PHAN IJGH C ic BIEU HIEN SIU U M CUA HOC SINH KHI THK HIlH GAC THAO TAC TH BUY 00 BAN IRONG BAY HOC OAI sd VA GIAI l)CH ThS NGUYEN THj MY H A N G * Trong day hqc toin d phd'''' thdng, d i cd rat nhilu qu[.]
PHAN IJGH Cic BIEU HIEN SIU U M CUA HOC SINH KHI THK HIlH GAC THAO TAC TH BUY 00 BAN IRONG BAY HOC OAI sd VA GIAI l)CH ThS NGUYEN THj MY H A N G * T rong day hqc toin d phd' thdng, d i cd rat eua bai toan la: x > -1; y > -1 nhilu quan did'm va y kiln neu v l nhi/ng Phuang trinh (2) tuong duong vdi: n (a+x) - x = sal lim cua hqc sinh (HS) g^lal cac bai tap n(1 +y) - y (3) Xet ham sd t(t) = n (1 +() - /cd dao toan.Chinghan,I.A.Komenskydakhingdjnh:"Bat ki mqt sal lam nao cung cdthelam eho HS hqc kem di h i m l a / ( ( ) = ^ nlu nhu giio vien (G V)_khdng chu y tdi sai lam Tnidng hgp 1:Mdit&{-'\ ;0) => t'(t)> => /f^/dong do, bing cich hudng din HS tunhin vasda chua, bidn Td (3) suy f(x) = f(y) x = y Do dd, bp khic phue sai lam" Thuc tiln eho thi'y, chat lupng day hqc toan d tmdng phd' thdng da quan tam dd'n phuang trinh trd ;t'-l2xi'+20/=0 he vd vipc phit hipn v i sda chda sal lam eho HS; nhidn, nghidm trdn (-1; 0) kha ning giai toin ciia cic em vin edn ban ehl Tmdng hgp 2: Vdi t e [0; ») =:> r{t) 0, y > 0; x < 0, chdng minh cie kd't qua toin hpe, hid'u ehua dung y < (mi'u chd't d day l i td (1) cd thd'suy x v i ban chi't ndn vipc van dgng kiln thuc vao giai bai tip ycung da'u) Nguydn nhin dan de'n sai lam cua HS la cac em chua n i m vdng npi dung kidn chua chit chd thde: "Nd'u ham so f(x) dan didu trdn (a; b) thi tu Vidg: PT dng dung tinh don didu eua him sd f(x) = f(y) vdi x, y e a; b) se tuong duang vdi Chung ta thu dupc kit qua: "Neu him sdt(x)dan dieu X = y" G V can luu y cho HS ring, ndi ham so trin a; b) thi td t(x) = i(y), vdi x,y& (a;b) se tudng ddng bie'n, nghjch bie'n thi ludn phai g i n vdi t i p ducmg vdix=y" Tuy nhidn, khdng nim vung ban xac djnh, nghTa la dong bie'n, nglijch bie'n tren chi't dan tdi HS chi nim dupc: "Neu him so t(x)dar\ khoang nao Khi giai he phuong trinh, xva ychua dl$u thi f(x) = (f(y) o x = y° ma khdng ehi rd f l i ham hin da cung thupc mdt miln, edn neu chung ttiupc so dan dipu tren (a;b) va x,y e (a; b); tddd, HS da mic mdt miln thi can ed su li giai x i c dang sai lim giai toan Ching han, vdi he phuang trinh | i - " f : ' f : ° ' " ,,>,HS giai nhu sau: dilu kien \H\*x)-H\*y) = x-y (2)' ' * Kkoa Toan, Tnftfni Bai hpc Vinh Tap ehi Gido due so 3011 43 (kil-1/2013)- Sai lam so sanh cac phep bien ddi cua phuong trinh sang phep bien Khi giai toan, ddi HS PT gia thilt cua bii toanddi cua bat phuongttinh;chuye'n td vipc giai bii tip sai din tdt khdngtimduqc hoictimsai da'u hidu chung,nay sang giai bai tip khic cung dang; chuyen td eie nhung dilm giong eua cic du kidn vi khdng phep bie'n doi cua day sdsang phep bidn