NGHIEN CIIU 1 ^ sur DONG DIEO D I I N TRUC OUAN Hd TRO DANH GIA NANG LOC TJNH TOAN COA HOC SINH TIED HOC I O I tvande Ning lye tinh toin (NLTT) I I mpt nang Iflc (NL) quan trpng trong tam NL chung cot[.]
NGHIEN CIIU ^ sur DONG DIEO D I I N TRUC OUAN Hd TRO DANH GIA NANG LOC TJNH TOAN COA HOC SINH TIED HOC GS TS DAO 1AM - TniiMg 6al hoc Vinh ThS PHAM TH! KIM CHAU - Tnriung Bai hpc Bdng Thip I.OItvande Ning lye tinh toin (NLTT) I I mpt nang Iflc (NL) quan trpng tam NL chung cot ldi ma Chflcmg trinh Giio dye thdng tong the 2015 de O l dinh gia (OG) mdt nhflng td cua NLTT cd nhieu phUOng thflc khic nhau, chung tdi tap trung vio d c h sfl dung bilu dien trye quan Qua do, hpc sinh (HS) dfldc trii nghifm vfla tim phflong I n gill quylt vin di (GQVD) vfla bdc Id cic bilu hifn cua NLTT l i m co sd phan bie cho thang OG Ddng thdi HS dupe phit triin NL ehuyen doi gifla ngdn ngfl thdng thfldng vdi ngdn ngfl trye quan va ngdn ngfl ki hieu 2.JC3C quan niem v l nang lu'c tmh t o i n cOa hpc sinh tieu hoc Cle nghifn cu\j vf NLTT trfn t h i gidi cd tfl rit l i u O Anh, ed quan nifm ve NLTT ciia Crowther (1959), Coekeroft (DES, 1982), DffiE (1998) Cic quan nifm vf NLTT ed diem tUong dong la sy hifu bilt v i ning lim vifc vcri nhflng eon so, nhan thfle khdng gian hinh hpc, bilu dien bing ngdn ngfl t o i n hpe nhfl ki hifu, dd thj, bilu dd, ti If phan trim, Chiln Iflpe d i thifn NLTT cCia Alien giai doan 2011 - 2020 md t i NLTT bao gom ning sfl dung sy hieu biet v i ki ning toin hpc di GQVO, d i p flng nhu d u cupe sdng mdi triidng xa hdi phfle tap Quan niem v l NLTT d Oc (2013) la kiln thflc, kT nang, hinh vi v i nang HS d n d l sfl dung toin hpc nhieu tinh hudng, Theo OECD (2008), NLTT l i nang sfl dyng, giii thieh va giao tiep thdng tin, 'j/ tfldng t o i n hpc tham gia vao cudc song xa hdi Theo Chflong trinh Gilo due thdng tong the cfla Bd GD&OT (2015), cic thinh t6 cfla NLTT bao gdm: - Sfl dung eic phip tfnh v i Ifldng cO bin: Sfl dyng dupe d c phep tinh sd hpc hpc tap; Ifldng dflpc kich thflde, khdi lupng, thdi gian d c trfldng hop don giin v i bflde d i u b i l t flde Iflpng - Sfl dung ngdn ngfl toan: Nhin bift v i sfl dung duoc eic thuit ngfl, ki hifu toan hpc, tinh chat dPn giin cHa sd ty nhien, mdt sd hlnh dOn giin; bflde d i u biet sfl dyng thing kf hoc t i p ; hinh dung v i vf phie hinh dang cfla cic hinh hinh hpc co bin; nhan bift v l bilu diln dflpe mdi lifn hf t o i n hpe gifla d c y l u td d c tinh hudng ddn giin hay b i i t o i n cd ldi van - Sfl dyng cdng cu tfnh toan: Sfl dyng dflpc d e dyng cy do, ve, tinh hpe tap; sfl dung dfldc miy tiiih d m tay vdi nhflng chfle nang tfnh toin don giin hoc t i p v i eupc songNguyen Thj Kilu Oanh da de xuat quan dilm phit triin NLTT d t i i u hpc gdm d c td sau [1]: -Thyc hifn thinh thao bdn phep tfnh sd hpe, tu tin flde IflcJng hpe tap v i cudc song; hiiu v i ed t h i