LUYEN TAP CHO HOG TRONG DAY HDC HINH« HOAT ODNG KET NOI TRI THUE iTRll i lNG TRUNG HOC PHOTHONG ThS PHAN THANH HAI* Abstract In this article, the author presents some points of view of connecting know[.]
HOAT ODNG KET NOI TRI THUE LUYEN TAP CHO HOG TRONG DAY HDC HINH« iTRllilNG TRUNG HOC PHOTHONG ThS P H A N THANH HAI* Abstract: In this article, the author presents some points of view of connecting knowledge andactim of connecting knowledge The students must mobilize knowledge to solve problem, discover knowledg learning geometry These acliuilies should be applied in teaching mathematics at high school Keywords: knowledge connection, geometry, students Ngdy nhgn bdi: 22/03/2016; sija chua- 25/03/2016; ngdy duy$t ddng: 25/03/2016 P hathien kien thire mdi la thudc ITnh vue tim tdi tri tueduoc mptso nha khoa tipc quan tam nhu: M.Cnjgliac;V.A.Cnjchetxki; Nguyen Ba Kim; Dao Tam; Bui Van Nghj; Cao Thi Ha; Trong hoat dpng tim toi kien ^ d c mdi hpc sinh (HS) gap nhung ktid khan chu yeu sau day: - Khd khan viec phat hien cac mau thuan npi tai gap cac tinh hudng cd van dede tudd tim each giai quyet cac mau thuan ni\'m kham pha tri thuc mdi; - Khd khan viec huy dpng diing kien thue de lam sang to nhiem vy nhan thirc, lam bpc 16 cac ddi tupng can kham pha; - Kho khan giai dap eau hoi: Dua tren co sd nao de huy dpng diing kien thdc da biet nh&m lam sang to van de.lap luan cdcan eirdechiem ITnh trithircmdi?; - Kho khan bien doi thdng tin cae tinh hudng m(^ dechuyenvedgngquen thupe, tudocothehuy ddng cac ki^'n thuc da biet nham xdli thong tin can tim,phat hien kien thdc mdi, Cac hoat dpng khSc phye nhOnp kho khan neu tren thupc pham tru hoat dpng ket ndi tri thUese duoc lam sang to qua noidung baivietnay, nh§m giiJp HS phat trien kien thuc mdi tron^ viec tim toi kien thdc toan hpc eung nhutrong thue tien Mpt so quan diem ve ket nd'i tri thuc l.l.Tdgoc triei hgc cho thay:y\ecketn6\]j'\ thup dacd vditiithuemdi thdng qua cae ptiuong thuc chuyeu sau: -Tochuc eho HS khao sat eae trudng hpp rieng, cac mdi lien he dac biet de tddd nhd hoat dong khai quat hoa chiing ta cd nhung tn thuc mdi tong quat hPn; - Phat hien mdi lien he nhan qua gida tri thdc da CO cua HS vdi tri tilde mdi can tim de dinh hudng each giaiquyetvan de Khidung tn/de mptvan de can^giai quyet, chiing ta sudyng mdi hen he nhan qua de hudng HS tim tdi cae tn thuc cpi nguon, iam tien de cho viec chung minh, lam sang to van de can giaiquyet, 1.2 TIJ goc tam Tihgc lien tuang cho ^^^ CalmdidUde phathien thdng qua hoatdoig lientifSfig va ehuyen hda cac lien tudng tu" ddi tupng sang ddi tuong khac Thieu kha nang lien tudng, HS se gap khd khan hoatdpng huy dpng kien thiJcde giai quyet van de, khd khan chuyen hoa cac van de khd sang nhdng van de quen tiiupe, kho khan quy la vequen Nha su pham G Polya dac biet coitiipng hoatdgng lien tudng nhim huy dpng tdi da cac kien thiJc da hpc lien quan den gia thietva