Ho Thj Mai Phuang Tgp chi KHOA HQC & CONG NGHE 94(06): 43-48
PHAT TRIEN TU* DUY CHO HQC SINH TRUNG HOC CO SO QUA DAY HOC GIAI BAI T^^P TOAN
Hd Thi Mai Phuang Trudng Dgi hpc Suphgrn- DH Thdi Nguyen TOM T A T
R6n luyen vd phdt triin tu duy cho ngudi hpc Id mdt nhipm vy quan trpng trong day hpc. Todn hpc Id mon khoa hpc c6 tinh trftu tupng cao vd tinh logic chat che. VI vgy, ngudi hpc phai c6 phuang phap tu duy khoa hpc vd mang tinh sdng tgo. Mon todn cd nhieu tiem ndng vd cung Id moi trudng tit nhit dl rha luypn vd phdt triin tu duy ciia ngudi hpc. Trong qud Ulnh dgy todn ben canh vipc dgy hpc sinh cdch tim Idi gidi bdi tdp nlu cd phuong phdp khai thdc hg thing bdi tap, cau h6i mpt cdch thich hgp dya tren nhftng nguySn tic ca bdn s5 giup cdc em biet tlm Idi giai bdi todn bdng nhilu cdch khdc nhau, khai thdc bdi todn theo nhilu hudng vd g6c dp khdc nhau, nhftng hoal ddng ndy slf g6p phdn rbn luy^n vd phdt triin tu duy d hpc sinh, ndng cao chat lupng dgy hpc ddp irng yeu cau dgy hpc phdt triin hifn nay.
Tir khda: Ren luy4n, phdt trien. lu duy, ngudi hpc, gido vien DAT VAN DE
Ren luyen va phdt triin tu duy (TD) cho ngudi hpc la m^t nhiem vu quan trgng trong day hgc. Toan hgc Id mdn khoa hgc cd tinh trftu tugng cao va tinh logic chdt che. Tri thuc trudc Id ca sd cho tri thftc sau vd tri thuc sau dya vdo tri thuc trudc. Vi vay ddi hdi ngudi hgc phdi cd mgt phuong phdp TD khoa hpc vd mang tinh sang tao. Ben canh dd vdi nhiing ddc diem ay, mdn loan cd nhilu tiim ndng va cung la mdt mdi trudng tdt de ren luyen vd phdt trien TD ciia ngudi hgc. Trong day hgc gidi bdi tap todn, ngudi hgc khdng chi tiep thu kien thftc, kT ndng ma cdn ren luyen each nghT, each tu duy, each hgc. Do vay trong qua trinh day hgc todn ndi chung, giai bai tap toan ndi rieng ngudi thiy khdng ehi dgy hgc sinh (HS) bilt each tim tdi loi gidi bdi tap ma cdn giiip cdc em bilt TD de gidi bdi toan bdng cac each khdc nhau, khai thac bai toan theo nhilu hudng, nhin bdi todn dudi nhieu gdc dg. Chinh nhung hoat dgng ndy se thiic day viec ren luypn va phat trien TD d HS.
TLTDUYLAGI?
Tu duy Id qua trinh nhdn thuc, phdn anh nhimg thugc tinh bdn chdt, nhung mot quan he cd tinh qui lugt cua sy vgt hipn tugng.
Tel. 0915590027; Email: [email protected]
Theo tft dien Tieng Viet (Hodng Phe, Nxb Khoa hpc Xa hgi, Hd Ngi, 1998). Tu duy la
"Giai dogn cao ciia qua trinh nhan thuc, di sau vao bdn chdt vd phdt hien ra tinh qui luat ciia sy vat bdng nhftng hinh thftc nhu bieu tugng, phdn doan va suy li".
Tu duy mang tinh khai quat, tinh gidn tilp, tinh trftu tugng. San pham ciia TD la nhiing khdi niem, phan doan, suy ludn dugc bieu dgt bdng nhiing tft, ngft, cau... TD la mdt hogt dpng tri tue vdi qua trinh bao gdm cdc budc sau;
* Xac djnh dugc van de, bieu dgt nd thdnh nhipm vu TD. Ndi each khdc la tlm dugc cau hdi can gidi dap.
* Huy ddng tri thuc, vdn kinh nghiem, hen tudng, hinh thanh gid thuyet vd each giai quyet van de, each tra Idi cau hdi.
* Xdc minh gia thuyet trong thuc tien. Neu gia thuyet dung thi qua budc sau, nlu sai thi phii djnh nd vd hinh thanh gia thuyet mdi.
* Quyet djnh, danh gid ket qud vd dua ra su dung.