sfl dyng eic kien thflc kT nang v l Ifldng nhi trfldng v i cudc sdng hing ngay; - Sfl dung chfnh xac, hifu q u i ngdn ngfl toin hpc nhfl d c thiiit ngfl, ki hifu toin hoc tfnh chit don giin cfla d c sd, tinh chat mot sd hinh hinh hpe, thdng tin thdng kf toin hpe d l GQVD niy sinh hpc tap v i cudc sdng; cd ning tfldmg tupng khdng gian nhU hinh dung, xle djnh v l sip xep, ve phic hinh dang d c ddi tuong don giin mdi trudng xung quanh, nim dupe tinh chit eo b i n eCia chflng; - Bilt vin dung suy luan logic, phan tfch va lya chpn dupe phuong an toi uu de GQVO ddn giin; xiy dyng md hlnh toan ve mdi quan he gifla d c dat Iflong, yeu td d l GQVD hpe tap va cudc sdng; - Sfldung hifu qua cdng eu, dyng cu ludng, tfnh toin nhfl d c loai thude, eke, compa, miy tfnh d m tay; bilt tinh t o i n vdi cac so Quan niem ca nhan ve nang liic tmh t o i n cila hoc sinh tieu hpc Tit c l nghifn eflu tren cd y nghTa quan trong vifc hinh thinh va phat triin NLTT efla HS tiiu hpe Tuy nhif n, de phfl hc^ vdi mue tifu OG, chflng tdi quan nifm NLTT gdm eae NL to sau: 3.1 Ndng liic tinh nhanh Cic bilu hifn chu yeu cua NL tinh nhanh bao gdm: Sfldungthanhthaoeic bifn phip tinh nham, biet ehuyen ddi hdp li d c h tinh phfle tap ve each ttnh ddn giin 3.2 Ndng luc sifdunp cdc ki thugt ttf Cac bleu hifn chii yeu cfla NL sfldung eic ki thuit tu bad gdm: Bift suy luan logic; bift dy doan v l kilm nghifm; bilt so sanh, phin tich, tong hpp, khai quit,.dl tim phUdng i n tdi flu GQVD; bilt quy la v l quen di tinh cac bieu thflc phfle tap 3.3 Nang lucsCrdung ngon ng&vd kihieu todn hge Cic bieu hifn ehfl yfu eiia NL sfl dung ngdn ngfl v l ki hifu toan hoc bao gdm: Biet ehuyin doi gifla ngdn ngfl thdng thfldng vdi ngdn ngfl trfle quan v i ngdn ngfl ki hifu; sfl dyng chfnh xae, hifu qui cic thuit ngfl, ki hlfu toin hpc, tinh chat ddn giin ciia cac sd va mdt sd hinh ddn giin; budc dau biet sfl dung thdng kf trdng hpc tap; hinh dung va ve phac hlnh dang eac ddi tfldng ddn giin moi trudng xung quanh 3.4 Ndng liicsitdung cdc phep tkih, quy tdc cong tfidt Cac bieu hifn chii ylu cGa NL sfl dung d c phfp tfnh, quy tic, edng thdc bao gom: Dim; thiie hifn thinh thao bon phep tinh sd hpc; van dyng dupe cic quy tie, cdng thfle eic tinh hudng cu t h i ; bilt flde Iflpng; hiiu v i sfl dung cic kien thfle, kT nang vf Ifldng n h i trfldng v i eude sdng 3.5 Ndng Iticsddung cdng cu tinh todn Cle bilu hien chti ylu cua NL sfldung edng ey tfnh toan bao gdm: Thuc hien thinh thao d e thao tic td, d t ghep, gap, ve, trfn eac cdng cy tfnh toan (thude thing, Ike, tranh inh, true sd, tia sd, sd dd, hinh ve, bing, bilu do, miy tfnh d m tay ); bilt sfl dung cac thao t i c tren cae cdng cu tinh toan de GQVD NLTT cd nhilu NL td vdi nhieu bilu hifn d d e mflc dp khae Khi tinh toin d l gill quyet tinh hudng hpc tip, HS phii trai qua rit nhifu hoat dpng v i thao tic tfnh toan Do