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MOT SO BIEN PHAP REN LUYEN Kl NANG TOAN HOC HOA TiNH HUONG THlfG TIEN CUD HOG SINH THUNG QUA UAY HUG NQI DUNG TO H0P XAC XUAT TS NGUY§N TH! C H A U G I A N G " LE THI KI§U D I E M " T oan hgc hoa tinh[.]
MOT SO BIEN PHAP REN LUYEN Kl NANG TOAN HOC HOA TiNH HUONG THlfG TIEN CUD HOG SINH THUNG QUA UAY HUG NQI DUNG TO H0P - XAC XUAT TS N G U Y § N TH! C H A U G I A N G " - LE THI KI§U D I E M " T oan hgc hoa tinh huong thuvtieniTHHIHJJ) la chuyen mot van dethuc tien bai toan desLTdungl^ieh thut toan hoc (TH)dabietnham nghien cutj giaiquyet Thuat ngir toan/tpc/jda [THH) dupc giai nghla la dua vedangTH(lylathematization: reduction to Mathematical) Ban chatcua hoat dong THH la motatinh huong thuc tiln (THTT) b§ng ngon ngiJTH Hoc sinh (HS) doi mat vcii nhifng van de cupc song se lien tuong den kien thUc TH phu hppdexay dung bai toan va tim Idigiai dap Ung nhu cau ban than Do la hoat dpng THHTHTT Viec ren luyen Iflnang THHTHTT clio HS tmng hpc plio thong (THPT) la can thiet, giup HS thuc hien hoat dong cohieu qua ngan gpn, mang tinh khoa hpc Ngoai ra, HS cat; co kha nang dien dat mpt van de, mpt dai luong bang nhieu hinh thflc khac IA Kinang xay dimg mo hinh TW; Kha nang bieu hien qua viec HS sfldung an so, kihieu, bleu thuc, dechuyen doi thong tin tUTHTT dflkien TH; s5p xep cac dukien bai toan phothong thuantuynhung van dam baoynghTacuaTHTT.HS dISn dat moi quan he giua cac dai lupng THTT bang thi, bieu do, tiinh ve, scf tom tat IS Kinang dieu chinh, danh gla mo hinh TH.-HS kiem tra tinh dung d i n , hpp li cua each kihieu an so, thiet lap phep toan gifla cac bieu thuc, mo hinh TH Trong quatrinh dieu chinh mo hinh TH, K i n a n g THHTHTT HS dudoan kel qua, tim gicfi han cua mohinhTH KTnang THHTHTT bao gom yeu to: KT nang Mpt so bien phap ren luyen k l nang thu nhan thong tin tUTHTT, kTnang bien doi thong tin T H H T H T T q u a d a y h o c T o h o p - X a c s u a t ( B a l s ' thuc tien dukien TH va kTnang xay dung mo va Giai tich 11) hinh TH cho THTT KT nang THHTHTT cua HS 2.1 Khai thac THTT de goi dgng ca THPT lakhanangHS van dung nhflng hieu bletTH day /tpc; Gop phan tao hflng thu hpc tap, phat huy cua minh dechuyen motTHTTthanh dang toan tinh tich cue, chu dpng cua HS thong Kinang THHTHTT cua HS THPT bao gom Vidu /.Trpng hoatdpng ngoai khoa cua trucfng, cacthanhto: Dpan thanii nien to chflc tro choi gieo mot sue 1.1 KTnang lien tumg, kit noi cac kieh thiic sSc can doi va dong chat Neu sue sac xuat TWAr/i/gap ran rfel/Hffiffen.HSquan sat, thu nhan hien mat CO so thong tin TH ti)thuc tien, huj; dpng, ket hpp klen thic cham la le thi TH se Slt dung de gial quyet van de Kha nang ngutJI chcfi se phuthupcvao kinh nghiem thuc te'cua ban than HS boc mpt vien ^ 1.2, Kinang phan tich, tong hgp nhung yeu bi hop to glathlet cda THTTKhanang HS danh gla (xem hinh i) moi lien hegifla yeu totrung tam,loai bo yeu tokhong Ban toehuc ban chat nliani dinh hucfng each giai quyet van de se trao glal Hlnh Con sue sac va hop bl chinh xac nhat Mflc dp phu thuoc gifla cac yeu to thflpng THTT ((uyetdjnh viec thiet lap bieu thilc, phuang ngucfi Choi boe duac vien bi Irang B?n Ngan thafti trinh, ham so, d I m o t a T H T T gia tro choi mpt lan Kha nang NgSn co dupe gial '% 1.3 Kinang sti dung ngon ngu TH thay the ngon ngu tu nhien de dien dat THTT: KT nang chpn an so, bleu diln dai luong bSng ki hieu, khai niem, menh de TH phu hcfp nhjm diln dat THTT 44 thfldng khong? 