Qud trinh TD dugc dien ra bang each chii the tien hanh cdc thao tac tri tup.
M O T S O NGUYEN T A C P H A T TRIEN TLT DUY
(1) Hieu thau vd ndm vimg kien thuc Cau phuong ngdn " cd bdt mdi got ndn hd" la kinh nghiem dugc nit ra tft cupc sdng cua nhan dan ta qua hdng nghin ndm vd dugc van 43
Ho Thi Mai Phuong Tap chf KHOA HQC & CONG NGH$ 94(06); 43 - 48 dyng vdo mpi hogt dgng ciia con ngudi.
Trong hogt dgng TD, phdi cd kiln thftc mdi cd CO sd de dya tren dd md TD diing ddn, Sy hieu biet cdng sau sic thi TD cang chinh xac Kiln thuc cang vftng vang thi TD cdng mgch lac Hieu Ihau vd ndm vftng kien thuc Id nIn tdng ciia TD trong hpc Igp vd gidi toan, la ca sd ciia vice tiep nhgn tri thftc mdi vd de phdt triin TD.
Cac kien thuc ciia todn hgc dugc sdp xIp theo mgt hp thong chdt che' tri thftc sau dya vdo in thuc trudc, chinh qua Irinh hgc tap lien tyc ndy Id mgt khau trong qud trinh phat trien TD.
Vi le dd trong dgy hgc ngudi thiy phdi thudng xuyen doi mdi phuong phdp dgy hgc (PPDH) de HS lilp nhgn kiln thuc mdi mgt each de ddng, nhanh chdng va khic sau dugc kiln thuc iy.
(2) Phdt tnen tu duy d\ra tren .su thirc hdnh va van dung kien thuc thudng xuyen De thau hieu va ndm viing kien thftc thi can thyc hdnh va van dyng kiln thftc thudng xuyen. NIU HS lam nhilu bdi tap, tim nhieu cdch thuc giai bai toan tlii kien thuc thudng xuyen dugc huy ddng, dugc cimg cd ngay cdng vftng chdc; ddng thdi luyen tgp giai bdi tap Id ca hgi d l HS tap luypn TD, tgo dyng kT ndng TD va vi thi TD ngdy cdng dugc phat trien. De ren luypn vd phdt trien TD cho ngudi hpc, GV phai day cdng nghien cftu, chgn loc dugc hp thdng bai tgp da dgng, ddo sdu dugc mgi khia canh cua kien thftc de HS thyc hanh, chinh hp thdng nhftng bai tgp iy ddi hdi HS phdi tgp luypn huy dpng kien thftc da hgc mpt each triet de. HS dugc ren luypn mgt phong cdch suy nghT sau sic ban va nhd dd dan hinh thanh dugc kT ndng huy dgng kien thftc gdp phin phat triin TD (3) Tich luy kinh nghiem vd ki ndng di phat trien tuduy
Mdi thao tac ciia TD diu phdi do ren luypn, cimg cd thudng xuyen, hgc tap ma ed.
Thuc te chftng td rdng qua trinh TD khdng phai llic ndo cung dugc di theo mgt con dudng thang tdp de tdi dich ma nd thudng quanh co khiic khuyu. Khi ta chgn dugc con dudng di din dich thing tip, day la liic qua 44
trinh TD ciia la sdng siia, mgch lac, mgi khdu trong qud trinh dd dd dugc sdp ddt mgt cdch toi uu. Khi con dudng di tdi dich quanh co khiic khuyu thi sau khi tdi dich ta can nhin lgi dl phan tich, phe phdn nhftng chd thieu sdt, logi di nhftng khau thua hodc sdp xIp Igi cac khdu trong qud trinh de TD dugc hgp li hon.
(iiai lgi mgt bdi todn theo mgt each khac, hay khai thdc bdi toan theo nhGhig hudng khac nhau chinh Id d l riit ra nhftng kinh nghipm ve vipc vgn dyng cdc thao tdc TD vd cung Id dl hodn thipn phuang phap TD.
Do vgy, v i ^ tich lu^ kinh n g h i ^ rat cin thiet cho sy phdt trien TD. Trong khi xem xd lgi each giai mgt bai to4n ta dd phai tgp luypn TD sdu sic hem. Vi thi, vipc due nit kinh nghipm khdng nhftng tgo cho ngirdi hgc ren luypn TD md cdn giup hg hoan thipn cac thao tdc TD ciia minh, Idm cho TD co chit lugng hon va day nhanh sy phat trien TD. Nhd todn hgc ndi tieng Pdlya dd ndi: "Chung ta hgc tap xuit phat tft kinh nghipm, hay ndi diing han, chiing ta phdi hgc tap tft kinh nghipm. Sft dyng kinh nghiem mgt each cd hipu qua nhdt la nhiem vy quan trong ciia con ngudi,..."
