jetJRNAL OF SCIENCE OF HNUE DQI 10 18173/2354 1075,2015 0033 Educational Sci , 2015, Vol 60, No 2, pp, 76 82 This paper is available online at http;//stdb hnue edu vn C A N N H A N H C H O N G DlTA LO[.]
jetJRNAL OF SCIENCE OF HNUE Educational Sci., 2015, Vol 60, No 2, pp, 76-82 This paper is available online at http;//stdb.hnue.edu.vn DQI: 10 18173/2354-1075,2015-0033 C A N N H A N H C H O N G DlTA LOAI TOAN GAN V l THl/C TlfiN VAO NOI DUNG GIANG DAY VIET NAM Td Van Ban Khoa Cdng nghi thdng tin, Hgc viin Ky thudt Qudn su Tom tat Bai viet phan tich tinh trang thieu hut loai bai toan gan vdi cac van de lien quan din thuc tiin cac giao trinh toan hien d Vigt Nam Mdt quy ttinh hdp H di van di dinh hUdng thUc tien cd vi tri xiing dang ttong giang day toan hpc, nhat la cac ttUdng ki thUtit dUdc di xuat Bai bao dUa mdt s6 kinh nghifim, cilng nhU mot vai khuyin nghi nhu dUa bai tap dmh hudng thUc tien vao npi dung thi tuyen sinh Dai hpc - Cao dang 7& khoa: Dinh hudng thuc tien, gidi quyet vdn de, lien nganh, cdi tiin gido trinh JVIci dau Cai tien giang day, hpc tap theo cac phUdng phap tien lien da dUdc nhieu tac gia nghien cflu va dang hinh mdt ttao lUu [3-8,15] Tuy nhien, ve long the, eac nghien cflu cdn ehua day dii, nhal la chUa ttien khai ap dung dUdc bao nhieu Chiing ta thay sU thieu but ro rang nhat d loai toan cd gan vdi cac van de hen quan den thuc tien Tren thi gidi, loai loan cd the tim thay d khap ndi thi d ta cdn nhu mdt cua liiim Sach giao khoa (SGK) dUdng nhu chUa ed chd cho nhung bai toan "SGK cung nhU IhUc le giang day hpe loan d ttUdng thdng "nhin chung mdi chi quan tam tdi mdt sd bai toan ciic tt; mot each khdng thudng xuyen, ttong dd rit it cac bai loan euc tti la cac tinh hudng lien mdn hay thuc te, du chi la nhflng tinh hudng ddn gian" [1] Theo kiem dim cua chung tdi, ttong so 1812 bai tap cua SGK toan PTTH chfldng trinh nang cao, clu cd 120 (chiem 6,6%) bai tap lien quan den thUc tien, ma chu yeu lai la nhflng thUe tien ddn gian Tinh hinh cdn te hdn d cac cuon giao ttinh toan cho dai hpc Trong so 549 bai tap cua tai heu [9], sach loan dUdc nhieu ttUdng sfl dung ebd sinb vien kl thuat, chi cd 20 (3,6%) bai tap lien quan din thuc tien, ma phan nhieu la tinh kich thUdc hinh Cd giao ttinh xac suit thong ke cho cac nganh ndng lam dUdc chinh sfla tfl giao ttinh cung loai cho ttUdng ki thuat Vdi mdt hpc heu nhu vay, kho cd the loi cuon mang ddng hpc sinh, sinh vien yeu thich toan Thiy mdt loat cdng thflc, phUdng trinh, dinh li khd khan thi hp hoac chan khdng hpc, hoac sinh tam li sd, ghet toan Cd em cdn cUc doan hdn nhan dinh: "Cd le dd la li de cae ban em thay tich phan, dao ham chi la nhflng thfl tu nhien nhay vao SGK "N^ rot cue sau 12 nam hoc, vdi nhieu ban, toan chi la mdn giup ngudi ta dim tien chfl khdng phai la mdt mdn giup ngUdi ed nhflng suy luan logic ttong ddi s6ng" Danh gia tinh binh giao due gin day, Van kien Hdi nghi lin thfl sau Ban Chap hanh Trung Udng Khda XI da khang dinh " npi dung giao diic cdn nang vi li thuyet, cd mat xa rdi thUc te PhUdng phap day va hpc cham do'i mdi " Bai viet nhan manh lai vai ttd ciia loai loan cd dmh hudng thUc tien, dong thdi di xult mdt so bien phap dd' loai toan dd dUdc ap dung rdng rai ttong giang day loan hpc d cae ttUdng