DAY HOC CHU OE YEU TO T H 6 N G KE 6 TOAN TIEU HOC THEO DINH HUONG HINH THANH VA PHAT TRIEN NANG Lire CHO HOC SINH Hoang Thi Cat* T 6 M TAT Thuc hien ddi mdi can bin, toin dien giao dye Viet Nara; gii[.]
DAY HOC CHU OE YEU TO T H N G KE TOAN TIEU HOC THEO DINH HUONG HINH THANH VA PHAT TRIEN NANG Lire CHO HOC SINH Hoang Thi Cat* T M TAT Thuc hien ddi mdi can bin, toin dien giao dye Viet Nara; giio due toin hge dang thyc hi|n doi radi phucmg phip day hgc theo hudng phit triln nang lue ngudi hgc Bii viet bin vl nang lyc toan hpc cin hinh va phit trien cho hpc sinh thdng qua dgy hpe ehu de yeu td thdng kl mon Toin d Tiiu hpc Bii bio dinh budng nghien cim vi dgy hpc Toin Tieu hpe theo ylu eau doi moi giio due hien Tie khda: nang luc toan hpc, ylu td thdng kl, tiiu hpc TEACHING THE TOPIC OF STATISTICAL FACTORS IN PRIMARY SCHOOL MATHEMATICS IN THE ORIENTATION OF COMPETENCE FORMATION AND DEVELOPMENT FOR PUPILS ABSTRACT Reaching the goal of basic and comprehensive iimovation ofVietnamese education, math teachers are now innovatmg teaching methods in the orientation of developing learners' competence This article discusses the learners' mathematical competence to form and develop through teaching statistical factors m primary school mathematics This article orientates the research and teaching of mathematics at primary schools toraeettiierequirements of education innovation at present Keywords:raatheraatiealcompetence, statistical factors, primary MdDAU Ddi mdi phucmg phip day hge (PPDH) dang thye hien bude chuyin tir ehucmg trinh giao due tiep can ndi dung sang tiep can nang lyc ciia ngudi hoc, nghTa li tir eho quan tim din viec hge sinh (HS) hge dupe cii gi din chd quan tim HS van dung dupe cii gi qua vigc hpc Di dira bio dupe diiu do, phai thuc hien ehuyin tir PPDH 'CN Truong Tieu hpc thuc hdnh 42 I TRUONG DAI HOC H A I P H N G theo ldi "truyin thy mpt chilu" sang dgy each hge, cieh van dung kiln thiie, ren luyen ky nang, hinh tiiinh nang lye vi phim chit Nang lyc ngudi hpc, kl ci nang luc ngudi day dang nhilu dieu ean phai lim rd de ed dinh hudng, giai phap td ehuc hogt ddng day hpe theo hudng hinh thinh vi phit trien nang lue ngudi hgc, nhit la HS Tliu hoe 2 NOI DUNG 2.1 Nang l\rc toan hoc (Mathematical competence) cin hinh va phat trien cho hpc sinh tiiu bpc 2.1.1 Ndng luc (Competence) Nang lyc (NL) dupe dinh nghta theo nhiiu cich khic su lya chpn diu hipu khic Theo tam ly hpc: "Ndng luc Id td hgp nhirng thupc tinh dpc ddo cda cd nhdn phii hgp voi nhimg yiu cdu ddc trung cua mgt hoqt dgng nhdt dinh nhdm ddm bdo cho hoqt dpng dqt hiiu qud cao " NL li kha nang ea nhin dap iing eae ylu ciu phirc hpp vi thyc hi|n edng nhi|m vy tiong mdt bdi einh cu thi (OECD, 2002) thdng tin vi tmyen thdng, NL thara mT vi NL the chat Cae NL dupe hinh thinh vi phat trien dua tien biu nang di truyin eua ngudi, qui trinh giio dye vi trai nghiem cudc sdng; dip img ylu eau eua nhieu loai hinh hogt dpng khae