!̂gl len piiru Khoa hpc Giao d^c THIFC NGHIEIVI DAY HOC TI/CHQN CAC CHU DE NANG CAO Of MON TOAN LOP 6 Day hpc tu chpn d l dUpc chinh thdc dUa vao chUdng trinh trung hpc cd sd (THCS) d nude ta tdnamhpe[.]
^!gl len piiru- -Khoa hpc Giao d^c THIFC NGHIEIVI DAY HOC TI/CHQN CAC CHU DE NANG CAO Of MON TOAN LOP TS.LEVANH6NG Trung tam Nghien cihj Cong nghe Giao dye D ay hpc tu chpn d l dUpc chinh thdc dUa vao chUdng trinh trung hpc cd sd (THCS) d nude ta tdnamhpe 2001-2002 bIng quyet dinh so 03/2002/ QD-GD&DT ngly 24/1 /2002 eua Bd trudng Bp Gilo due va DIo tao va chi dupc thUc hien d ele Idp va Theo quylt djnh dd, day hpc tU chpn d mdn TolnTHCS dupe thUc hien bang d c chu de tuehpn theo loai: bim sat, nlng cao vl dip Ung Den nam hoc 2006-2007, day hpe tU chpn d mdn Toln THCS da dupe thue hien d toan d p hpc, ke cl d c Idp v l 7, nhUng gidl han d hai loai chu de bIm sat v l nang cao.Tuy nhi§n, vlec thuc hien day hpc tUehpn d mdn Toln THCS, tren thuc tien, van cdn khd khan Tai edng vIn hudng dan thUe hien nhiem vu nam hpc 2009-2010, Bp GD&DT da lUu y rang "trong dilu kien chua ban hanh dupe t l i lieu chCi 6i nlng cao, can dinh thdi lUpng day hpe tU chpn de thUe hien chu de bIm sat nham dn tap, he thong hda, khIc sau kien thUc"(Bp Giao due v l Dao tao, 2009) Bli viet nly gidl thieu mot thue nghiem nham gili quyet khd khIn ve tai lieu day hpc tuehpn eho chu de nlng cao d mdn Toln Idp / Noi dung thiTc nghiem 1.1 Nghien culj cua Nguyen HQu Chlu v l edng su (Nguyin HCfu Chlu 2005 a, trang 42) da md t l kha rd v l muc tiiu, npl dung, d u true chung ve tai lieu day hpc cho ehu di (theo loai bai hpc va loai bai tap) va d c h thdc tiln hanh day hpc tU chpn d THCS Vdi mdn Toan, nghien cCfu d l chi mdt danh sach d c chu de nang cao d mdn Toan Idp va Idp Nghiin cCfu tiep theo ve day hpc tUchpn mdn Toln THCS (gdm d c Idp 6,7,8 va 9) Vien Chiln lupe va ChUdng trinh gilo due, la Vien Khoa hpe gilo due Viet Nam thuc hien, d l gldi thieu eae chu de nang cao d mdn Toan Idp gdm lOchudela: ChU de 6: So sanh hai phln sd Chu de 7: Day cle phan sd viit theo quy luat Chu de 8: Mdt so phUpng phap gili toan sd hpc Chu de 9: Tinh sd dilm, sd doan thang, sd dUdng thang ChCide 10:Tinhsddogdc Do danh mue d e ehu 6i tren chua dugc phe duyet v l tli lieu day hpe kem theo ehua dupc bien soan chinh thUe, nen tiln hanh nghien eC^, chung tdi lua chpn xay dung tai lieu day hpe cho chU di vdi ten gpi nhu sau; Chu de 1: Dly sd Chu d l 2: Chia hit Chude3:Phansd ChCi de 4: Tinh sd dilm, sd dUdng thing vl so doan thang Cd the thay, ten chu de ma chung toi lUa chpn gan gui vdi tin ele ehu de 1,4,7 vl ma Vien Khoa hpc Gilo due Viet Nam d l 6i xuat nIm 2007 1.2 Hai loai tai lieu day hpe eho chCi d l tren dupc thuc nghiem II: -Tli lieu dung ehung eho hpc sinh va giao vien (eho hpe sinh II chfnh) -Tai lieu danh rieng cho gilo vien a) Tai lieu dung ehung cho hpc sinh v l giao vien dUdc ehung tdi xay dUng theo hinh thUe he thdng d e bai tap Sau thUe hien cac bai tap dd theo