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DAY HOC CHU DE GIOI HAN LIEN TUC (j DAI SO VA GlAl TiCH 1 1 THEO DINH HUONG HINH THANH VA PHAT TRIEN NANG LITC CHO HOC SINH THPT Pham Van Trao* T 6 M TAT Giao dye Toan hpc dang thyc hien ddi mdi phuon[.]
DAY HOC CHU DE GIOI HAN - LIEN TUC (j DAI SO VA GlAl TiCH 1 THEO DINH HUONG HINH THANH VA PHAT TRIEN NANG LITC CHO HOC SINH THPT Pham Van Trao* TAT Giao dye Toan hpc dang thyc hien ddi mdi phuong phip day hge theo hudng phat trien nang lye ngudi hpc Bii bio bin ve nang luc toin hge can hinh thinh va phat trien eho hge sinh thdng qua day hpc chu dl gidi han - liln tuc a Dai sd va Giai tieh 11 T6M Tu khoa: nang luc toin hgc, gidi ban - hen tye TEACHING THE TOPIC OF LIMITS AND CONTINUITY IN IITH GRADE ALGEBRA AND CALCULUS TEXTBOOK IN THE ORIENTATION OF ABILITY FORMATION AND DEVELOPMENT FOR HIGH SCHOOL STUDENTS ABSTRACT Math teachers are now innovating theh teaching methods in the orientation of developing learners' competence The article discusses raatheraatieal competence to form and develop for high school students through teaching the topic of Limits and Continuity in 11th grade Algebra and Calculus Key words: mathematical competence, Limits and Continuity Md flAu , , , , De thyc hien ddi mdi phuang phap day hpe theo hudng phat triin nang lye ngudi hgc, cie trudng su pham cin phai thyc su di diu ,., ! *A i, •-• w *u i,s« nghien ciiu va de xuat cae giai phap thuc hien , , , , , »i , - , - I, s L- u Nghien eiiu day du nang luc toan hgc ean hinh thinh vi phit triin cho hgc sinh, di xuit eic dinh hudng day hpe chu di gidi ban-Uen tye d mdn toin THPT; dinh hudng eho nghien cihi vi giang day d DHSP theo hudng phit triin nang '^c ^^° ^ i ^ ^'™' ^^p "^8 y^" ^^^ 8*^° ^^^ p'^° thdng hien _ „ i _ niikj/2.1 Ndng luc (Competence) vd nang l^rc s i /todn hoc (mathematicalcompetence) 2.1.1 Nang luc (Competence) Theo tira ly hpc: "Ndng luc Id tS hgp nhieng thugc tinh dgc ddo cua cd nhdn phii hgp vai nhimg yiu cdu ddc trung cua mpt hoqt dpng TAPCfflKHOAH0C,Sd21,thdiig03/2017 | 35 nhdt dinh nham ddm bdo cho hoqt dpng dqt hiiu qud cao " Ndng luc chuyin mdn lien quan din timg mdn hgc riing biet Vi dy nhdm nang luc chuyin radn m6n Theo Nguyin Van Chrdng [3, tr 14]: "Ndng luc, thudng ggi Id ndng luc hdnh dpng Id khd Toin bao gdra cac nang lue sau diy: ndng thuc hiin hieu qud mpt nhiem vy/mpt hdnh dpng cu the, liin quan den mpt linh vuc nhdt dinh dya trin casd hiiu biit, kindng Id xdo vd su sdn sdng hank dpng " Nhu viy, ndi din nang luc li ndi den nang tiem in mdt ci tbi, mgt thii phi vgt chit Song nd thi hi?n duac qua hinh dOng vi danh gia dupe no qua ket qui ciia boat dpng Thdng thudng, mgt ngudi dupe gpi li cd nang lye niu ngudi dd nim viing tri thiie, ki nang, ki xao ciia mgt loai hogt ddng nio dd va dat dupe kit qua tit hem, cao ban so vdi trinh dp tnmg binh eua nhiing ngudi khac cimg tien hanh hogt dgng dd nhiing dieu kiln vi hoan eanh tuong duong ditf HI So* 1.1 Cic nang lye chuyin mon mdn Toan Mdi td hpp eic