NL dac thii la nhiing NL dupe hinh vi phit trien tien ea sd cie NL ehung theo dinh hudng chuyin siu, rieng biet tiong cic logi hinh boat dpng, cdng vile hoae tinh hudng, mdi trudng dae thu, ein thilt cho nhiing hoat ddng ehuyin bilt, dap iing yeu eiu han hep hcmciia mOt hogt ddng nhu Toin hpc Am nhgc, MT thuat The thao, NL ehung va NL dac thii diu duac hinh thinh va phit trien thdng qua eic radn hpe, hogt ddng NL li kha nang van dung ddng bd eic kiin giio due; NL dgc thii vua la muc tieu viia la "don thiic, kT nang, thai dp, pham chat da tich luy dupe vi thao tie"tiongeic boat dpng day hpe, giio dye; de ling xir, xii li tinh hudng hay di giai quyit vin gdp phan hinh va phit trien eie NL ehung de mpt cieh ed hieu qua (Ll Diic Ngpe, 2014) 2.1.2 Ndng lyc todn hgc (mathematical Vgy, ban chat eiia NL Ii kha nang huy ddng competence) cdn hinh thdnh vd phdt triin cho tdng hgp eic kien thire, kt nang vi cac thupc tinh hgc sink tiiu hoc tam Ii ci nhin khic nhu himg thii, niem tin, y Theo V A Kmchetxki: " NL todn hgc dugc ehi, de thye hien thinh edng mdt cdng viee tiong bdi canh nhat dinh Bieu hi|n eua NL la hiiu Id nhimg dqc diem tdm li cd nhdn (trudc biet sir dyng cic npi dung vi cie kT thuit tiong hit Id nhimg ddc diem cua hoqt ddng tri tue) ddp mpt tinh hudng ed y nghTa, chii khdng tiep thu ung nhieng yiu cdu cua hoqt dpng hgc tap todn, vd nhihig dieu kien vieng chdc nhu lupmg tri thiic rdi rae thi Id nguyin nhdn cua sy thdnh cong viic Ndng luc chung vd ndng lyc dqc thit nam vimg mpt cdch sdng tqo todn hgc vdi lu NL chung li nhiing NL ca bin, edt Idi lim cdch Id mgt mdn hgc, dqc biit ndm vitng tuong nin tang eho rapi hogt ddng ciia ngudi tiong doi nhanh, de ddng, sdu sdc nhimg lain thiec Id cudc sdng va lao ddng nghi nghipp Tgi Hdi thao ndng, ki xdo linh vye Todn hgc" [6, ti.l3] Nhimg npi dung chinh cua Chuong trinh gido Cdu triic cua ndng lyc loan hgc: dye phd thdng tong thi chuang trinh gido dye phd thdng moi (\2'\yAI20\5) dz^xzc dvcihZ Theo Kiuchetxki thi cdu true cua ndng luc NL chung, dd li: NL ty hpe, NL giai quyit vin todn hgc bao gdm nhung thinh phin: Thu nhpn di vi sang tao, NL ngdn ngu vi giao tiip, NL thdng tin, chi biin thong tin, luu trie thdng tin vd hpp tic, NL tinh toan, NL sir dyng edng nghe thdnh phdn tong hgp chung T A P C H K H O A H O C , S 21, thdng 03/2017 | 43 Cac yiu to inh hudng den sy hinh vi phat triin nang lyc toan hgc; Yeu td tu nhien sinh hgc; Yeu to moi trudng xd hpi vd gido dye; Yeu td npi dung cua todn hgc; Yiu to hoqt dong cda hgc sink Theo Dd Tiln Dgt vi nhdra nghien cihi Vien Khoa hpc giao dye Viet Nara (2012), cd nhieu each liet ke NL dupe hinh thinh vi phit trien qua hpc tgp toan xuat phat tii nhiing gdc dp khae Chung ldi xdc dinh nhimg NL dqc thu cua mon Todn, Id: (1) NL tu duy: li tdng hpp nhiing nang ghi nhd, tii hien, trim tupnghda, khii quit hda, tudng tupng, suy luin - giii quyet van de, xii Ii vi hnh cim qui trinh phan anh, phit triln tri