi bd't cu fhdi dilm ndo TS chi edn chgn dung bdi thi dd ddng ki, hf fhdng se hien thj mdn hinh sdn sdng fhi vd TS bdt ddu Idm bdi Cdc budc Idm bdi thi thdt ed td cht/c tuong ty nhu ede budc Idm bdi fhi that ty d tren Sou hodn thdnh bdi fhi, fhi sinh cd f h l xem video hudng ddn gidi de thi bdng edeh click chgn vdo fob «video hudng ddn gidi" St/ dyng hf thd'ng e-learning fodn 12 td chuc ihl frye tuyen de OG kit qud hgc tgp mdn Todn ctJo HS nhdm hinh fhdnh nhdn thue dung ddn ciJo HS v l ede ki fhi ddng thdi tgo d i l u kifn cho HS h/ OG Tif dd, hinh fhdnh cho HS ede kT ndng: hf Tap chi Glao due so 9 (ki i la/aoiai thdng hod, quo kit qud cuo kilm fro vd hr kilm tro dd phdn logi cdc kiln thifc v l gidi tich vd hinh hgc Idp 12; phdt hien nhifng chd thieu hut v l mgt kiln thuc, nhifng soi Idm gidi todn vd duo bifn phdp khde phye; kT ndng h/ rut kinh nghifm ve each hgc, phuong phdp hgc tdp mdn todn cho bdn thdn vd tim cdch dilu chinh cho chinh minh • Tai lieu tham khao Nguyfin Ba Kim Phuung phap day hoc m6n Toan NXB Dai hpe suphpm, H 2004 Dao Tam (chu bien) - Tr4n Trung Td chirc hoat dpng nhan thiic day hpc mon Toan a truvng trung hpc phd thong NXB Dpi lipc suphpm H 2010 Tran Trung (chil bien) - Dang Xuan Cuung - Nguyfin Van Hflng - Nguyin Danh Nam Ung dung cong ngh^ thong tin vao day hpc niOn Toan u tnrung phd thOng NXB Gido due Viet Nam H 201 I SUMMARY The use of E-learning in teaching and learning to meet the diverse needs of students: study anywhere, study anytime, lifelong learning, learning in an open and flexible way This paper presents the design and implementation of online test tools used in E-leaming system to test and evaluate the learning outcomes in Mathematics of Grade 12 high school students Boi diTffng tir thuan nghich (Tii'p theo Irang 58) Tai li^u tham khao Nguyen Ba Kim (chii biOn) Phmmg phap day hpc mon Toan NXB Dpi hpe suplipm H 2004 Thai Thj Hdng Lam "MfHsdbidu hi^nciJa tuduy thuan nghjch Irong day hpc Toan d truong phd thflng" Tap chi Gido due sd 272 (l^i 2, i 0/ 2011) Nguyin Van Thuan Gdp phdn phdt tri^n ndng luc tuduy logic vd sii- dung chinh xde ngdn nga Todn hpc cho hpe sinh ddn cd'p trung hpc phd tlidng day hpc dpi sd Luan an lien si Giao due hpc, Trucrng Dai hpc su pham Vinh, 2004 Tran Van Hao (tdng chu bien) Dai so va giai tich 11 NXB Gidoduc Vift Nam, H 2011 SUMMARY High school, forming firmly a system of concepts for pupils is very important This article refers to some measures of teaching concepts in order to help pupils understand and use them firmly, simultaneously contnbute to foster reversible thinking for pupils ... duong Vi dy: dgy hgc khdi nifm hinh chop deu d Idp 11, GV nen eho HS thief lap sy h/ong ifng frj sou: «Hinh chop diu" # ifng vdi tdp hgp cdc thudc tinh: «/d hinh chop ed ddy Id da gide diu, nghTa... ddy: Cdch 1: Cho hdm sd / : ,v -> /?;x i-> i = /u), tdp gid frj Clio hdm sd f Id tdp hgp r = [y = /{iiiiiX), hoy ndi each khdc Id fdp tdt ed ede gid fri f(x) vdi VATE.V- Cdch 2: Cho hdm so /... hf fhdng khdi nifm vd mdi quon hf giifa chiing Tdp luyen cho HS dien dgt djnh nghTo theo ede cdch khdc nhou vd tim djnh nghia h/ong duong Trong mgt khdi nifm todn hgc, chung to thudng chgn mgt