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PHA! TRifN NANG lllGTOUYVATIiiTlfiliTllllNGKIIONe CHO HOC SINH TI^D HOC QUA B A I HOC T O A N V ^ CAT GHEP Q ThS NGUYEN THI XUAN Yl ^ bfii dudng vd phdt triln cdc ndng lye lu duy cho hgc sinh (HS) HIU[.]
PHA! TRifN NANG lllGTOUYVATIiiTlfiliTllllNGKIIONe CHO HOC SINH TI^D HOC QUA B A I HOC T O A N Q l ^ bfii dudng vd phdt triln cdc ndng lye lu cho hgc sinh (HS) HIU hgc dgy hgc cdc ylu tfi hinh hgc mdn Todn d tllu hgc Id mfit cde nhl$m vy eo bdn eua qud Hinh dgy hgc cdc ylu ifi hinh hgc d hiu hgc, dfing thdi Id ydu cfiu thudng xuydn vd cfin thilt nhfim thyc hi^n myc Hdu gido dye Myc dfch dgy hgc cdc ylu tfi hinh hgc d HIU hgc vdo cung cfip cho HS nhOng hllu bilt cfin thilt v l hinh dgng, v{ tri vd kfch thude cOo edc vfil h'ong khdng gian tilp xuc vdi edc «Wn/) hudng todn hgd* Hong cufic sfing rfiudng ngdy, vda chufin bj cho v l ^ hgc ede bdi todn hinh hgc d frung hgc CO sd (THCS) Trong dd, cdc bdi hsdn hinh hgc d trudng THCS cd cfiu true logic tuang doi chfit chd, muon Irnh hfii dugc edc kiln thuc hgc sinh, HS phdi cd mfit Hinh dfi phdi h'iln tu nhfil vd so sdnh dfii chilu glOa cdi dd cho vdl cdi cfin Hm Hudc cfii - ghdp) Kll qud cOa phdp ihu sd dua din cdc ihao tdc tilp iheo, hofic Id bdi todn da dugc gidl hofic phdi dilu chinh h> sy phdn Ifch, lfing hgp lllp Ineo VI vfiy, d l gidl dugc cdc bdi todn v l C-GH, HS phdi huy dfing hfiu hit cdc ihoo Ide hi co bdn: phdn tfch, ting hgp, so sdnh cung trf tudng tugng ld)dng gian Kit qud sou gidl bdi todn Id HS phdt Hiln dugc cdc ndng li/c hr vd Hf hidng h;gng khdng glon cua HS cung dugc hinh Hidnhvd phdt Mln Khi gidi cdc bdi todn C-GH d Hiu hgc cfin ddm bdo cdc ydu cfiu co bdn sou: - Cdt hinh: Khi cfit hinh cho hvdc thdnh hinh nhd cfin luu f: dudng cfit phdi Id dudng cfit ihfing hofic gfip khue, ddm bdo dung sd' nhdl cfit hofic dung si mdnh nrtd bdi lodn ydu cfiu, lfing d l ^ Hc^ cdc mfii cfit dung bfing di$n Hch hinh ban dfiu; - Ghip hinh: Ghdp cdc mdnh dd cfit d l dugc hinh mdi phdi dung hinh dgng cOa hinh md bdi todn ydu cfiu vd tfing dl$ntfchcOa cdc mfit ghdp dugc dOng bfing didn Hch hinh ban dfiu Quy hinh hudng dfin HS gidi cdc bdi lodn v l C-GH HIU hgc bilu tugng v l dlfin h'ch cOa mfit hinh gfin liln vdi cdc vudng dl^n tfeh (don vj do) Do dd, gido vidn (GV) cd i h l dua hogt ddng C-GH v l v i ^ C-GH Hdn cdc d vudng se glOp cho HS gidi cdc bdi lodn vi C-GH, GV can tfi chi>c cho liln hdnh iheo quy H-inh sou: - Budc 1: Ve hinh dd cho Hdn giay kd d vudng (sao cho cd thl nhfin thd'y hinh ve gfim bao nhidu d vudng); -IMiflfikfcHifNb Tap chi Blao due s6 (ki i • T/aom - Budc 2: Nhgn xdt Hdn