nang lye thinh phan tao nen nang lye toin hpc eua mdi ea nhin 2.1.2 Ndng lice todn hgc (mathematical competence) Theo Nguyin Hmi Chau [2, tr 32]: "Nang Mo hinh cdu true ndng life luc todn hgc Id khd ndng nhdn bietp nghia, vai Nang luc duac dinh nghia theo nhilu each trd cua kiin thuc todn hoc cugc sdng; khae nhau, thude vio bdi cinh vi raue dich khd ndng van dung tu todn hgc de gidi su dung nhiing nang luc dd Vi vay, cie nhi quyit cdc vdn de cua thyc tiin ddp ung nhu cdu nghiin cim tren the gidi da sir dung nhiing md ddi song hiin tqi vd tugng lai mpt edch linh hinh nang lye khic tilp can ciia minh: hoqt; khd ndng phdn tich, suy luqn, lap luan khdi qudt hoa, trao ddi thong tin mpt cdch hieu Md hinh nang luc theo OECD: qud thong qua viic ddt ra, hinh thdnh vd giai Trong eic ehucmg tnnh day hpc (DH) hi|n quyit vdn di todn hgc cdc tinh huong, eua eae nude thude OECD, ngudi ta sii dyng hodn cdnh khdc nhau, " md hinh nang lye dem giin hcra, phan ehia nang Cdu true cua ndng luc todn hgc: lye hai nhdm chinh, li cdc ndng lyre chung vi cdc ndng lye chuyin mon Nhom ndng luc chung bao gom: ' Kha nang hinh dpng dOc lap thinh cdng; Theo KoTuteexki thi cdu true cua ndng lifc todn hgc bao gdm nhiing phan: Thu nhqn thdng tin, chi biin thong tin, luu trie thong tin va thdnh phdn tdng hgp chung • Kha nang sir dung cic cdng eu giao tiip vi Cac yiu ti anh hudng den sy hinh thdnh vd edng cy tri thirc rapt cieh ty chu; phdt triin ndng luc todn hgc: • Khi nang hinh dgng thinh cdng cie Yiu td tu nhien - sinh hgc: Nang lye toan cua nhdm xa hdi khong ddng nhit 36 I TRUONGDAIHOCHAIPHONG hpc sinh dupe di truyin tii eha me, mi ehung ta hay gpi la ndng khieu todn Yeu to mdi trudng xd hpi vd gido due: Mdi hpc sinh (HS) diu sdng (hogt dpng) mOt radi tnrdng xa hpi nhat dmh Mdi trudng gdp phin tgo nen ddng ca, myc dich, phuang ti|n, hinh ddng eua ci nhan, dd giio dye ddng vai trd ehii dao Cym tdi tqo: Nhd Igi cic ddi tupng, khai nilm, dinh nghTa va tinh chit toin hpe Thyc hipn dupe mdt cich lira quen thupc Ap dyng mgt thuit toan tieu ehuan Cum niy gom miic trinh dp: - Trinh dp 1: HS bilt tr^ ldi ciu hdi ve bdi cinh quen thupc, dd cd cie thdng tin lien quan va cau hdi duac neu ro Yeu to ngi dung cua todn hgc: Chinh ban than radn toin hpc vdi ngi dung ed dae tinh triru tuong, Idgic da gdp phan hinh va phat trien eae nang lye toin hgc eho hpc sinh - Trinh 2: HS biit diln giii vi nhan biit tinh hudng tiong bdi einh mi khdng cin kit luan trye tilp trinh niy, HS biet su dung eic thuit toin ca bin, cong thiic, phucmg phap (PP), Yiu to hoqt dgng cua hgc sinh: Hoat ddng eua hoae quy ude Cac em cd kha nang bien luan hpc sinh ddng vai trd quylt dinh trye tiep din su tryc tiip vi giii thieh y nghta kit qua hinh thinh va phat triln nang luc toin hpc Mudn hinh vi phit triin nang luc toan, hoe sinh Cum lien kit: Kit ndi, tieh hgp thdng tin di can phii duac true tiep thao tic, hogt dpng vdi giii quylt eae van de dan gian Tgo nhiing ket cac ddi tupng, npi dung toin hgc mgt each tieh nii eic