ket luan eua bai toan, chgn Ipc cac nhdm tri thde can thiet eho viec thyc hien cic hoatdpng giai bai toan mdi Chii trpng lien tuong bai toan can giai vdi cac bai toan gde quentiiupcmaHS da biet,timeach bien ddi bai toan ve bai toan goc, TiJ ddhuy dpng kien thdc nh^m ket ndi gia thiet vaketpi cua bai toan, nh&m giup HS d i d a n g huy dong kill thirc de giaiquyetvan dedat batoan.G,P^a cung coitrpng ket hpp gida dac biet hoa vakb&pl hda, chu trpng khuyen HS xem xet cae trucmg hdp rieng de tddd c d c p s d khai quathoa tdi bai toan tong quat han, tao eo hpi dedang ttiiet lap mdi Pen hegiOa kien thue can tim vdi cae kien thtJc da cd M.Cnjgliac da nhan manh: Nhung tri thdc da finh hpi dupc lai tham gia vao qua trinh tu nhu lam^ yeu tdcua tu de tiep thu nhung tri thdc men khac [1;tr 64-65] Nhu vay, tu di tCrhe thdng tri thiic da bietjJai cactrithucmdican tim.Noi each khac.tu dak^no he thdng tri thdc da biet den cac tri thuc can biei D^ day ehiing taxetmptvaividy day hpc toan Ket no! tri thuc Tren eosdphantich cac quan diem tri^thoc,larn li hpc ve hoat dpng ket ndi tri thdc, baivietnay * Tnrong Trung hoc phd thong Tnrdng Chinh - Dah Nong 481 Tap chi Gido dye so 381 (hi 1-5/2016), chungtoiquan niem: Ket noi tri thirc da CO voi tri thiic moi can phat hienlrong qua trinh tim toi tri tue la viec chgn Ipc CO tinh quy luat cac tri thuc da CO va to Chile Chung voi tucach de dir doan cac van de, van dung Chung de lap luan lam sang to nhiem vu nhan tliilc Ihong qua cac tinh huong ll,S,WC,/1C,C/W la cac hinh binh hanh va tudo suy tam giac edba canh lan luat b^ng AA,, BB^ CC, Khidd ttieo quy t&c ba diem ta ed: ^^+¥B, + CC, = AA,+Aji^ + MA^AA=Q Nhu vay, viee ket ndi tri ttidc d day dupe diln thdng qua cac hoat dpng lien tudng tdi quy tac ba diem, ddi vdi phep toan cpng veetp, tinh chat hinh binh hanh, dudng tnjng binh tam giac Nhdcac tinh chatnayvatiidng qua hoat dpng dung hinh, suy Chiing ta co the nhan thay dieu thong qua dupc fam giac AA,M co dp dai ba canh lan lupt viec phan tich vi du sau day; b&ng dp dai ba dudng trung tuyen, V i d u : Chiing minh rSng tam giac ABC Cae tri thdc duoc ket ndi d tren bao gom tri thde bat ki, ta luon CO X f + B [ + C C ; = 6, Irong AA,; gde: Tong ba vecto djnh tren ba canh cua mpt tam BB,; CC, lan lupt la cac ducmg trung tuyen xuat phat giactiieomptchieu quay nao ludn b^ngvectp tii cac dinh A.B^C Hoat dpng ket ndi tri thuc Cach 1: Dang thiic vecto can chiing minh; Chung toi quan niem hoat dpng ket ndi tin tuc la ^4i + BB^+Cc: = lien quan I6i ba dudng trung nhOng hoat dpng cua HS tim kiem eac tri thuc cpi nguon, cac tri ttidc tnjng gian duac ket ndi mpt tuyen va trpng tam G cua tam giac gpi cho HS lien he thdng theo cac moi lien he nhan qua, lien he phy tudng tfllmenhdequen thupc; a + G B + G C = Sii thupc nham lam sang td nhiem vu nhan thdc, de ehu dung kien thiic thexam nhap vao ddi tupng, xam nhap vao van dede da biet ^ chiem