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TO CHIIC DAY HOC THEO 0 0 AN TOONG OAY HOG MDN T O A N CHO HOC SINH TRUNG HOC PHO THONG TS TRAN VIET CLTONG* ThS NGUY§N N G O C TRANG" ThS NGUY§N PHUC BINH**'''' 1 Day hoc theo du an (DHTDA) cho hpc sinh[.]
TO CHIIC DAY HOC THEO 00 AN TOONG OAY HOG MDN TOAN CHO HOC SINH TRUNG HOC PHO THONG TS TRAN VIET CLTONG* - ThS NGUY§N N G O C T R A N G " ThS NGUY§N PHUC BINH**' Day hoc theo du an (DHTDA) cho hpc sinh (HS) trung hoc phd thong (THPT) DHTDA l i hinh thdc tdehdc day hpe nhifng duan hpc tip (DAHT) dudi su hudng din vadieu khien eua giao vien (GV) Trong day hpc mdn Toan d trudng THPT, GVedthetdchue van dung DHTDA theo quy trinh sau: • Budc Xac (Jjnh chu de, nhiem vu hpc tap va nghien cifu gan vdi yeu cau cua mon hpc hoac mpt chii de kien thtrc cy the sach giao khoa co lien he vol thuc tien; (co the khdi dau bang ytirong cua HS hoac nhiJng djnh htfdng, chidin cua GV) • Budc Cac nhom hinh fle cuong va lap ke hoach thi/c hien, xac djnh muc tieu cua du an (DA) Hinh dung chi tiet cac eong viec cu the, each thifc thuc hien, cac dieu kien can thiet nhu: nguon tu lieu, thiet bi can thiet, kinh phi, ngudi tham gia •Budc3 Cac nhom thi/c hien nhiem vu: thu th^p thong tin: ti/sach bao, tap chi, mang Internet, khao sat, dieu tra, phong van, ; xilithong fetong hop, phan tich dtflieu (cdthe bieu hien bang so do, bieu ), thao luan thudng xuyen giCra cac vien nhdm de giai quyet van de va kiem tra tien dp; xay dung san pham :%^ hpp cac ket qua mpt san pham cuoi cung • Budc Gidi thieu san pham trudc tap the Idp; nhdm tn/dng trinh bay, gidi thieu san pham bang cac each: sir dung bai viet, PowerPoint, ban do, tranh anh, md hinh - Budc Banh gia ket qua dat dupe so vdi muc tieu xac djnh: HS turut nhung bai hpc To chdc DHTDA noi dung "He bat phuang trinh (BPT) bae nhat hai an" cho HS THPT 1) Tieu decua DAHT: "Sd dung kien thdc ve he BPT JDie nhat hai an giai quyet eac bai toin ddi sd'ng" 2) Thdigian thuc hien: tuan 3)Muc tieu DAHT: • Vekien thucHS neu dupe eic ndi dung nhu: khai niem BPT, nghiem eua BPT, hai BPT tuong duong, mdt sd phep bien dd'i tuong duong cua BPT, he BPT bae nhi't hai an, nghiem va tap nghiem cua nd,^cie budc giai BPT bae nha't, he BPT va he BPT quy ve bic nhait, bic hai; giai v i bien luan dung BPT v i he BPT bae nhi't, bae hai don gian ed ehua tham so 4) Xay dung bg ciu hoi dinh hudng - Cau hoi khai quat:K\en thdc ve he BPT bae nha't hai an ed thegiai quyet cic bai toan thue tiin nhu the nao? - Cac cau hdi bai hqc: 1) Khii niem BPT bae nha't hai an?; 2) Bieu diin tap nghiem eua BPT bae nha't hai an nhuthenao?; 3jCaeh bieu diin mien nghiem cua he BPT bic nha't hai i'n?; 4) Bieu diin hinh hoc mien nghiem eua he BPT sau: 2x+y0 - Cac cau hdi ndi dung: 1) Mpt cdng ti can thue xe van chuyen 140 ngudi va tan hang hda Noi cho thue xe chlcd 10 xe hieu Mitsubishi va xe hieu Ford Mpt chiecxe hieu Mitsubishi cd the chd20 ngudi va 0,6 tan hang Mpt chiecxe hieu Forded thecho lOngudiva 1,5 tan hang Tien thue mot xe hieu Mitsubishi la trieu dong, mpt xe hieu Ford la trieu