cich biiu dat khae Cum niy eye, say ml, cdng vdi y ehi, nghj lye va sy kiln gdm trinh dd: tri de vupt qua eie trd nggi, din din chiira linh - Trinh dp 3: HS biit thyc hinh eie PP quy cic tri thiic toan hpc Dilu dd khang dinh, nang lye, tai nang cua radi eon ngudi chi cd thi dupe dinh rd rang, gdra ed vi|e ylu ciu quyet dinh hinb thinh "trong hoqt dpng, thong qua hoqt tuin ty Cic era bilt ehpn lya va ip dung nhieu ki hoaeh giii quyet tinh hudng dan gian O trinh dgng vd bang hoqt dpng " eiia mdi ei nhin dp niy HS biit diln giii vi trinh bay dua vao Cdc cdp cua ndng luc todn hgc • nhiiu ngudn thdng tin vi li le eua ehinh rainh Chuang trinh dinh gia hpc sinh qudc tl PISA - Trinh dp 4: HS biit lim viec cy thi vdi eae de cap den cip dp nang lye toan hpc gdm cym rad hinh cu the va nhiing tinh hudng phirc tap eu tii tgo, cyra lien kit vi cym phan anh vdi trinh thi ed thi liln quan tdi khd khan, hgn ehe hoae dp nang luc phan: nlu Iln gia dinh trinh dp HS biit sii dyng ki nang toin dien va suy luin hpp li, cung vdi tu ttieo bdi cinh Cae em biit xay dung vi giii thich ciing nhu biln luan dua vio sy dien giai, li luin va hanh dgng eua minh Cymphdn dnh: Nhan biit ndi dung toan hpc tinh hudng cd vin di phii giii quyet Van dung kiin thiie toin hpc de giai quylt cic van dl thyc tiin Biit phan tich, tdng hap, suy luan, lip luan, khai quit hda ehiing rainh toan hpc Cym niy gdm trinh dp: Sa 1.2 Bieu di^n cac ckp dd nang lux toan hpc - Trinh dg 5: HS biit phit trien vi lira viec vdi cie md hinh tinh hudng phirc tap, xac dinh TAP CHi KHOA HOC, Sfi 21, thiiiig 03/2017 37 dupe hinh chii yeu qua eic mdn hpe/ tren ldp hpe/ nhi tnrdng, tren nin ciiaragtmoi trudng hgc tgp than thien, tich cue hda ngudi hpe, vdi cic li thuylt dgy hge hien dai nhu: day hgc kien tgo; dgy hgc trai nghiem; day hpe tuang tac, - Trinh dp 6: HS biit cich khii nilm hda, Nhdm eie nang lye phi nhintiiiic(edt loi) bao g&n: (1) Nang lye vuot khd; khii quit hda vi sii dung thdng tin dya vao vile tim hiiu va rad phdng nhung tinh huong phiie (2) Nang lye thich img, nang lye iing phd stress; tap Cl trinh dp niy, HS cd nang suy nghT va (3) Nang lye thay ddi suy nghT /tgo niim tin suy luin toan hpe cao eip Cic em cd kha nang tieh eye; ip dung nhan thiic va hieu biet vi|e am hieu cac (4) Nang luc quan sit; nang luc tapttungchii y; ki hieu, cdng thiic vi mdi quan he toin hpc dl xay dung nhilu PP tilp ein va ehien lupc mdi (5) Nang lyc quin Manh dgo/phat trien bin than vi?c giii quyet nhilu tinh hudng Ig Mdi nang lye phi nhan thiie cdt loi niy lai khd khan vi nlu phucmg in giai quyit tiinh dp nay, HS biit lira vile cd ki hoaeh, su dung suy nghT, tu duy; trinh biy ed sy liln kit phu hop, eae dac diim biiu tnmg, cd tu siu sic ddi vdi tinh hudng 2.2 Ndng lire todn hgc cdn hinh thdnh vd gdm mdt nhdm eae nang lyc eu the/nang lyc phdt triin cho HS THPT thinh phin Moi nang luc ehung va eic nang 2.2.1 Ndng lye cdn hinh thdnh vdphdt trien luc thinh phan cua chiing cung dupe hinh thinh qua mdn hgc, nhung chd yeu qua