Tap chi KHOA HOC DHSP TPHCM Duang Minh Thdnh BAN VE MOT SO YEU TO HINH THANH NEN MOT CHlTONG TRINH KHUNG QUOC GIA MON TOAN DUaNG MINH T H A N H * TOM TAT Trong bdi bdo ndy chung toi diem lgi nhitng ye[.]
Tap chi KHOA HOC DHSP TPHCM Duang Minh Thdnh BAN VE MOT SO YEU TO HINH THANH NEN MOT CHlTONG TRINH KHUNG QUOC GIA MON TOAN DUaNG MINH T H A N H * TOM TAT Trong bdi bdo ndy chung toi diem lgi nhitng yeu to quan tgo nen mot ehuang trinh khung mon Todn a phS thong Sau chung toi se trinh bdy tdm hrac chuong trinh khung mon Todn cua Singapore nhu Id mot vi du Cuoi cimg chiing toi so sdnh hai ehuan trinh ciia Singapore vd cua Viet Nam de de xudt mot so y tudng cho viec thiet ke ehuang trinh khung mon Todn a Viet Nam Tu^khoa: chuong trinh Toan, sach giao khoa, thiet ke chucmg trinh ABSTRACT A discussion of the fundamentals for the formation of a national mathematics curriculum In this article, we discuss some fundamentals for the formation of a national mathematics curriculum Then, a summary of Singaporean mathematics curriculum is presented as an example Finally, the two nations' curricula are compared to propo.se some ideas for the design of Vietnam's mathematics curriculum Keywords: Math, textbooks Curriculum design Gioi thieu Giao due Viet Nam da co nhieu thay doi lan hon niia the ki qua, nhung ngi dung va phuang phap day toan, hgc toan thong thi thay doi kha cham Mgt nguyen nhan de thay la Viet Nam thieu nhimg nghien ciiu sau ve ehuang trinh va thilt kl xay dung chuong trinh Bat dau tii nam 1950, Viet Nam da trai qua bon lan thay dll sach giao khoa nhung lan gan day nhat nam 2002 chiing ta mai thuc hien mgt each "bai ban", la xay dung chuong trinh truac, bien soan tai lieu day thii nghiem roi moi lam sach giao khoa chinh thiic' Tuy nhien, ca chiing ta da co mgt chuong trinh khung quoc gia thi chuong trinh van chua thuc su hoan chinh, nhat la ehuang trinh danh cho bac thong ca so va thong trung hgc^ Khi dat chuong trinh canh mgt s6 chuong trinh Toan nhieu nuoc tien tien tren the giai, ta co the nhan thiy nhiing khac biet ro ret: Tir co so li luan, quan diem giao due cho den ngi dung, chu dl kiln thiic, phuong phap giang day, phuang phap hgc tap va phuang tien h6 trg Su cin thilt va tim quan trgng ciia mgt chuong trinh khung qu6c gia d6i voi viec dinh huong cho nln giao due thong da dugc khang djnh tren cac nghien ciiu qu6c tl vl giao due Chuong trinh khung qu6c gia khong don gian chi la mgt tai lieu bit bugc CO tinh phap li chira nhung ngi dung giao vien can day va hge sinh cin phai hgc " TS, Truing Bai hgc Su- pham TPHCM Tap chi KHOA HOC BHSP TPHCM Sd 65 ndm 2014 raa no eon djnh huong each day cua giao vien va each hpc ciia hpc sinh ciing nhu each danh gia qua trinh day va hpc Anh qu6c, chuong trinh khung quoc gia dugc chuan hoa, cap nhat lien tuc theo timg giai doan phii hpp, va cong b6 rpng rai tren trang web ciia Bp Giao due Day la chuong trinh quy djnh nhimg npi dung bat bupc den Icjp {giao due bit bupc), eae trucmg hpc dugc nha nuoc tai tro dugc yeu cau phai eo chucmg trinh khung cua rieng minh dua tren chucmg trinh khung qu6c gia va phai cong bo cong khai tren raang [English Department for Education 2013] Ci MI, khong co chuong trinh khung cap quoc gia ma raa chi co chuong trinh khung cua timg tieu bang Tuy nhi§n, cac chuong trinh tieu bang phai dupe xay dung tren nhimg chuan rave NCTM Hpi dong quoc gia cac giao vien Toan - quy djnh [A.C Burris 2014] O Viet Nara, chuong trinh khung quoc gia chu yeu de cap den nhiing npi dung va thcyi lugng danh cho giang day va danh gia bac tieu hpc, chiing toi cho rang nhiJng nguiri thiet ke chucmg trinh da co nhimg no luc dang ghi nhan de dua dupe mot chuong trinh Toan vol nhihig chu de kien thuc kha hoan ehinh Sach giao khoa toan tieu hpc eiing da cong viee phat trien cac chii de Ket qua danh gia giao due Pasec 10 (ciia Pasec Confemen, chuong trinh phan tich cae he thong giao due cua Hpi nghi cac Bg truong giao due cac nuac sir dung tieng Phap) cho thay hgc sinh tieu hpc Vipt Nam tiep thu tot cac ehii de kien thirc, co cac ki nang tir cip dp thip ddn cip dp cao^ Tuy nhien den bac thong co sir va ph6 thong trung hpc thi diSu khong dugc tri tot toan hpc va nhiiu mon hpc khae dupe thiit kS nhiing b6 mon khoa hgc rieng le Yiu t6 khoa hgc dugc dat len tren yiu t6 cong cu va ling dung vo tinh da bien toan hgc rapt mon khoa hpc li dua thuin treacae suy lu^n toan hoc' Vai muc dich nghien eiru de ciing xay dung mpt chucmg trinh khung qu6c gia mon Toan phii hpp viji nhung chuin rauc qu6c te va tipm can nhiing chuong trinh toan rapt s6 nuoc co nin giao due tien tiin, ehung