hinh vd v l ede dfic dilm dugc edl h> hinh chu thdp vd sou dd chOng ciia hinh eho (di$n tfch - sfi d vudng, hinh dugc ghdp Igl thdnh hinh mdi cd phdi Id hinh dgng, gdc, cgnh ); - Budc 3: Dd'i chilu vdl ydu vudng hay khdng hodn lodn dya vdo trye glde ciu cOo hinh phdi kio thdnh, cd ydu cfiu ndo dd md khdng thl chung minh bfing phuong phdp dugc thda mdn h> cdc d vudng d Hong hinh vd vd suy diln Tuy nhidn, vdi GV cfin hllu rd ca sd If dfic dilm cua hinh dd cho; - Budc 4: Xdc djnh lufin Clio cdeh C-GH dd GV phdi hinh dung dugc bfi phfin ndo cOa hinh cfin phdi efit ghdp (boo dfi ddi cgnh cua hinh vudng trudc thyc hdnh gfim cdc d vudng cd lidn quan) Phdn tfch vd so C-GH Vi dl§n Kch hinh vudng Id vufing ndn sdnh moi lidn h§ giua cde d vudng, chO y su dyng cgnh hinh vufing Id V5 don vj ddi Ta cd = 2^ + cdc dinh vd cgnh cua hinh ban dfiu d l h;io ' , ndn theo djnh If Pitago, cgnh cua hinh vudng hinh mdi; - Sudc 5: Cfit ghdp cdc d vudng lidn ed dfi ddl bfing cgnh huyin cua tam gidc vudng quan dya trdn sy phdn Ifch eua budc cd hoi cgnh gdc vudng Id vd don vj ddi Mfit s^ bdi lodn cy t h l N l u bdi todn khdng ydu cfiu v l sfi nhdl cfit hofic v l so mgnh nhd dugc cfit thl cd t h l cd 1)Bditodn J.Chohlnhchu nhilu cdch C-GH khde nhou, hiy nhidn nlu bdi thfip nhu hinh vd Hay cfit hinh chu ihfip ihdnh cdc mdnh nhd i ' ' lodn ydu cfiu ihdm v l sfi nhdt cfit hofic v l sfi mdnh vd^idp ihdnh mfit hinh vudng | | nhd sou cfii ro bdi H)dn Hd ndn khd khdn hon 2) Bdi todn 2: Hdy cfit mgt hinh chu thfip bfing Hudng ddn: I i hoi nhdt keo thfing roi ghdp cdc mdnh nhd d l - Budc 1: Vd hinh chu thfip I ' Hdn g i ^ kd d vudng Hinh chu thfip chiim hinh dugc mfit hinh vudng Hudng ddn: Ggl M , N Id trung dilm cuo cgnh vudng (coi mfii hinh vudng dd Id don v| di^n Kch vd dd ddi mfit cgnh hinh vudng Id don vi CD vd EF Nd'i M vd N , A vd B, cfit theo dudng M N d l tdch noi hai mdnh, efit dfii phfin cdn Igi ddl) - Sudc 2: Di$n tfch hinh chu thfip bdng d theo dudng AB d l dugc mdnh vd ghdp nhu hinh ben vuong - Budc 3: Vi hinh vudng ghdp dugc cd didn Kch bfing hinh chu nhfit, ndn di$n Kch hinh vuong cung bfing d vudng Do dd, ^ i h l giQ nguydn d vudng '-\P- d glua vd cfit ghdp d vudng xung quanh - Budc 4:1^1 giu fi vudng d glua vd efit d A E vudng xung quanh, cfin chO ^ dfnh ndo dd cua N hinh i u ihfip cd Igo thdnh mfit hinh vudng khdng? (dung thudc, dke d l thu - cd Hil ggi jr mfii dinh Trong bdi lodn ndy, hinh vudng gh6p dui?c cy thl vd HS h; Hm cdc dinh cdn Igl) GV ggl y HS nd'i bfin dfnh cua hinh chu thfip d l cd hinh cd kich thudc dung bdng hinh vudng ghip duqc h-ong bdi lodn J, nhiSn, h-ong cdch C-GH d vuong, xem xdl dl§n