thixc va van dyng chiing vao thuc tien vi giai quyet cic md hinh toan hpe, thi hien va dinh gii ldi giai tiong ngft canh thuc ti (4) NL giao tiip todn hgc: li nang sii dung cic dang ngdn ngii ndi, viit vi biiu diln toin hpc dl lira thuylt trinh vi giai thich lam sang td van de toin hpe NL giao tiip HIn quan tdi viec sir dung ngdn ngii toin hpc (ehii, ki hi^u, biiu do, thj, cae Hen kit Idgic, ) kit hpp voi ngdn ngii thdng thudng NL dupe thi hi$n qua viec hieu eic van bin toan hpe, dat eau h6i, tra ldi eau hdi, lap luin giai toin, (5) NL su dqng cdc cdng cy, phuang tiin hgc todn (bao gdra cie phuomg tien thdng thudng va bude dau lira quen vdi sir dyng edng nghe thdng tin) 2.1.3 Ndng lyc tu thdng ke Tu thdng ke (Statistical thinking) Theo Robert H Miti;hell (2000): "Tu NL tu cua hgc sinh tieu hgc iroitg qud trinh hgc todn thi hipn qua cdc thao tdc chu yiu thong ki (TDTK) Id triit li hgc tap vd hdnh dong nhu: phdn tich vd tdng hgp, so sdnh vd tuong tu, dya trin cdc nguyin tdc ca bdn: Tdt cd cdc cong ddc bi$t hda vd khdi qudt hda, buoc ddu chu viic diin mgt hi thdng cua nhihig qud y din NL tu logic suy luqn tiin chimg trinh lien quan vai nhau; Sy biin doi ton tqi minh; cdc NL tuduy phi phdn vd sdng tqo, cung mgi qud trinh do; Rut ggn vd nhqn thuc dugc su nhu cdc yeu to du dodn, tim tdi ke cd tryc gidc biin ddi Id chia khda ddn tdi thdnh e6n^\ todn hge vd tuang tugng khong gian Tbeo TS Trin Diic Chiln [1, tr.21]: TDTK (2) NL gidi quyit vdn di: li kha nang ci nhin Id qud trinh nhdn thiec, phdn dnh vd vqn di^ng su dung hieu qua cic qui trinh nhan thiic, hanh nhihig quy ludt thong ke (QLTK) biiu thi moi ddng vi thai dp, ddng ca, xiic cam &^ giai quyit liin hi gida tdt yeu vd ngau nhiin, giiea chdt vd nhiing tinh hudng c6 vin di rai d dd khong ed lugng cua dam dong cdc hiin tugng ngau nhien san quy trinh, thii tye, giai phap thdng thudng Hoat ddng TDTK thuc chit Ii cic thao tac Diy li mdt tiong nhiing NL rai mdn Toin ed lua chgn kiln thirc thdng ke - xae suit (TK - XS) nhiiu thuan Igi de phit tiiin eho ngudi hge qua phu hap vdi nhiera vu nhin thiic dupe dit vifc tiip nhin khai niera, quy tie toin hpc vi dgc Kiin thirc TK - XS vira li cd hich ban diu, vira biet li qua giai toan la phuang ti|n eo bin, viia la kit qui eiia qua (3) NL md hinh hda hay cdn gpi li NL toan trinh TDTK Nhung kiin tiiiic TK - XS tham hgc hda li kha nang ehuyin hda mot vin dl thuc gia vao qui trinh TDTK ciia HS cip THPT c6 ti sang mgt vin di toin hgc bing cich thiit lap thi chia lim hai loai: Nhiing kiln thiic thu nhgn 44 I TRUCJNGDAIHOCHAIPH6NG D^c diem the hien Soi t i r ^ g phii bap ckp dg I Chu the TDTK nhan bi^t v6 Sir ton tai cila tinh QLTK sir gan lien voi quan sat n lan ldn cac hifn tirgng ngau nhien cy the Hgc smh tieu hgc sau hoc cie yeu t6 TK CO thg dat trinh d6 ciia NL TDTK cap dp II Bang Nam cap dp nang lijrc TDTK Chli thS TDTK nhan biet cac QLTK an giau sau cac hif n tugtug ngau nhien don gian, chu yeu