dai Ngay nhan hai: 15/08/2014 Ngay nhan dang; 12/03/2015 Lien hS; T6 Wn Ban, e-mail: tvban_hvkt@yahoo.coin.vn Can nhanh chdng dua loai loan gan vdi thuc tiin vao ndi dung gidng dgy d Viit Nam hoc nUdc ta, nhat la cae trUdng dai hpc ki thuat, bao gom cae van di lien quan den bien soan giao trinh, to chflc giang day, cd eau de thi Noi dung nghien cihi 2.1 Danh gia vai tro cua loai toan dinh hil6ng thu'c tiin Nhiiu hpc gia va nha sU pham danh sU quan tam dac biel din vai ttd cua loai loan dinh budng thuc tien Theo thfl tU md rdng dan eua khai niem dd la: (a) t a i toan ed din giai (story problems), (b) bai loan lien quan din thi gidi thuc (real word problems), (c) giang day hpc tap theo phUdng phap giai quyit van de, (d) xem xet md hinh loan hpc Tfl thud giao thdi gifla the ki 19-20, John Dewey, nha tam li hpc va nha giao due Iflng danh cua Hoa Ki da de chu ttUdng thay va ttd ciing ehuyen ddng, cung "giai quyet vin di" Ong la ngUdi diu tien ebong lai mdt kieu nha trUdng, d dd hpe sinh nhai lai nhiJng Idi giang cua thay giao "hpc sinh din trUdng khdng phai de tiep thu nhflng tti thflc da dfldc ghi vao ttong mdt chUdng ttinh ma roi cd le se khdng bao gid diing den, ma ehinh la de giai quyet cae van de, giai quyit cac "bai loan" cua nd nhflng thuc te ma nd gap hang ngay" Nha tu tudng khai sang d Nhat Ban Fukuzawa Yukichi (1835-1901) ndi: "Du cd nhoi nhet day kien thiic ttong dau nhimg khdng the flng dung vao thuc ti thi cung vd nghia ma thdi" Theo [12], mdt ttong nhflng tieu chuan cua cuon giao ttinh khoa hoe la "Kiin thflc li thuyit dupe gan Uen vdi ap dung thuc tien, tfl dd dUa den y nghia cung nhu dam bao tinh vflng chae eua li thuyit" Doivditoanhpe, CO the kera cdng trinh khdi dau cua Polia "How to solve problems" (1945) - d dd neu len cac phUdng phap tiem can de giai quyit bai loan, bay hfldng din day each giai bai toan, nhiing suy luan ed li va thuc diy qua ttinh sieu nhan thflc [11] va gin day hdn, md rdng giai quyit van de sang nghien cflu ve md hinh toan hoc [10,13] V.V Fttxov da khang dinh: "Vigc giang day loan d IrUdng thdng khdng the khdng chfl y din su cin thiet phai phan anh khia canh flng dung cua khoa hpc Toan hpc Dieu dd phai dfldc thuc hien bang viec day cho hpc sinh flng dung Toan bpc de giai quyit cac bai loan cd ndi dung thuc te" Rdi ghi nha trUdng di vao cudc song, ngUdi ta thUdng lien tudng din nhflng gi da hpe dUdc "Mac du hp vidn din nhflng kien thflc hpc tSp d ttUdng, nhflng nhan viin dd lam diiu mot each linh hoat va sang tao, thudng la tao hoac tai tao nhflng kiin thflc loan hpc phu hdp vdi tinh huong cua vin di hien hflu, khong giong nhfl each ma hp da ttai qua toan hpc nhu nhflng hp hpc d trudng" [13] NhU vay hoe lap theo loi giai quyit vin de cd y ngliia Idn lao, Ngoai niem vui cua ngUdi biit tim kiem va sang tao, hp se cd kha nang chu ddng tu kham pha kien thflc va giai phap cho nhung bai toan ma minh cd the gap phai ttong cudc ddi Mat khac khdng cd "hieu flng phu" cho hoc tap theo phUdng phap giai quyet vin de Khdng cd bang ehflng cho thiy chung ta phai lo lang rang sinh vien bi mat di nhflng ki nang cd ban eua hp niu giao vien (GV) tap ttung vao phat ttien ki nang giai quyit vin di loan hpc Chung la cung khdng ngai bai loan thUc tiin lam mat di sU chat