toi de xuit viec xem xet \d.x chuong trinh toan a thong ma truoc hit la chucmg trinh Toan b?c tiiu hpc da dugc Bp Giao due va Dao t?o ban hanh n5m 2006 b6i canh dat e ^ chuong trinh Toan ciia rapt nuac CO nin giao due dugc cgng dong qu6c ti cong nhan, la Singapore' Chiing toi chi tap trung vao nhimg npi dung dugc quy dinh nam diu tien cua bac tieu hpc, nhihig phuang phap giao due co thi dupe huy dgng mpt each da d^ing va linh hojt Chung toi khong di sau vao giai thich nguyen nhan ciia nhimg tin tai viee xdy dung chucmg trinh Toan ma chi nhin manh nhiing yiu ti lam nen mat ehuang trinh toan chuan cho giao due thong Bai bao dupe trinh bay theo ciu tnic nhu sau: muc diu tien danh di tra lai cau hoi chuong trinh Toan la gi va no dugc thiit ke nhu thi nao? Trong muc tiip theo chiing toi trinh bay chuong trinh khung mon Toan ciia Singapore Di dgc gia co eai nhin toto di?n, chiing to; se ttinh bay ting thi chuong trinh nhung o goc torn luge, neu nhiing diim chinh, nii bat va sau dimg lai nhimg npi dung danh cho lap Chi tiit cua chuong trinh dpc gia co the tham khao tai lieu [Singapore Ministry of Education 20 Tap chi KHOA HOC DHSP TPHCM Dteffng Minh Thdnh 2012] Phan cuoi ciia bai bao danh cho nhung danh gia ve chuong trinh toan a bac tieu hgc, sau de xuit mgt s6 cai tiln thilt ke xay dung chuong trinh toan bac tieu hgc a Viet Nam Nhimg dl xuit co the sg la ggi y cho viec thilt kl chuong trinh Toan cho nhiing bac hgc tiep theo Cau true cua mot chu'ong trinh Toan Chiing ta bat diu voi cau hoi "chuong trinh giang day Toan la gi?" Dau tien, chuong trinh giang day Toan la mgt bg gom cac kinh nghiem dugc thiet ke de thiie day viec hgc Toan va thii hai, la duang toan hgc ma hgc sinh se di theo suot giai doan thong [J Kilpatrick 2011] Co nhilu each hieu ve duang toan hgc Theo J Kilpatrick, neu toan hgc dugc hieu la mgt mien da chieu thi day chinh la duang tuyen tinh xuyen qua mien da chieu Nhu vay khong the dua vao truong hgc mgi thii mien toan hgc da chieu ma chiing ta can phai can nhac lira chgn, lam tim mgt duong phii hgp de di qua nhung n6i dung can phai hgc Va nhu tat ca chiing ta deu biet, la mgt nhi$m vu khong dan gian goc ling dung toan hgc, duong toan hgc danh cho hgc sinh phai co nhieu nga re vao nhung ITnh vyc cua doi song hang Dong thoi sau moi ngi dung toan hgc dugc hgc, hgc sinh tim thSy dugc nga re va dii tu tin vao kien thiic toan hgc de di vao moi nga re Goc lam tang them ap lire cho nhimg nguoi thiet ke chuong trinh lua chgn nhung ngi dung toan hgc chiia dung nhihig ling dung dai song va tao nhiing nga re thich hgp Theo mgt nghien ciiu ciia Hiep hgi quoc te ve danh gia tuu giao dyc^, mgt chuong trinh Toan phai bao dam yeu to: duoi goc nha quan li no phai la chuong trinh c6 muc tiSu, duoi goc giao vi^n no la chuong trinh kha thi ap diing dugc, va duoi goc hgc sinh thi no phai la chuong trinh hoan dugc Cau tnic ciia mgt chuong trinh toan toi thieu phai bao gom: muc tieu, quan diem, phuong phap lam nln tang, quy tac va each thiic ap dung, ngi dung va nhiing huang dan, each danh gia' Trong cac yeu to cau nen mgt chuong trinh, muc tieu dugc danh gia la quan trgng nhit nhu kilu "muc tieu nao chuong trinh iy" Viec dua nhiing mue tieu giao due can phai nghien cuu, can nhac kT luong va phai chii y den nang lire ciia nguoi hgc Viec dat muc tieu nham muc dich kiem soat dugc ket qua va san phim day hgc, CO nghia la moi muc tieu it phai lugng hoa dugc danh gia va co kha nang thuc hien dugc ChiroTig trinh Toan cua Singapore Chuong trinh khung mon Toan ciia Singapore (Mathematics Teaching and Learning Syllabus - MTLS) dugc Bg Giao due Singapore ban hanh va ap dung tir nam 2013 (cap nhat tir Chuong trinh khung mon Toan nam 2007) Mo diu, MTLS nhin manh: "Hgc Toan la chia khoa quan trgng tit ca cac he thdng giao due nhim chuin bi cho cong dan ciia minh mgt cugc s6ng thi ki XXI Mgt su hilu biit t6t vl toan se cin thilt cho bat cii noi nao co tinh toan, luong, hga, phan tich thdng ke Viec hgc Toan cung cip mgt phuang tien tuyet vol dl dao tao tam h6n, phat 21 Tap chi KHOA HOC DHSP TPHCM Sd 65 ndm 2014 triin nang lire, suy nghi logic, trim tupng, 6c phe phan va sang tao" [Singapore Ministry of Education 2012, trang 2] MTLS cho ring khong phai tit ca hpc sinh se ciing so thich va kha nang tu nhien di hgc Toan, mgt s6 se thay no thii vi, mgt so se thiy no thaeh thiic, ragt s6 se phat hien dugc nhiing vin di hip din, mot so se thay roi rim Do MTLS di den kit luan ring cin phai cung cip nhOng duong khac biet va them cac lira chpn di nguai hpc tii da hoa tiim nang eiia hp, dat dugc mpt mirc dp iam ehu toan hpc di phuc vu tit