eic boat dgng cho HS THPT giao due ngoii mdn hpc/ngoii ldp hpc trln nen Theo nhdm chuyin gia tu vin cho chuang eiia mOt mdi trudng tuang tic van boa xa hgi trinh giio dye Viet Nara sau 2015 [6], thi cac tich eye (giau tinh tucmg tic, liln tye dupe trai nang lye can hinh thinh va phat trien eho HS PT nghiim, khdng ip dat tii giio viln/phy huynh, bao gdm: hoc sinh dupe ty bay td y kien, ludn tdn trgng Nhdm cac nang lye nhan thiie (cdt Idi) gdra y kiln hpe sinh, giao vien ludn khuyin khich, cie nang lye: nudi dudng cam xiie tieh eye), vdi cic li thuyet giao due hien dai nhu: trii nghiem; tuong tie; (1) Nang luc ngon ngii; trd ehai, (2) Nang lye tinh toan va suy luin Idgie/tu 2.2.2 Ndng luc todn hgc cdn hinh thdnh vd triru tuang; phdt triin cho HS THPT (3) Nang lye giii quyet van dl; Phin tich cic nhdra nang luc va dae diem (4) Nang lue sing tgo; ciia radn Toan eho thay mdn Toin c6 vai tio rat (5) Nang lye cira xiie; quan trgng gdp phan hinh ci nhiing ning lyc cdt Idi vi phi cdt loi Thdng qua hpc tip mdn (6) Nang lye tuang tic xa hpi; Toan, ngudi hpc cd thi tryc tiip hinh thinh cac (7) Nang lye ty hpe/ hpe suit ddi; nang luc: Nang lye tinh toan vi suy luin Idgic/ (8) Nang luc sieu nhan thiic (nghT vi cieh tu tiiu tupng; Nang lye giai quyit vin de, suy nghT) Nang lue sing tgo; Nang lye tu hpe/ hge suot Mdi nang lye nhin thiic lai gim mgt nhdra ddi; Nang lye sieu nhan thiie (nghT vl cieh suy eae nang lye cu tbi/ nang lye thinh phin Mdi nang nghT); Nang lyc vupt khd; Nang lyc quan sat; lye chung va cae nang lye thinh phin eiia chiing nang lyc tap tmng chii y 38 I TRUONG DAI HOC H A I P H O N G Chuin nang lyc toin hpe ciia hgc sinh phd thdng (PT) dupe hieu li nhiing nang lyc can ed hpe sinh hgc xong chuang trinh radn Toin PT 2.3 Dinh hudng DH chu de gidi hqn-lien tuc d THPT theo hudng hinh thdnh vd phdt trien ndng luc todn hgc cho HS - Khuynh hudng, nang toan hpe hda cic tinh hudng Chuang IV: Gidi ban (9 tilt): Day sd cd gidi han 0; Day sd cd gidi hgn hihi hgn; Day so cd gidi 2.3.1.Ngi dung DH chu de gioi hqn - lien tuc Trln ca sd thuyit da tri tul (do Gardner a THPT (1993) di xudng) va Li thuyit tuang tae van hda Xu hudng ehung eua giio dye toan hpc PT - xa hdi (Social-cultural Theory) cua Vugdtsky, hien tien the gidi la tang cudng hudng toan cie nghien ciiu eua Koruteexki chiing tdi nhin hpc ling dyng va nang cao nang lye thye hanh, thay nhiing nang lue sau diy li nhiing nang lyc van dyng toin hpc eho HS Vi vgy nhiing tii thiie ma giao dye toin hpc PT can hudng tdi: giiu tilra nang img dyng ciia gidi hgn-Iien tye (1) Nang luc thu nhan thdng tin toan hpc: da dupe dua vio npi dung dgy hpc d trudng PT Chli dl gidi hgn - lien tye cung cip nhiing Nang lyc tri giic hinh thiie hda tai lieu toan hpc, kiln thiie rad diu, ca bin, nen tang ciia Giii tieh nang lyc nam cau true hinh thiic cua bai toan Ngi dung xoay quanh hai khii nilm ea bin la (2) Che biln thdng tin toan hpe: gidi ban va Hen tue Nhiing khai niem vi cae - Nang lyc tu Idgic tiong ITnh vuc eae phep