^!gl len piiru- -Khoa hpc Giao d^c
THIFC NGHIEIVI DAY HOC TI/CHQN CAC CHU DE NANG CAO Of MON TOAN LOP 6
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 8 va 9. Theo quylt djnh dd, day hpc tU chpn d mdn TolnTHCS dupe thUc hien bang d c chu de tuehpn theo 3 loai: bim sat, nlng cao v l 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 6 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 6.
1 / 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 nay d l chi ra mdt danh sach d c chu de nang cao d mdn Toan Idp 8 va Idp 9.
Nghiin cCfu tiep theo ve day hpc tUchpn mdn Toln THCS (gdm d c Idp 6,7,8 va 9) do Vien Chiln lupe va ChUdng trinh gilo due, nay la Vien Khoa hpe gilo due Viet Nam thuc hien, d l gldi thieu eae chu de nang cao d mdn Toan Idp 6 gdm lOchudela:
Chu di 1: Day so tu nhien viet theo quy luat.
Chu de 2; So sanh hai luy thUa.
Chu di 3:Tim sd tan cung cua mot luy thCte.
Chu d l 4: Cac van de nang eao ve tinh chia het, Ude va bdi.
ChCi de 5: Mdt so dang bli tap ve sd nguyen td.
TS.LEVANH6NG Trung tam Nghien cihj Cong nghe Giao dye
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 khi tiln hanh nghien eC^, chung tdi lua chpn xay dung tai lieu day hpe cho 4 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 v l so doan thang.
Cd the thay, ten 4 chu de ma chung toi lUa chpn gan gui vdi tin ele ehu de 1,4,7 v l 9 ma Vien Khoa hpc Gilo due Viet Nam d l 6i xuat nIm 2007.
1.2 Hai loai tai lieu day hpe eho 4 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 khi 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 ra.
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 hpc trong day hoc. Trude hit, la elc luan dilm ve eae ehUe nang day hpe, giao due, phIt trien va kiem tra dinh gil cua bai tap Toln da dupe cle tac gil Nguyen BI Kim v l Vu Duong Thuy nghien edu td nam 1980, gldi thieu d nam 1992 (Nguyen BI Kim va Vu DUdng Thuy 1992, trang 206) va sau nly dupc Nguyen Ba Kim nhin nhan lai theo quan diem hoat
KHGD so 69, thdng 6 - 2011 23
K h o a hpc G i d o d u e -
ddng: eoi bai tap Toan ed vai trd I I " g i l 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 trong 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 T o l n 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 t d ehUe, hUdng dan hpe sinh cd dupe kien thdc, kT nang va thai dp ma d c ehCi di nay mudn neu ra.
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 c l e bai tap trong 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 4 t i l t . T r o n g phan thU hai cd gpi y d c h t d 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 c l e bai tap sau do v l van dung lau dai. NhUvay, tai lieu nay 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 do di hpe sinh h o l n t h I n h elc bai tap da dat ra.
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 t h e m ve loai t i l lieu thU nhat da dupc thue nghiem.
Chu de 7 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 thanh d c edng thUe so hang tong q u i t v l sCf d u n g chung trong giai m d t so b l i toan khdng qua phCfc tap. Mot so bai tap trong chu de nay I I :
Bai tap 1: Hay d u doan edng thUe tinh sd hang t o n g q u i t eua d c day sd:
a ) 2 , 4 , 6 , 8 , 1 0 , . . . b ) l , 3 , 5 , 7 , 9 , . . . e ) 1 , 4 , 7 , 1 0 , 1 3 , . . .
B l i tap 13; Djnh nghTa: Ta gpi n! la tfeh eua*n sd t u n h l l n dau tien.
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 , 2 7 , 2 5 6 , 3 1 2 5 , . . . 3,6,29,258,3127,...
0 , 3 , 2 6 , 2 5 5 , 3 1 2 4 , . . .
Chu dS 2 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 6 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. N h u 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 trong g i l l t o l n ve chia h i t . Cu the, cd mot sd bai tap nhU:
Bli tap 1 :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 - 3 ) h) 2(a-4) d ) x ( a - b ) i ) 7 ( 2 - c ) Bai tap 7 : Chdng minh r a n g : 6 ^ ^ 6 e ) 1 2 ' » M 4 4 7 ^ ' ^ 4 9 g ) 2 ^ ' ' M 6 8 ^ N 6 4 h)3«^N81 1 3 ^ ' M 6 9 i ) 5 i ^ « M 2 5 Bli tap 15: Chdng minh rang 1-1-3-1-3^-1-...-|-3«M3
Chu de3 duge x l y d u n g 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 trong chij di n l y :
B l i tap 1: (trieh 2 d u d i u )
, 1 1 1 , 1
a ) — - + h — - I - ... +
1.2 2.3 3.4 999.1000
b)
J_
5.7" ... + -
1.3 3.5 Bli tap 2:
J_ _1_
1.2"^ 2.3 n(rt + l ) Bai tap 8:
1 9 .101
1
3 13.22
9 66.31
40 9331
24 K H G D s o 6 9 , thdng 6 - 2 0 1 1
^ 1 idHUCru-
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 khi 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 trong tong sd 22 bai tap cua chu d l nly II:
Bli 1 / Cho 3 diem phan biet.