hon cupc sing hoac theo duoi toan hpc a mirc eao nhit MTLS quy dinh mon Toan la chii di quan trpng chuong trinh giang day cua Singapore va mpi tre era phai co it nhat 10 nara hpc thuc sir ve Toan 3.1 Quan diim nen tdng Trong MTLS, sir thay dii vi npi dung khong phai la don bay quan ttpng Thay vao diiu quan trpng la trao cho hpc sinh nhiing kl nang va nang lire, dan tcii qua trinh hpc tap cin thiit han nhimg gi dugc day va ghi nho Nhu vay chuong ttinh MTLS dupe viit voi quan diera khong chi nhim thong bao cho giao vien ve nhirng gi hp se giang day ma no anh hucmg den each day ciia giao vien va each hpc ciia hpc sinh Mgt diiu quan trgng khac ma chucmg trinh de cap la giai thich kinh nghiem hpc tap ben canh ket qua hpc tap va hucmg dan giao vien lara dieu a) Muc tieu: Muc tieu t6ng the: Bao dam hpc sinh se dat dugc rapt mirc dp lam chii toan hge nham phue vu tot nhat cho cuge song cua hg Doi veil nhiing nguai quan tam va co kha nang thi se theo duoi toan hpc cr miic eao nhat co the Muc tigu chinh: Tiep thu va ap dung cac khai niem va ki nang toan hpc, phat trien kl nang nhan thirc sir dung toan hpc de giai quyet van de, phat trien thai dp tich cue doi veil tpan hpc Muc tieu a b^c tieu hoc: ' Co dugc khai niem va kl nang toan hgc de ap dung cupc sing hing va tiep tuc hpc toan mpt each lien tue; • Phattriin tu duy, li luan, giao tiip, ung dung va ki nang nhan thirc thong qua giai toan; Xay dung long tin va nuoi duong sir hilng thu ve toan hpc Nhiing rauc tieu cr nhimg bac cao hon, dpc gia co thi tham khao o tai lieu [Singapore Ministry of Education 2012] b) Phan bo chuong trinh toan or cac bSc hoc ciia Singapore d bae tiiu hpc, theo sa di ben tren, PI-4 Maths (Toan tiiu hgc tir lap din lop 4) chung eho tit ea hpc sinh P5-6 Standard Maths phat triin nhiing npi dung cua Pl-4 Maths P5-6 Foundation Maths xem xet lai mgt si khai niem va kl nang quan trgng Pl-4 Maths Nhiing khai niem va kl nang dugc giai thieu Foundation Maths la tap cua Standard Maths O nhimg bac cao han, dgc gia co thi tham khao (Singapore Ministty of 22 Dutmg Minh Thanh Tgp chi KHOA HOC DHSP TPHCM Education 2012) N(A)-Level nghia la Normal (Academic) Level (danh eho hgc sinh co nang luc ve hge thuat) va N(T)-Level nghia la Norraal (Technical) Level (danh cho hpc sinh co nang lire vi ki thu^t) Giai thich: t : di thing true tiip; —>: chuyin tiip dupe bo sung them kien thire va kl nang H3 Maths HI Maths —> H2 Maths Pre-University ,^ + S3-4 Additional Maths (0-Level) + -I S3-4 Additional Maths (N(A)Level) ] Secondary + S1-4 Maths (0-Level) Sl-4Ma ths (N(A)-Level) P5-6 Standard Maths SI-4 Maths (N(T)-Level) P5-6 Foundation Maths Primary Pl-4 Maths Hinh Phdn bd ehuang trinh Todn a cdc bdc hgc cita Singapgre 3.2 Md hinh cho khung ehuang trinh Chi tiit vi mo hinh nay, dpc gia co the xem [Singapore Ministry of Education 2012], a day chiing toi chi de cap mpt so yeu ti lam nii bat quan diim va muc tieu giao due ciia chuong trinh Nhimg yeu to bao gim; Sieu nhan thirc (Metacognition), thai dp (Atthudes) va tiin trinh (Processes) Sieu nhfln thiic (Metacognition): Sieu nhan thirc di cap din nhan thiic va kha nang kiem soat qua trinh tu cua rapt nguai, dae biet la viee lira chgn va sii dung cac chiin luge giai quyit van de No bao gom kha nang giam sat suy nghi ciia chinh minh va tu dieu chinh hanh vi hge tap 23 Tap chi KHOA HOC DHSP TPHCM So 65 nam 2014 Thai (Attitudes): thai de cap khia canh tinh cam cua viec hgc Toan nhu: Niem tin doi voi toan hgc va tinh him dung ciia no, su quan tam va thich thii hgc toan, danh gia cao ve dep va siic manh ciia toan hgc, sir ty tin viec sir dung toan hgc va tinh kien tri viec giai quyet mgt van de Tien trinh (Processes): Tien trinh de cap nhiing kT nang lien quan den viec dat dugc va ap dung nhiing hieu biet toan hgc No gom co li luan, giao tiep va kdt n6i, ap dung va mo hinh hoa, kT nang tu va tim giai phap qua thii nghiem • Li luan toan hge de cap den kha nang phan tich tinh huong toan hgc va xay dung lap luan logic; • Giao tiep de cap din kha nang sii dung ngon ngii toan hgc dl thi hien y tuang toan hgc va lap luan chinh xac, siic tich va hgp li; Ket noi de cap kha nang nhin thiy va lien kit nhiing y tuong toan hgc, giua toan hgc va cdc mon hgc khac, giiia toan hgc va thi gioi thuc; Niem tin Svquan t ^ , hiing thu Danh gia cao gia tri S\irinc^y S\r kien nhan Giam sat suyngbi cda chinh minh ~ "euchinhhanhvihQct^ Tinh toan so hi?c Bien doi d^i so •y lu^, giao t i ^ vili£a h$ TuAng tupng khong gian dungvim6hlnfah6a Phan tich (to li^ Ki n&ng tu v& tim giii Etodgic ph^ quathdnghi^ V|n dyng cong c^ toan h^c Udchi^ng Sd