dudri daag quy tac trung binh cqng Sau hgc xong TK, HS cdp THCS cin va c6 thg d^t dugc tiinh dO ciia NL TDTK Cap dp III dupe tryc tiip d cic chii dk TK - XS; Nhiing kien thiic da dupe thu nhan tir trudc, ching hgn cic kiln thie liln quan tdi Toin hpc, Vgt ly, Hda hge, Sinh hpc, Dia li, Vi nhu vgy tiii ehu thi TDTK cin hieu, biet vi dupe ren luypn kl nang van dung tri thiec TK-XS Chli the TDTK c6 thg phan anfa, v$n dung cua cac QLTK don gian an t ^ g khong gian mau W; cac so li?u TK dugc mo ta khAc Sau hge xong TK XS, HS cip THPT cSn va CO the dat trinh dg cila NL TDTK Chli th^ TDTK phan anh, nghien ciiu cac QLTK an tang khong gian XS cua cac d?ii lugmg ngau nhien (Tu toan hgc triiu tuong) Sinh vien Djii hgc co the CO trinh dg cOa NLTDTK Ndng lire TDTK Ndng lyc TDTK Id mgt NL cy thi a HS, di ren luyin ndng lyc TDTK cho HS, phdi ren luyin cdc ky ndng chuyen biet thupc cdc thdnh phdn cua ndng luc TDTK Dl hinh thinh vi phit triln nang lye TDTK eho HS phd thdng, chung ta cin quan tira tdi eic ky nang (KN) chuyin bi|t ed quan be hiiu ea vdi Cac KN ehuyen biet nhara ren Iuy?n nang lye TDTK eho HS phd thdng: KN 1: Van dung tri thiec TK - XS vdo cdc tinh huong cy thi; KN2: Nhqn biit, phdn biet cdc hien tugng tdt yeu ' ngdu nhien, > i KN3: Phdt Men tinh QLTK dn giau dam ddng cdc hiin tugng ngdu nhien; KN4: Phdt hiin vd gidi quyit vdn de lien quan tdi nhung tinh huong mangy nghia TK - XS Cin chli y rang ragt HS phd thdng cd nang lue TDTK tbi khdng chi cd cic kiin thiic, KN, ky xio ma cdn phii cd tinh cira, nguyen vpng, hiing thu, dpng ca, dgc diim tara sinh ly Ilia tudi, dd la cic dac dilm ve nhin each Nhung dac diim niy cd anh hudng rd ret din hogt ddng TDTK Cdc cdp dp cua ndng l^c TDTK Theo TS Trin Diic Chiln, ed thi rao ta su phit triin nang lyc TDTK theo nam cap dp nhu d Bing sau day > Cic d^i tugng tinh toan Nha loan hgc c6 trinh dugc trim xuat hoa khoi dg cua NLTDTK ban chat cu the; cac phfip toan dugc triru xu^t khoi nghia thong thudng QLTK dugc nghien ciiu hg suy diSn triru tugng ngoai mgi su thg hi^n cu the (Tu toan hgc - triru tugng a mure d§ cao) Nhu vgy, HS Tiiu hpc cin hinh thinh vi phit triin NL TDTK d eip dp cip dp I: chu thi TDTK nhqn biit sy tdn lai cua nhieng QLTK qua quan sdt tryc tiep so ldn du Ion cdc hien tugng ngdu nhiin cu thi De hinh thinh vi phat trien nang lye TDTK cho HS tiiu hge, DH ein quan tim rln luyen cac ky nang chuyen biet vdiraiiedo thich hop TAPCHiKHOAHQC,S621,thSi^03/2017 [ 45 Vi dy: Khi DH bai: Lam quen vdi so lieu (ti.l34,Toan3) rd hon cic img dung thiit thuc eua yiu ti thing ke vdi cupe sdng Tir vi du: Do ehieu cao ciia bdn ban Anh, Phong, Ngin, Minh ta cd cic sd heu sau Nhu vdy, dd giup HS hinh thdnh vdphdt triin ndng luc TDTK Anh Phong Ngin Minh Ndi vi thing kl va TDTK, tir nam 1920 nha eao 122 cm cao 130 em eao 127 em eao 118 cm khoa hpe ngudi Anh H.G.Wells da viit: "Trong mgt tuang lai khdng xa, kien thiec thong ki vd Viet cic sd ehieu cao eua