'TriRfngD^itipcViDb "Cao hQC K 21, PhiTtfiig phap d^y hgc Toan - Imng D^i hgc Vinh Tqp chi Gide due so 361 (ki - 7/2015) A Khong Ihe; B It kha nang (5Q%); E C h i c ehan CO giai til irdng Tinh huong tr§n khong giong nhirng bai tap xac suat ma HS da hoc sach giao khoa HS lien taong den bai toan tinh xac suatcua bien co, cu the la bien co X: "Ban Ngan thSng tro choi de nhan di/oc glalthi/ong" nen dinh hirdng dung cong thuc tlnh xac suat P{x) Gieo sue sac va boc mpt «{n) vien bitrong hop xay dpc lap Do xac suatth^ng tro choi la xac suat cua liai bien co dpc lap nen su dyng quy ^ c nhan xac suat Sau tinli xac suat cua hai bien co noi tren ta tim dupc cau tra Idl cho tinh huong thuc t i l n Giao vien (G V) can luu y viec HS hieu nham tu "va" nen diing quy t^c cpng xac suat d i n den ket qua sal 2.2 Ren luyen cho HS kinang su dung ngon nguttf nhien va ngon ngu TH dediin dat THTT m dt each ehinh xac 2.2.1 Luyen tip cho HS diin datbaitoin, THTT bin^g nhieu hinh tiidc khie nhau:TmnQ chuong trinh phothong, nhieu khai niem TH dupc dinh nghTa b^ng nhQng each khac nhau, do, G V t^ng cucffig cho HS phat bieu djnh nghla, djnh ii, menh deTH, theo each hieu ri§ng cua ho Dieu giup eac em nam viing klen thuc, ban chatcua doi tupng TH nhGng dm klen thay doi Vidu 2: Phan Gial tich {Sal so va Glai tich 11) trinh bay quy tac cpng: "Mpt cong viec dupc hoan boi mpt hai hanh dpng Neu hanh dpng iiaycomcach Ihuc hlen.hanh dpng CO/J each thuc hl^n kh6ng tnJng vdi bat ki each nao cua hanh dpng thu'nhat thl cong viec ed (m+n) each thuc hien" Quy t§c cong cothe mdrpng eho nhieu hanh dpng Quy t i c cpng dupc phat bleu a tren thuc chat la quy t i c dem so phan te'cua hai tap hpp khong giao nhau, phat bleu nhu sau: "Neu >1vaSla cac tap hpp hthj han khong giao nhau, thi n{AyB)=n(A)+ô(a)" Do ddquytĐc cpng CO the phat liieu dang khac: "IVIpt cong viec A dupc hoan bdi cac hanh dpng Hanh dpng 1,2, /flan lutjl c6 n,, n^ ,/)j^caeh thuc hien Trong khdng cd bat ki each thuc hien nao cua hanh dpng tmng vdi each thuc hien cua hanh dpng Khi dd cdng viec A cd (n, + n^+.,.+ n^ each thuchien' 2.2.2, Ren luyen kha nang phan biet ngon ngdti/ nh^n va ngdn ngd TH: Ngdn ngi? TH cd dac diem bid'u dat ngan gpn, loplc, khdng mang s i c tliai bleu cam, doi khdng dong nhatvdl ngon ngu"tunhien HS ng^i glai bai toan cd npi dung tiiuc liln vi gap khd (ki - 7/2015) khan chuywitungdnngu'tunhlen sang ngdn ngi? TH G V can phan biet cho H S cai bieu dieri (ki hieu) va cai dupe big'u diln (cai dupc ki hieu), dieu rat can tiiietgiup ngudi hpc mo taTHTT bang ngon ngi? TH mptcach chuan xac Vidu 3: Gieo mdt sue s^c tren mat phang n i m ngang.T[nhxae suat de: >4;''Matchanxuathien";S;"Xuat hien mat cdso Cham chia het cho 3"; C-"Xuathlen mated so cham khdng be hon 3'\ GV hudng d i n HS phan biet ngdn ngi?tunhien va ngdn ngi?TH b i n g bang sau: Cai 6ijc^ bilu dign ( C ^ duoc ki hi$u PhSp thuT Giso sCic sSc Cdi bc^u di§n (ki hi^u) n = {1,2.3.4,5,6} A "M§tch3nxuahi$n" /* = {2.4.6} Kha nfing xay b i l n c^ A & L n^)={ B: "Xuat hi$n mgt c6 so cham chia hgt cho T Kha nang xay bi^n co la • C: "Xuat hi#n m$t c6 so c h ^ S = {3.6} HB)-'C = {3,4,5,6} khong b6 hon 3", Kha nSng xay biSn co C 1^ ^ P(C) = ^ 2.3 Ren luygn kinang xac dinh mo hinh TH eua THTT qua day hge To hgp -Xac suat 2.3.1 Tangcudng hoatdgng tiiLic nghiem keth^ tiiao luan nhdm :HS tiep xue vdi THTT dupc tap dupt cac kTnang thuc hanh J H : thu thsip so lieu, dudoan ketqua,ttiaotactrensolieu dekiem tra ketqua Budc dau HS lam quen vdi viee van dung TH vao thuc tidn, chu ddng tich cue trao doi tiidng tin, chia se khd khan, cung xay dung baihpc K/'di/'^.'Ban th Lfnhatedmpt dong tien, ban ttiu'hai ed sue sac (deu can do'l, dong chat) Xet phep thir "ban thu'nhat gieo dong tien, sau dd ban thii'hai gieo sue s§c" Tinh xac suat cua cac biS'n co sau: ^.•"D6ngtienxuathienmatsap";S.'''Con sue s5e xuat hien mate cham"; C: "Con sue s i c xuat hien mat le" - Lop hpc dupe chia tiianh nhdm, td'chuc cho HS thuc hien gieo dong tien va sue sic (vdi quy udc m a t s ^ l a m a t ghi gia tri dong tien),ghiketqua15 lan gieo dau tl§n - Tir ket qua cua eac nhdm, hudng d i n HS su dyng phuong phap tn/c quan dephan tich kha nang xay cua tirng bien eo A B, C phep thu HS Tgp chi Giao due so 3611 45 thay rang: bien c6/4 va b i a i co C cd kha nang xay m b ^ g nhau, bien co B cd kha nang xay it hon bien ed'^ va C Neu kl hieu S lamatsap, N la mat ngi)a thi ta ed ket qua: n (A)= 6, n (B)= 2, n (C) = G -Thdngquatiiuc nghiem, HS nhan thay viec gieo dong tien vacon sue sac 1^ hoan toan dpe lap HS s u dung eae budc tinh xac suat cho tung bien co'de tim k^qua - HS dd'i chieu ketqua tim Suae vdl dudoan ban dau va rut ket luan 2.3.2 Bo sung vi du minh hga, bai tap co ngi dung tht/c tien: Npi dung To hpp - Xae suat chuong trinh phd' tiidng the hien rd net nhat ung dyng TH vao ddi song thyc tien Do dd, can khai thac khia canh tiidng qua viec minh hpa kien tiiirc b4ng vidu, bai tap cd ndidung thue tien Day la phuong tien giup bai giang trd nen sinh dpng, HS d§ tiep thu klen tiiue Vidu5:\/d\ cac chi? so 1,2.3,4,5,6 Cd the lap dupc bao nhieu so tunhien gom sau chi?soddl mdt khac nhau, chL?so1vachi?so4khdngdimg lien ke? HS su'dung kien tii ife hoan viva ehinh hpp degiai baitoanti-en GVedttieneu bai toan til ucte(cijng mo hlnh TH) nhusau: "Cd4 HS v a G V dupc xep ngoi vao day ghe hang ngang Hoi cd bao nhieu each s l p xep cho G V khdnp ngoi canh nhau?" HS lien tudng nhi?ng dae diem ehung cua bai toan Viec xep "2 G V khong ngoi canh nhau" gid'ng nhu lap so eho "chi? so va chir so klidng ddng lien ke" Mdi each xep tiida man yeu cau tuong tu nhu tim duoc mot so tu nhien thoa man bai toan HS thdng hieu cae bai toan cd cung md hinh giup cac em ren luyen nang lyc khai quat hda tinh hud'ng thuc tiin 2.3.3 Kiem tmmdcdg tiep tiiu bai hgc, van dung km) tilde cuaHS tiiong qua rH7T;Baikiem tra dirpc long ghep THTT ttiiic day HS tim hieu, nghien ciiii, khai ttiac cac kien ttiifc TH lien quan Hoatddng luyen tap img dung TH vao THTT dien thudng xuydn giiip HS li'nh hdi va cung cd kien tiiii'c sau sac hon Qua G V danh gia tinh hinh hpc tap, ren luyen kT narig THHTHTT eua cac em; dong thdi phan anh chat lupng giao dye Vidu 6: Bai toan "Bang trd ehoi d Hdi chp": mdt hpi chp, ngudl