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Tu lieu tham khao So SO nam 2013 PHAT HUY TINH TICH ClTC VA SANG TAO CUA HQC SINH TRONG MOI TRITONG KHAO SAT TOAN NGUYEN THI DUVeN'''' T6M TAT Khdo sdt todn Id mgt liip egn dgy hge ldy hge sinh ldm Irung[.]
Tu- lieu tham khao So SO nam 2013 PHAT HUY TINH TICH ClTC VA SANG TAO CUA HQC SINH TRONG MOI TRITONG KHAO SAT TOAN NGUYEN THI DUVeN' T6M TAT Khdo sdt todn Id mgt liip egn dgy hge ldy hge sinh ldm Irung Idm Tiep can ndy dd vd dang dugc nghien ciiu vd dp dgng cdc Ihue hdnh dgy hge de ddi mdi viic hoc lodn eua hge sinh Bdi viil ndy trinh bdy tdc dgng ciia liip can khdo sdt lodn den tinh lich cue vd sdng Igo cita hoc sinh Irong qud trinh hge todn cita cde em dga tren mdi nghien cim dinh tinh ve tiep cdn ndy Tir khoa: khao sat loan, quy trinh khao sat loan, mdi trudng khio sat toin ABSTRACT Promoting students' being active and creative in mathematical investigation environment Mathematical investigation is a student-centered teaching approach This approach has been being studied and applied to teaching practices lo innovate students' mathematics learning This paper presents Ihe impact of mathematical investigation approach on students' being active and creative during their mathematical learning process from a qualitative research on this approach Keywords: Mathematical investigation, mathematical investigation process, mathematical investigation environment I Md dau Phat huy tinh tieh eye va sang tao eiia hpe sinh qua trinh hpc toan li mdt nhitng yeu ciu cap thiit ciia nln giio dye nudc ta giai doan hien nham dap iing yeu cau ddi mdi viec day hpc toan nha tnrdng phd thdng va theo kip xu hudng tiln bp giio dye toin fren thi gidi Mac dii chuong trinh toan da duac ddi mdi hucing din viec phit frien tu toan hpc eho hpc sinh, nhien viec hpc toan cua mdt bp phan cac em hpc sinh van chua dim bao dupe ylu td tich cue vi sing tao [2] Nghien eiiu cua tic gii niy ehi ring hau het hpc sinh, ke ca cac hpc sinh cd TiiS Trudng D^i hpc Su pham Hue nang khieu toan chi dupe giao nhitng bii toan mang tinh quy trinh la ehu yeu Cac em it cd ca hpi khim phi nhiing bii toin mang tinh thieh thuc, yeu eau kha nang giii quyet eac van de thyc tien va cie loai hinh tu bac cao Vi the hau hit hpc sinh it cd himg thu vdi eac gid hpc toin cua minh Trong luc dd, nhieu nghien cim da chi rang hpc sinh th|t sy bj cudn hilt vio mpt gid hpc toin neu cac em dupe hpc toin mdt mdi trudng ehua dung nhieu ylu td thach thuc va kich thieh tri td md, tudng tupng cua cic em [4] Nhilu tilp can day hpc da dupe dl xuat dl tim kiem cic mdi trudng hpc tap tuang tac nhim thiic diy vipe hpc toan ciia hpc sinh nhu: tilp can hdi-tim, giii quyet vin dl, khio sat toin Trong Tap chi KHOA HOC DHSP TPHCM dd, khao sat toan dugc xem la tiep can day hge cd the mang lai nhieu co hgi cho hge sinh hoc toan mdt each tich cue va sang tao Tiep can dgy hoc da va dang thu hut su quan tam, nghien ciiu ciia cac nha giao due tren the gidi nham tim kilm each thiic de cai tien viec hoc toan ciia hge sinh va phat trien nang luc toan hoc cho cac em Tuy nhien, d nudc ta ti£p can van chua dugc quan tam nghien ciiu va ap dung mdt each rdng rai vao thuc