do, viee phan hoach NLTT cic NL thinh td chi cd tfnh tUdng ddi v l giao thda Tuy nhien, vife phin chia la cd sd cho viec xly dung d c tifu chi cung nhfl hlnh vi OG NLTT eiJa HS cudi d p Tiiu hpe Sifl28-TWyiGS/2016-9 I NGHIEN CDUCan sfl dung tinh toan qua bilu diln trye quanpt Tinh toin qua bieu dien trUc quan Toan OG NLTTcfla HS tieu hpc vi nd phfl hpp n g u j ^ | j tiiu hoc 4.1 Biiu diin todn hge vd edc hinh thdc eda bieuday hoe Toin t i i u hpc die dilm tfl cfla HS tiiu hoc, nguyen t i c day hpe tfl true quan sinh ddng den tu diin todn hge Theo PISA, NL toin hoe phd thdng gdm nhilu NL trflu tflpng v i giii quylt nhflng khd khin cua HS tieu phin ma bleu dien toin hpe II mdt NL cd bin v i hpc troiig vifc tim nghTa cua tri thflc Vife tinh toan tren quan trpng Bilu dien toin hpc phin thinh pham trfl bleu dien trfle quan khdng chi l i eo hdi deOG NLTT eda nhfl saii: ThUc tf Gdm cic bilu dien thye t l d mfle dp HS m l cdn l i tinh hudng giflp HS phat trien NL sfl dung thip, thao tic trfle t l l p bing tay; Bieu tugng: Cae bilu ngdn ngfl toin hpc OInh gii nang lUc tinh toan cua hoc sinh tieu diln true quan sti dung cle hinh Inh, dd thj, sd do, bieu bing, ; Kl hiiu: Gdm d e btlu diln ngdn ngfl v i bieu hoc qua bilu diln trUc quan dien kf hifu [2] Bilu difn tnic quan ddng vai trd trung Mi^c dfch cfla Chflong trinh OG HS quoc te (PISA) la gian k i t ndi bilu dien thyc t l vdi bleu diln kf hifu DG NL ciia HS nhfl; NL sfl dung ngdn ngfl toin, NL mfl Tadao phin loai cle bilu diln giao due Toan hinh hoi va d c kT nang GQVO O Vift Na_m, NL sfldung ngdn ngfl toin dflpe xem l i mdt td cfla NLTT Mit thinh5 dangsau: - Biiu diin thuc ti: Cic bilu dien dUa tren trang thai khic, dfla vio d c bilu hifn cfla NLTT, ngdn ngfl toan thyc cfla ddi tUpng, tic ddng tnic tiep, cu t h i v i tfl nhien hpc dfldc hieu khdng chi gom cie thuit ngfl, kf hieu toan - Biiu diin bang md hinh thao tdc dugc Chflng nhfl hoc m i cdn md rdng tdi cic lo^i ngdn ngfl so dd, hlnh nhflng cdng cu hd tro day hpe Dd l i sy thay the hay cie vf, tranh Inh, bing, bilu dd Do do, vife thiet ke cic tinh hudng bleu dien trfle quan vfla cd t i c dung ho trp DG md hinh^il ve doi tfldng m l HS t i c ddng trye tilp - Bieu dien bdng hlnh dnh (bieu dien true quan): Cie mdt sd thinh td NLTT ciia HS t i i u hpe vfla dip flng muc btlu dien sfldung tranh minh hpa, sO do, d^ thj, bleu tieu OG cOa PISA Vidu: Vnh hudng phdn sdtrin dogn thang Diy l i loai bilu difn giiu tinh true quan v l sinh ddng - Biiu diin bing ngdn ngd: Cic bilu difn sfl dung ngdn ngfl hing ngiy d l dien dat Loai bleu dien bj chi phdi bdi cle quy udc nhflng thilu tfnh ngan gpn Bieu dien cd tinh md t l va tao d m giac quen thupc (vdi 2"= 2.2.2 gdm n thfla sd 2) Vdi HS trung hpe thdng, bai toin giai bing - Biiu diin bdng ki hiiu: Cic bilu difn sfl dyng kf cich sfl dyng gidi han n d i n tdi vd eUc Trong tinh hifu