JOURNAL OF SCIENCE OF HNUE Vol 56, No 5, pp 117 123 D A Y H O C NHUTNG KHAI N I E M C U A H I N H HOC K H O N G G I A N 6 T R U C J N G T R U N G H O C P H 6 T H O N G T H E O Q U A N DIEM HOAT D O N[.]
JOURNAL OF SCIENCE OF HNUE Vol 56, No 5, pp 117-123 D A Y H O C NHUTNG K H A I N I E M C U A H I N H H O C KHONG GIAN TRUCJNG TRUNG HOC THEO Q U A N DIEM HOAT P H THONG DONG Tran Trung Trudng Du bi Dgi hoc Ddn toe Sdm, San E-mail: trungt.dbdhss@moet.edu.vn Tom t a t Theo Nguygn Ba Kim [1], vice van dung quan diim hoat dgng vao day hgc mon Todn cho hgc sinh dUdc thi hien qua cdc tu tudng chu dao sau: Cho hgc sinh thuc hien vd tap luyen nhflng hoat dgng va hoat dgng thdnh phan tUdng thich vdi npi dung va muc dfch day hgc; Gay dgng cd hgc tap va ti6n hanh hoat dpng; Truyen thu tri thflc, dac biet la nhflng tri thflc phiTdng phdp, nhu phUdng tien vd ket qua cua hoat dong; Phan bac boat dgng ldm ch5 dua cho viec diiu khiin qud trinh day hoc Bdi bao trinh bay viec van dung quan diem hoat dgng vdo day hoc khai niem hinh hgc khong gian, mgt nhflng tinh huQng diin hinh day hgc mon Toan d trudng ph6 thong Md dau Mdi ndi dung day hgc diu lign he mat thiet vdi nhflng hoat dgng nhat dinh da dugc tiin hdnh qud trinh hinh va van dung ndi dung dd \^i vay, bat ddu mgt ngi dung day hgc gido vign can phdt hien nhflng boat dgng lign he vdi nd rdi can cfl vdo muc dich day hgc ma Ifla chgn d i tap luyen cho hgc sinh mgt so nhflng hoat ddng da phat hien dflgc Viec phdn tich mgt hoat dgng nhflng boat dgng thdnh phan giup giao vign td chflc cho hgc sinh tiin hanh nhflng boat ddng vdi mflc vfla sflc, giup cdc em thflc hien va tap luyen nhflng boat ddng phan tUdng thich vdi ngi dung vd muc dich day hgc Ddng thdi, chu trgng ggi ddng cd d i hgc sinh y thflc rd rdng vi sad thflc hien boat dgng hay boat dgng khac Viec tiin hanh nhflng hoat ddng ddi hdi nhflng tri thflc nhdt dinh, ddc biet la tri thflc phfldng phap Nhflng tri thflc nhfl vay cd lai Id kit qua cua mdt qua trinh boat d'gng K i t qua ren luyen d mdt mflc nao dd cua mgt hoat dgng cd t h i la tien d i d i tap luyen va dat kit qua cao hdn cua cac hoat ddng tiip theo ngn cdn phan bdc hoat ddng theo nhflng mflc khac lam cd sd cho viec chi dao, dieu khiin qua trinh day hgc 117 lYdn Trung 2.1 Noi d u n g n g h i e n c\iu Quy trinh day hoc khai niem hinh hoc theo quan di^m hoat dong \ a n dung eiuan diem liocit^ dgng viio diiy hgc- mon Todn d irudug trung hgc phd thong, giiio \'i(''ii ed the td chflc cae- boat dgng day hgc khai nicun hinh hoc- theo ciuy trinli sau: Budc L Uttili thdnh ht.c'u tugng vc kh.dt nirin: Ciiko vieu xky di.mg (-iie boat dgng g(.)i (ho hgc- sinh nhu ci'iu nhiiii thflc ve khiii niem mdi CJhang licin cd the t i elifl(- (-ho lig(- sinh thfle hieu Ciie lioiil dgng iiliU v("'' dgc Imili v(''- tfl eld tim Ciie thuoc tiuh bdn chat eiiii khdi iiifuii mdi Budc Xdy dung dinh nghia khdi ntrni: Giao \i(''n dua tmh budng mdi, td chflc cho hoe- sinh licMi hiinh (iie hoi.ii ddng phdn tich, so siinb doi eliiiu bra chgn (iic doi tugng ed nhflng dau hieu biin chat (iia khiii niem ed Bifdc Sau dd, bdng thao tiic khdi eimit hda, hgc sinh trinh bii.