tien day hge d trudng phd thdng Vi the, can tien hanh nhieu nghien Cliu hudng den viec tim hieu tac dgng cua tiep can khao sat toan len qua trinh hoc toan ciia hoc sinh nh4m phat huy tinh tich cue va sang tao cua cac em qua trinh hge toan Phuong phap nghien ciiu chinh dugc Sli dung nghien ciiu la phuang phap dinh tinh Hai hoat ddng chinh nghien ciiu la quan sat hpc sinh cac em hge tap mdi trudng khao sat toan va phdng vdn cac em trudc va sau cac tiet hoc dd Thanh phan tham gia vao nghien ciiu gdm cac hge sinh cua nhirng lap chgn ban tu nhien 11 A,,11 A, va 12 A, d mdt trudng trung hoc phd thdng viing ngoai d Hul Cdng cu ciia nghien ciiu la cac tinh hudng khao sat toan va bang cau hdi phdng \kn hoc sinh De thu thap du lieu eho nghien ciiu nay, cac cugc phdng van ban d^u se dugc thuc hien nham tim hieu v6 mdi trudng hge toan hang cua hge sinh Tilp den, cac quan sat va ghi chu \h cac chii diem du dinh thiic day tinh tich cue va sang tao ciia hoc sinh se Nguyen Thi Duyen dugc thuc hien cac em lam viec mdi trudng khao sat toan Sau do, cac cugc phdng vdn hge sinh se dugc tiln hanh nham tim hieu tac ddng ciia moi trudng khao sat toan len viec hge toan ciia cac em Du lieu thu dugc tu nghien Cliu se dugc phan tich mdt each djnh tinh Giai doan dau tien qua trinh phan tich dii lieu Men quan den viec viet cac ghi nhd tir viec xem lai cac bang ghi hinh va ghi am cung nhu dgc lai cac ghi chii dugc thuc hien quan sat va phdng van hoc sinh Nhiing ghi nhd la cac md ta tdm tat ve thdng tin thu dugc tir cac bang ghi am va cac ghi chii va dugc sir dung nhu nhung thdng tin ban dau de tim hieu ve ca hdi hge tap da sinh giiia cac hge sinh tham gia vao nghien ciiu cac em lam vi?c mdi trudng khao sat toan Viec ma hda do- lieu se dua tren nhihig ghi nhd va dugc thuc hien bang each diing cac tir khda ia dgt cdu hoi, dua cdc y tudng vd cde gid thuyei, thu thgp vd xir li dir lieu, dua cdc kit ludn vd cdc tong qudt hoa, sir dung suy lugn quy ngp vd suy lugn ngogi suy Nhung tir khda la nhiing thuat ngu Men quan den cac td quy trinh khao sat toan ma hge sinh se tiln hanh cac em hge tap mdi trudng day hge liy khao sat Iam trung tam Chiing cung la nhihig td cd mdi lien he mat thiet vdi tinh tich cue va sang tao cua hge sinh qua trinh hge toan Mgt tiep can diln giai se dugc sii dung phan tich dit lieu dl riit nhtmg kit luan tir nhiing thdng tin thu dugc Sd 50 ndm 2013 Tu" li§u tham khao Phat huy tinh tich circ va sang tao cua hpc sinh moi trirdng khao sat toan 2.1 Quy trtnh khdo sdt todn Khao sat toan la mgt tiep can day hoc da dugc cac nha giao due tren thi gidi quan tam nghien ciiu va ap dung vao thuc tiln day hoc tir nhung nam 1970 Tuy nhien, hien cac nha giao due van chua tim dugc su thdng nhat quan niem vS thuat ngii Mgt sd nha giao due ling hg quan dilm cho rang khao sat toan la tilp can md [3, 7] Hg eho ring khao sat toan la qua trinh hge sinh kham pha cac bai toan md bang each tiep can tir nhilu dudng khac nhSm dua din nhilu y tudng toan va nhilu ldi giai khac Ndi each khac, khao sat toan la qua trinh hge sinh tien hanh kham pha cac bai toan cd mue dich, quy trinh va ldi giai mang tinh chat md Trong dd, mdt sd nha giao due khac lai dua quan niem khac