tfeh eua hinh vudng vua tgo dugc cd di^n Kch cung bfing d vudng Tu dd, i>dl lodn I, i6 nhdl c6\ a khdng ddm bdo yiu c6u Vdn dS Id nhdt c6t d^l d vi hi ndo cua hinh rul ggi >' cdch C-GH cho th$p thi ddm bdo ydu cdu cua bdi todn, ndn nhdt ciil d bdi lodn AK/C ddt cdc vj hi khde (xem binh v§) W ^ 31 Bdi lodn 3: Hoy ciit mdt hinh chu thdp chi bdng hoi nhdi c6l roi ghep cdc mdnh nhd d l duvc mdt hinh chu nh^t cd chilu ddi gd'p ddi chiiu r^ng - Buiie 5: Tlivc hanh C-GH Iheo goi ^ d bulk M i v6i HS lilu hpc, v l ^ gidi bdi lodn frSn hodn todnldsi/mdmfim.HS looy hooy md nDSm cIS tim cdch cM g h i p soo cho thda man ySu dbi dijt cuo di bdi Vi#c xem x i t cdc mdnh lap till Blao due so 289 m i • 7/»on) Hudng dBn: - N^l A vdl B, cdt theo dudng n6\ AB; - Noi C, D Doqn ihSng CD cdt AB d O Cdt iheo dudng CO Hinh chu ihdp d\tgc cdt ihdnh mdnh G h i p cdc mdnh |nhv hinh ve) ta duvc hinh chu nh0t thda mdn y i u cdu cOa bdi todn _ # Trong bdi todn ndy, hinh chO nhfit ghdp dugc phdi ddm bdo hoi ydu cfiu (sfi nhdl cfit vd hinh dgng cOa hinh ghdp dugc Id hinh chO nhfil cd chilu ddi gfip ddl chilu rfing) D l hinh ghdp dugc id hinh cha nhfit cd chilu ddl gfip dfll chilu rfing, GV phdi tfnh dfi ddt mSi cgnh cua hinh chij nhfit: Ta chia hinh chO thfip thdnh 20 hinh vudng nhd thi di§n tfch hinh chO nhd'l bfing 20 d vudng N l u coi chilu rfing Id x Hil chilu ddl Id 2x Khi dd, dl|n Hch hinh chJ nhfil ki 2x' - 20 - > x^ - 10 1^ + 3' Vfiy, chilu rfing cOa hinh chO nhfit ddi bfing dfi ddi cgnh huyin cua mfit lam gidc vudng md, hai cgnh gdc vudng Ifin lugl Id vd don vj ddi, cdn chilu ddi cua hinh chO nhfit bfing ddl cgnh huyin cua mfit tam gidc vudng ed hai cgnh gdc vudng vd d don vj ddi 4) Bdi todn 4: Cho hai hinh cha Hifip bfing Hdy cfii mfii hinh thdnh hai mdnh cho ghdp bfin mdnh Igl to dugc mgl hinh vudng Hudng dSn: - Cfit hoi mdnh theo dudng AB, CD ta dugc bfin mdnh; - Ghdp bfin mdnh, ta dugc hinh vudng Theo cdch Ifip lufin d Irdn, cgnh hinh vudng ghdp dugc bfing dfi ddl cgnh huyin cOa mfii tam gidc vudng, md hoi cgnh gdc vudng Ifin lugt Id vd don vj ddl, dOng bfing dfi ddl dogn ihfing A6, CD D l ghdp dugc hinh vudng ihda mdn ydu cfiu bdi todn cfin phdi xoay cdc mdnh cho AB, CD ro phfa ngodi d l chung trd thdnh cgnh cOa hinh vudng Bdi vilt ndy dfi chi d l cfip bdi tadn v l C-GH chQ thdp vdl dl^n Kch khdng thay dfii, nhung quo dd, cho Htfiy ig phong phu vd da dgng cOa cdc bdi lodn C-GH d tflu hgc Td vide gidl cdc bdi lodn ndy, ndng Igc Hr vdfrfh/dng higng khdng gian cOa HS sd dugc bfii dudng rdn luy|n vd phdt h-lln a T&i li^u tham khtlo VQ Qutfc Chung M(yt stf vtfn Ak d^y hpc c i c ytfu ttf hinh hQC nh&m b l l