hoc, Dyisd, Hinh h^c, Udng k£, Xic suit, Giii tich Hinh Mo hinh cho khung chuong trinh 24 Tgp chi KHOA HOC DHSP TPHCM Ducmg Minh Thanh Ung dung va mo hinh hoa The gioi thuc • Tim hiiu vin di The gicii toan hoc • Dua cac gia dinh de dan gian hoa van de • Mo ta van de duoi hinh thiic toan hge Bai toan the gioi thuc » Phan chieu giai phap the giai thue • Cai tien mo hinh M6 hinh toan hgc Lua chgn, sii dung phuong phap, cong cu toan hgc thieh hgp Giai quylt vdn de, trinh bay giai phap ; Giai phap trong the gidi thuc Loi giai toan hgc • Giai thieh loi giai toan hpc boi canh bai toan th\rc te • Trinh bay Icri giai cho bai toan thuc te Hinh Qud trinh md hinh hda todn hgc theg MTLS 3.3 Ba quy tde gidng dgy, ba giai dogn hoc todn vd ddnh gid irong l&p hpc Ba quy tic giang day Quy tde Giang day nhim rauc dich hpc tap; hpc tap la di hiiu biit; bit diu tii li luan sau ap dung va cuoi ciing la giai quyet van de Quy tde Giang day nen xay dung tren kiin thiic ciia hpc sinh, mang din hpat dgng nhan thiic dua tren hirng thii va kinh nghiem va mang hpc sinh vao hoat dgng hge t?p tich cue co phan hii Quy tac Giang day n6n ket n6i hgc tap vgi the gicM th^c, khai thac cac cong c\i cong ngh? th6ng tin va nhin manh nhttag nang luc cua thi ki XXI Ba giai doan hpc Giai dogn Sin sang sin sang hpc la bucic chuan bi quan trpng de hpc tap cong Giao vien cin chii y din vai tro cua kiin thiic chuan bi, boi canh thiic day di tao dgng luc va moi truong hpc t$p 25 Tap chi KHOA HOC DHSP TPHCIVI S6 65 nam 2014 Giai dggn Tham gia Day la giai doan chinh cua viec hpc nai ma giao vien sir dung mpt "tiet muc giao due" di thu hiit hpc sinh vao viec hgc Co ba phuong phap su phjim lam xuong song: Hpc tap dua tren boat dpng, tuc la hpc bing each lam: phuong phap dae bipt CO hieu qua cho giang day cae khai niem va kl nang toan hgc bac tiiu hpc va trung hpc CO so Xem vi du [Singapore Ministry of Education 2012] Hpc tap theo nhihig yeu ciu co huang din eua giao vien: thay vi dua cac cau tra icri, giao vien hucing din hpc sinh kham pha, dieu tra va t^ tim thay cau tra Icri Hge sinh hpc each tap trung vao cau hoi hoac y tuong cu the, dugc tham gia vao giao tiep, giai thich va phan xa tren cau tra loi cua hp Hpc sinh eung hpc each dat cau hoi, xir li thong tin dii lieu va tim kiem cac giai phap phii hpp Xem vi du [Singapore Ministry of Education 2012] • Hpc tap theo su huiing din true tiip ciia giao vien: huong din tryrc tiip hieu qua nhat hpc sinh dugc biit nhiing gi hg se dupe hpc tSp va nhimg gi hp du kiin se lam dugc Dieu giup hgc sinh tap trung vao cdc mye tieu hgc t^p Giai dogn i.am chu Day la giai doan cuii ciing cua qua trinh hpc tjp ngi giao vien giilp hgc sinh ciing CO va raa rpng viec hpc Cac phuong phap tiip can chu yiu bao gom: Thuc hanh tao dpng lire; Xera lai c6 phan anh; • Mo rpng hpc tap a) Vai trg cua ddnh gid Danh gia la mpt phan cua qua trinh tucmg tac giang day va hge tap tai giao vien thu thap thong tin phan hii vi viec hpc tap ciia hpc sinh di thong bao va hi trg cho viec giang day Ngugc lai qua danh gia hgc sinh biit nhimg gi hp dang co va nhiftig gi hp cin lara di cai thien viec hgc cua hgc sinh b) Phgm vi ddnh gid Danh gia co the dugc phan loai bao gim ting kit, dinh hinh va chin doan c) Tich hgp ddnh gid vdo dgy hge Dieu quan trpng la giao vien biit nhimg gi va nao danh gia viec hpc ciia hpc sinh, va Iam the nao de dua danh gia qua trinh hpc tap Vi du, giao vien eo thi xem hpc sinh giai quyit vin de va di nghi hpc sinh giai thich chiin luge cua hp Giao vien cung cho phep hgc sinh tham gia vao viec danh gia cong viec cua chinh hp, tu phan anh viee hpc cua rainh va lam thi nao di cai thien no Co hai each danh gia: danh gia linh boat tiiy thcri diim (vi du bing each dat cau hoi) va danh gia theo ki hoaeh (vi du bang phiiu danh gia) 26 Du-ffngMinh Thanh Tap chi KHOA HOC DHSP TPHCM 3.4 Chtrffng trinh Todn tieu hoc MTLS So hgc va dai so Do dae va hinh hoc Thong ke Tien trinh toan hoc Tien trinh toan hoc So Tien trinh thiitu MPI Li luan, giao • Sir dung nhirng ki hieu thich hgp, nhung bieu tugng va tiep va ket quy uoc de trinh bay va truyen dat y tuang toan hgc noi • Neu cau hoi dua tren quy nap va suy luan theo: Mau quan sat, tuong dong va khac biet Nhiing ket luan hgp li va suy luan Giai thich hay bien minh cho cac giai phap, viet cac giai phap toan hgc • Ket noi toan hgc va giua toan hgc vdi cugc song MP2 Ap dung MP3 Nhung kT • Sir dung nhung kT nang tu nhu: phan loai, so sanh, sap nang tu xep trinh tu, tong quat hoa, suy dien, nit ggn, phan tich, tong va nhirng hgp phuong phap • Sii dung mgt mo hinh giai quyet van de nhu cua Polya danh