ve cdng viec khao sat toan [5, 9] Trong nghien ciiu ve qua trinh nhan thirc ciia hge sinh cac em hoc tap mdi trudng khao sat toan, hai tac gia Yeo va Yeap cho rang khao s^t toan la qua trinh hoc sinh kham pha cac bai toan bang nhirng thao tac nhu dac biet hda, phdng doan, kiem chung va tdng quat hda Vi khao sat toan dirge xem xet tren gdc dd la mot quy trinh nhan thiic nen nd khdng bd hep vao cae bai toan md ma cd the tich hgp vao cac bai toan ddng Tir hai quan diem neu tren, cd the xem khao sat toan la qua trinh hge sinh tim tdi, giai quyet cac tinh hudng toan hge phiic tap thdng qua cac hoat ddng nhu nghi van, thii nghidm, kiem chimg, khai quat hda va phan anh Mgt quy trinh khao sat toan gdm cac buac theo sa dd sau: Dat cau hdi gia thin-et /" Phan anil, da J ill gia ^4 Thu thap liir heu tnu kiem idi giai ^ t/ Ket hiiin tdng quat hda Hinh Quy trinh khdo sdi lodn Budc diu tien frong qui trinh khio sat toin lien quan din viee tim hilu tinh hudng ban diu dl dat cic cau hdi, tim kiem cie myc dich dl khim phi, xay dyng eac gia thuylt bing cic hoat ddng thye nghipm toan nhu dac biet hda, doin va thu, tim kilm quy luat Budc tilp theo lien quan din cic boat ddng nhu thu thap dit lieu, tim phucmg in dl giii quylt van de, kilm chimg hay bic bd cac gia thuylt Budc kl tilp lien quan din viec nit cic ket lujn va tdng quit hda Bude cudi cung quy trinh lien quan din cac hoat dpng nhu thao luan, Tap chl KHOA HQC DHSP TPHCM danh gia ve cac phucmg an giai quylt vin dl, md rdng cac ket qua tim kilm dugc d^t cac cau hdi de tiln hanh nhung kham pha xa han Qua trinh khao sat toan khdng dimg lai d budc ma vSn tilp tuc vdi nhiing chu trinh tilp theo Cac budc quy trinh khao sat toan khdng dua cac chi din cu the cho viec kham pha cac tinh hudng ri^ng le ma chi cung cip cac ggi y mang tinh dinh hudng dl kich thich ngudi hge theo dudi cac nghi van cua minh qua trinh kham pha kien thiic Nguyen Thj Duyin 2.2 Moi trudng day hpc ldy khdo sdt todn ldm trung tdm Mdi trudng day hoc liy khao sat toan lam trung tam la mdi trudng su pham ed dae trung the hien d viec hge sinh tiln hanh cac hoat ddng khao sat toan eac em giai quylt cac nhiem vu hoc tap dugc yeu cau Cd bdn ylu to ciu nen mdi trudng day hge liy khao sat toan lam trung tam: tinh hudng khao sat, khao sat toan, hoc sinh, giao vien theo sa dd sau: Hinh Moi trudng dgy hpe ldy khdo sdt ldm trung tdm IChi hoc t$p moi trudng khao sat toan, hge sinh bj cudn hiit vao cac tinh hudng khao sat ddi hdi cac em phai dat cac cau hdi, dua cac gia thuySt, thu thap dii lieu va tien hanh nghien ciiu Kiln thiic toan se dugc chilm linh bdi nhiing hge sinh tich ci^c tham gia vao qua trinh khao sat toan de tim kilm cau tra ldi cho nhCing cau hdi ciia minh Van de ca ban nhat qua trinh khao sat toan khdng phai la viec hge sinh dua dugc cau tra ldi diing ma viec cac em dat dugc cac cau hdi va tim kiem eho minh mdt muc dich de kham pha tinh hudng ban dau Khi tien hanh qua trinh khao sat toan, eac em se dat cho minh cac cau hdi cd dang nhu nhirng van de nao dugc dat tinh hudng nay, dieu gi se xay neu ta xem xet phan hay phan ciia tinh hudng, nhiing chiln luge giai quylt vin dl nao se dugc sir dung, nhtmg phucmg an glal quyet