Hnh tri thdc mditrong toan hpc cijng nhutrong thuc tien Tren ca sd phan tich cac quan diem triet neufl = thi f hpc, tam llhpcve hoat dpng ket ndi tri thdcvakhaithae -a = Khi cau tnJc cua hoatdpng tim toi tritue, chung tdi dua he thong tri * mptsdhoatdpng ttianh phan eua hoatdpng ketnditri thiic dupc ket thdc ITnh vue tim tdi tri tue nhim phat hien va noi nhim giai chiem finh cac kien thuc mdisau day: baitoancothe 3.1 Hoatdgng xac dfnh cac mau thuin mo ta Iheo so sau; {hinh 1) cac tinh huong tri tht/c mdi nham lam bgc 16 nhiem vu nhan thdc qua trinh chi the hoat GA*GB*CC^O AGi-BC*Ca^O GB.Gr = 2G^ dgng ttr duy, xam nh$p vao do) tugng nghien CIIU, xam nhap vao tinh huong mdi -:*G+|BC+|CG-O ll-io.BO.CGJ.i Xuat phat td gdc dp tam li hoc nhan thdc; tam li A^»Bfl,*cc,^a hoc tri tue va td gdc dp tu bien chdng cijng nhu Cac/72.-ViecChung minh AA, +BB, +CC, = O gdi phuong phap luan nhan thuc toan hpc, cd the thay cho HS lien tudng tdi AA^, BB^, CC, la^dp dai ba ring: hoat dpng nhan thdc ndi ehung, nhan thdc toan canh cua mottam giac AA^I\/I, tddd co the dyng tam hpc noi rieng dupc b i t nguon tuviee phat hien eac mau thuin de tudd tao dpng lue cho hoatdpng giai gi^c cd dp dai ba canh la AA^, BB^, CC, nhu sau: Tap chi Gido dye so 381 (kil-5/2016) 49 Baygidta xet bai toan tdng quat cuabaltoanlren' quyet cac mau thuin do.Tdcac mau thuan day hoc toan sinh cac nhiem vu nhan thdc, cac doi Cho hinh hop chu nhat ABCD.A'B'C'D'ziickYyi\ thudc AB = a; AD = 'b;AA'=c Tinh theo a;6;c tupng cua hoat dong, ddi tuong cua tu thuc day khoang each giua hai dudng thing SDva/lS'.' hoatdpng Xac dinh mau thuan cac tinh hudng trittiucmfflva viee giaiquyet cae mau thuan ddi hoi Mau thuin sinh HS tiep can vdibaitoan giaovien dmh hudng eho HS huy dongcactn thucva tdng quat la: HS khong the ap dgngtri/cliep kinh nghiem da biet, de tirdo tim each khic phyc eacquy trinh da xet bai toan tren, noi each khac, quy trinh tren khong tuong thich vdi bai toan md'i mau thuan, phathien cac tnfhUc mdi, la: CA 'khong phai la phuang vuong goc v6i (/IS'D), Mptsdmau thuin thudng bieu hien cua HS tronjkhid6(/ie'D)//00 Cdthe khic phuc mau day hpctoan:-l\/lauthuanhJnguyen nhan HS khong thuan nhd dinh hudng eho HS sudung gian chu trpng ve sucan ddi gida hai matcii phap va ngutiep the tich cua hinh chop D'/4fie'c6 dien tich day nghia cua cac ddi tupng quan he toan hoc; - Mau thuin thong qua khao sat HS tuang tac vdi tinh s = -BABB- = -ac the tich hinh chop hudng tn thuc phuang phap mdi; - Mau thuan giua tri thuc phuang phap da co eua HS khong tuong D'ABB'\aV = ^abc thich vdi phuong phap van dung tinh hudng dupc khaiquat, Tu khoang each can tim bing dai di/arg cao h vetddinh Sden mat phing (AB'D)va(i\er\k\\ K/dt/^.