Hly ve 3 diem va dat kf hieu eho chung.
Hly ve cac dudng thang di qua 2 trong 3 diem do. Hdi cd t h i cd may dudng thang?
Bli 2/ Cho 3 diem phan biet. Hay ve cac doan thing di qua 2 trong 3 diem dd. Hdi ed the cd may doan thing?
Bli 3/ Cho 4 diem phan biet. Hay ve d c doan thing dl qua 2 trong 4 diem dd. Hdi cd the cd may do?n thing?
Bli 4/ Cho 4 dilm phln biet. Hly ve cac dudng thing dl qua 2 trong 4 diem dd. Hdi ed the cd may dudngthing?
Bli 5/ Mdt gill bdng da "TU hung" cd 4 dpi bdng d l , ki hieu II A, B, C, D thdng nhat to chu'c dau vdng trdn c l lupt di va lupt ve de chpn dpi Vd djch. Hly lap bIng md t l mdt d c h 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 5 dilm, trong dd khdng cd 3 dilm nIo thing hang. Tfnh so dudng thing di qua 2 dilm trong 5 diem da eho.
Bli 9/T6ng quit bli toln 8 cho n diem Bai 14/ Ba dudng thing cd 1 dilm chung dupe gpi II3 dudng thing ddng quy. Cho 5 dUdng thing ddi mdt d t nhau m l trong do khdng cd 3 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 trong bIng
S6du'ejngthangd6l m^tcSt nhau, nhung khfing c6 3 di/dng
d6np quy 2 4 S 6
S6 giao diem
1 3 6 10 IS
So giao tang them 0 2
Qu/ luSt cOa day so glao
diem 1 3=1+2 6=1+2+3 10=1+2+3+4
Bli 16/ Hay ve hinh tUdng ijfng vdi moi ddng trong bIng tren
Bli 17/ Hay md rdng them d c so trong bIng va ve hinh tUdng tfng.
Khoa hpc Gido dye 2/ T 6 chuTc thUc nghiem va ket qud ban dau
2.1 Thue nghiem nay dupe ehung tdi tiln hanh hai lupt tai trudng PTCS Thuc nghiem thudc Vien KHGDVN. Lupt thU nhat thuc hien trong nam hpc 2008-2009 vdi 3 chu de dau tien. LUpt thU hai thUc hien trong nIm hpc 2009-2010 vdi d 4 chu de d l neu. Chung tdi eCing gpi y giao vien phIt trien mdt so kT thuat chi tilt d l dU kien trong 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 v l 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 trong d e gid hpc ma nha trudng bo trf de day tang cudng moi tuan 2 tilt cho mon Toln theo d c trinh dd cua hpc sinh.Trinh dp hpe sinh d nhdm thuc nghiem la khi trong Ian thUe nghiem thUnhat v l II gidl trong 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 ra nhU he thdng d c bai tap, djnh hudng to chUe, hUdng dan giai, phan bd thdi gian cho 4 tilt theo tirtig cap 2 tilt (Bd GDStDT quy dinh day hpe tU chpn 2 tiet/tuan)
(2) Giao vien d l cu t h i hda dupc dinh hUdng thiet k l trong tai lieu dinh rieng cho giao vlen bIng neu ra 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 trong 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 trong 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.
KHGD s6 69, thdng 6-2011 25
Khoa hpc Gido dgc •
(5) Ndi dung thUe nghiem ve4chu de nang eao mdn Toan vdi he thong bai tap d l di ra dupe nhdm hpc sinh thUe nghiem tilp nhan vdi sU ham thich.
b) Vl kit qui kiem tra cudi dpt thuc nghiem, ehung tdi xin neu ra de bai kiem tra, kit qui va mdt sd nhan xet nhu sau:
(l)Debdi (thdi gian lam bli 60 phut)
(thdi diem kiem tra: 15/5/2010, sau khi kit thuc thucnghiem 1 tuan)
Bdi 1 (3 diem) Du doln edng thUe tong quit eho day so sau
1;4;9;16;25;...
2;6;12;20;30;...
4;10;28;82;244;...
Bdi2 (2 diem) Chdng minh ring:
5100. 5 « + 598 1^21
ed/3(1,5diem) ChoS-1-H2-i-2^-t-2^+ -1-2""
Tfnh sdsd hang eua S Chdng minh S chia hit eho 7 Bd/4(2dilm)
1 1 1 1
TTnhS^-—+ + + ...-+
1.5 5.9 9.13 97.101 Timxbiet + + -I-....+ =
1.6 6.11 11.16 x.(x + 5) 56
Bffl5(1,5diem)
Cho 7 diem phln biet bat ki, khdng ed 3 diem nao thing hIng. Ndi hai diem bat ki de tao thanh ele doan thang. Hdi cd bao nhilu doan thang dupe taothinh?