van de nao cd the chap nhan, phuang an nao la tdi uu Cac em ciing sir dung hai kieu suy luan dac trung kham pha toan dd la suy luan quy nap va suy luan ngoai suy Neu 189 Tu" li§u tham khao nhu suy luan-quy nap dupe xem la qui trinh suy l u ^ nhim dua din ket qui tdng quit tu hOn ban cic kit qua tuong ty tit mdt sd trudng hpp dat biet thi suy l u ^ ngoai suy li qua trinh suy luan nham tim kiem hoac xay dyng mpt gia thuyet phii hpp nhat de giii thich cho nhiing gi quan sat dupe [1] Mac du khdng cd gi dam bio gia thuyet tren li dung nhtmg cic kieu suy luan cd the mang den sy sing tao hpc toan Vai frd cua ngudi giio vien la cung cap cho hpc sinh cae tinh hudng khao sit toan mang tinh van de eao vi chira dyng nhieu co hpi cho hpc sinh khim pha kien thirc toan Giao vien li ngudi dua cac chi dan mang tinh dinh hucing that sy can thiet de trp giup hpc sinh lim sing td eae nghi van nham giup eac em theo dudi nhirng kham phi xa hon qui trinh khio sat toan 2.3 Dgc trung cua Ilnh hudng khdo sdt todn Cic tinh hudng khao sit hop li va ldi cudn la yeu td co bin nham dam bao thinh cdng cua mdt gid hpc toan mdi trucmg day bpc liy khio sat lim trung tam [6] Cic tic gii niy cung chi rang xay dyng mdt mdi trudng thiic diy viec hpe vdi nbieu ca hdi dl hpc sinh tranh luan va phin anh li cin thiit nhung chua du nlu tinh hudng khio sat khdng dii thach thiic vi thilu tinh kich thieh qua trinh khim phi toan eiia hpe sinh Vay mpt tinh budng khio sit toan phai dim bao nhdng ylu td gi dl cd thi thue diy viec khim phi toin eua hpc sinh nhim phit huy tdi da tinh tich eye nhan thirc cua cac em? Mdt tinh hudng khio sit 190 SS 50 nam 2013 toin duoc xem li ed tinh thiie day viee kham pha toin cua hpc sinh neu nd tich hop dupe mpt sd dac trung sau: Kieh thich hpc sinh dat cac nghi van va cac gii thuyet qua trinh kham pha kien thirc Tir dd, cic em tich cyc thu thap, xir li cic dd lieu de tim cau tra ldi cho nhitng nghi van cua chinh minh, khang dinh hay bac bd nhihig gii thuyet da dupe dua ra, tim kiem eic quy luat hoac di din cac tdng quit hda, tilp tuc de xuat nhung cau hdi hay nhiing gii thuyet mdi de theo dudi nhirng khim phi xahan Mang lai nhieu ca hdi de hpc sinh phat huy tri tudng tuang vi phit trien thdi quen suy nghT mdt each sang tao Mdt hpc sinh cd the tiep can tinh hudng hpc tap dudi nhieu gdc dp, dat dupe nhieu nghi van vi gii thuyet khic de md rdng tinh hudng khao sit ban dau thi cac em cd nhieu ca hdi de phat huy thdi quen suy nghT mpt cich phan ki vi nang luc sing tao cua bin than Ddi hdi hpc sinh phai tich hop mdt each sing tao cic kiln thitc va kT nang khdng ehi cua mdn toin ma cua cic mdn hpc khac Hpc sinh cd co hdi sir dung cic kien thire vi kl nang lien mdn theo each thyc tl nhat khim phi kiln thuc toan hpc Dieu cd nghTa li each thirc mi hpc sinh suy nghT de giii quyet eic nhiem vu hpc tap phai gan gidng vdi cich mi cac em suy nghT ddi mat vdi tinh hudng tuong ty eudc song hang Vira dem lai himg khdi cho hpc sinh nhung vira du thich thiie dl kich thich cae hpc sinh theo dudi nhimg thic mac, nghi vin cua minh qua trinh Tap chi KHOA HOC DHSP TPHCM kham pha kien thirc Mdt mat, hge sinh phai cd hiing thii va thay viec kham pha linh hudng hge