toin hpc nhfl sd, ki tu, bieu tupng Trong ChUpng trinh Toin tifu hpe, phan Idn cac hudng niy, chflng tdi mudn nhan manh vai trd hd tro kiln thflc dupe trinh biy dfldi dang trfle quan (tranh inh, ctia bieu dien trye quan viec ^ n h hfli^g HS tiiu trtic sd, tia sd, sd dd, hlnh ve, bing, bleu do) cung d c yfu hpc quy la v l quen d l tim k i t qui Chiing tdi minh hoa d u vf thao tic (dim, td, e l t ghfp, gIp, ve, flde Iflpng, gia trj phan sdqua bieu dien trfle quan, HS tfl vife quan sit • thao tie - dfl doin - khii quit se nhin thiy ket qui do, lufmg) 4.2 Quan niim cd nhdn vi Biiu dien trUc quan bai toin Todn tiiu lige vd tinh todn qua biiu dien trde quan Todn tiiu hgc Tfl cic kit q u i nghifn eflu vf bilu difn toan hoe v i dac dilm chuong trinh Toin tiiu hpc neu trfn, chung tdi d l xult hai quan nifm sau: Hlnh 1: Cde md Mnh bdng gidy trdng - Biiu diin tn/e quan Todn tiiu hoc la viec md Gil sfl Idp hoc ehia thinh 04 nhdm, phat cho moi t i hay bilu diln cie doi tflpng Toan tieu hpe qua cae md nhdm 01 md ninh 04 md hlnh d Hlnh l.Yeu clu hlnh trye quan nhU:Tranh Inh, true sd, tia sd, so do, hlnh moi nhdm gill quylt d c cau hdi tinh hudng trfn ve, bing, liilu dd bing cic thao tie dim, td, d t ghep, md hlnh cua nhom minh, sau dd trinh biy kit qui v i giai gap, ve, flde Iflpng, do, Ifldng thich each lam - Tfnh todn qua biiu dien tn/c quan Todn tiiu hgc l i vile thflc hifn nhung thao tic dfm, td, d t ghfp, gap, ve, flde Ifldng, dd, ludng; sd sanh, ddi chilu, phan Hinh Hlnh Hinh tfch tdnc| hpp, khii quit; thyc hifn cic phep ttnh sd hpc NLTT cfla HS t i i u hpe ehi dupc the hifn qua cie trfn mien g i i tri eua md hinh trye quan; cie thao tie ehuyen ddi gifla ngdn ngfl thdng thudng vdl ngdn ngfl hoat ddng giii quylt tinh hudng Chflng tdi thiet ke toin hpc v i ngdn ngfl trfle quan tren md hinh trye quan tinh hudng vdi nhilu hoat ddng Bing 1: Bdng 1: Cde hogt dgng gidi quyit tinh hudng cua HS cau h6i cia giio v\in Hoat dpng cua HS Bilu hifin tfnh toan cia HS (X^t mo hinh bing giay] (Lim cd sd phfin bac cho thang SG) 1, Hay thyc hien thao tic tren - GIp ddi bang gily - Lfdc Ifldng, chia bang gily lim 02 md hlnh d l xic djnh gii trj -Tfi mpt phan (Hinh 2) phin bing - Chua nhin each tfnh tdng theo edng thflc - Chuyin tfl ngdn ngfl kf hieu sang ngdn ngfl gii tri phan sfi teen bang phin sd — va ghi cdng thflc O-i) giay tfnh gii tri phin sfi —, IO*KHIIAH9CGIIIODyC NGHIEN CUU ^ - Chuyen tfl ngfin ngfl ki hieu sang - Phin tich: Phan bang gily ehfla td l i — Mudn cd ngdn ngfl gia trj phan sd tren bang giay — phii gap de ehia phan bang giay ehfla td lim 02 - Chuyfn tfl ngfin ngfl ki hlfu sang ngfin ngfl gia trj phan sfi tren bang gtay - Cach 1: HS khdng biet chuyen tfl ngfin ngfl gii tri trin bang giay = sang ngdn ngfl ki hifu - Cach 2: HS bift chuyin tfl ngdn ngfl gii trj tren bing giay sang ngdn ngfl ki hieu; bift phan tieh