\- dinh nghia khai niem Budc Ndm vUng khdi niem,: Gido vien tc') chflc cho hoe sinh tien hdnh boat deing nhan diing khai niem ndi bg toan hgc va nhflng tinh hudng thflc tiin cudc sdng (niu cd) mdt mflc nao dd cd t h i yen (du hgc sinh tir xdy dirng cdc vi du t h i hien khdi niem vfla mdi dugc hinh Cuoi cung giao vien thflc hien khau "thi chi boa" bdng viec phdt biiu chinh xae- dinh nghia khdi niem cfing vdi cac ky hieu Budc 4- Cung co, van dung khdi niem: Trong budc giao vi(''n nen to chflc cho hgc sinh boat ddng \an dung khdi niem vfla hgc viio cdc tinh budng eu t h i nhu: thflc hanh gidi todn, chflng minh dinh ly, xdy dirng eac khdi niem khac van dung khai nie"'m vdo thuc tiin T i i p theo, ed t h i cho bgc sinh xe\ cke trudng help riemg, ting eiuat Cuoi cung, sap xip logic ciie khai nie^ni va mdi lie~m he gifla khai niem mdi vdi eke khdi niem da hgc- trUdc dd 2.2 D a y h o c k h a i n i e m c u a p h a n Hinh quan di^m hoat dpng hgc khong gian theo Sau day la vi du the hie;^n vi(;'e vkn dung quan diim boat ddng diiy hgc mgt so khai nie^m eua IPinh Iwc khdng gian ldp 11 d trudng trung hgc phd thdng: Vi du Day hgc khdi niem hai mat phdng song song Budc Hinh thdnh bieu tuang vi klidt nicm: De hinh khiii nic^^in hai niiit phdng song song, giao vien cd t h i ddt vdn dk: Trong khdng gian (ho hai mat phang phdn bie^t (a) va (/J) .Nc^t cac trfldng hc?p cd the xay ddi vdi so diim ehung eua chung? Can tra ldi mong ddi: 118 Day hoc nhUng khdi ni$in ciia Hinh hgc khdng gian d trUdng trung hgc phd thdng Trfldng hdp 1: (ev) vd (/:/) khdng cd diim chung nao Tnrdng hgp 2: (ei) va (J) cd vd sd diim chung thuge: giao tuyin cua chung Budc Xdy dung dinh nghia khdi niem: Khi dd giao vign xay di.rng dinh nghia khai niem hai mat phang song song: Trong trudng hgp 1, ta ndi (cv) vd (0) song song, kf hicm lii {n)//{p) Budc Nam vUng khdi niem: Dg nhdn dang khdi niem hai mdt phdng song song, gido vign ddt cdu hdi: Trong phdng hgc hay quan siit va iky vi du vi hai mdt phang song song? Budc 4- Cimg co khdi niem: Dg cung CO khdi nie^ni hai mat phing song song, gido vign ngu van de: Cho hai mat phang (P) va [Q) song song vdi nhau, d C (P) Hdi d ed song song vdi (Q) hay khdng? Hgc sinh lap ludn: d//{Q), vi niu ngugc lai d vd (Q) ed mdt diim chung M thi (P) va (Q) cd diim chung M diiu nav mdu thudn vdi gid thiit (P)//(Q) ^ Tfl dd giao vign ddn ddt hgc sinh kien tao tri thflc dac biet Id tri Hinh thflc phfldng phdp nhu phudng tien vd kit qua cua boat dgng bdng each dat cau hdi: Neu mdt vai flng dung cua khdi niem nay? Cdu tra ldi mong dgi Id: Di chflng minh dfldng thdng d song song (Q) ta tim mgt mat phing (P) chfla d ma (P) song song (Q) Vi du Dg.y hgc cdc khdi niem khodng cdch Di binh thdnh khdi niem khoang each tfl mgt diim den mdt mat phdng, gido vign cho hgc sinh lam bai tap: Cho hinh chdp tam gidc diu S.ABC cd AB = a, mat bgn tao vdi day mot gdc bdng 45° Hay tinh chiiu cao SH cua hinh chdp Qua viec hgc sinh thflc hien phep chiiu vudng gdc dinh S trgn mat phdng {ABC) vd tinh ddi SH, gido vien dan ddt hgc sinh