ddi cua him hie'u dupc mue dich nhin thde eua vide so sanh (soso, thi khdng phai tat ea eie thao tic dd deu dung sanh de lim gi, so sinh nhu the nio) nen liet ke mdtTuy nhien, nhieu HS da mac nhidn cdng nhin cac cich khdng cd he thd'ng eac di'u hidu eua cic dd'i ket qua tuangfc/dd.Dudi diy, chung ta PT mpt sdsal tupng dupe so sinh ma khdng nit dupe kit luan lam eua HSttidngqua cac vi dg sau: nio la canttiiltva ca ban nhat Vidu:Tm dieu kidn cin va du debit phuong trinh Vidu:So sinb hal cich glal eua bai toan sau: Mgted nghiem nhdmHS ISemgdm 7HSndva8HSnam Cdbao Cd HS giai nhu sau: Oleu kidn cin va du d l bat nhieu cich chgn HS nhdm eho ed it nhi't phuang trinh ax'+bx+cs:0.(a*o) ed nghipm la mdtHSnQ A = b'-4ac>0Cich /.-Chpn HS cd it nhat mdt HS nd xay HS da ip dgng tuang tudilu kidn ed nghipm ciia eiefai/dnghppsau:-1 HSnuvi4HSnam,sdcich batphuong trinh bic hal nhuddivdlphuang trinh bae chpn la: c]ci=490; - HS nu va HS nam, sd cichhai Trong tmdng hop nay, dieu kipn A = *= - 4ac s chpn la: c^C, = 1176; -3 HS ndvi HS nam, so cich chi la dilu kidn du chu khdng phai li dilu kipn cin de chpn li: c,'c;=98o; - HS ndvi HS nam, sdeachbit phuang trinh ax^ +ftx+c> 0, (a 9s 0) cd nghidm ehpn li: c,'cj = 28o;-5HSnu,sd'cachchpn la: c,' = 21 Ching ban, ddi vdi bat phuang trinh x'+X+1 >0, blet Khi dd, sdeich ehpn thda ydu elu bii toan thuc A = -3 < nhung bit phuang trinh edngbi^m vdi mpl;r la: c',ci+c-c^+c,cl+c^c',+c,' = 2947 Khi day hpc chu dl Phuang trinh vi ehii dl Bit Cich ^.'Sdeich ehpn HS bit ki nhdm la:phuang trinh ed nhieu net tuong tu nhau, nhien c,',; sicich ehpn HS khdng cd HS nd nao (hay khdng phai sutuong tunao eung dung Ching ban, HS thudng ngd nhin ve nhdng phep biln dd'i sau toin HS nam) li: c,' Suy sdeach chpn HS ed it(chu y ring cae phep biln dd'i sau dd'i vdi phuang trinh nhi't mdt HS nd la: c,'i - Q' = 2947 laaung()an):^.o=^„.,;^.^.|„„., ; H S so sinb v i ehi thay dupe ca hal each giai dlu dung, eie cich glal khae nhun^ cung cho mdt |/(^£|g(l)|o dip so Tuy nhien,GVcan giup HS nim duoc vi'n dl f(x)i:-g(xy ddiy li ndn lua chpn cich giai nao ddng tmdc mdt «(jr)ao bai toan dim? Khi nio thi lua chpn cich (dim tmeA/7W 2gU)«r;;_;;'.,,.,; Ax)ig-ixr a"'" " > a " " o /(x)^ g(x); tilp), nio thi lua ehpn cich (dim gian tilp)? GV cdthehudng HS vio mgc dieh so sanh tmdng log./U)2 log.,«U)llAx)ig(x) [glx)iO [g hop niy la vide lua chpn cich giai phu hop Neu dim so phan tuttongtip A cdtinhchat T la khd khan vi Do dd, day hpc chu dl bat phuang trinh, GV phai xet qui nhieu tmdng hpp din tdl ed the mie saiphai hinh dung tmdc nhung sai lam HS ed the mic lim li dim thda, dim thilu; dd, ta sedd'm sdphin phai de khic phgc kjp thdl eho eac em tu A khdng edtinhchat T, sau dd lay sd'phln td Sal lam khai quit hoa cua A tnidisd'vda dim dupe ta se thu dupe dap so Oe khai