dong Hdi phai thue bao nhieu xe moi loai de chi phi thap nhat? 2; Mpt xudng san xua't hai loai san pham Moi kilogam san pham loai I can 2kg nguyen lieu va 30 gid, dem lai mi/c Id! 40000 ddng Mdi kilogam san pham loai II can 4kg nguyen lieu va 15 gid, dem lai miJo Idi 30000 dong Xuong cd 200kg nguyen lieu va 120 gid lam viec Nen san xuat mdi loai san pham bao nhieu de cd miJc Idi cao nhat? 3) Nhan djp tet Tmng thu, xi nghiep san xua't banh Trang muon san xuat hai loai banh la banh dau xanh va banh deo nhan dau xanh Be san xua't hai loai banh nay, xi nghiep can: dudng, dau, bdt, triJng, miit Gia sd'so dudng cd the chuan bj dupe la 300kg, dau la 200kg, cac nguyen lieu khac bao nhieu cung cd San xuat mdt cai banh dau xanh can 0,06kg dudng, 0,08kg dau va cho lai ngan dong San xua't mdt cai banh deo can 0,07kg dudng; 0,04kg dau va cho lai 1,8 ngan dong Can BPT bae nhi't mdt an, djnh li ve di'u eua nhj thue bae nhait va di'u cua tam thdc bae hai; - Vekinang: HS ed the'v$n dgng cac dinh li ve di'u eua nhj thdc bae nha't v i di'u eua tam thdc bic hai giai eic bai toan ve 44 Tap chi Gido due so 325 * Tnroing Dai hoc sir pham - ll^i hpc Thai Nguyin " Tnrcing Cao d h g ki thuat Ly Tir Trong TP HCM *** Tnriing Cao dang cdng thuong TP Ho Chi Minh (kil 1/2014) lap ke ho?ch san xuat mdi loai banh bao nhieu cai de khong bj dpng ve dudng, dau va to'ng so lai thu dupe la Idn nhat (neu san xuat bao nhieu cung ban het)? 4jCdng ti Bao bi Dupe can san xuat loai hop gia'y: di/ng thuoc B,, di/ng cao Sao vang va dung "Quy sam dai bd'hoan" Be san xua't cac loai hop nay, eong ti dung cac tam bia cd kich thude giong Moi tam bia cd hai each cat khac Cach thu nhat cat dupe hop B,, mpt hop cao Sao vang va hop Quy sam Cach thu hai cat dupe hop B,, hop cao Sao vang va hop Quy sam Theo ke hoach, sdhdp Quy sam phai cd la 900 hpp, so hop B, tdi thieu la 900 hop, sd hop cao Sao vang td'i thieu la 1000 hop Can tim phuong an cho tdng sd tam bia phai dung la it nha't? hien eau hdi bii hpe v i eau hdi ndi dung 2;+/V/;/em vu3:Thuc hien eau hdi bai hpc va cau hdi ndi dung 3;^+ Nhiem vu4:'ihuc hien eau hdi bai hpc va eau hdi ndi dung c) Lap ke'hoach trien khai DA: • Thdng bio den tiJTigHS ndi dung cua DA, thdi gian thue hien, cac yeu cau eua DA HS chua'n bj DA khoang tu2-3 tuan vdi day du cie phuang tien, edng eg hd trp thue hien DA; - Theo ddi sit eac phan viee d nha eua HS: tang bud'i nghe bio eao de cuong ndi dung va tien dp eac DA (viec phan ehia edng viec, thdi gian, kinh phi, tien hanh DA, len ke hoach tiep xue td'i thieu 5) Xay dung ke'hoach trien khai DAHT hai lan tren tuan, edbao eio thu ); - Hudng din HS a) Lap ke'hoach DHTDA: - Xay dung nqi dung bao cao tai Idp va thao luan; - Ket thue DA va phan hdi DA:Xay dt/ng bd ciu hdi djnh hudng, giao ntiiem vg DA; - Rut bii hpe kinh nghiem tu DA eho tifng nhdm, tifng thinh vien eua nhdm; - Trinh 6) Quy trinh kiem tra, hudng din, hd tra HS baysinpham cua HS:M6\ nhdm tim hieu vithu thap thuc hien DA ddlieude thie't kevi bien soan tai lieu trinh biy Giai doan I.Lua chqn detai va xac dinh muc tieu eic kien