gia, nit • Sir dung nhirng phuong phap nit tia kinh nghiem: Ve so tia kinh do, tao bang bieu, phan doan va kiem tra, lat ngugc van dh, don nghiem gian hoa van de, xem xet truang hgp dae biet Cau true ngi dung chirorng trinh giang day Toan a lop Mot: phan ehung toi chi torn luge va giii lai mgt so ngi dung ma theo chiing toi danh gia la noi bat N9i dung LOfPMOT S HOC VA DAI SO CHU DE: SO Cac so pham vi 100 Phep cgng va phep trir 2.1 Phep egng va trir pham vi 100, tinh nham phep cgng va phep tru pham vi 20 Ph^p nhan va phep chia j Kinh nghiem hoc tap Ngi dung ve mat toan hgc khong khac biet so vol chuong trinh ciia Viet Nam Hoc sinh nen co co* hoi de Lam viec theo nhom de ke nhimg eau chuyen vl phep egng va phep trir sir dung cac d6i vat/hinh anh cu thi; so sanh hai so pham vi 20; lam chu dugc phep cgng va phep trir pham vi 20 thong qua nhimg dang tro choi Hoc sinh nen co co" hgi de 27 T?p chi KHOA HOC DHSP TPHCM 3.1 Khai niem ve nhan va chia 3.2 Nhan pham vi 40 va chia pham vi 20 3.3 Bai toan eo loi giai buoc ve phep nhan va phep chia vdi hinh anh true quan CHU DE: TIEN Tien 1.1 Dem tien: dem theo xu den la, dim theo la din 100 la 1.2 Giai bai toan co lai giai buoc lien quan den cgng va trir tien chi bang la (hoac chi bang xu) DO DAC VA HINH HQC CHU DE : DO D^yC Chilu d^i 1.1 Do va so sanh chieu dai cua nhirng vat nhirng dan vi khong tieu chuan S6 65 ndm 2014 (a) Tao cac nhdm bang dimg nh&ng doi tugng cy the va dim tong so doi tugng cua cac nhom bang each I5p l^i lien tiep cdc phep cgng, sCr dung ng6n ngii nhu "2 nhom 5" va "2 lan 5" (b) Chia mgt s6 nhiing d6 vafhinh dnh cu thi dugc cat va giai thich each chia; phan chia mgt tap cae vat cu thS cac nhom bing nhau, va thao luan khai niem phSn chia Hgc sinh nen co ctf hgi de (a) Giao tiep va chia se kinh nghi?m mua sam (b) Nhan thiic dugc tien xu (giay), ghi chii nhung loai tien khac nhau, dim tien tir menh gia cao den thap (c) Quy doi mgt loai tien xu hoac tiln giay, so sanh so tien (dung tiln Ah choi) (d) L ^ vi^e theo nhom dimg tien ehai de cgng, trir v^ doi tien cac hoat dgng mua sim Hgc sinh nen co ctf hgi de Lam vi?c theo nhom de chieu dai sir dung nhieu don vi khong ti^u chuan nhu cac bg phan ca the, kep giSy va nhung v^t bien moi truang gan giii xurfg quanh va gi^i thich viee lira chgn don vi va phep dugc thuc hi$n nhu the nao; uoc tinh dai cua mgt dl vat truac va sii dung hi "khoang" dl mo ta phep Thfii gian Hgc sinh nSn co ca hgi de 2.1 Dgc thoi gian theo Dgc thai gian tir ding h6 va lien he din nhimg su kien thai gio/nua gia gian ciia mgt su dung "gio" va "gia ruoi"; sap xip su kien theo trinh tu thai gian, giai thich sir phii hgp hay khong Clia su kien tai cac thai dilm khac ngay, vi du an trua liic gia ehilu CHU DE: HiNH HQC Hinh ehilu Hgc sinh nen co cff hgi de 1.1 Xac dinh, dat ten, mo ta (a) Nhan biet, ggi ten va mo ta loai hinh ehilu co ban va phan loai nhiing hinh tir nhiing vat va hinh anh thuc; theo ddi each thu hinh chiSu chieu tir dl vat ehilu; xac dinh va mo ta hinh ehilu cac kich ea va huong khac nhau, tao mgt hinh • hinh ehii nhat chieu tir nhiing manh cat va doan mgt hinh ehilu tir mo hinh vuong ta hinh dang • hinh tron 28 Tgp chi KHOA HOC DHSP TPHCM • hinh tam giac 1.2 Thuc hien/hoan nhiing hinh chieu theo mgt hoac hai so cac thugc tinh sau: kich thudc, hinh dang, mau sac, huong Dui/ng Minh Thdnh (b) Nhan biet va mo ta su khac nhau/glong giiia hai hinh chieu; lam viec theo nhom de sap xep cae hinh chieu theo nhiing each khac va giai thich (c) Sir dung hinh chieu hoae nhiing chuong trinh ling dung nhd de tao mo hinh va mo ta cac mo hinh (d) Lam viec theo nhom de tao mgt mo hinh va mai cac nhom khac doan hinh bi mat mo hinh THONG KE CHU DE: MO TA VA GIAI THiCH Dtr LI|:U Bang dii' lieu hinh anh Hgc sinh nen co co hgi de 1.1 Dgc va giai thich dii (a) Lam viec theo nhom de thu thap dii li6u tCr lop hgc, tra li?u tir bang du lieu hinh lai eac cau hdi nhu "Chiing toi thich nhihig loai trai cay anh nao?" va sii dung bang dii lieu hinh anh (b) Thao luan va mo ta dii lieu dugc trinh bay mgt bang dii lieu hinh anh bang each sii dung ngon ngii nhu "nhat", "it nhat", "Ion nhat", "nhieu nhu" (c) Bieu dien bang dii lieu hinh anh ca hai hinh thiic dgc va ngang, va tao mgt cau chuyen sir dung thong tin tir mgt bang dii lieu hinh anh Mot sd ban luSn ve nhirng yeu to hinh nSn m6t chirong trinh khung quoc gia mon Toan 4.1 Mot so diem Ithdc giira chwtmg trinh Todn bge tieu hgc ciia Viet Nam (CTTTH) va chirong trinh toan bae tigu hoc ciia Singapore (PMTLS) Quan diem gi^o due va hf th6ng muc tieu Quan diem giao due cua PMTLS chi rang qua trinh hinh