hudng dan cua gilo vien, hpe sinh se dat duac kien thdc, kT nlng v l thai dp dat Co sd cho viec xay dUng ndi dung chu de bang he thdng bai tap dupe ehung tdi xle djnh d n cCf vao eae luan diem ve chUe nang cua bai tap Toln Chu di 1: Day so tu nhien viet theo quy luat hpc day hoc Trude hit, la elc luan dilm ve eae ehUe nang day hpe, giao due, phIt trien va kiem Chu de 2; So sanh hai luy thUa tra dinh gil cua bai tap Toln da dupe cle tac gil Chu di 3:Tim sd tan cung cua mot luy thCte Nguyen BI Kim v l Vu Duong Thuy nghien edu td Chu d l 4: Cac van de nang eao ve tinh chia het, nam 1980, gldi thieu d nam 1992 (Nguyen BI Kim Ude va bdi va Vu DUdng Thuy 1992, trang 206) va sau nly dupc ChCi de 5: Mdt so dang bli tap ve sd nguyen td Nguyen Ba Kim nhin nhan lai theo quan diem hoat KHGD so 69, thdng - 2011 23 K h o a hpc G i d o d u e ddng: eoi bai tap Toan ed vai trd I I "gil mang hoat ddng cua hpe sinh"va cd the khai t h i e vai trd cCia bai tap tren nhieu binh dien day hpc nhU: mue dich day hpe, npi dung day hpc va phUdng phap day hpc, (Nguyen Ba Kim 2002, trang 384) Chung tdi eung dua vao nhUng nghien eUu va thUe nghiem q u i trlnh thUe hien de tai d p Bp"BUdc dau thCf nghiem hinh thUc t u chpn d trung hpe cd sd; m l so B 92-45-01 Vdi de t l i tren, dUpe nghiem thu nam 1995, ehung tdi da xay dUng d c c h u y i n de day hpc cho hinh thUe t u chpn dudi dang he thdng d c bai t i p Toln hpc b) T l i lieu danh rieng cho g i l o vien nham giup g i l o vien sd dung dupe tai lieu dung chung cho hpc sinh va g i l o vien (neu tren) de td ehUe, hUdng dan hpe sinh cd dupe kien thdc, kT nang va thai dp ma d c ehCi di mudn neu Di thUe hien d i l u dd, tai lieu n l y ed hai phan ehfnh: (1) Idi giai h o l e gpi y ve Idi giai cle bai tap he thdng va (2) gpi y ve tien trinh day hpe ele bai tap d l neu theo thdi gian d l quy djnh eho moi chu de tilt.Trong phan thU hai cd gpi y d c h td ehUe day hpe, eleh thUe giao nhiem vu eho hpe sinh v l to ehUc hudng dan, danh g i l k i t qua edng v i l e hpc sinh da thuc hien Dae biet, phan n l y luu y mot sd diem g i l o vien can nhac n h d hpe sinh ghi n h d k i l n thdc, kT nang cd dupc tU bai tap d d hay m d t sd bai tap da l l m de van dung g i l i cle bai tap sau v l van dung lau dai NhUvay, tai lieu n h u I I b i n ke hoach t o ehUe edng viee cho hpe sinh de giao vien se t i l p tuc cu the hda chung cd the b I n g d u hdi gpi y hay ehu y n I o di hpe sinh h o l n t h I n h elc bai tap da dat 1.3 Dudi day I I mdt sd bai t i p t d eae ehCi d l t r I n n h u I I vi du de hinh dung them ve loai t i l lieu thU nhat da dupc thue nghiem Chu de v l d l y so dupc thiet ke vdi mong mudn hpc sinh se cd dugc k i l n thdc ki nang ban dau ve quy nap de k h I i q u i t tinh quy luat eua d l y sd d c edng thUe so hang tong q u i t v l sCf dung chung giai m d t so b l i toan khdng qua phCfc tap Mot so bai tap chu de I I : Bai tap 1: Hay d u doan edng thUe tinh sd hang tong q u i t eua d c day sd: a)2,4,6,8,10, b)l,3,5,7,9, Khdng diJng m I y tinh h l y tfnh: 1!.21,31, 7! Bai tap 15: Hay d u d o a n edng thdc tinh so hang t o n g q u i t eua c l e d l y sd: 1,4,27,256,3125, 3,6,29,258,3127, 0,3, 26,255,3124, Chu dS dupe \Ua chpn n h I m giup hpe sinh p h I t t r i l n k i l n thOfc kT n l n g v l chia h i t d l hpc ehUPng trinh chinh thdc vdi mde dp sCf dung dUpc m d t sd kT nang edng cu ve b i l n ddi bleu thu'c chiJa ehU Nhu vay, se cd d c bai t i p 6i hpc sinh c6 kl n l n g edng cu ban dau v l b i l n doi bleu thdc chiJiS chUva d c bai tap sUdung chung g i l l t o l n ve chia h i t Cu the, cd mot sd bai tap nhU: Bli tap :ThUc hien phep t o l n : a)a(x-i-y) e) 3(a-b) b)b(x-i-1) g)5(x-y) c) a ( x - ) h) 2(a-4) d)x(a-b) i)7(2-c) Bai tap : Chdng minh rang: 6^^6 e)12'»M44 7^'^49 g)2^''M6 8^N64 h)3«^N81 13^'M69 i)5i^«M25 Bli tap 15: Chdng minh rang 1-1-3-1-3^-1- -|-3«M3 Chu de3 duge x l y dung n h I m p h I t t r i l n e^e kT n l n g tinh t o l n ve phan sd nhUng vdi yeu d u b i l t sd dung dupc kT thuat p h I t hien quy luat Mdt b l i tap chij di n l y : Bli tap 1: (trieh d u d i u ) , 1 a)—-+ 1.2 b) 1.3 , h —-I- 2.3 999.1000 J_ 3.5 + 3.4 5.7" + - 101 Bli tap 2: J_ _1_ 1.2"^ 2.3 n(rt + l ) Bai tap 8: e)1,4,7,10,13, Bli tap 13; Djnh nghTa: Ta gpi n! la tfeh eua*n sd t u n h l l n dau tien 24 13.22 66.31 40 9331 K H G D s o 69, thdng - 1 ^ idHUCru- Khoa hpc Gido dye Chu d44 bao gdm eae bai tap vUa eung eo d c kiln thu'c kT nang da cd theo yeu d u eua chuong trinh VLfa phIt trien chung de dip Ung nang va hdng thCi eua hpc sinh HPn nUa, mot vai bli t i p cdn dupc lUa chpn nhIm eung cd phIt trien ve khIi quit, ve quy nap da hinh thInh, ren Iuyen tU d c chCi d l d l cd Cd 11 tong sd 22 bai tap cua chu d l nly II: Bli / Cho diem phan biet Hly ve diem va dat kf hieu eho chung Hly ve cac dudng thang di qua diem Hdi cd t h i cd may dudng thang? Bli 2/ Cho diem phan biet Hay ve cac doan thing di qua diem dd Hdi ed the cd may doan thing? Bli 3/ Cho diem phan biet Hay ve d c doan thing dl qua diem dd Hdi cd the cd may do?n thing? Bli 4/ Cho dilm phln biet Hly ve cac dudng thing dl qua diem dd Hdi ed the cd may dudngthing? Bli 5/ Mdt gill bdng da "TU hung" cd dpi bdng d l , ki hieu II A, B, C, D thdng nhat to chu'c dau vdng trdn cl lupt di va lupt ve de chpn dpi Vd djch Hly lap bIng md t l mdt dch quy dinh thu" tU ele tran diu cCia gili Neu gili dau quy djnh chi thi dau mdt lUdt thi gili dd se cd bao nhieu tran dau Bai 8/ Cho dilm, dd khdng cd dilm nIo thing hang Tfnh so dudng thing di qua dilm diem da eho Bli 9/T6ng quit bli toln cho n diem Bai 14/ Ba dudng thing cd dilm chung dupe gpi II3 dudng thing ddng quy Cho dUdng thing ddi mdt d t m l khdng cd dudng nIo dong quy Hay ve hinh va cho biet ed t h i ed bao nhilu glao diem? Bli 15/ Diln vao d trdng bIng S6du'ejngthangd6l m^tcSt nhau, nhung khfing c6 di/dng d6np quy S S6 giao diem So giao tang them 10 IS Qu/ luSt cOa day so glao diem 3=1+2 6=1+2+3 10=1+2+3+4 Bli 16/ Hay ve hinh tUdng ijfng