ehoi nem dong xu vao mdt bang dupc ke nhirng d vudng Neu mdt dong xu dinh vao bien, nd bj loai Neu lan khoi bang, no se dupc nem lai Nhung ne'u dong xu nam Ipt vao d vudng.ngudichoittiangdupcddngxuvathem mpt 46 Tqp chl Gido due so 361 Hinh Bang vuong va dong xu suatcLJa bien ed Xac suat de tiiang trd ehoi phu tiiupc vao kich thudc eua dong xu va mdt d vudng bang HS can xay diAig mohinhTH cho THTT tiong tnrdng hpp cy the de tim cau tra idl cho van de Ching han,baitoancdban kinh euadongxula2 cm va canh cua hlnh vudng la cm HS hieu ring de tiiang tidehoi thi tam eiia ddng xu phal each moi canh hlnh vudng it nha't cm; nguoc lai thi canh cua hinh vudng se c5t dong xu Ne'u thang thi khdng gian lai la mpt hinh vudng canh em (gpi la hinh vuong khdng bie'n ed) (xem sddS^ Xacsuatdetii^nglatisdglira dien tich hinh vuong khdng bien co va dien tich hinh vudng^ (trong vi du tren />=^) HS tien hanh ttiyc nghiem deddiehleu ket qua cua md hinh TH vdi ttii/c tien, dong ttidi ap dung md hinh TH cho cae dong xu (hoac d vudng)cd kieh thudc khac Sau ciing HS tim md hinh TH tdng quatcho THTT Quy trinh THH bil toantren,1) Van de xuat phat tur TIHTT: Xac suat de thing trd choi d Hpi chp; 2) Diln datvande ttieo eac khainiSmTH; Bang coke nhi?ng d vudng thehien cac hinh vuong, d6ng xu the hien hirih tidn Hinh vudng chu'a hinh trdn till ngudl ehoi thang, edn ne'u canh eua hinh vudng cat hinh ti'dn thi ngudi choi ttiua; 3) Loai bd cae yeute'khdng ban chat, ehii trpng yeu td'TH de chuyd'n van de tiianh bai toan dai dien eho THTT: Tinh hud'ng duoc chuyen tiianh md'i lien hegiiia dien tieh hinh trdn (dong xu) va dien tich eua hinh vudng;4) Glal bai toan: Diing cdng thde tinh dien tich hinh trdn, dien tich hinhyudng Tinh tisd'giija dien tich hinh vudng khdng bien co va dien tich hinh vudng ban dau Ketqua tim dupc la xac suatcua baltoan;5} Lam cho Idlgiaicua bai toan cdy (ki - 7/2015) nghia ddi vol THTT: Thuc nghiem lai tinh hudng de doi chieu vdi ketqua tim dupc ntiam danh gia Idi glai Xac suat de tiiang trd choi la tuong ddi thap (25%) Cac yeu to canh hinh vudng, ban kinh dong xu anh hUPng den xac suat tiling trd ehPi Ban kinh dong xu cang nho hay eanh hinh vudng cang Idn thi xae suat thangtrd choi cang cao 2.3.4 Deeap den ung dung cua To hgp - Xae suit tiong mon hgc khac nhu Vitii, Hda hgc, Sinh hgc, : Dieu tiie hien sy Hen mdn gii?a TH va cac mdn hpe khac nhatrudng GV cdthetien hanh hoat dpng day hpe mdn toan cQng nhu GV bp mdn khac ien hanh day hpc mdn dd, gdp phan dua TH ung dyng rpng rai thue tien Vidu 7: Bai toan mdn Sinh hgc "Lai hai gid'ng hoa mau hong va mau ngudi ta dupc ba ket qua: cay dthe he sau ed hoa mau hong, hoac canh sen vdi ciing kha nang Ch9n ngau nhien hat hoa lai dem gieo Tinh xac suat de: a) Cd dung cay hoa mau do; b) Cd cay hoa mau do, cay mau canh sen va eay mau hdng" Bai toan s u dung khai niem to hpp, cdng thirc tinh xae suat, quy tac nhan xac suat THHTHTT la hoatdpng can thietvaquan trpng, thudng dupc thuc hien theo quy trinh sau: T H T t - > md hinh TH - > si} dung klen thdc TH de gial bai toan md hinh - > dleu ehinh md hinh phii hpp vdi THTT KT nang THHTHTT tao dieu kien ctio HS van dung nhifng klen thu'c TH trudng thong vao eudc sdng, giiip HS hieu dupe ban chat kien