kien thire quan trpng hon npi dimg dugc hgc, dieu ma CTTTH khong he nhic toi Trong thuc ti trucmg hgc Viet Nam ngi dung giang day dugc kiem soat chat che^ va co ve truang hgc quan tam nhiiu din viee ghi nha kiin thirc cua hpc sinh ban la trao cho hgc sinh nhitng kT nang va nang luc CTTTH co phan cap he thong rauc tieu tit mue tieu ting thi cho din cac muc tieu chi tiet nhung he thing mue tieu eua hai chuong trinh vi co ban la khac Trong PMTLS nhin manh muc tieu trang bi ki nang phuc vu cupc song (xem lai phin 2.1.) thi CTTTH di sau vao nhihig muc tieu raang npi dung toan hgc va phat trien nang luc tu duy, cu thi: (1) Co kiin thiic ca ban ban diu vi si hgc, cac dai lugng thong dung, mgt s6 yiu ti hinh hgc va thing ke don gian; (2) Hinh cac kl nang thuc hanh tinh, luong, giai bai toan m nhiiu ling dung thiit thuc dcii sing'; (3) Buac diu phat triin nang luc tu duy, kha nang suy luan hgp li va diln dat dung Dieu din toi sir khac biet viec thiet ki hai chucmg trinh'" 29 Tap chi KHOA HOC DHSP'TPHCM Sd 65 ndm 2014 Mo hinh giao due, phan bo va thiet ke chirong trinh Ca hai chuong trinh deu cho rang kiin thirc, kl nang, himg thu, thai dp va hanh vi hpc tap ma hpc sinh co dugc' xuat phat tir viec giai quyet cac bai toan Tuy nhien, PMTLS nhin manh din vai tro ngang giiia cac yeu to va dua dugc mgt mo hinh cu thi nhu a hinh 2, tit trien khai vao nhimg ngi dung tiip theo (tuc la chi cho nguoi ta biit phai lara the nao) CTTTH ciing de cao viec hinh phuong phap suy nghi, phuong phap hgc tap tich eye, chu dpng, khoa hpc va sang tao eua hoc sinh thong qua viec giai toan Tuy nhien, thuc ti truong hpc Viet Nara, chinh kiin thitc va phuang phap giai toan moi la nhimg yeu to dugc uu tien Nguyen nhan la tinh trien khai eiia ehuang trinh yeu (tire la nguoi ta khong biet trien khai the nao va van loay hoay voi bai toan tim kiem nhiing phucmg phap day hpc cho phat huy tinh tich eye, chu dpng, khoa hpc va sang tao ciia hpc sinh - ma dang li lai giai ciia bai toan phai nam chinh chuong trinh) Vai quan diem giao due can phai cung cap cho nguai hpc nhieu eon ducmg va nhiiu lira chgn, MTLS da thiit ki nhiiu chuong trinh khac tit cuoi bac tiiu hpc O Viet Nam, len den bac thong trung hgc, hpc sinh raoi tiip can cac chucmg trinh khac nhung nhin chung sir phan chia chucmg trinh cho phii hgp timg dii tugng dugc coi la that bai" Do la chua ke chucmg trinh cho timg bac hgc dugc thiit ki dpc lap boi timg nhom tac gia va khong dugc trinh bay mot he thing nhit xuyen suit tir bac tieu hpc den hit bac phi thong trung hpc'^ Phu-ong phap day hoc va danh gia kit qua hoc tf p Ca hai chuong trinh deu nhin manh yiu t i phuang phap day hpc va danh rapt phin quan trpng di noi vi danh gia kit qua hpc tap Trong PMTLS, vin di ciia giao vien la lam tich hpp danh gia vao boat dgng d£iy hgc di dat hieu qua nhu da chi thi CTTTH, yeu to khong phai la vin di cua giao vien ma yiu t i danh gia loan dien, khach quan, cong bing, phan loai tich cue dii tugng hpc sinh mai la yiu ti uu tien hang dau (tien the, danh gia kit qua hpc tap hien a truang hpc Viet Nam da theo mpt quy trinh, eho ring chuin kiin thitc cin thiit han nhiing chuin muc khae, danh gia npi dung can thiit ban danh gia qua trinh, di cao danh gia djnh ki hon danh gia thuong xuyen linh hoat, di cao danh gia tren phiiu ban danh gia qua cau hoi, thing nhat mpt each thirc danh gia ban la giao vien chii dpng lua chgn each thitc danh gia) Npi dung kiln thuc, each ti chuc va phirong tifn day hoc Ta CO the de dang nhan npi dung kiin thiic, each ti chiic va phuang tien day hpc dupe de cap PIVITLS da dang, phong phii va gin vol thuc ti cupc sing hon so voi CTTTH Ro rang thiit ki chuong trinh ciia PMTLS phii hop vcii rauc tieu ban diu cua no, mac dii CTTTH co nhic din rauc tieu phuc vu cupc sing nhien each thiet ke cua no chi dimg lai nhimg bai tap thuc ti don gian dugc lap di lap lai va khong CO nhieu nhimg bai tap gan vai nhimg boat dpng hang cua tre em Ching ban yeu ti hinh hpc chiiu CTTTH liip chi gim nhimg vi du sau: Viit ten moi 30 Tap chi KHOA HOC DHSP TPHCM Dwomg Minh Thdnh hinh vao eho eham; to ciing mau nhirng hinh ciing hinh dang (hinh ve); minh hga mat cai co hinh tron, mat siic sac co dang hinh vuong (tac gia bai bao khdng hieu li tai nguoi ta lai lay vi du siic sac dua vao chuong trinh toan lop du no gan vdi tro choi may riii khong thieh hgp vdi liia tuoi), khan quang cd dang tam giac; ghep hinh hinh mdi (hinh ve) That theo nhu PMTLS, ta co the lay cac vat va hinh anh thuc de day ve hinh ehilu, \iy mat cat tir nhiing vat ehilu de thu dugc hinh ehilu, lam viec theo nhom dl phan loai hinh ehilu, choi