-Cactilthuc phuang phap xac dinh khoang each giua hai dudng thang cheo a, b duoc neu tam giac y4S'£>'ia S, va dd ^ = y = ^ Bai loan qua hai quy trinh chu yeu sau: Quy trinh /."Bao gom cac budc quy ve tinh dien tich tam giac AB'D' theo - Xae dinh mat phang (P) ehua b va (P) // a; a;b;e • Tinh khoang each td mot diem M thupc a 3.2 Hoat dgng bien ddi thong tin vecac den (P) tugng, cac quy luat can kham pha theo nti Quy trinh ^.'Gom cac bude hudng khac nhau, nhim gitip chu the huy kien thuc theo nhieu each khac - Dyng mat phing (P) ehua a va (P) lib; -Dung mat phang (O)chLfa dva{0)//a; Bien doi thong tin toan hpe la hoatdpng cua chu - Tinh khoang each giua hai mat phing "(P) the lam thay doi hinh thdc dien dat cua thong lin de CO the huy dpng kien thuc da CO lam bpc !p cac npi va(0) Van dyng quy trinh tren de giai bai toan sau: dung, cac mdi quan he an chda cac thong tin de tiep nhan tn thue mdi mot each hieu qua Cho hinh lap phuong ABCD.A 'B'C'D'canh bing a Tinh khoang each giua hai dudng thing BD [12;tr43-44] Vi du 3: Cho ba diem A, B, C cd dinh tren ma! waAS: phang (a) va A la diem di dpng khong gian, Theo quy trinh 1, S z (a) GpiJ fa trung diem cua ;4Cva/lacacdiBm ehung ta cb the xac th6amanhethu'c:3M^-2/B + 7c-oQ.XacW dinh mat phing giao tuyen eua mat phang {S>1i)va mat phang (SSJ) (AB'D)chuaAB'va HS da CO vdn kien thuc ve khai niem giao tuyen (ABV) // BD Do cua hai mat phing phan biet la dudng thang& hinh lap qua haidiem chung cua haimatphangddhoacia phuang dudng thing dudng thang di qua mgt diem ehung va co vec CA'l{ABD)raiH ,-,„,, - chi phuang a nen khoang each Haimatphing (S/^/)va(SSJ)phan bietvacoSIa can tim bing dp dai doan 0J,OJ LAO\^ e A0\ 0' la tam cua mat A'BC'D', dd diem chung, ta ean xac dinh diem ehung thu'liai Vol bai toan nay, ndu giir nguyen giathidt{*) khongt^^ Qi=-c//=ir.r=:^ doigithiHSseratkhdkhantrongvleetimdiinchvng Do thifhaihoac tim phuong cua 501 Tap chi Gido due so 381 (kil-5l20W d6,xuathiensumateanbing.Tuy nhien,bang hoat dpng bien ddi thdng tin, hudng dan HS tdng bude bien ddi gia thiet {*) de lam boc Id cac ttiuoe tinh, quan he an ehua ben ddi tupng nhusau: (') '^2/A^AB+AB-~AC 'AJ = BJ- Vay glao tuywi can tim la dudngthanga di qua S va song song vdi BJ{hinh4) Nhd hoat ddng bien dot thong tin giup cho HS kha nang chuyen ddi giua hinh thue va npi dung cua ddi tupng de tim thay mdi lien he giua tn thuc mdi vdi nhung tn thuc da CO eua HS,tddd tim hudng giaiquyetvan de 3.3 Hoat dgng chuyen hda cac bai tap sach giao khoa cac bai toan md, tao cohgi Cho HS kham pha kien thdc mdi tren cosd huy dgng tdi da cac tri th dc da cd Hoat dpng ehuyen bai toan sach giao khoa Ihanh bai toan md nham tang eudng hoat dpng phat hiwi tim toi kien ttiirc mdi cua HS, qua dd phat tnen nang lyc tuduy sang tao,tao cahpi cho HS huy dpng twda cae kientfiLfcdadupc hpc.Baig thditich cue hda hoatdmg cua HS, khPiday kha nang tylap, chudpng, sang tao cua HS Nham nang eao nang tuc phat hien vagiaquyetvan de, tac ddng den tam li,tinh cam, dem lai niem say m e va thu hoe tap eho H S Wdu^.'Tucong thiic iupng giac ca ban daduoc h x ' |cosj+sin-T]