vdi moi ddng bIng tren Bli 17/ Hay md rdng them d c so bIng va ve hinh tUdng tfng KHGD s6 69, thdng 6-2011 2/ T6 chuTc thUc nghiem va ket qud ban dau 2.1 Thue nghiem dupe ehung tdi tiln hanh hai lupt tai trudng PTCS Thuc nghiem thudc Vien KHGDVN Lupt thU nhat thuc hien nam hpc 2008-2009 vdi chu de dau tien LUpt thU hai thUc hien nIm hpc 2009-2010 vdi d chu de d l neu Chung tdi eCing gpi y giao vien phIt trien mdt so kT thuat chi tilt d l dU kien til lieu gilo vien nhu dung may ehilu, phan mIm powerpoint, hay dung phieu hpc tap de djnh rd nhiem vu cCia hpe sinh Qua thue nghiem lUpt thU nhat, ehung tdt dieu chinh bo sung v l tli lieu thUe nghiem hole bIng nhIc nhd giao vien hole bIng bd sung tren tai lieu Cu the, vdi thuc nghiem lupt thU hai: tli lieu dung ehung eho hpc sinh vl gilo vien dupe lam rd hdn ve npi dung kiln thUe ma eae bai tap the hien di hpc sinh cd chCi y sd dung chung lau dai; cdn vdi tai lieu giao vien dupc chung tdi trinh bay kT hdn ve muc tieu gid day va dieu hinh hoat dong nhdm Chung tdi chap nhan thUe nghiem mdt dch tU nhien d e gid hpc ma nha trudng bo trf de day tang cudng moi tuan tilt cho mon Toln theo d c trinh dd cua hpc sinh.Trinh dp hpe sinh d nhdm thuc nghiem la Ian thUe nghiem thUnhat v l II gidl Ian thUe nghiem thU hai 2.2 Kit qui ban dau cho thuc nghiem lUpt thd hai dupe md t l theo hai phUdng dien quan sat gid hpc va danh gil kit qui bai kiem tra sau thuc nghiem a) Ve quan sit gid thUe nghiem, chung tdi thay; (1) Gilo vien d l tuin thu d c tai lieu day hpc ml chung tdi dUa nhU he thdng d c bai tap, djnh hudng to chUe, hUdng dan giai, phan bd thdi gian cho tilt theo tirtig cap tilt (Bd GDStDT quy dinh day hpe tU chpn tiet/tuan) (2) Giao vien d l cu t h i hda dupc dinh hUdng thiet k l tai lieu dinh rieng cho giao vlen bIng neu philu hpc tap, sif dung phUPng tiln edng nghe thdng tin ho trp, cu the hda ele gpi y day hpe bing khich le hay danh gia (3) Hpc sinh hlo hUng hpc tap d c gid thuc nghiem va nghiem tuc vdi bli kiem tra danh gil cudi dpt thuc nghiem, (4) Viee to chUc cle hoat ddng nhdm day hpe elc chu de nlng cao dupc thiet ke theo phucmg phap he thdng bai tap dan xen vdi cac hinh thdc, phUdng phIp day hpc khie nhu phat van, neu van di la cd the chap nhan dupc 25 Khoa hpc Gido dgc • Ng en y (5) Ndi dung thUe nghiem ve4chu de nang eao (3) Vai nhan xet ve kit qui bai kilm tra mdn Toan vdi he thong bai tap d l di dupe nhdm 1/ Dilm toan bli td diem trd len ed tl le 703 hpc sinh thUe nghiem tilp nhan vdi sU ham thich b) Vl kit qui kiem tra cudi dpt thuc nghiem, % va dilm trung binh eua d nhdm thUe nghilm ehung tdi xin neu de bai kiem tra, kit qui va mdt la 7,22 eho thay bai kiem tra phu hpp vdi hpe sinh sd nhan xet nhu sau: kha, gldi (l)Debdi (thdi gian lam bli 60 phut) 2/ Chenh lech diem toln bli Idn (diem eao nhat (thdi diem kiem tra: 15/5/2010, sau kit thuc 10, diem thap nhat 3,5), vay ed phan hda cao ve ket thucnghiem tuan) Bdi (3 diem) Du doln edng thUe tong quit qui kilm tra du hpe