cac tro choi doan hinh, sir dung nhiing ling dung tren may tinh 4.2 Mgt s6 di nghi thiit ki chu&ng trinh Todn bac tiiu hgc • Trinh bay ro quan diem giao due va xay dung lai mgt each co he thong cac muc tieu giao due ctia day va hgc toan, phan tach ro muc tieu hgc toan gan vdi ung dung thuc tl va muc tieu hgc Toan dl theo duoi cac nganh khoa hgc (trong co toan hgc) Trinh bay chuong trinh mgt he thing nhat tir bae tieu hgc din hit bac thong trung hgc Lira chgn mgt md hinh giao due tir nhiing mo hinh san co hoac xay dung mgt md hinh giao due phii hgp vdi quan diem va muc tieu giao due Viec lua chgn mgt mo hinh san CO da dugc kiem chiing ve chat lugng do! vdi mon Toan (hoac xa hon la nhung mon khoa hgc ty nhien) van tot hon la tu xay dung mgt mo hinh khong dua tren mgt quan diem giao due tien bg nao'^ Vi du ta cd the nghien ciiu, lua chgn, cai tien va ap dung chuong trinh Toan tieu hgc eua Singapore • Trinh bay ro rang va cu the viec lira chgn phuong phap va each thiic tien hanh boat dgng day hgc Quan diem coi giao vien la nhiing nguoi am hieu ve phuong phap day hgc va cho rang giao vien tu minh co the lua chgn dugc mgt each thiic phii hgp de tien hanh mgt bai day c6 the dan den mgt nhan djnh rang: giao vien khong cSn phai cd su ho trg ve mat giao due ciia cac chuyen gia giao due (tiic la cac nha nghien ciiu vl giao due), hg cd the tu lo lieu dugc That cac chuyen gia ve giao due mdi la nhung ngudi dugc trang bi day dii cac kien thtic, cac cong cu nghien ciiu, thir nghiem va lien tue cap nhat nhiJng kien thiic mdi thong qua nhung nghien ciiu cua hg Do do, hg chinh la nhirng ngugi true tiep lam cong viec nghien ciiu, tim toi, phat hien de sau lira chgn mgt phucmg phap phii hgp vdi moi bai hgc, ggi y va hudng dan giao vien each thirc tien hanh bai hgc do'"* • Ngi dung kien thiic cho tirng bac hgc va cho timg tuoi phai lua chgn dua tren nhiing nghien eiru ve su phat trien va boat dgng hang cua tre em Vi du tre em lam quen vdi choi cd dang hinh hgc khdng gian, tien bac, thdi gian, hoat dgng mua sim, bai toan nhan, bai toan chia phan, bai toan thdng ke sdm hon so vdi trudc day Do dd c4n nghien cuu dua nhung ngi dung toan hgc tucmg ung vao nhiing lap nhd hon Tap chi KHOA HOC DHSP TPHCM Sd 65 nam 2014 • cln da dang hda nhirng dd diing va phuang tien hd trg day hgc; vi du nhu tien, choi, dd hinh, bang dii lieu hinh anh va dua thing vao ehuang trinh Toan • Nghien eiiu, xay dung lai each thiic danh gia trudng hgc, chii trgng nhiing chuin muc khac ngoai chuin kiln thiic, nhin manh viec danh gia qua trmh, danh gia thudng xuyen, danh gia qua cau hdi, tang tinh chu dgng cho giao vien viec lira chgn each thiic danh gia ' Theo tac gia Nguyin Minh Thuyet (T6ng chii bien mot s6 SGK) v4 difiu niy chi dung vdi mpt s6 mon hpc ^ Tac gia Nguyin Huy Doan (chu bien mpt s6 SGK toan): "Sau hoan thien SGK, dem giang day r6i thi Vian Khoa hpc gi^o due Viet Nam moi dirac B^ giao nhiem vu "xau lai" chuong trinh ciia cSp voi Ddy 1^ vi^c lam da r6i chii khong phai viec lam khoa hpc" ' Theo Pasec 10, !6p 2, ik ca cac hpc sinh Vift Nam, kS ca c^c hpc sinh y^u nhat, d^u l^m chu dupe nSng l^rc d p dp thSp v^ cao dupe lucmg qua c^c bai ki^m tra m6n tiing Vi?t va mon Toan; a lop 5, 90,7% hpc sinh da co dupe c^c nang luc dupe luong bii kiem tra m6n Tiing Viet, 50,1% hpc sinh dS d^it dupe tat ca nhflng nang luc dupe bai kilm tra mon Toin Su giam siit ro ret vl nhihig nang lire dupe bAi kiSm tra m5n To^ ciia hpc sinh tii 16p din Idp cung la mpt van de dang tim hieu * Tat ca c^c bai kilm tra nang luc hpc toan ciia hpc sinh edp vi cap deu xoay quanh viee chung minh eac tinh chat toin hpc, tim kilm cac ylu t6 to^n hpc dg:a hoan toin tren tinh chat toan hpc (nghiem, dai doan thing, di?n tich hinh ) hoSc don thuSn la c^c ph^p biln d6i toSn hpc (tinh toan, riit gpn ) Kh6ng co bat ki mpt ling dyng nio vupt khoi toan hpc, tham chi la qua mon hpc khac Cng dung toan hpc khSng dupe coi trpng chfnh mon Toan ma duoc "ngam hieu" la nhiem vu ciia nhiing mon hpc khac ' Theo kit qua ddnh gia PISA nSm 2012, Singapore xip hang 2, Vift Nam xip hang 17 MEA; Robitaille 1980; Travers & Westbury 1989 ' Chucmg trinh Toan cua Viet Nam vdn c6 ddy dii cdc yeu to da neu Tuy nhien ylu t6 npi dung chuong trinh va chuin kiln thuc, kT nang chilm phdn ion chuong trinh, Bp Giao dye va Dio tao chi danh m6t phdn rdt nho dp vai trang de dl cap nhung ylu t6 lai * Chuong trinh giao due ph6 thong edp tilu hpc, Bp Giio dye va Dio tao (2006) quy dinh ro o trang 116: "Vi^c day hpc va kilm tra kit qua hpc tap Toan phai c5n cii vao chuong trinh, sich giao khoa, d^c bi?t la chudn kiln thiic va