thiic lien quanden DA thgc hien (trong khoang D/4 Ke'hoach hudng din, hotroHS:-Cung cap thdng thdigian lOngiyj.Mdinhdm HS trinh bay san pha'm tin, gpi y HS chu y den nhifng van de lien quan den cua nhdm minh vdi thdi gian l i 15 phut trudc Idp, cie kien thue ve he BPT, tao dieu kien eho HS xae djnh de nhdm cdn lai se gdp y, sau dd, ca Idp thao luan tai va mge tieu eua DA; -Tap hua'n kinang thuc hien 10 phut, thdi giari cdn laiGV v i H S rut kinh i/ghiem va DA cho HS: kining thu thap va khaithae thdng tin, ki hpp thdc hda kien thdc ' nang xay dung va bieu diin bai thuyet trinh bing b) Thiet kenhdm va lap ke'hoach cijio HS hoat PowerPoint ddng:- Thiet ke nhdm :Ldp duqc chia eac nhdm, Giai doan Trien khai DA va xay dung kehoach mdi nhdm ed khoang tu -16 ngudi Viec phan chia thue hien: • G V hudng din cic nhdm lap ke hoach can dam bao tinh ddng deu ve trinh dp nhan thue, thuc hien DA, xie djnh nhiem vu hpc tip dua tren bp tinh tieh cue boat ddng giua eac nhdm Nhdm eau hdi khung djnh hudng; - Gpi y eho eac nhdm trudng G V chi djnh hoic cd the eic vien trudng phuang thdc dieu hanh nhdm va phan edng nhdm bau chpn ed chdc ning dieu hanh va nhiem vg den tung thinh vien nhdm; - Chi quan li edng viec ehung eua nhdm Cin cdvao ning dan HS each thue lien Iae, trao ddi vdi G V thdng qua luc va tinh tich cue eua mdi vien, nhdm trudng mang Internet (xiy dung eho mdi nhdm mdt hop va cae thinh vien nhdni chia nhdm cac thu dien tu ) Giai doan Thue hien DA, gdm eac budc: - Ke "td'hoatdong"y.hac nhim giai quyet eic cdng viee eg the thue hien DA Mdi "td'hoatdqng"\ubau hoach hudng dan /7d to-f C u ng cap cac tai lieu va dja mdt to trudng de' bao cio hoat ddng cua td eho chi thdng tin hifu ieh lien quan den ndidung DA tren Intemet; + Thdng qua hop thu dien tuhoic dien thoai, nhdm tardng Trong sudt DA, eic nhdm tardnp vatdtardng ngoai GV ed the thudng xuyen giim sit, kiem tra, ddn dde nhiem vg glim sit va dieu hanh "tdhoatdqn^', cdn cd cac nhdm HS hoat ddng, kjp thdi dua nhifng chi chdc ning trao dd'i, baocio kjp thdi nhung thuan lpi din, djnh hudng hoatddng; -i- Hudng din HS ehinh v i khd khan vdi GV nhim nhanh chdng tim bien sua, hoan tai lieu li thuyet va san pha'm minh hpa, phuong phap ehuyen the, chpn Ipe mpt tai lieu li phip thao gd - Thiet lap nhiem vu hqc tap:^cA mdi DA, ein cd thuyet mdt bai thuyet trinh l^ing PowerPoint; vio mgc tieu vabpciu hdi djnh hudng eung nhuyeu - Kehoach kiem tra:-\- Hing ngay, cie nhdm trudng cau ehung cua DA, eic nhdm HS thao luan, xac djnh bao eao lich lam viec, tinh hinh hoatddng eua nhdm, ndi dung, nhiem vg phai thuc hien, kien thue trpng tam eac cdng viee da lam duoc va ehua lam dupe, ket qua cdng viee cua tdng vien nhdm cho GV; cin dat sau DA Tddd, xay dung cae giai doan va lip + Sau mpt tuan thu'e hien, eic nhdm nop ban tai lieu li ke'hoach boat ddng, phin edng nhiem vg eg the den thuyet (so thao) trinh bay nhifng kien thue trpng tim, cac "t6hoatdqn^': + Nhiem vu 1:lh\sc tiien eau hdi CO ban lien quan den ndi dung DA ea nhdm eiing bii hpe v i ciu hdi ndi dung 1; + Nhiem vu2:lh\4c (kil-112014) Tap