tap la dang lam va cd y nghTa TLT dd cac em mong mudn tien hanh viec khao sat va mong mudn thuc hien cdng cac qua trinh khao sat Mat khac nidi hge sinh phai nd lire tdi da de tiep can tinh hudng tiiy theo kha nang ciia ban than minh Dieu ddi hdi linh hudng hoc tap phai cd nhieu diem bat dau phu hgp vdi trinh dd khac ciia cac hoc sinh lap hoc Thiic day qua trinh giao tiep va thao luan gitra cac hoc sinh tdp hoc Nhiem vu HQC tap truyen thong - Cau hdi dugc dat bdi giao vien - T^p trung vao cac hoat dgng ghi nhd nhan biet va ap dung mang tinh quy trinh - Khuyen khich cac hoat dgng nhd lai va Ihuc hanh - Tap trung chu yeu vao kien thirc va kT nang mdn toan - Thieu tinh thuc te va it dugc dat vao mdt ngu canh cu the - Viec md rdng bai toan dugc thuc hien sau giai bai toan ban dau - Cho phep ngudi hoc sir dung it chien luge hge tap giai quyet van de • Hge sinh chii )eu lam viec mdt each ca nhan giai quyet cac bai toan Nguyen Thi Duyen Tinh hudng phai mang lai ca hdi de hge sinh giao tiep va tranh luan vdi ve eac y tudng toan hge mdt mdi trudng tuong tac d cae em lam viec mgt each ca nhan va hgp tac, ciing chia se cac y tudng de tien hanh cac khao sat xa ban Cd the thay rd sir khac biet gitra mgt tinh hudng khao sat toan va mdt nhiem vu hge tap mang tinh tiuyen thdng so sanh chiing vdi nhau: Tinh huong khao sat toan - Tinh hudng ban dau co the giao vien hoac hoc sinh dua nhiing cau hdi kham pha tinh hudng tiep theo thudng dugc dat bdi hge sinh - Khuyen khich cac hoat ddng kham pha kien thiic bang viec thir nghiem, tien doan dac biet hda tdng quat hda vdi trgng tam la giai quyet van de - Khuyen khich viec suy nghT, tudng tugng va phan anh - Mang den cho hge sinh ca hdi sir dung kien thiic \a kT nang lien mdn bang each tich hgp cac tinh hudng thuc te vao mdi trudng khao sat toan - Mang tinh thue te va dugc dat mgt ngir canh nao dd - Viec md rgng bai toan dugc chiia dung tinh hudng ban dau - Ddi hdi ngudi hoc phai sir dung nhieu chiln luge hge tap khac - Khuyin khich su hgp tac cua cac hoc sinh vao viec kham pha tinh hudng 191 Tu' lieu tham khao Mdt quy trinh kha him ich viee giiip giio vien lim quen vdi viec thiit kl cic cau hdi hieu qui day hpc toan duoc dl xuit bdi Sullivan va Lilbum [8] se dupe v§n dung de thiet ke cic tinh hudng khao sit toan Quy trinh niy gdm ba budc nhu sau: Budc 1: Nhan mpt chil de cin day Bude 2: Thiet kl mdt cau hdi ddng vi tim cau tri Idi cho cau hdi dd Budc 3: Thiit kl tinh hudng khio sit toin tuong img mi qua trinh kham phi tinh hudng bao him viec tim cau tri ldi cho cau hdi ddng ndi tren Xet vi dy ve viec thiet ke mpt tinh hudng khao sat toan: Budc 1: Chu de bai hpc li sd trung binh Budc 2: Cau hdi ddng cd the li: Biem thi lot nghiep cudi cdp cdc mdn Todn, Vdn, Li, Sinh, Sir vd Anh vdn cua bgn An ldn lugt Id 7, 8, 6, 5, vd Biem trung binh cdc mdn thi lot nghiep cua bgn An Id bao nhieu? Budc 3: Tinh hudng khao sit toin tucmg img Ii: Biem irung binh edc mdn Ihi lot nghiep cuoi cdp Todn, Vdn, Li, Sinh, Sir vd Anh vdn cita bgn An Id Biem thi mdi mdn cita bgn An Id bao nhieu? Rd rang viec khim phi tinh budng niy se giiip hpc sinh tim dupe nhieu Idi giai khic trpng dd cd ea cau tri ldi cho cau hdi ddng tucmg