toan ve gidi han - HIn tuc la ea sd cho viec quan he sd lupng vi khdng gian, he thdng ki nghiin eiiu cae npi dung khic cua Giii tich (dao hieu sd vi diu Nang lyc tu bang cic ki him vi phan, tieh phin, ) Dac bilt, chimg cho hieu toin hpc phep giii quylt nhieu bii toin eua khoa hpe va - Nang lyc khii quit hda nhanh va rdng cie thuc tiln, ma ta khdng the giai quyet dupe neu chi diing eie kien thiic eua Dgi sd, Hinh hpc Do ddi tupng, quan he toin hge vi cac phep toan ehinh la nhung bai toin lien quan den sy vo ban - Nang lyc nit ggn qui trinh suy luan toan hpe Theo ehucmg trinh giio dye PT, ngi dung vi he thdng eic phep toan tuang iing Nang lye gidi ban va lien tye dupe dl cap den nhu sau: tu bang cie eau tnic nit gpn - SGK Dai si va Giii tich 11: Chuang IV: (3) Luu trii thdng tin toan hgc: Gidi ban (9 tiit): Gidi hgn hiiu ban cua day sd; - Tri nhd toan hgc (Tri nhd khai quit vl cic: Dinh ly vi gidi hgn hiiu ban; Tong eua cap sd quan he toin hpc, dgc diem ve cae logi, so dd nhin liii vd hgn; Gidi hgn vd eye Phan gidi hgn, suy luin vi chiing minh, phuang phip giai toan, lien tue eiia ham sd gdm cac ngi dung: Dinh nguyin tie, dudng Idi giii toan) nghia gidi han hiiu hgn ciia hira si tai mpt diera; (4) Nang lue vgn dyng toan hoe vio giii Dinh ly vi gidi hgn hiiu han; Dinh nghia gidi hgn mgt ben; Dinh nghia gidi ban biiu han eua quyet van dl: - Nang lue van dyng eae tri thiic Toan nhu ham sd tai vd eye; Dinh nghTa gidi ban vd eye ciia him sd; Mdt vai gidi ban dae biet; Mdt vii cdng cu hpe tip quy tic vi gidi han vd eye; Dinh nghta ham sd - Nang lyc giai rapt sd bii toin cd tinh thyc lien tye tai mdt diim; Dinh nghta him sd lien tye tien dien hinh yen rapt khoing; Mdt so dinh ly ca ban vi him - Nang lye van dung tri thiire va phucmg PP tu sd Hen tue Toin vio thye tiin - SGK Dai sd vi Giai tich nang eao 11: TAP c m KHOA HOC, S6 21, t h a c ^ 03/2017 | 39 hgn vd cue; Gidi hgn vi Uen tye cua hira bao gdra: Gidi hgn ciia hira sd tgi mpt dilra (Gidi hgn hiiu ban; Gidi hgn vd eye; Gidi hgn eiia hara sd tai vd eye); Mdt sd dinh ly ve gidi ban hiiu hgn; Gidi hgn mdt ben (Gidi han hiiu ban; Gidi hgn vd eye); Mpt vii quy tac tim gidi^ hgn vd eye; Cic dang v6 dinh (Dang — va —; Dang °° ; Dang oo — oo ); Him sd liln tye tgi rapt dilm; Hira so liln tuc trln rapt khoang, rapt dogn; Tinh chit ciia him sd lien tuc (dinh ly, hi qui, y nghta hinh hpc eua dinh ly, y nghta hinh hge ciia he qui) trinh, ), dac biet hda eie dgng gidi hgn - liln tuc tdng quit cho nhiing bii eu thi; + Phit trien tu thugt giii: Tim ldi giai vi trinh biy cie bai toin tim gidi ban day, gidi ban him, hira sd liln tye theo cac budc ehung Phit triin nang lye trinh bay ldi giii, nang lyc sii dung ngdn ngu vi ki hieu Phit triin nang lyc sing tao bii toin gidi han, liln tuc radi; Vi du: Tir bii tap trang 135 vdi tam giac diu, cd tbi rad rpng bii toan sang hinh vudng hay luc giic diu, + Bii tgp vi gidi ban - HIn tye rit phong 2.3.2 Dinh huong DH chu de gidi hqn - liin phii ea ve PP vi Id thuit, the hien