chi Gido due so 325 45 1) Nghiem thu DA bien soan GV ein cdvio detien hanh soan thao mdt 'Bao eio DA: - Chuan bibio cao:GV dang ki bii kiem tra trie nghiem khieh quan, yeu eau ti't ca HS eua cie nhdm tap trung hoan thinh tai Idp hpe muon hdi trudnp, may chieu, may ehgp anh, miy khoang thdi gian 15 phut; + GV tien hanh kiem quay phim, ehuan bj cae bii kiem tra, dinh gii; chpn va phan edng HS lam thu ki, ehgp anh, quay phim tra dot xuat boat ddng eua mdt vai nhdm Giaidoan4 Trinh bay sin pham DA:-Kehoach va chua'n bj hdi trudng, bdtri ehd n^di eho eac nhdm; Bao eao DA: Trinh tu thuyet trinh DA bing hudng din h6trg:QM hudng din HS eic budc trinh biy bai thuyet trinh, phuang phap Idieud'n ngudi nghe PowerPoint dupe td chuc nhu sau: cac nhdm tJutJc Dinh hudng HS dat eau hdi tim hie'u, phan bien vi'n phin cdng thuyet trinh theo thututu nhdm rdi lan deeung nhucich giai thieh va bao vequan diem ;-/Ce lupt den nhdm Cie nhdm can trinh biy rd kien thue trpng tam, nhifng van de gin vdi thuc te Thdi hoach kiim tra:GN dua mdt vai cau hdi lien quan gian bao cio va trinh bay san pha'm minh hpa eua den cac kien thdc co ban cua DA va chi djnh mpt mdi nhdm j i 15 phut; sau bai bio cao, cie thanh vien bat ki cac nhdm tra Idi vien eua mdi nhdm cdn lai tien hanh dat ciu hdi hay Giai doan Danh gia DA: - Kehoach hudng din neu cic van de cdn khiie mic qui trinh bao hdtro:GN gidi thieu v i hudng din HS thue hien eac cio, nhdm bio eio cd nhiem vu giai thieh hoac tra tieu chi dinh gia DA, gpi y giiip HS suy nghi va tu Idi true tiep trudc tap the Neued qua nhieu eau hdi dinh gia qui trinh hpe tap cua ehinh minh; -Kehoach dit ra, nhdm bio cio phai tien hinh ghi nhan tren kiem tra:+ HS giifa cie nhdm eiing vdi GV se dinh gii'y v i the hien cie eau tra Idi bing vin ban, gui den gii ket qua dat dupe; + Cud'i DA, tat ea H S phai hoan cic nhdm sau bud'i thuyet trinh thinh mdtbii kiem tra 45 phut tai Idp hpe de G V danh * Yeu cau ve sin pham DA: - Tii lieu li thuyet: gii mdc dp tiep thu kien thife, ki ning giai quyet van -I- Hinh thdc trinh biy: gdm cae phan gidi thieu ve de cudc sdng lien quan den DA eua eic em DA, mge Ige, npi dung v i phan ket luan Su dgng 7) Ho sa danh gia font chif Times New Roman hoac Arial,cd ehua 13, a) Phieu danh gia eanhan:M6\ HS duqc phit mdt cd minh hpa hinh anh; -i- Nqidunp:Jmh bay kien phieu tudinh gia, HS dua vaoeic tieu chi, ndi dung, thife CO ban ve BPT bae nha't hai an; each bieu diin thang diem tdi da v i hudng din dinh gii de tu danh tap nghiem eua BPT bate nhi't hai an va hp BPT bae gia ve kha ning v i ning lue lam viee cua ban than nhi'thaia'n;tien hinh bieu diin hinh hpemien nghiem HS tu dinh gii bing cich cho diem vao cae edt tu cua he BPT: dinh gii, quatrinh dinh gii phai dam bao tinh trung thue GV dua vio ket qua bao eao eua cie nhdm va 3x + yQ b) Phieu danh gia cua nhdm trudng: - Phieu x>Q danh gia vien nhdm: M di nhdm trudng duqc phat mdt phieu dinh gii eic thinh vien -Baitrinh diin PowerPoint: + Hinh thdc trinh bay: nhdm Nhdm trudng dua vio tieu ehi, ndi dung, mau sic cic slide, font chif v i miu chif phai dexem; thang diem td'i da va eho die'm vao edt (Jiem e i sudgng cac hieu dng trinh chieu don gian, hinh anh nhan eua mdi vien nhdm Phieu danh minh hpa phai dep, rd ring Nen chen them cic doan gii cua nhdm trudng danh eho cac thinh vien video clip m inh hpa; + A/p/dung'.