sinh dupe chpn ban dau deu eho day so sau kha gidl 1;4;9;16;25; 3/ HS biet dUdoan quy luat day so (bai 1), biet 2;6;12;20;30; van dung edng thC^c cho ddi tUpng hinh hpc (bli 5) 4;10;28;82;244; vdi mUc dp chae chin, the hien nang eua hpc Bdi2 (2 diem) Chdng minh ring: sinh gidl 5100 « + 598 1^21 ed/3(1,5diem) ChoS-1-H2-i-2^-t-2^+ Tfnh sdsd hang eua S Chdng minh S chia hit eho Bd/4(2dilm) 1 TTnhS^-—+ 1.5 1 + + -+ 5.9 9.13 Timxbiet + 1.6 -1-2"" 97.101 + -I- + 6.11 11.16 = x.(x + 5) 56 4/ HS da bude dau vIn dung suy luan v l chUng minh (qua elc bai 2; va 4), t h i hiin mijfe dp eao eua hpe sinh gidi ve mdn Toln Tuy nhien, hoc sinh chua the thao vdi suy luan va chdng minh nhu d l thao ve tfnh toln v l dU doan (so sanh eae bai bai v l bai vdi cac bli vl 5) Kit qui thuc nghiem neu tren cho thay cd the thUe hien dugc viee xay dung npi dung day hpe tu! chpn ehu de nang eao bIng hinh thUe he thdng bli tap va tli lieu the hien phUPng phIp cd tinh thi Thuc nghiem cung gpi y mdt sd nhu d u ve Bffl5(1,5diem) nghien eCru mde dp khd cho cle bai tap tli Cho diem phln biet bat ki, khdng ed diem lieu day hpe va vay eung dat yeu d u cdn phli nao thing hIng Ndi hai diem bat ki de tao ele doan thang Hdi cd bao nhilu doan thang dupe holn thien ca hai loai t l i lieu day hpc d l cd (bao gdm cl he thdng bai tap, nhat la bli t i p mang tfnh taothinh? gidi thieu kiln thdc mdi v l gpi y bo sung de giao (2) Ve kit qui (Xem bang va bIng 2) theo diem todn bdi Bdng 1- Tong hep Oiem 10 9,5 8,5 7,5 6,5 2 5.5 4,5 So bai •ni^% 29,6 3,7 7,4 11,1 3,7 7,4 7,4 3,7 3,7 11,1 3,7 7,4 3,5 Bang - Tong hap theo diem trung binh Ket q u i diem cOa 27 hoc sinh Olem toan bai Olem t i f n q bai 1/ 2/ 3/ 4/ 5/ 1.5 1.5 Olem toi da 10 O i l m toi thleu 3,5 0 Oiem trunq binh 7.22 2.74 1.37 0.98 135 1.24 Lech so vcn toi da 2,78 0.26 0.63 032 0.65 026 TIIelechsovcfit6lda(%) 27,8 31 34 33 17 0 (Xem tiep trang 22) KHGD so 69, thang 6-2011 Khoa hpc Giao due • 5.4 Cde logi dudn hoc tap (Project works): Day hpc d u I n cho phep ngUdi hpe lam viee THirC NGHIEM (Tiep theo trang 26) mot each ed tfnh hop t i e vdi cac ban hpc va ngudi hudng dan eua mlnh mot mdi trudng lay hpe sinh lam trung tam, ndi ma hpc sinh dUdc khuyen khfch kham pha elc chCi de khae ma chung vien cu the them t l i lieu eho rieng hpe sinh nhu phieuhpetap) quan t i m Cle dU I n ed e h i l u s l u , cd giai doan va ed tfnh phUe tap se thue day ehung x l y dung k i l n thCfc N h U v a y , d a y h p e k h l m p h l e d dang khie Moi dang ed nhCfng dac diem, yeu td rieng nhUng chung deu ed nhCfng diem ehung I I giup hpe sinh k h I m p h i tri thUe eua n h i n loai d l bien tri thUc eua rieng minh Day hpe theo ele dang k h I m p h i I I xu hudng eua nen giao due hien dai, dua tren sUtham gia eua ngUdl hpe v I o viee g i l i quyet van de v l nhCfng suy nghT ed tinh phe phan (tu phe p h l n dupe p h I t huy) hoat ddng m l hpe sinh thay phu hpp va hUng thu TAI L i f U T H A M KHAO Bd G i l o due va Dao t a o Dgy kJnang