mdi liln hi tye d THPT theo hudng hinh thdnh vd phdt trien raat thiet giiia nhilu raing kien thiic toin (dgi s6, ndng lyc todn hgc cho HS lupng giac, giai tich, phuang phap tinh), do Nhiing diera can luu y nham phat tiien nang nd li mpt tiong nhiing npi dung giiip ren luyen luc toin hpc thyc hien dgy hpc gidi hgn - lien vi phit triln nang lye toan hge eho ngudi dgy va tuc, li: ngudi hpe Qua trinh DH PP va kt thuit tun gicti + Tang eudng thdng tin, ehi dan Ueh sii vl hgn, lien tye gan lien vdi vile day giai bii tap opt dung "gidi hgn - liln tye" de gay hiing thu toan eu the Day li qui trinh liu dii, no khong vdi ngi dung day vi hge, dl tri giic ve dep ndi tai the dien tiong chi mdt hay mot vai tiet hgc cua toan hgc, li tien d% phit trien nang lye toin Qui trinh DH bii tap GV cin chii y: hge, tie ddng tdt tdi tu tudng va tinh cira cua HS Phat trien nang lyc nhin dgng, nang luc thi hi|n PP va ki thuit tim gidi hgn, lien tuc; Vi dy: Cd the nlu vi du vl day sd Phi-bd-na-xi; Bii toan tra luang cho cdng nhan; Doin nhgn gidi ban eiia day so thuc bing hinb hge, + Phat tiiin nang luc boat dpng tri tue phi biin yong giii Toin: Su phan tich bii toan, phat hiin eie yiu td ca bin va eic yiu td dac bilt bai toin, bilt phan doan each thire giii bii vi tu phin biln cich lam; - / \ (-1)" Vi du: Xlt day sd ("„) vdi "« - " ^ , cho n thay ddi ldn din, ta thay cic diim biiu dien chura quanh diem Day se co gidi ban + Phat tiiin nang luc hogt dpng tri tue chung: Khii quit dang bai tap, khai quit kT thuit giai cac bai toin ve gidi hgn - Uln tuc, liln h$ giiia cac thao tie va dau hi|u tiong dang toan vi gidi han - liln tuc vdi npi dung toan hpc khac (ding thiic, bat dang thiic; phuang trinh, bit phuang 40 I TRU6NGDAIHOCHAIPH6NG - H | thdng hda kien thiie ea bin nhit (doi vdi hpe sinh khdng ddi hdi li thuyet qui chuyin sau vi gidi ban - lien tye li mpt ndi dung phiic tap cua toin sa cip vi cao cap; d phgm vi THPT chi dimg Igi d muc dp: Gidi han, lien tye dupe xem nhu li khai niem ban dau, chi cin ap dung dugc cie cdng thiie da dupe trinh biy Ciing vdi dd, h? thdng eic biln ddi chung cho timg PP; - Doi vdi mdi bai toin cu the, can tuin thu bdn bude giai toin ndi chung Diy li diem dac biet quan trgng quylt dinh sy hinh thinh vi phat triln cie nang lyc toan hpc d ngudi lim toan Thye hien eic biln phip van dap, dim thoai, tir vin dip; qua hogt ddng ngdn ngii niy se kich thich tu hudng dieh ciia ngudi lira toin 2.3.3 Yiu cau cua ngudi gido viin DH ehu de gidi hqn - lien tuc a THPT Dl giiip HS nam dupe mdt cieh he thong nhiing kiln thiic, kt nang, hinh vi phat triin nang lye toin hgc hpe chii dl gidi han bin tuc ngudi giao viln cin phai: + Nim chic cac kiin thiie vi gidi hgn day sd, gidi hgn him, ham sd liln tuc vi eae khai nilra liln quan K^T LUAN Chuyin manh qui trinh giio due tu chii yeu tiang bi kiln thiic sang phit triln nang luc > + Hiiu vi vgn dung duac PP nghien ciiu gidi phim chit ngudi hpc la rapt dinh hudng tit ylu han, hentiacdd li PP tu toin hoc radt cich , i