Tgp chi KHOA HQC DHSP TPHCM So 37 nam 2012 Dl/DOAN VA GIAI T H I C H NGUYEN NHAN SAI LAM CUA HpC SINH KHI HpC CHU DE PHAN S6 DU^6l N G 6 N NGU CUA DIDACTIC TOAN DUONG HOU TQNG'''' T6M TAT Sira chaa sai l[.]
So 37 nam 2012 Tgp chi KHOA HQC DHSP TPHCM Dl/DOAN VA GIAI T H I C H NGUYEN NHAN SAI L A M CUA HpC SINH KHI HpC CHU DE PHAN S6 DU^6l N G N NGU CUA D I D A C T I C TOAN DUONG HOU TQNG' T6M TAT Sira chaa sai ldm cdmdty nghia quan trgng trgng viic phdt triin lu HS, cing cd kiin thirc ki ndng ciia cdc em Qua sua chua sai ldm, nhdn thirc dung cua HS si ciing eo chdc chdn han Hiiu rd nhang sai ldm mdc phdi HS cd y thuc han Irgng ldm bdi tap di phong nhiing sai ldm khdc hgc tip Sai ldm cua HS biiu Men mudn hinh mudn ve vd nhiiu nguyen nhdn khie Tuy nhiin, chiing tdi chi mgng mudn du dodn vd giai thich sai ldm cua hgc sinh dudi ngdn ngu ciia didactic Todn thdng qua dgy hgc chi ii phdn sd Tu khda: sai lim, nguygn nhin, phin sd ABSTRACT Predicting and explaining the causes of students' mistakes in learning fraction using didactic mathematics Correcting mistakes has a very important effect in developing students' thinking enhancing their knowledge and skills Through correcting mistakes, students' perception will be more reinforced Understanding these mistakes clearly, students are more cautio when doing exercises, avoiding other mistakes in learning Students' mistakes are varied and due to various causes However, we only want to'predict and explain students' mistakes in learning fraction using didactic mathematics Keywords; error, cause, fraction Dit van de Ttt vifc nghign cim chucmg trinh vi thyc tg giing dgy, chung tdi da md hinh hda cic nguygn nhin sai lim cua HS hpc chu dl phin si Sai lam cua HS lign quan dgn cdc dgng bii tgp phin so phdc tgp Dilu niy cung ding nghTa vdi ngudn gic nguygn nhan sai lim cung rat phong phu Do dd, vin dl giii diich chung cung khdng dan giin Vi vgy, qua bii bio niy chiing tdi chi mong muon mft NCS, Tru'dng Bgi hpc Su phgnn TPHCM 130 phan nio dd lam ro nguygn nhan cic sai lim cua HS dudi gic df cua didactic Toin Sai lim nghiin cihi didactic Toin 2.1 Cic quan niim vi sai lam cic li thuyet hpc t^p Hpc thuylt vg hinh vi coi sai lim la sy phin inh ciia sy thiiu higu bilt hay su vd y, bit cin m i thdi Trong do, hpc thuylt kiln tgo lgi xem sai lim va phdt hifn sai lim la mft ylu td quan ttpng ttong vifc xiy dyng boat dpng nhin thdc cua HS vdi li Tgp chi KHOA HOC DHSP TPHCM nhu sau: tao sir mSt cSn' bang he tu ciia chii thd, vide nh|n sai lam tao didu ki^n thuan lpi dk vupt qua no va lam sinh m^t thd can bSng gia tang m6i Nguai ta cho ring sai ^ khdng phai la mot su kidn thii yiu xay mSt qua trinh No khdng nim ngoM kien thiic ma chinh la bieu hien cua kiin thuc Brousseau cung nhan manh den tim quan ciia viec nghidn cuu sai \km day hgc thong qua hai doan trich duoi day: "Sai ldm khdng chi dem gidn thieu hieu biet, ma hd hay ngau nhien sinh ( ), md cdn Id hgu qud mot kiin thicc trudc day dd tirng td cd ich, dem lgi thdnh cong, nhung bdy gid lgi td sai ldm hogc dom gidn la khong cdn thich hop niia Nhimg sai ldm thupc logi ndy khong phdi thdt thudng hay khdng du dodn duac Chiing tgo chudng nggi Trong hogt dgng cua GV cung nhu hogt ddng cua HS, sai ldm bao gia cung gop phdn xdy dung nen nghia cua kiin thirc thu nhdn duac." [l,tr.57] 