bdn ban ta duge tu thdng ki se tra thdnh mdt yiu td khong day sd lifu; thi thiiu dugc hgc vdn phd thong cua mdi 122 era, 130 cm, 127 era, 118 cm cong ddn, gidng nhu Id khd ndng biit doe biit viit vqy " Nhin vio diy sd lieu trln ta biet: 2.1.4 Ndng lyc todn hgc cdn hinh thdnh vd Day sd lipu tien ed sd (day chinh Id kich phdt trien cho hgc sinh dqy hgc chu diyiu id thuoc cua mdu) So lieu thir nhit, thii hai, thii ba, thir tu tuang thdng ki d Todn Tieu hgc ling li: 122 em, 130 cm, 127 cm, 118 cm (ddy chink Id cdc gid tri cdc so lieu cua mdu) Theo phan tich d trln, ehiing toi xic dinh nang luc toan hpc can hinb vi phat triin Nhu vqy, da giup HS hinh thdnh vd phdt triin eho HS Tieu hpe dgy hge (DH) ehu di ylu ti thdng ke d Toin Tiiu hpc la: ndng lyc TDTK Tiep theo, dl di din bang thdng kl cic sd lipu; trang 136, Toin cd trinh biy: (1)NL tuduy; Diy li bang thing kl sd hpc sinh gidi eda cic Idp d rapt trudng tiiu hpc: (3) NL gidi quyit vdn di; L*p 3A 3B 3C 3D S6 hge sinh gioi 1R 13 25 15 Nhu vdy, SGK da neu ro khdi niim bdng thong ki so lipu Khi DH bai ein khic siu cho HS: + Dgc bing sd li|u va dya tren sd li|u eiia bing de biit eic thdng tin HIn quan thuc hi|n eae phep tinh tir eie thdng sd da eho ciia bing (2) Ndng lycTDTK; (4) NL md hinh hda; (5) NL giao tiep todn hgc; (6) NL ste dyng cdc cdng cu, phuang tien hgc todn Tiiy theo timg bai hpc cy thi ngudi giio vien ed thi triin khai DH theo hudng hinh va phit tiien nang luc cho HS theo cie mire dp c6 thi dl dgt dupe muc dich, yeu ciu ciia mdn hgc 2.2 D|nh hirdng day hpc chu de yeu to thong kl mdn Toan fr Tiiu hpc theo hirfrng hinh thinh va phit triin nang I^c cho hpc sinh + Xac dinh mdi liln h | giira cae cgt, eae ddng 2.2.1 Npi dung dqy hgc yiu to thong ki tiong bing; y nghTa ciia bing sd lieu; radi lien he vi thdng tin vi xa hpi KT nang niy giiip HS ed mon Todn d Tiiu hgc kha nang nhan di?n bing sd li|u nhanh ehdng, Ngiy nay, khoa hge Thdng kl vi Ly thuyet tangtiiemhiiu biit va nim tiidng tin xa hpi, hiiu xic suit da xim nhip ragt cich cd h | thdng vi ei 46 I TRUdNG DAI HQC H A I P H N G nhilu ling dung thiit thye vao tit ea cie ITnh vye ciia cudc sdng Mdn hge XS - TK da dupe dua vio nha trudng tgo co sd ban diu cho viec nang cao nang lyc img dyng toin hge vao tiiyc tiin cho HS Trong ehuang tiinh giio dye PT mdi d nude ta, XS - TK da duge dua vio tir cip tiiu hge, cip THCS vi cip THPT Npi dung ca ban cua chii di yiu td thing kl tiong chuang trinh Toin Tiiu hpe bao gdm: Toin vdi hai yeu ciu dan giin dk HS bit diu lira quen vdi thdng kl sd Heu, dd la: Gidi thieu bing sd Hlu dan gian vi tgp sip xip cie sd lieu eiia bang theo mye dieh, ylu cau eho trudc nhanh chdng, tang thera hiiu biet va nara thdng tin xa hpi De giup HS CO khd ndng nhdn diin vd cd ki ndng dgc, xii li, nhdn xet tren bdng sd lieu, SGK da cd mpt sd bdi tap vdi cdc bdng cu the di giiip HS hinh thdnh kfndng vd xu li thdng tin + Nhan xet tren biiu dd: Nhgn xet trln bieu dd