-The'hien dugc nhifng nhdm l i mpt nhung can ed quan trpng de ndi dung cO ban eua tai lieu li thuyet GV dinh gia va cho die'm ve su' tien bd cua cie 2)Banh gia vatudanh gia:-Danh giasin pham thinh vien nhdm; -Danh gii sin pha'm nhdm: nhdm: GV ein ed vio tai lieu bien soan, bay thuyet Mdi nhdm dupfc phit phieu danh gii san phi'm trinh, san pha'm minh hpa eua mdi nhdm dua eua nhdm minh Nhdm trudnp l i ngudi dai dien dinh gii v i tien hanh eho die'm vio phieu dinh gia eho nhdm cd nhiem vg trao ddi, thao luan vdi cic danh cho mdi nhdm Sau do, ket hop vdi phieu danh vien nhdm dua nhirng dinh gii gia eua mdi nhdm, GV tien hinh phin tich v i cho vecae nhdm cdn lai diem eg thecho mdi nhdm; -Danh qia nhdm trudng: c) Phieu danh gia cua GV.gom:- Phieu danh gii Dua tren ket qua san phi'm eua mdi nhdm eung su san pha'm nhdm; - Phieu dinh gii nhdm trudng; cdng viec dieu hinh nhdm hoat ddng, GV eho diem vio phieu danh gia nhdm trudng theo - Phieu dinh gii tdng vien ctla eac nhdm Ket qua thuc hien DA (Xem tiep trang 53) 46 Tap chi Gido due so 325 (kil 1/2014) lupt la tiep die'm cua cic canh AB, BC, CD, DE, EF, vao day hpe de truyen eho HS niem say me hpc tap FA vdi dudng trdn (0) Khi dd, theo djnh li Pascal dd'i va cang yeu thieh mdn hpe • vdi Ige giic i\4NPQRS ndi tiep dudng trdn: hJINnQR =X, PQi-^SI\/l= Y, NPnRS=Z ta cd ba diem X, Y Z Tai lieu tham Ichao thing hang Michael de Villiers Some adventures in Euclidean D l tha'y eic die'm X, Y, Zlan lugt l i cue eua cac geometry University of Durban-Westville, Durban, dudng thing BE, AD, CFdd'i vdi dudng trdn (0) Vi X, South Africa, 1996 Y, Z l i ba die'm thing hang nen cie dudng ddi cue Michael de Villiers Generalizing van Aubel using cua nd l i BE, AD, CFddng quy tai mdt die'm Die'm duality Mathematics Magazine, Vol.?."! (4), pp 303nay chinh liege cua dudng thing Pascal dd'i vdi dudng 307 2000a Michael de Villiers ,4 dual, and generalisations, trdn |0) ^ (J bai toan nay, neu chifng minh tore tiep ba dudng of a sharp resuh KwaZulu-Natal Mathematics Journal, thing BE, AD, CFddng quy se rait pliue tap Khi van Vol.5(2), pp.16-18, 2000b dung thao tic tuduy TDN dexem xetdkhia canh khie Nguyin Ba Kim Phuong phap day hpc mon Toan NXB Dai hpc supham, H 2004 thi bai toan lai trd nen don gian hon Cg the, nhd cip khai niem dd'i ngiu: cue v i dudng dd'i cue, ddng quy va thing hang, bii toan dugc chuyen ve chifng minh ba SUMIVIARY die'm thing hing di/a vio ket qua cua djnh li Pascal *** The concept of duality plays an important role in mathematics However, this concept is not popularly Quy tie TDN yeu eau HS phai cd kha ning tuduy used in the secondary school because duality princid mdc dp eao Vi vay, diy la bien phip bdi dudng ples are not true in Euclidean geometry Tiierefore, nang luc tu toin hpe eho HS gidi