kT nang ciia mon hpc " Qua trao d6i vdi nhiing giao vi^n tilu hoe theo hpc Idp liSn thdng dl idy bSng dai hpc tai Trudng DHSP TPHCM, viee d^y "ngoai chuong trinh" la khong dupe ph6p Giao vien cClng khong cdn phai day ngoai chucmg trinh vi du6i theo chuong trinh da met, hon niia thi cir chi idy kiln thiic chuong trinh Trong d6i vdi PMTLS, nhu ta thay d cOt thir 2, ndi dung giang day chi mang tinh de xuat hay gpi y cac bai toan d day da dupe mo hinh hoa dudi dang cac bai toan c6 ldi giai theo kilu phat bilu san va tim dap so chii khong phai dupe m6 hinh hda tCr mpt tinh hu6ng that sy ma hpc sinh phai ddi m?it nen x^t vl tinh img dyng d day la kha yeu Hon nQa nlu chu y din thii ty mye tilu ta se thay tinh uu tign ciia timg loai mye tiSu CTTTH, dl day ph^p cong, chuong trinh yeu cdu gido vien sir dyng cdc md hinh, hinh ve, thao tac dl minh hpa, nhan biit y nghTa cua phep c6ng Con d6i vdi PMTLS, gido vien dupe gpi y t6 chuc hpc sinh iam vi?c theo nh6m de kl nhirng cau chuyen vl phep cpng \k Idm chu phip cpng thong qua nhiing dang tr6 choi Chuong trinh THPT phan ban dupe thi dilm vdi hai ban khoa hpc t^r nhien (KHTN) va khoa hpc x2 hpi nhSn van (KHXH-NV), ap dung dai tra thi b6 sung them ban co ban (danh cho hpc sinh khdng co thien hudng d mdn hpc nao ed) vdi du kiln ban ddu: khoang 50% hpc sinh chpn ban co ban, 30% chpn ban KHTN va 20% chpn ban KHXH-NV Tuy nhien, theo thing ke cua Sd GD-DT TPHCM cho biit ti Ip hpc sinh ddng ki hpc ban ca ban tdng timg nam: Nam hpc 2006-2007, nam ddu tien triln khai d^i trd chucmg trinh phan ban THPT, TPHCM cd 75% hpc sinh hpc ban eo ban, 22% hpc sinh hpc ban A, 3% hpc sinh hpc ban C Din nSm 32 Tap chi KHOA HOC DHSP TPHCM Duffng Minh Thanh hpc 2012-20U, dii khdng thdng ke cy t h i nhung dai dien Phong Giao dye Trung hpc cua Sd GD-DT TPHCM eho biet hdu hit hpc sinh dSng ki hpc ban co ban " Theo danh gia mdi day nhdt vl chucmg trinh - SGK hien hanh, Bp GD-DT thda nh$n: "Viec xay d^mg chucmg trinh cdn lam theo kilu cdt khue: Cdp tilu hoc dupe tiln hanh nam 1996, THCS nam 1998 nhung din nam 2000 mdi xay dyng dl an ting thi vl d6i mdi chuong trinh, SGK giao dye p h i thong'" ' O day tde gia liai bao khong c6 y phe phan chuong trinh toan cua Viet Nam la khong dua trfin mpt quan diem gido dye tien bp O l xudt ciia tac gia la ndi ehung thilt kl mpt chucmg trinh nao dd chpn mpt chuong trinh da dupe kilm chimg tdt hon hay la tu thill kl mdt mo hinh mdi (ma khong dua tren quan dilm giao due tifin bp nao) la t6t hon Tac gia khong co y coi thudng dpi ngu giao vien va cdng tac dao tao giao vien ma chi khiing dinh lai rdng giao vien luon cin co su hd trp cdn thilt, lien tyc ttr cac chuyen gia giao due vl mat phuong phap v i each thiic tien hdnh hoat dong d^y hoc ca rdi trudng d^i hoc Nhu cdu cdn sy ho trp cCia giao vien la cd that, dieu thi hi6n ro qua nhilu dien dan chia se kinh nghiem va tai lieu giang d^y tren internet TAI LIEU THAM KHAO Bg Giao due va Dao tao (2006), Chuong trinh gido due phd thong cdp tiiu hgc, Nxb Giao due Ha Ngi Bg Giao due va Dao tao (2013), Huang ddn thuc hien chudn kiin thuc, kT ndng cdc mon hgc a tieu hgc, Nxb Giao due Viet Nam, Ha Ngi Bg Giao due va Dao tao (2009), "Tai lieu phan phdi chuong trinh trung hgc co so va trung hgc phi thong" (ap dung tir nam hoc 2009-2010), Ha Ngi, http://www moet.gov v« A.C Burris (2014), A Brief History of Mathematics Education and the NCTM Standards, Pearson Allyn Bacon Prentice Hall English Department for Education (2013), "National Curriculum in England" (Framework document), http://www.education.gov.uk/schools/teachingandlearning/curriculum J Kilpatrick (2011), Slouching Toward a National Curriculum, J of Mathematics Education at Teachers College, Spring-Summer, Vol 2, pp.8-18 Singapore Ministry of Education (2012), "2013 Primary Mathematics Teaching and Learning Syllabus", http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2013.pd (Ngdy Tda so^n nf)$n difoc bdi: 13-3-2014 phin bi$n danh gid: 08-9-2014; ngdy chip nt)$n dSng: 22-12-2014) 33 ... djnh rang: giao vien khong cSn phai cd su ho trg ve mat giao due ciia cac chuyen gia giao due (tiic la cac nha nghien ciiu vl giao due), hg cd the tu lo lieu dugc That cac chuyen gia ve giao due... la giao vien biit nhimg gi va nao danh gia viec hpc ciia hpc sinh, va Iam the nao de dua danh gia qua trinh hpc tap Vi du, giao vien eo thi xem hpc sinh giai quyit vin de va di nghi hpc sinh giai... mo ta phep Thfii gian Hgc sinh nSn co ca hgi de 2.1 Dgc thoi gian theo Dgc thai gian tir ding h6 va lien he din nhimg su kien thai gio/nua gia gian ciia mgt su dung "gio" va "gia ruoi"; sap xip