2.2 Moi quan he cua sai lam vd cdc khdi niim khdc li thuyet didactic Todn 2.2.1 Sai ldm vd quy tdc hdnh dong Duffng Huu Tong Vi dii: wh vin dd sip thii tu cac s6 thap ph^n, ta da thiy 1^ su gin ket giua nhiJng c^u tr^ 16i sai cua HS cho phep ta nghi rang nhiJng sai lim phO hgp v6i vi?c dp dung mpt quy tic hanh dgng dugic ciu tir hai quy tic sau day: IVIgt algorit so sdnh cdc s6 nguydn Sy phdn bidt giGa cdc chG s6 truoc vd sau diu phiy Cdc quy tic hdnh dpng - dugc chi r6 qua vide nghien ciiu nhiJng cau tra loi sai ciia HS, vdn co thd mang lai cau trd 16i diing mgt s6 tinh hu6ng Nhirng tinh hu6ng xdc dinh pham vi hgp thiic ciia quy tac hanh dgng Tong quat hon, quy tac hanh dgng la nhimg kien thirc cua HS Nhirng kien thiic ndy co phgm vi hgp thuc cUa nd Mgt cdu trd ldi sai thudng den tic viec dp dung mgt quy tdc hdnh dgng a ngodi phgm vi hgp thicc ciia no 2.2.2 Sai ldm vd dinh U hdnh dong Trong li thuyet truong quan niem, cac dang thiic se cho phep mo hinh hoa hoat dgng cua HS, chi ro dac tnmg cua "t6 chiic bit bidn ve each iing xii cua HS mpt 16p tinh huong" Cac tdc gid ciia "Nhung ydu to co bdn cua Didactic Todn",[l,tr.85], cho ring chinh Gerard Vergnaud dd dd nghi phan tich cac dang thiic theo bon thdnh phan: Mot qt^ tdc hdnh dgng la mot mo liinh dugc xSy dung nham giai thich va chi ro nhirng kidn thiic ma HS da sii dung - Nhiing muc dich vd muc dich Quan nifm niy cung cho phep giai thich nguon goc cua mpt si khd khin vifc hpc tfp khii nifm cin bfc hai vi sau niy vifc hilu cic so thyc Nhu viy, lpi ich cua vifc md hinh hda bing thuit ngtt quan nifm cho phep giii thich mpt sai lim dn djnh ciia HS Giai thich sai lam cua hpc sinh hpc chii de phan so dudi ngdn ngii' cua didactic Toin 3.1 Kliu nhiim vj/ T,: "Tim phan so bing phan so dacha" SGK dl cap nhilu bii tip cd lien quan T, Ching ban, cau b bii tip nhu sau: b) ' 60 • ' 32 ' *Ki thudt r,.+ Ngu phan sd mdi cho bigt miu s6, tim sd dg miu sd cua phin sd thd nhat nhin (hofc chia) vtH si dd bing vdi miu sd cua phin so thu hai Sau dd, nhin (hogc chia) bl sd cua phan sd thu nhit vdi sd vtta tim dupc de cd dupc tu sd cua phan sd thu hai + Ngupc lgi, nlu phan s6 mdi cho bigt ttt sd, tim sd dg tu so cua phin sd thii nhat nhin (hofc chia) vdi so dd bing vdi ttt sd cua phin sd thd hai Sau dd, nhan (hogc chia) miu so cua phin si thu nhat vdi sd vua tim dupc dl cd dupc miu si cua phin so thd hai Tap chi KHOA HOC DHSP TPHCM Vi du: - = — HS co thd dua lai giai la HS thuang tim mpt so cho s6 cpng vai se bdng (3 + D = 6) va sau cpng tii s6 cua phan s6 v6i s6 vira tim dugc dd co dugfc so can tim (2+3 = 5) Hay noi khac di, dd tim mot phan s6 ma bdng vai phan s6 dd cho, cdc em thucmg suy Iuan "cgng" hon la suy luan "nhan" 3.2 Kieu nhiem vu T^: "So sdnh hai phansd" Dac trimg ciia kidu nhiem vu: hai phan so co cimg mdu so, hai phan so co cung tii, hai phan so khdc mau so Dya trdn dac tnmg tren, chiing toi cilia thdnh kieu nhiem vu nhu sau: So sanh hai phan so cung mau so, so sdnh hai phan so khdc mdu so, so sdnh hai phan so cung tii so Kieu nhifm vu T2a- "So sdnh hai phan so ciing mau so" Chiing toi dua mgt vi dy SGK Toan dai didn cho kidu nhiem vu: , Vidu: So sanh hai phdn so — * fS thudt Tj^ dugc trinh bay tucmg minh SGV nhu sau: Mudn so sdnh hai phdn so co ciing mdu so, ta chi cdn so sdnh hai tu so: phdn