tuduy H I Ndi, 2000 (Tai lieu cua d u an Viet Bi "Ho trp day hpetCfxa") David WJohnson & RogerT Johnson Learning Together and Atone: Cooperative, Competitive, and IndividualisticLearning.JhWd edition Prentice Hall, Englewood Cliffs, NewJesey 076323(1991) Phd Diic Hda Dgy hgc tich cue vd each tlep dgy hoc tieu hgc NXB DHSR 2009 J Samuel Rethinking Barkin Realist international TAILI|UTHAMKHAO / Bp Giao due va D I o tao, Hudng ddn thuehien nhiem vu Gido ducTrung hgc nam hgc 2009-2010.Hh Ndi, 2009 2/ Nguyen HQu C h l u (2005a, chu bien), Mdt so vdn de ve dgy hoc edc chCi de tu chon chuang trlnh tdp trudng THCS, NXB G i l o dye Ha Ndi 2005 3/ Nguyen HOfu C h l u (2005b), NhUng vdn died bdn ve chuang trinh vd qud trinh dgy hgc, NXBGD, 2005 4/ Nguyen Ba Kim (chO bien) - Vu DUdng Thuy(1992), Phuong phdp dgy hoe mdn Todn (phan dai eUdng), NXB G i l o due, H I Npi, 1992 5/ Nguyen BI Kim (2002), Phuang phdp dgy hgc mon Todn, NXB Dai hpc SU pham, H I Npi, 2002 6/Trung t i m Cong nghe g i l o due, Bdo edo tong kit di tdi cap Bg "Budc ddu thCl nghiem hinh thdc tU ehgn d trung hoc ca s&', ma sd B 92-45-01, H I Npi, 1995 7/ Vien Khoa hpe Giao due Viet Nam (2007), Chuang trinh dgy hgc tu chon mdn Todn THCS (lUu hanh npi bd), H I Npi, 2007 Constructivism: Relations Theory, Cambridge University Press, UK 2010 SUMMARY Constructivism Theory allows learners building knowledge for themselves through testing ideas from available experience and knov\/ledge, then apply SUMMARY This paper introduces an experimental instructionfortwokindsofthe&^grademathematlcs materials to meet a demand on the self-selected teaching materials with the appropriate enhanced topics Pupils' handbook is developed in the form of selected system of mathematical exercises to make this knowledge to other situation relating to new full use of the role of exercises as pupils' knowledge Learning with forms of Inquyry teaching holder and meeting the aspects of purpose, content is trend of modern education, based on participation and teaching method Teacher's guide lets him/her of learners in solving problem and critical thoughts help pupils ta the above activities with a view (critical thought is promoting) in activity that pupils to achieve the demand of knowledge, skills and find relevant and interesting attitudes of teaching topic activities K H G D s d 69, t h d n g - 1 ... vao d trdng bIng S6du''ejngthangd6l m^tcSt nhau, nhung khfing c6 di/dng d6np quy S S6 giao diem So giao tang them 10 IS Qu/ luSt cOa day so glao diem 3=1+2 6= 1+2+3 10=1+2+3+4 Bli 16/ Hay ve hinh... 1.37 0.98 135 1.24 Lech so vcn toi da 2,78 0. 26 0 .63 032 0 .65 0 26 TIIelechsovcfit6lda(%) 27,8 31 34 33 17 0 (Xem tiep trang 22) KHGD so 69 , thang 6- 2011 Khoa hpc Giao due • 5.4 Cde logi dudn hoc... g)5(x-y) c) a ( x - ) h) 2(a-4) d)x(a-b) i)7(2-c) Bai tap : Chdng minh rang: 6^ ^6 e)12''»M44 7^''^49 g)2^''''M6 8^N64 h)3«^N81 13^''M69 i)5i^«M25 Bli tap 15: Chdng minh rang 1-1-3-1-3^-1- -|-3«M3 Chu de3