che, mil di ve dep ciia loan hpc Khdng mot md hinh nao chfla dung dUdc hit dUdc mpi dang ve cfla thue tiln Md hinh nhiiu lam la giai thich dUdc phan cot loi cua thi gidi thuc Einstein da ndi "As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they not refer to reality", tam dieh la: Dung cham den thuc ti, toan hpc khdng cdn chat che - cang chat che, toan hpc cang xa rdi thUc ti Trong boi canh phat ttien manh cua ki thuat va canh ttanh loan clu, giai quyet vin di can quan tam dac biet din nhflng yiu to cd tinh chit hen nganh [14] Cin eho sinh vien tiip xiie vdi nhflng bai toan khdng nhat thiet chi lien quan den nganh, nghi eua hp Chang ban, bai toan Uen quan din mSt din chuyin ddng cua cac hanh tinh khdng chi danh cho sinh viin hang khdng vu ttu hay diiu khien; bai loan loi Uu lUu lUdng ddng chay den eac turbin nude khdng chi danh cho T6 Van Ban sinh vien nganh dien Di nhiin, kien tiiflc sat vdi nganh, nghi la tot Song, ngfldi can tti thflc rat rdng nhflng kinh nghiem eua giai quyit vin de cang ddi hdi nhflng tinh hu6ng va each ; tiep can mang ti'nh lien nganh 2.2 Cai tien giao trinh theo hirdng can ban, thiSt thu'c, tang vi du, bai tap gan v6i thurc tien Chung tdi chu tifldng tang dang ke ti le eac vi du bai tap gan vdi thuc tiin, cd mat d nhieu nganh, nghi khae nhau, d nhieu ehuyen de loan hpc khac va d nhieu cap dp khd dl khac Bai loan can cd mfle thach nhat dinh, khdng nin chi dung thUc tiln tam thudng Neu vi du cua xac suit thong ke xoay quanh tung sue sac thi hpc sinh nham tudng day chi la mdn hpc ciia cac ttd chdi may rui Neu vi du ap dung eiia phep tinb vi phan xoay quanh tinh dp dai, dien ti'ch, the tich thi ngUdi hpe se eho rang, giai ti'ch la mdn tinh kich thudc hinh Gia nhU cd nhflng vi du ap dung da dang, cflu sinh vien eua chiing ta khdng phai keu than: "Nhflng thfl em hpc nhu tich phan, vi phan ham so, flng dung ti'ch phan, phfldng ttinh vi ph&n, da tap hinh hpc Riemann cao sieu qua, nen em khdng nhin thay nhflng flng dung dii nho nhd de hieu sau va thiy bet dUde cai hay, cai dep cua nd hpc sinh, sinh vien hdi em, hpc loan d ttUdng dai hpc cd tac dung gi?" Cd nhiing vi du tudng chiitng la thuin tfly li thuyit niu chung ta cd nin kiin thflc Id thua^ van cd the nliin nd dfldi ngon ngfl cua flng dung [3] Chang ban, bai loan xel phan bo eua phep bien doi eosin eua phan bo deu Y = cos X, X cd phan bo diu tten doan [0; 2TT\ Day la bai toan cd tinh eh|t loan hpc thuIn tuy, Song niu giao vien cd nhflng kiin thflc ve Vat U dpc mdt s6 tai Ueu ve ki thuat dien, se ed the hfldng dan cho sinh vien gan X vdi gdc pha cua cuon dSy quay diu ttong mot tfl trUdng, Y la ddng di£n phat sinh thi bai loan da cd mdt dien mao mdi, vi tti bai tap dUdc khang dinh linh yeu mdn hpc dupe ciing c6 Xet cae bai tap thdng thudng va cd ap dung thUe ti d Bang Bang Mdt so bdi todn todn hgc thuan ttiy vd bdi todn thuc tien lien quan Toan hoc thuan Gan vdi thUc te Khi ca boi vdi van toe tUdng doi v so vdi nirdc, nang lUdng san cua no tten mot ddn vi thdi gian la j;^ Ngudi ta thay rang ca di cU CO gang cUctieuhda nang lUdng long the de bdi mot khoang Tim cuettiham so each nhat dinh Niu van tdc ddng nUdc la a va ca bdi ngUdc dong nudc (a < v) thi thdi gian can bdi dUdc khoang each L la E{v) = -!^, {a