so ndo cd tu sd be han thi be han; phdn so ndo cd tu sd ldn hon thi ldn han; neu tu so bang thi hai phdn so bang Kieu nhiem vu T2b- "So sdnh hai phan so khdc m&u sS" * KT thudt r^j dugc phat bidu SGK nhu sau: Dirang Hieu Tong Muon so sdnh hai phdn sd khdc mdu so, ta cd thi quy ddng mdu sd hai phdn sd do, roi so sdnh tu sd cua hai phdn so mai Mgt dac tnmg khd li thii cho kidu nhi?m vu ndy: hai phan s6 dugc cho, CO mpt phan so 1cm hon vd phan so lai nho han Vf du dai di?n cho kidu nhidm vu nhu thd dugc dua phdn luydn tap ciia SGK: Bdi tap So sdnh hai phan so bang hai cdch khdc nhau: , 28 a) — va —: b) — • va — 21 Mpt each la so sanh theo ki thuat r^h, vay each lai tac gia mong muon a HS Id gi? De tim cau trd lai cho cdu hoi ndy, chiing toi trich dan doan trich sau SGV: Cdch 2: Ta cd: — > (vi tif so lan han mdu 7 ' ~ so) ; — < hay > — (vi tic sd be han mdu sd) o n Tif — >1 va 1>— tacd: — >— 8 Qua doan trich trdn, chiing toi dd xuit mgt kT thudt r^^ so sdnh hai phan s6 ma co mgt phan s6 lorn hon va phdn s6 lai nho han *Kt thugt T^^ Dem so sanh hai phdn s6 vai Phan s6 ndo Ion hon thi phan s6 lorn han phan so lai 133 sS 37 nim 2012 Tgp chl KHQA HQC DHSP TPHCM 12 14 VI du: So sinh — vi — Ldi giii 16 29 cua HS cd thi nhu sau: 12 < 14 ; 16 < 29 nen — < — Diy li sai lim rat biln 16 29 cua cic em Li cd thi giii thich li cic di quen vdi md hinh so sinh hai so ty nhign, ngn cic em di dp dyng md hinh dd vio bii toin trgn dan din Idi giii khdng chinh xic Kiiu nhiim vfi T2c "So sinh hai phin so cung tU so " Ndi chung, kilu nhifm vy niy khdng dupc trinh biy phin hinh thinh kiln thuc mdi nhu hai kilu nhifm vy tren Nd chi dupc nhic dgn thdng qua bai tip SGK: Bii t^p So sinh hai phin so cd cung tusd: b) So sinh hai phin sd: , , — va — ; — va — 11 14 11 *KX thudt r^^: + So sinh hai miu sd cua hai phin sd, -I- Phin sd nao cd miu so ldn ban thi nhd ban Nhieu em se cho ring mau so cua phan sd ldn hon thi phin sd dd ldn hon Vi cic em thiy tu sd cua chung bing roi nen chi cin so sinh miu sd nhu so sinh hai sd ty nhign 3.3 Kiiu nhifm v(i T3: "Sip xip day cic phin si theo thit tif tit bi din ldn " Sau diy li mot minh hpa cho kilu nhifm vy niy Nd dupc ttinh ttong SGK: 134 Bii t4p Vilt cic phin sd theo thit ty ttt bg din Idn: 6,4.5 2.5.2 b) a) 3'6'4 7'7'7 * Ki thugt fj.- + Kllm tra xem, cic phan so dupc cho cd cung miu so hay khdng? + Nlu cic phin so cung mau sd thi sip xip cic phin so dupc quy ve nhu li sip xip cic tu so + NIU cic phin so khdng ciing miu so thi phii quy dong mau sd Sau dd, tilp tyc thyc hifn nhu budc Ndi chung, hai kigu nhifm vy T2 vi T3 cd thi dupc gpi tat li sip thu ty dp Idn cua cic phin sd Mpt quan nifm sai tim cua nhieu HS li cic phin so cd tu sd va mau sd nhd hon thi phin sd dd nhd ban Ddi khi, vifc so sinh cic phin so mi chi xem xgt dgn vifc so sinh mau so cua cic phin- sd Dilu niy cd thi dupc giii thich li HS xem tu sd vi miu sd cua mpt phan sd nhu hai s6 ty nhign khdng lign hf gi Vidtf: s i p xip cic phin so sau theo 2 thu ty tu bg dgn Idn: —;—;— Cau tti Idi cd thi cd cua HS la: Chung tdi dy doin sg cd nhieu 3'5'9' HS mic phii sai lim nhu thi Li cd thi cd khiln HS lim nhu vgy bdi vi cic em cd khuynh hudng cho ring phan si ldn hon phin s6 nlu cd miu si ldn hon Hay ndi khic di, tdn tgi d HS mft djnh li hinh dpng chua chinh xac: Nlu < c thi —