(2) Ve kit qui (Xem bang 1 va bIng 2) Bdng 1- Tong hep
Ng en y (3) Vai nhan xet ve kit qui bai kilm tra 1/ Dilm toan bli td diem 7 trd len ed tl le 703
% va dilm trung binh eua d nhdm thUe nghilm la 7,22 eho thay bai kiem tra phu hpp vdi hpe sinh kha, gldi.
2/ Chenh lech diem toln bli Idn (diem eao nhat 10, diem thap nhat 3,5), vay ed phan hda cao ve ket qui kilm tra du hpe sinh dupe chpn ban dau deu kha gidl.
3/ HS biet dUdoan quy luat day so (bai 1), biet van dung edng thC^c cho ddi tUpng hinh hpc (bli 5) vdi mUc dp chae chin, the hien khi nang eua hpc sinh khi gidl
4/ HS da bude dau vIn dung suy luan v l chUng minh (qua elc bai 2; 3 va 4), t h i hiin mijfe dp eao eua hpe sinh khi gidi ve mdn Toln. Tuy nhien, hoc sinh chua the thanh thao vdi suy luan va chdng minh nhu d l thanh thao ve tfnh toln v l dU doan (so sanh eae bai 2 bai 3 v l bai 4 vdi cac bli 1 v l 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 nay cd tinh khi thi.
Thuc nghiem do cung gpi y mdt sd nhu d u ve nghien eCru mde dp khd cho cle bai tap trong tli lieu day hpe va do vay eung dat ra yeu d u cdn phli holn thien ca hai loai t l i lieu day hpc d l cd (bao gdm c l he thdng bai tap, nhat la bli t i p mang tfnh gidi thieu kiln thdc mdi v l gpi y bo sung de giao theo diem todn bdi
Oiem So bai
• n i ^ % 10 8 29,6
9,5 1 3,7
9 2 7,4
8,5 3 11,1
8 1 3,7
7,5 2 7,4
7 2 7,4
6,5 1 3,7
6 0 0
5.5 1 3,7
5 3 11,1
4,5 1 3,7
4 0 0
3,5 2 7,4
Bang 2 - Tong hap theo diem trung binh
Ket q u i diem cOa 27 hoc sinh Olem toi da O i l m toi thleu O i e m t r u n q binh Lech so vcn toi da T I I e l e c h s o v c f i t 6 l d a ( % )
Olem toan bai
10 3,5 7.22 2,78 27,8
Olem t i f n q bai 1 /
3 2 2.74 0.26 9
2/
2 0 1.37 0.63 31
3 / 1.5 0 0.98 0 3 2 34
4 / 2 0 1 3 5 0.65 33
5/
1.5 0 1.24 026 17
(Xem tiep trang 22) KHGD so 69, thang 6-2011
K h o a h p c G i a o d u e •
5.4. Cde logi dudn hoc tap (Project works):
Day hpc d u I n cho phep ngUdi hpe lam viee mot each ed tfnh hop t i e vdi cac ban hpc va ngudi hudng dan eua mlnh trong mot mdi trudng lay hpe sinh lam trung tam, ndi ma hpc sinh dUdc khuyen khfch kham pha elc chCi de khae nhau ma chung 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 5 dang khie nhau.
Moi dang ed nhCfng dac diem, yeu t d 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 thanh 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 duy phe p h l n dupe p h I t huy) t r o n g hoat ddng m l hpe sinh thay phu hpp va hUng t h u .
TAI L i f U T H A M KHAO
1. 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").
2. David WJohnson & RogerT. Johnson. Learning Together and Atone: Cooperative, Competitive, and IndividualisticLearning.JhWd edition. Prentice Hall, Englewood Cliffs, NewJesey 076323(1991).
3. Phd Diic Hda. Dgy hgc tich cue vd each tlep con trong dgy hoc tieu hgc. NXB DHSR 2009.
4. J. Samuel Barkin. Realist Constructivism:
Rethinking international 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 this knowledge to other situation relating to new knowledge. Learning with forms of Inquyry teaching is trend of modern education, based on participation of learners in solving problem and critical thoughts (critical thought is promoting) in activity that pupils find relevant and interesting.
THirC NGHIEM...
(Tiep theo trang 26)
vien cu the t h e m t l i lieu eho rieng hpe sinh nhu phieuhpetap).
TAILI|UTHAMKHAO
1 / 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 trong chuang trlnh tdp 8 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 B I 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.
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 full use of the role of exercises as pupils' activities holder and meeting the aspects of purpose, content and teaching method. Teacher's guide lets him/her help pupils ta do the above activities with a view to achieve the demand of knowledge, skills and attitudes of teaching topic.
K H G D s d 6 9 , t h d n g 6 - 2 0 1 1