ehuang trinh Toin Tieu hpe ehu yeu tiln biiu dd hinh ept (bieu cdt hinh chii nhit) vi bieu dd hinh qugt Biiu d i hinh ept ehii nhgt duge ciu triic tiong dgng d ludi vudng ed true ngang vi cdt doe biiu Toin 4: Gidi thieu budc diu vi sd tmng binh thi cae dai lupng cd radi lien he vdi Qui eong; Lip bing sd Heu vi nh|n xet bing sd li|u; trinh DH giio viln hudng dan HS phat hien mii Gidi thilu biiu dd; Tap nhin xet tren biiu dd lien he niy va dua tiln dp eao eic hinh edt chir Toan 5: On tap eiing cd cic kT nang nhu: Dge nhit de thye hien eie yeu eiu eiia bii toin bing sd lieu; Nhan xlt trln biiu dd; Tinh sd + Chli y hinh thinh cho HS y nghTa thing ke tiimg binh cpng; Gidi thilu ve bieu di binh quat vi y nghia thye te eua nd; Tip dpc biiu dd hinh eua biiu di: The hi|n sy tap tmng hay phin tan qugt; hpc sinh eung dupe gidi thilu va biit ve eie so lieu thdng ke - BH s6 trung binh cpng mdt s6 bieu dd dang dan + Tir vi dy la cac bai toin thuc ti, dan dat cho HS ed khai niera ve sd trung binh cdng, cieh - Bay hoc nhqn biit vd ren luyin cdc kindng tinh sd tmng binh cpng; Soc bang so lifu; nhqn xet trin bieu dd + Hinh y nghia thdng ke ciia trung binh + Bang so lieu thudng li bing hinh ehii nhit cpng cho HS Sd trang binh cpng dai diln cho cd eae ddng vi cic ept; cic ddng vi cdt li eie eic sd lieu cua mdt bing thdng kl thdng tin da cho hoae dl diln vio, c6 raoi liln h | - DH biiu hinh quqt biln thien vdi 2.2.2 Mgt sd yeu cdu DHyeu to thdng ki + Dpe bing sd li|u: dpe bang sd lieu la viec HS duac hudng dan va thye hanh trln eie bing hinh chii nhat tien dd da cd cic thdng sd cho trudc ylu ciu HS dpe va dya tien sd lieu cda bang dk biit cac thdng tin liln quan thuc hien eic phep tinh tCr cac thdng so da eho cua bing + Trong DH giii toin vl bieu dd hinh quat chii y tap cho HS cd kT nang ve xac dinh muc dieh mi biiu dd cin thi hifn Tdng phin tram tiong biiu hinh qugt luon li 100% NghTa li TONG cie phan thdng ke (ddi tupng) hinh tidn bang 100% + Cho HS xae dinh radi liln he giiia cic ept, + Cic logi toin tren bleu hinh quat: Cho eie ddng tiong bing; y nghTa eiia bing so lilu; biet ti 11 phan tiara ciia thinh phin vi tdng sd mdi liln hi vi thdng tin vi xa hgi KT nang niy lupng eua eic thinh phan, tim si lupng ciia giup HS cd nang nhan dien bing sd ligu phan dd; Cho phan tiara trln biiu dd vi TAP c m KHOA H p c , Sd 21, t h d n g 03/2017 | 47 - Hinh thinh vi phit trien nang lyc TDTK: Phii coi day la mdt nhiing ylu ciu trgng tam cua DH ehu de Nhimg ngi dung DH c6 Mgt vdi luu y dqy phdn Biiu hinh quat chu dl diu cd ea sd vi ea hgi di khai thie, ren luyen nang lyc TDTK cho HS Ve kiin thuc: Xic dinh raue dich biiu thi Vi dy: Trong bii Lam quen vdi sd lipu TK hien; Nhgn biit y n^Ta ciia eie hinh ve hoae ki (tr 134, SGK Toan 3), trudc cic bii toin chiiu hieu tuang iing; Nhgn xet, tinh toan so lieu - tia cao HS; Hay sd kg tiong bao gao; Hay day ldi yeu eau ciia bii toin s6 lieu ciia day sd GV cin kheo llo gpi