toan rat hifu this paper proposes the potential of applying the concept of quasi-duality in geometry at the secondary hieu, die biet, giup HS he thd'ng hda v i md rdng tri school level and presents its application in systemathdc toan hpc mdt each chu ddng, tich cue Dieu tizing knowledge and discovering new results These la CO sd cho su sing fao frong nghien cdu v i hpe tip activities also make a contribution to develop stutoan Do dd, G V can van dgng linh boat quy tie TON dent's thinkingin solving mathematical problems quyet vi'n de, ning lue giao tiep, ning lue lam viee nhdm Do dd, DHTDA gdp phan nang eao cha't (Tiep theo trang 46) lupng giang day mdn Toa'n frong trudng THPT v i hudng din; -Banh gii tdng vien mdi nhdm:gin nha trudng vdi thuc fien.Q Qua tren ket qua danh gii san pha'm eua ca nhdm Tai lieu tham lihao eiing vdi phieu dinh gii eua nhdm tn/dng danh eho Trin Viet Cuong - Trin Trung Tiep can hien dai cac vien, phieu tudinh gia ban than, GV eho ren luyen nang luc sirpham cho sinh vien nganh die'm va tinh die'm vao phieu dinh gii eua mdi HS toan a trud'ng dai hpc NXB Dai hoc su pham, Trong quatrinh thuyetfrinh DA, GVed thecincu H.2013 vao tinh tieh cue phit bie'u, kha^ning tham gia ddng Buck Institute for Education Introduction to gdp vao st/thinh cdng cua bud'i thuyet trinh ma eho Project- Based Learning Project based learning hand cac em them die'm thudng book, 2007 3) Danh gia kit qua cua DA: Dinh gia John W Thomas A review of research on Project cdng DA dua tren cic tieu ehi: nang luc lam viee, tinh Based Learning California, 2000 than, tie phong lam viee nhdm va chat lugng san phi'm Mat khae,GV can cin cdvao chua'n kien thdc, SUMMARY kinang ma HS dat dugc sau DA ke't thue Project based learning is a form of teaching aimed To chirc day hoc theo dir an *** at learners, learner-centered This article has proposed the ways of organizing students project based Van dgng D HTD A vao day hpe da dat dugc m ge learning in Mathematics for high school students The tieu kep: giup HS dat chua'n kien thdc, ki ning va experimental pedagogical results were initially demonstrated that project based learning in Mathematics thai dp theo yeu cau eua mge tieu bai hpe, hieu rd for high school students is appropriate and meet the cie dng dgng eua foan hpe frong thuc tien; ngoai ra, requirements of innovative teaching methods in high sciiools nowadays HS cdn dugc ren luyen va nang eao ning luc giai (kil-1/2014) Tap chi Gido due so 325 53 ... thao luan vdi cic danh cho mdi nhdm Sau do, ket hop vdi phieu danh vien nhdm dua nhirng dinh gii gia eua mdi nhdm, GV tien hinh phin tich v i cho vecae nhdm cdn lai diem eg thecho mdi nhdm; -Danh... eua nhdm tn/dng danh eho Trin Viet Cuong - Trin Trung Tiep can hien dai cac vien, phieu tudinh gia ban than, GV eho ren luyen nang luc sirpham cho sinh vien nganh die''m va tinh die''m vao phieu... Sao vang va hop Quy sam Theo ke hoach, sdhdp Quy sam phai cd la 900 hpp, so hop B, tdi thieu la 900 hop, sd hop cao Sao vang td''i thieu la 1000 hop Can tim phuong an cho tdng sd tam bia phai