Idgic va he tiidng ' ' '^"^ '^°^^ ^^^^ ^°^ "^°'' '^^^ ''^°' ^°^" '*^^" S'^° dye Viet Nam Tir viec xic dinh khung nang + Xac dinh rd cic nang lyc toan hpc cin hinh lye chung vi nang luc chuyen bi|t liln quan tiianh vi phat tiiin eho HS.CdPPDH tiiich bap; ^ „ , ,; thuc biln mdi Uln he hop ly vdi thue tiln dk HS ^'^ "^°" * ° ^ ^ ' " ""^l ^ ^ ^ "^^'^S tnnh, ndi cd ky nang thuc hinh, tinh toan va ip dyng cae *^""S, PP, dinh gia mdi mdn hpc li rapt ehudi tri tinic gidi han day sd, gidi hgn hira vi ham sd ^^^ "^S^*^" ^*^ ^^ ^^^vrc nghipm De xuat nang liln tuc vio thyc tiln 'v^ toan hpe cin hinh thinh va phat triln cho HS + Cin phit triin eho HS nang lye toin hoc, giup HS nira bit va lim chii dupe cie PP vi kT thuit giii toan da dang Diiu dd khiin HS tich eye hem tiong vi|e hpc, gpi ddng ea yeu thich mdn hpe vi dap iing dupe cie miie dp yeu eiu khac cita mdn hpe ^""^ "^^ !"^' '^ ^^^ '^^^ ^^^ " ^ ^ ^ ^^"^ ^'^" ° " '^^^ ^^ g^^' ^f' " 1'^" ^ ^ ^ ™PT ^ ca ^^ nghien ciiu, triin khai DH theo dinh hudng hinh thinh vi phat tiien nang luc cho sinh viln su phgm toan tiong xu thi doi radi giio dye dgi hpc dap iing yeu ciu ciia giio dye PT hien TAI LIEU THAM KHAO Bg Giao due vi Dao tao (2006), Tdi liiu boi dudng gido viin thyc hiin chuong trinh sdch gido khoa ldp 11 trung hgc phd thdng mon Todn hgc, NXB Giio due Nguyin Hiiu Chau (2005), Nhimg vdn di co bdn ve chuong trinh vd qud trinh dqy hgc NXB Giio due Nguyin Van Cudng, Bemd Meier(2010), Mptsd vdn de chung ve ddi moi phucmg phdp dqy hgc a trudng THPT, NXB Giao dye Nguyen San Ha (2010), Ren luyen hgc sinh trung hgc thong khd ndng todn hoc hda theo tiiu chudn cua PISA, Tgp ehi Khoa hpe giio due, sd Tran Van Hgo (Tong chii bien), Vii Tuin (Chu biln), Dao Ngpe Nam, Le Van Tien, Vii Viet Yen (2007), Dqi sd vd gidi tich 11, NXB Giao due Nguyin Cdng Khanh (2012), Ndng lyc vd ddnh gid kit qua gido dye theo ndng luc chuong trinh gido due phd thdng sau ndm 2015, NXB Giio dye Nguyin Van Khue (1997), Todn cao cdpAl, NXB Giao due Nguyin Thi My Lpe (2010), Dqy hoc phdt trien cdc nang luc cua hgc sinh the ky 21, Hdi tiiao khoa hpc Dgi hpc Giao dye, DHQGHN Doin Quynh (Tdng Chu bien) - Nguyen Huy Doan (Chii biln), Nguyen Xuin Liera, Nguyin Khic Minh, Dgng Hiing Thang (2006) Dqi so vd gidi tich 11 ndng cao , NXB Giao due Ngdy nhqn bdi: 09/12/2016 Ngdy PB ddnh gid: 09/01/2017 Ngdy duyet ddng: 12/01/2017 TAP CHt KHOA HQC, Sd 21, thdi^ 03/2017 | 41 ... lyc toin hpe ciia hgc sinh phd thdng (PT) dupe hieu li nhiing nang lyc can ed hpe sinh hgc xong chuang trinh radn Toin PT 2.3 Dinh hudng DH chu de gidi hqn-lien tuc d THPT theo hudng hinh thdnh... ''^^^ ^^ g^^'' ^f'' " 1''^" ^ ^ ^ ™PT ^ ca ^^ nghien ciiu, triin khai DH theo dinh hudng hinh thinh vi phat tiien nang luc cho sinh viln su phgm toan tiong xu thi doi radi giio dye dgi hpc dap iing... phdp dqy hgc a trudng THPT, NXB Giao dye Nguyen San Ha (2010), Ren luyen hgc sinh trung hgc thong khd ndng todn hoc hda theo tiiu chudn cua PISA, Tgp ehi Khoa hpe giio due, sd Tran Van Hgo (Tong