img Trong viee tri ldi cau bdi ddng hucing hpe sinh din viec ap dung kiln thue mang tinh quy trinh tbi tinh budng khio sit toan niy se mang lai nhieu ca hpi dl cac em thyc hinb ve khii niem sd trung binh 192 SS SO nam 2013 nhim hilu sau ban vl khai niem niy 2.4 Tinh tich cifc vd sdng Igo cua hoc sinh moi tru&ng khdo sdt lodn NhOng tinh hudng khio sat toan cd tinh thuc diy viee bpc se mang den hirng khdi eho hpe sinh va kich thieh eic em kien tri tim kilm nhtJng khim phi xa ban Kit qua tir viee quan sit lap hpe da eho thiy nang lye suy luan, dac biet la suy luan quy nap va suy luan ngoai suy dupe phit huy cac em kham pha cac tinh hudng khao sit toan Khi tiln hinh cac boat dpng khio sat toin, hpc sinh se diing suy luan quy nap de de xuat cic gia thuylt thdng qua viec tien hanh cae boat ddng dy doan, thir nghiem, tim kilm quy luat, tdng quit hda Cic em se diing suy luan ngoai suy dl dua eac gii thuylt phu hpp nhit tir nhirng dit lieu da cd de khim pha tinh hudng ban dau Cd the thay ro dieu niy qua viec phan tich dap img cua hpe sinh cac em lim viec vdi tinh hudng sd hinh Tinh hudng (so hinh) Du dodn sd hgng tdng qudt cua cdc ddy so lam gide hinh vudng, ngU gidc Tinh hudng niy dupe thiet kl de day tiet ty chpn chuang Day sd, cap sd cdng va cap sd nhan, Dai sd vi Giai tich Icip 11 Nang cao Muc tieu cia tilt hpe niy la nham giiip hpc sinh lim quen vdi chien lupc tim kiem quy lu|it, cu the li tim kilm quy luat de du doan ket qua cua mdt sd bai toin frudc day dupe phat bilu dudi dang ehimg minh cic dang thirc d bii Phep quy nap Giio vien se diing md hinh bieu diln tryc quan tit cie philu hpe tap dl giii thich cho hpc sinh thuat ngu sd hinh Dyng mdt da giic Tap chi KHOA HOC DHSP TPHCM Nguyen Thi Duyen deu ldi k dinh (k>3) vi canh li dem vj A la mdt dinh eua da giic dd, thyc hien cac phep vi ty tim A ti sd 1, 2, , n-1 (n > 2) se thu dupe nhirng da giac diu k eanh vi ty vdi da giac ban dau Tren cic canh ciia da giic dd, xuat phit tir dinh A danh dau eie diem each deu mot khoing bang don vi Sd cic diem dupe dinb dau tren tat ca cic mien da giic dyng dupe gpi la sd k-giac thit n cua day sd k-giac Tiep din hpc sinh Idp dupe phan thinh cic nhdm vi dupe giao cac philu bpc tap cd chita md hinh bilu dien trye quan cua cie sd k-giae dl ty khim phi Day sd tam giic: Hpc sinh dim sd chim tren mdi hinh bleu diln vi tim sd hang thit n cua day sd niy li tdng n so bang dau ciia mdt cap sd cdng cd sd hang dau li vi cdng sai li 1: " 1, = t , = l + t, = l + + t, = l+2 + + t =1+2+3+4+ •+n-n(n+l)/2 Day sd hinh vudng: Hoc sinh dem sd cham tren mdi hinh bieu dien va tim sd hang thu n eua day sd la tdng n sd hang dau ciia mgt cap sd cgng cd sd hang diu la va cdng sai la Mdt sd hge sinh thi phat hien quy luat khac, cac em nhan sd hang thii n day sd la sd chinh phuang n": s, = Sj=l+3 s,=l + + s,=l+3 + + ^ = l+3 + + + - + ( n - l ) = n' S, = I s, =2= s, =3= s,=4= s„ =n" Day sd ngu giac: Tuang tu hoc sinh tim sd hang thii n ciia day sd la tdng n sd hang dau cua mdt cap sd cgng cd sd hang dau la va cdng sai la 3: p = l + + + + - + ( i l - ) p,-l P,!