tong hpp, van dung eae ph^p tinh ehUa td la — Phin da td bing trfl phan chua tfi edng trfl phin sfi, phin bi^ va eae phan bang eiia don vi Hay thye hien thao tae tr§n phin bing md hinh vfla thyc hifn d Bflde -Tfi mdt phan (Hinh 3).Tinh tong: di xic dinh gii tri cfla tdng -Cich 1:Tinh true t i f p : - + i = ^ 4 gii tri eiia tong 4 Thflc hien thao tie tren md Cac hoat ddng cfla HS tfldng ty nhu eiu hdi Cac bieu hifn efla HS tUdng ty nhfl hinh vfla thye hien d Bflde 2 (Hinh 4) eau hfii d l xic djnh gia trj eiia tdng 1 • ,.- —+ —-i va ghi cong thflc tfnh gii tri cfla tong •- Cich 1: Tinh trye tifp tfing eua phin sfi theo -Bilu hien nhfltrong cich cua cau cieh quy dong mlu sfi hdt Tinh theo dch vat vl, sal - Cich 2: HS bilu diln tren doan thing lin Iflpt dfn sfit mat thfri gian - Bilu hien nhfltrong cich efla cau hdi d bflde thfl n, ta cd tdng sau: - Cieh 3: Nhay bin kT thuat tu i l l - Cach 3: HS khdng bifu dien tren doan thing, d e duy, bilt quy la vf quen de dfla bieu - +— + -I- + em phin tich: thflc phfle tap vf ddn giin, sing tao 2.2 2.2.2 2.2 ; Budc tfing bing each GQVO (phin sd thfl n eo mau sfi gfir Bflde tfing bing ( n thfla sd 2) Hay tinh tdng i bude thfl Cich gap trfn md hlnh hlnh trdn va md hinh hlnh vudng thflc hifn tflong tu (Hinh 5,6) Cach gap trfn md hinh hinh tam giie nhu sau: Gap ddi mdt canh d l cd trung diem, kf doan thing dl qua dinh cdn lai efla tam giic v i trung diem viia gap; tam giic dflpc chia lam hai phin bing (Hinh 7) Chung tdi ehi minh hoa cich gap m l HS t i i u hoc thudng sfl dung MA Vidu 1: Tinh hudng ludi tam gidc diu Hmh Hinh Hmh 10 Hinh 11 Chiing toi thilt ke tinh huong theo cic cau hdi ning dan dp khd Bing Vcfl HS t i i u hpe, clu hdi moi tinh hudng trfn tuong ddi khd Cach thiet ke d e ciu hdi theo t r i t ty ngu y quy luit cflng cic bilu dien trye quan tflong flng Urn HS thay van de dOn giin, cd the giii quyft dflOc Kit luan Hinh Hinh Hinh? Khi quan sat mdi nhdm trinh bay kit q u i v l giii Chung toi da tifn hinh phin tieh hifu qui cfla vifc sfl thieh d c h lim, HS c l ldp phit hifn dii thye hien trfn d e dijng bieu dtin tmC quan DG NLTT cfla HS cudi d p md hinh khic nhflng d c h GQVO tUOng ty nhau.Tfl (Xem tiep trang 22) dd, HS khii quit d c h GQVO eho loai toin niy sfi 128-THilN65/2016 • 1 ... hoc sinh tieu diln true quan sti dung cle hinh Inh, dd thj, sd do, bieu bing, ; Kl hiiu: Gdm d e btlu diln ngdn ngfl v i bieu hoc qua bilu diln trUc quan dien kf hifu [2] Bilu difn tnic quan. .. trj phan sdqua bieu dien trfle quan, HS tfl vife quan sit • thao tie - dfl doin - khii quit se nhin thiy ket qui do, lufmg) 4.2 Quan niim cd nhdn vi Biiu dien trUc quan bai toin Todn tiiu lige... hinh trye quan; cie thao tie ehuyen ddi gifla ngdn ngfl thdng thudng vdl ngdn ngfl hoat ddng giii quylt tinh hudng Chflng tdi thiet ke toin hpc v i ngdn ngfl trfle quan tren md hinh trye quan tinh