quit hda td't, dilu quan trpng nhat la HS Mpt nhdng da'u hieu denhan bilt each giai theophaitimra dupe di'u hidu chung va ban chat eiia cic each dim giin tilp thudng la dl bai cd ydu eaudd'i tuongriengle Mpt nhdng bleu hien sal lam "cd it nhat mdf phan tu thda dilu kidn nio dd" eua HS la khdng tim duge dau hieu bin chat, ngd nhin giQa dilu hieu ehung vi dau hieu bin c/)a/(ttijru Sai lam tuong tu hda Trong hpe tip, HS rat hay sudung thao tie tt/ongtupng hoi sal); khdngtieniugng dugcmdtsdtn/dng ti/ hda nhung cae em ddi khdng hie'u ring tuonghgp suy bi&i cua cii tdng quit ttJfhda ehi mang tinh dudoan, mpi kit c)ua ciia tuang Vidu: Khi day hqc khii nidm gkii ban eua him so tu hda dlu phai ehung minh mdi khing djnh dupe (Xem dep trang 59) tinh dung din cua nd Ching hpn nhu vide chuyd'n "'•'—£".,.,; 44 Tap chi Gide due so 301 (kil-1/2013) ttidi gian cho ca ngudi day v i ngudi hpe, m i cdn lam thu ttiap v i xu li thdng tin, kT ning tinh toan, kT ning sinh dpng bai hpc, tao dupe hdng ttiu hpe tip cho phin tich, td'ng hap ) • ngudi hpc Tii lieu tham khao Od'i mdi khau kid'm b-a - dinh gia kit qua Debbie Candau - Jennifer Doherty - Robert Hannafin hpc tap cua ngudi hoc John Judge - Judi Yost - Paige Kuni Intel teach to Trong qui trinh kid'm tra - dinh gii, nd'u nhin ttiay kit qua lam bai eua S V ehua tdt, ngudi day ed the the future (Chuong trinh day hpc cho tuong Iai cua dieu chmh phuong phip dpy va nqudi hpc dilu ehinh Intel) NXB Thanh niin, 2007 phuong phip hpe eho phu hop dd dat dupc mge tidu NguySn Thtf Hung - Hoang Vin Hai "Phat triln cac kl nang nghien cuu khoa hpc cho hpc sinh thOng qua day hpc da d l Phuang phap kid'm tra dinh g i i can phu bop, d?iy hpc theo du an" Tgp chi Gido dfic, sO' 274/2011 vdi cic binh thde phong phu (tu luin hay trie Trin Dinh Long Li thuyA hf thtfng NXB Khoa nghiem khich quan, kid'm tra vidt bay vi'n d i p , hgc vd kl thu4t, U 1999 kilm tra c i nhin hay theo nhdm ) Trong qua Le Dire Long Tai lifu bien so?n Phuong ph4p dsiy trinh ttiuc hidn chuang trinh mdn Tin hpc, chung m6n Tin hpc Dgi hgc suphgm Thdnh phdHS Chi Minh, tdl da thue hipn klhoaeh kid'm tra - dinh gii thudng 2006 xuyen thdng qua cic bai tip, bai thuc hanh v i eac SUMMARY chuydn d i c g thd' This paper presents a system of effective measDd'i vdi bii thi kit thue mdn hpc, ehu yd'u td' chde ures to enhance the quality ofeducaUon In informatics cho SV thi bing hinh thde thuc hanh Tuy nhidn, ndi at Hanoi University ofNatural Resources and EnviThese measures have totally reformed sevdung kid'm tra - dinh gii can phai bao quit dupe ndi ronment eral elements ofthe teaching process: curriculum, dung chu yd'u eua mdn hpc, trinh tinh trang dinh gii teachers, detailed course ouSine teaching methods khdng dung kit qua hpe tip ciia SV Ngoii ra, k l and methods ofassessing