dirOng nftng li;c t v d u y cho hQC sinh tiiu hflc NXB Di?i hqc suphrfm, H.I998 H& ST Hd NhOng vfl'n 6k cff sd cda phmmg ph^p d^y vA h^c toftn tl^u hpc NXB Gi&o dvc H 1990 Dfi Trung Hif u - Dfi Dinh Hoan - H i Si H6 Phiroog phftp dvy hyc toftn i\iu hpc NXB Gido dvc H 1993 Nguyfin Titfn THi (ctiu biftn) - Chu Van Quang Toftn (Gi&o trinh ddng cho c&c trudrng su ph^m d^o I90 gifto viftn liiu hpc) NXB Gidodnc H 1994 SUMMARY Article refers to the problem of cross-shaped cutgrafted area does not change Thereby, sho\t^ tt^e richness and diversity of the cut-puzzle problem In elementary school From ttie solution of this prot^em, the capacity of thinking and spatk^ imaglnanon of the students v/lll be training and developement practice Dmh hudng hinh \x\ thvc (Tlip theo trang 38) Tdi li^u tham khdo Howard Gardner Ca cfiu tri khdn - U thaylt vi nhiiua^ngtrlldtbD.NXB Gidodfic.H 1997 NguySn B& Kim Phinmg phftp d^y bpc DIOD Toftn NXB Ddi hoc suphpm Hd N^i, 2003 Phan Trgng Ngg (chd bifin) - Nguyfin Diic Hubng Cftc 11 thuydt phftt tri^n tfim U ngodi NXB D^i hgc suphpm HdN0i,2Qm Nguyfin Vftn Ttiifim "Tudng tugng khOng gian, phftt huy trf tudng tugng khOng gian cOa hpc sinh d^y tilnh hgc ph&ng" T^p clif Nghiin cuu gido dfic, s i l l Ihfing 12/1984 Clements, D., Swaminathan, S., Hannibal, M., and Sarama, J Young childrens' concepts of shape Journal for Research in Mathematics Education, 1999 Dolan, D., Williamson, J., and Muri, M Mathematics Activities for Elementary School Teachers, A Problem Solving Approach ON: Addison-Wesley,Inc,I997 Mc Gee, Human spatial abilities New York, NY: Preager, 1979 8.Van Hiele, Piem M A Child's Thought and Geometry National Science Foundation, Washington D C , 1984 SUMMARY The author studies the geometry thinking of late kindergatern and early primary children through activities The auttmr tjuitt some understandings of methodology which are good tor soMng problerDS This artk:le contributes to r&iovdte curriculum and mettKxl of teaching at school Tap chi Blao due s6 (ki i • r/aoia) ... giQ nguydn d vudng ''-\P- d glua vd cfit ghdp d vudng xung quanh - Budc 4:1^1 giu fi vudng d glua vd efit d A E vudng xung quanh, cfin chO ^ dfnh ndo dd cua N hinh i u ihfip cd Igo thdnh mfit hinh... khdng gian cOa HS sd dugc bfii dudng rdn luy|n vd phdt h-lln a T&i li^u tham khtlo VQ Qutfc Chung M(yt stf vtfn Ak d^y hpc c i c ytfu ttf hinh hQC nh&m b l l dirOng nftng li;c t v d u y cho hQC sinh. .. ngodi NXB D^i hgc suphpm HdN0i,2Qm Nguyfin Vftn Ttiifim "Tudng tugng khOng gian, phftt huy trf tudng tugng khOng gian cOa hpc sinh d^y tilnh hgc ph&ng" T^p clif Nghiin cuu gido dfic, s i l l Ihfing