thdc, tranh hieu cac van de TH mdt each hinh thu'c TH Td' hpp va Xae suat ed dng dung nhieu linh vyc khoa hpo va cupc sd'ngi, dd thdng qua day hoc ndi dung nay, GV cdthe gdp phan ren luyen kTnang THHTHTT cho HS THPT Q Tai li^u tham k h a o BO GD-DT PISA v^ c^c d a n g cSu hoi NXB Gido difc H 2008 D&o Tam (chu bien) - Lfi Kiin Duong Ti^p cSn cac phmmg ph^p day hpc khdng truy£n thtfng day hpc toan it truong dai hpc va truioiig phd thdng NXB D(ti hpc su phfim H 2008 Tr^n Vui D^nh gifi hieu bi^t todn ciia hpc sinh 15 tudi (Chuong trinh ddnh gid hpc sinh qudc ti PISA) NXB C/dorf{ adjusted models suitable for practical situations Mathematization skills for practical situations enabling students to apply tbe knowledge of mathematics in high school to life This helps students to understand the nature of knowledge, avoidance of math problems a form Combinatorics and Probabihty bas applications In many fields of science and life, so that through tbe teaching this content we present some method to tram mathematization skills for practical situations for high school students Mpt Sfl bien phap nhilni nang GBD (Tiip theo trang bia 3) nen viet nhieu lan de nhd lau hon (vi^t ttiu, viet bai luan ); - Khuyen khich HS tich cyc tiao da, tiiao luan vdi ban de cdttie viia ren luyen dupc cac kTnang vda giup HS ciing edtiitillie tdtnhat;-Yeu cau H S g h l c h ^ ciJng la each giup HS nhd lau hon nht?ng gi dupc hpe (hpe tdmcri khdng chl nhin matchumaphai viet ndra nhieu lan vadua vao mptngiJcanh eutiie); -Cdtiieday tiimdi, cau tmc eau thdng qua nhiing bai hat ngan, vui nhdn hoac mdt trd choi don gian, vua lam cho ngudi hpc bdt cang thang met mdi, vita kich tiiich hiing ttiu hpctap;-Trong gidhpc, HS khdngchinganghe vaghl chep ma quan trpng hon phal phat huy tinh tich eye tiong hpc t ^ Trong hoat ddng hpc tap, tinh tich cue ddng mdt val trd quan trpng giup ngudl hpc kham pha, n§m b i t tri tilde mdt each td'tnhat, hid'u sau va md rdng sy hieu bie't cua minh nhieu ITnh vue; quan trpng hpn, giup HS dap dng dupc yeu cau cua xa hdi la ngudl nang ddng, sang tao, linh hoat, tich cue, chuddng • Tai lieu tham khdo Hd An Phmnig p h a p mCfi n^m nhanh v^ vung tiengAnh NXB Gido dye H 1999 Aristova.L Tinh tich cue hpc t a p cua hpc sinh NXB Mo^tva 1986 COvaliop.A.V T a m li hpc xa h6i (i^lp 1,2,3) NXB Gido due, U 1976 Hd Ngpc D^ii x a m li hpc d^y hpc NXB Gido due, H 1983 SUMMARY The paper analyses positive situation of English leaming of students In cultural and artistic fields In Gla Lai Through analysis, tbe article proposes measures to enhance positive learning for students of English Tap chi Gido due so 361 47 ... ket qua: n (A)= 6, n (B)= 2, n (C) = G -Thdngquatiiuc nghiem, HS nhan thay viec gieo dong tien vacon sue sac 1^ hoan toan dpe lap HS s u dung eae budc tinh xac suat cho tung bien co''de tim k ^qua. .. nghiem deddiehleu ket qua cua md hinh TH vdi ttii/c tien, dong ttidi ap dung md hinh TH cho cae dong xu (hoac d vudng)cd kieh thudc khac Sau ciing HS tim md hinh TH tdng quatcho THTT Quy trinh THH... cau tra Idl cho tinh huong thuc t i l n Giao vien (G V) can luu y viec HS hieu nham tu "va" nen diing quy t^c cpng xac suat d i n den ket qua sal 2.2 Ren luyen cho HS kinang su dung ngon nguttf