=l+4 p, = l + + p, = l + + + 10 Hge sinh khdng dimg lai d viec tim kilm sd hang tdng quat ciia cac day sd tam giac, hinh vudng va ngu giac ma cdn t\r minh dat cac eau hdi de kham xa han ve tinh hudng eac sd hinh Cac em thSc mic lieu cd the du doan sd hang = n(3n-l)/2 tdng quat cua mdt day sd luc giac va day sd k-giac vdi k >3 tir tinh hudng hay khdng Mdt sd hge sinh da nhin dugc su tuang tu tim kilm quy luat du doan sd hang tdng quat ciia day sd tam giac, hinh vudng va ngu giac Cac em 193 SS SO nam 2013 Tu' lieu tham khao nhan thiy t„ la tdng n sd hang dau cua mdt cip sd cdng cd sd hang dau la vi cdng sai li din s„ la tdng n sd hang diu cua mdt cip sd cdng cd sd hang dau la va cdng sai li vi p„ la tong n sd hang diu ciia mdt cip sd cdng cd sd hjng diu li va cdng sai li Tit dd cac em dua gii thuylt cua minh ve sd hang tdng quit h_, ciia mdt day sd iyc giic: Cd the ndi hpc sinh da sir dyng kieu suy luan ngoai suy md rdng kham phi tinh hudng niy Tir viec nhan quy luat ddi vdi sd bang tdng quit ciia day sd tam giic, blnb vudng va ngii giac, bing cich tucmg tu hpc sinh di den gia thuylt ve sd hang tdng quit cua day sd Iyc giac Cac em cung nhan thay sd hang tdng quit cua day sd tam giac, hinh vudng, ngii giac vi luc giic deu ed sd hang dau Ii va edng sai bang sd eanh eiia cic hinh dd tru di nen cic em ciing dl xuit mdt gia thuylt vl sd hang tdng quit ciia mdt day sd k-giac vdi k>3 li tdng n sd hang diu cua mdt cip sd cdng cd sd hang diu la vi cdng sai la k-2 M; s =t„_i+t„ Co the thay nang luc giao tiep toan hge bang cac bieu dien bgi eua hoc sinh se dugc phat huy cac em lam viec mdi trudng khao sat toan Hge sinh khdng nhiing lam toan vdi cac bieu dien dai sd ma cac em cdn dung cac bieu dien hinh hoc nhu mgt phuang tien de tien hanh qua trinh suy luan ngoai suy nham tim kiem cac gia thuylt tien hanh qua 194 hay u.=l(2 + (n-l)(k-2)) Mdt sd hpc sinh cdn tiln hinh nhimg khim pha xa hon ed gang tim kiem mdi lien he giira cac sd hinh niy Cac em dua mpt sd du doin tbu vi ed gang tim kiem mdi lien he giira cic sd hinh dya tren bieu dien hinh hpc cua chung: • # p„ =n+3t„_| trinh khao sat toan Ben canh do, viec co gang tim kiem bieu dien bgi qua trinh khao sat toan da lam cho tri tudng cua hge sinh phong phii hon Hoc sinh da dua dugc mdt sd dang bieu dien khac cua day sd (n') Tir day cac em cung tim mdi lien he giiia cac dang bieu dien khac cua da\ sd (nM vdi mo Tap chi KHOA HOC OHSP TPHCM hinh hinh hpc bieu dien tdng S =l'+2-+ +n- Cie em da sudung mdi lien he giiia cic bieu dien hinh bpc dd de dy doin ket qui cua S, nhan thay Mdt sd hpc sinh cdn tien hinh nhirng khim pha xa ban cd ging tim kiem phuong phip tinh tryc tiep S, Cac sd hang ]-, 2- n- tdng Iam cic em lien tudng den viec su dung cic bang dang thitc dang (l + xf vdi x=0,l,2 , Tuy nhien eic em edng eie hang dang thirc 3'- (-ttJ)-'- ^'r t ?^ < Nguyen Thi Duyen 3S,=(l+2+-+n)(2n+l) nen s n(n+l)(2n+I) Sau dd eae em diing phep chimg minh quy nap de kiem chimg dy doin cua minh ve theo ve thi eic sd hang ]-, 2', , n- bi triet tieu nhtmg lai tim tdng S, = ! + 2+ +n Dieu dd Iam eho eie em nghT den viec diing cic hang dang thifc dang tuong ty nhung bac phai cao hem don vi la (i + x)\ Cac em thay x = o i, ,TI vio hang dang thiie dang (i + x)': !'-,}' ^ Ij y , *" n -(1*4^ J = ^ fj)i.=fatjXffl-ltir ruT f ,