the academic performance of learners Survey results show that these meashoach kid'm tra - dinh gia khdng chi ehu y dd'n kiln ures have brought remarrkable training results In a posiUve direcUon ttidc, ma cdn phai quan tim ca cic kTning (kTning Trong day hpc mdn Toin, GV can tim cich ban checic nguyen nhin giy sai lam eua HS ea sai lam ehua xuat hidn GV ein du doin tmde (Tiep theo trang 44) nhdng sal lam HS cd t h i gap phai day hpc tdng tpi mpt did'm, sich giao khoa thudng bit dlu chu d l de cd nhihig bidn phip nhim ban chd, sda chua eho eie em; die bidt, HS khdng dupc sudgng , f(x) bing viduxetmpt him hdu tied dang ^ , t r o n g dd, nhdng khai quit khdng ed suy kiin, nhung phep h/ong g(x) l i ham so khdng xic djnh tai x=x^ nao dd Vi du, tu khdng cd co sd Nd'u GV ed eie phuong phip day Irong Oai so'va Giai tich 11 (ning eao) xet ham sd hpe phu hop se khie phgc duqc sal lim cua HS quitrinh giai toin • dup: cho bdi cdng thde/(x)=^^-y • Sau PT vide Phantichcac bieu hien sal iam llympldiysox,,x,, x^ max„5t2,v«eA''saoeho Tii lifu tham khao lim x„ = 2, liic dd ta ed lim f(xj = Khi dd, ta ndi ham Nguygn Ba Kim (chu bien) Phuong phip d^y bpc mdn Toin NXB Dgi hgc suphgm, H 2004 sd /cd ^Idl ban la x d i n dd'n HS se ehi cic TrSn Van Hao (tdng chii bien) Dai sd va giai tich 11 i^c didm vi dg d trdn l i : kit qua eua gidl han NXB Gido dvc Vift Nam, H 2011 khdng phg thupc vao cdng thde t(x), f(x) khdng xic SUMMARY djnh tai gii trj ma ;f dan tdi Tddd nhan thde sai lam la gkii hpn eiia him sd' cho bdi cdng thde t(x) xdan Basic logical operations Include analysis, synthetdi die'm nio ttii tai did'm dd ham so phai khdng xic sis, comparison, slmilarization abstraction and generalization Analysis and synthesis are two conflictdjnh Sal lim d diy l i HS da ngp nhin di'u hidu ing operaUons but are two sides of a single process: abstraction is necessary condition of generalization f(x) = ^ i l ^ khdng xic dlnh tai x = di'u hidu In this paper, we have analyzed the manifestations of high school pupils' mistakes in performing basic logical operations For each operation, we present ban chat some common mistake manifestations and examples (ki 1-1/2013)- Tap chi Gide due so 301 59 ...2 Sai lam so sanh cac phep bien ddi cua phuong trinh sang phep bien Khi giai toan, ddi HS PT gia thilt cua bii toanddi cua bat phuongttinh;chuye''n td vipc giai bii tip sai din tdt khdngtimduqc... xet qui nhieu tmdng hpp din tdl ed the mie saiphai hinh dung tmdc nhung sai lam HS ed the mic lim li dim thda, dim thilu; dd, ta sedd''m sdphin phai de khic phgc kjp thdl eho eac em tu A khdng edtinhchat... bin chat, ngd nhin giQa dilu hieu ehung vi dau hieu bin c/)a/(ttijru Sai lam tuong tu hda Trong hpe tip, HS rat hay sudung thao tie tt/ongtupng hoi sal); khdngtieniugng dugcmdtsdtn/dng ti/ hda