hinh biiu tugng vi khai niem khoang cdch tfl mot diim din mgt mdt phdng va din mdt dfldng thdng thong qua phep chiiu vudng gdc Gido vign ngu tinh chdt di hgc sinh cung cd khdi niem: Khoang each tfl mgt diim O din dfldng thdng d la khoang each be nhat cdc khoang each tfl diim tdi mdt diim bat ky cua dfldng thing d 119 Ti-an Trung Ci'ui tlii ldi mong ddi Id: Ggi H \k hinh chif'u viibiig gde cua C Wen dudng tlii'mg d gc.)i M thugc- (/ lit mot diim biit- ky kluu- // NcMi O ^ (I thi AHOM la tam giiic vudng liii H nen OH < O^P, N(^>ii O € e/ thi DM > OH = Hinh Giiio xic'ii tiep tue gpi md c-ho bgc sinh cii(- tuih clug liej) theo: Khoiiug c-iicli gifla dudng tliiiug vii iiii:il phang song song lii khoang ciieli bc^ nhal c-ac- khoiing c-ach tfl mot diem biit ky thugc- dudng thfmg tdi mot diim bat k.v eiia (ei) Hay xiie dinh khodng each dd t yen hinh ve' n Hinh Hinh Tfl dd hay so sdnh khoang eacb gifla dfldng thang d va (o) vdi khoang each tfl diim 1/ bat ky thudc d den (o)? Can tlii ldi mong dgi lii: Ibii khodng (iieh nig- bfmg Di hoc- sinh dinh nghia khoang e-iich gifla luii mat phdng song song, gido vign ggi ddng cd md dcdu vdi ggi y: Bdng ciich hiiu tUdng tfl dinh nghia tren hay dinh nghia khoang cdch gifla hai miit phing song song? Can trd ldi mong dgi la: Khoang eaeli gifla bai mdt p h i n g song song la khoang cac-h tfl mgt dic'un bat ky ciia mat phing niiy din mat phing De the hien c-ac khai nic'^ni tre*Mi, giiio vien bdi tc\p: Cho hinh lap phflOng ABCD.A'B'C'D' canh a Hay xac dinh khoang each: a Tfl A din dudng t h i n g CD, h Tfl A din [CDD'C), [BDD'B') c Gifla dfldng t h i n g B'D' vk d Gifla hai mat phing: {ABCD) 120 BD {ABCD) vd {A'B'C'D') Day hgc nhiing khdi niem ciia Hmh hgc khdng gian d trudng trung hgc plio thong Gido vign ggi dgng ed md dilu nhdm hinh khai niem khdang each gifla hai dudng thang chcd nhau: Neu hiiu khddng each nhu tren, thi khoang cdch gifla hai dudng thing cheo a, b khdng gian la dai doan MN e^ho M e (i,N € b,MN I a.MN /; Song, li(Mi doi vdi hai dudng tbiiig (IUH) bc^it kv a b khdng gian ed phai bao gid cung ton tcii eluy iihi~il eludiig thing A eiit vii vudng goc- a b? B;; ' > " ;' A' p: ! Bl 'D Hinh Ne'ni hgc sinh e-hua dua duge cdu tra ldi, giao vien cd t h i Im thdp ye'ui can bang Ciic- ggi v sau: - Dudng thing A nhu \ay da xac- dinh dugc \'iii td ndo chua? Ygu can hgc sinh nhan xet: phuong cua A dd biit, dd la phUdng vuong gdc vdi (P) Trong dd ( P ) la mat phing nhdn hai vec td chi phudng cua a,b lam cdp vec td chi phucJng - Dg xac dinh A ta can xdc dinh thgm viu to ndo nfla? (Xdc dinh mdt diim thugc A) Hay xdc dinh diim H la giao cua A va (P)'.^ Gido vien gdi v: Giii sfl da di.rng dflgc A cbo A ekt a.6, (P) lan lugt tai 1/ A'', / / Hay tim moi lien he"' gifla ba diim dd? Tfl dd suy cdch xdc dinh H? Yen can bgc sinh tra ldi: H la dnh cua M, A'^ qua phep chiin theo phudng vudng gdc trgn (P) Ngn H la giao cua a',b' vdi a',b' lan lutJt Id hinh chiiu cua a,b trgn (P) Hinh Hay tra ldi can hdi dat ban ddu? Yeu cdu hgc sinh trd ldi: Vay, ddi vdi hai dudng t h i n g cheo bdt ky a khdng gian bao gid cung tdn t