(4) Biel cdch huy dpng va vgn dung kien thuc vd kinh nghiem vao vi^c phdt trien TD Thau hieu vd nim vimg kien thirc va thudng xuyen thyc hdnh van dyng chung, dd ta nhftng ca sd vgt chat cho sy phdt trien ciia TD, do chinh la "bgt" de ggt nen "hd". Qud trinh tich lu^ kinh nghipm la co hgi de phat trien TD.
Neu da cd mgt qud trinh hgc tap vdi phong cdch thudng xuyen rut kmh nghipm thi qud trinh huy dgng kien thuc cdng mau le va nhihig kiln thuc dugc huy dgng la nhirng kien thftc thyc sy can thiet.
Trong dgy hgc giai bdi tap todn d trudng THCS cac nguyen tac tren can dugc quan tam mgt each tript de, nhu vay se gdp phdn tich eye trong ren luypn va phat trien TD.
MOT SO BIEN P H A P G O P P H A N P H A T TRIEN TU' DUY T O A N HOC CHO HOC SINH
Tu nhung nguyen tdc ciia TD de gdp phin phat trien TD cho ngudi hgc cin thyc hien tren ca sd cua mgt s6 bien phap sau.
Ho Thj Mai Phuong Tap chi KHOA HQC & CONG NGHE 94(06): 43-48.,
* Gido vien luon tim tdi nhirng phuang phdp dgy hoc lot vd luon doi mai PP dgy - hpc GV cd phuong phdp day hpc (PPDH) tot va ludn ddi mdi PPDH se giup HS nam vftng vd hieu thau kien thftc. Can lya chgn mgt he thdng cau hdi cho timg bai hgc, cho tftng khau trong qua trinh dien ra cua gid hgc mgt each kheo leo, ed tinh kich thich TD, phat huy sang tao va gay hung thii hge tgp cho HS. Ben canh vipc trau ddi nhftng tri thftc loan hgc qui dinh iTong chuang trinh, cin quan tam din vipc trau deli cho HS ve phuang phap hgc tgp, phucmg (Aap suy lugn.
* Lira chon he thong bdt tap tot vd throng xuyen cung co kien thuc cho HS Mdt he thdng bai tgp dugc coi la tot neu nd ddm bao viec soi sdng, cung cd, dao sau dugc nhftng kien thftc ma HS da hgc, gay dugc hung thu hgc tap, Idm cho HS ham me hgc tap, nang dan trinh dp hieu biet, kT ndng gidi loan, do dd phat trien dugc TD loan hgc cho HS. Can tranh thu mgi ca hdi de cimg co mgi kien thftc cho HS: cung cd khi day mgt kien thuc mdi cd lien quan, cung cd khi giai mgt bai tap can van dung mdt kien thuc nao dd, ciing cd trudc va sau khi thi het hpc kl hoac het nam hgc.
* Thuang xuyen tap luyen cho hpc sinh suy dodn vd tudng tugng, hudng ddn HS biel phe phdn vd tich luy kinh nghiem.
Can tgo nhieu co hgi, nhieu tinh hudng buoc HS phdi suy doan; Suy dodn ve ket luan ciia mot dinh ly, ve ket qua eua mgt bai todn, ve kha nang giai bai todn,.. Sau mdi bai loan kho hogc mgt bai loan hay, HS biet danh thdi gian de nhin lai each gidi, nhan biet each giai tdt, phe phan nhftng cho rudm rd, tim each cai tiln phuong phap giai, dl xuit nhftng cdch giai hay, dong thdi phan tich, khai thac bai toan tuong tu, bai loan tdng quat ( neu cd).
Dieu ndy giup ren luyen cho HS dgc lap suy nghT, tu dat cac cau hdi vd tu tim each giai dap chung, dong thdi khuyen khich nhimg boat dgng tri dc nhu dgt cau hdi hodi nghi khoa hgc; tgi sao? nhu the nao?..
REN LUYEN VA PHAT TRIEN TD QUA, DAY HQC GlAl B A I TAP T O A N Bai tap todn hgc cd vai trd quan trgng trong, mdn Toan. Bdi tap cd vai tro Id gid mang hogt dgng cua hgc sinh, Bdi tap loan dugc su dyng vdi nhieu dyng y khac nhau, cd nhieu y nghTa
Hinh thanh, cimg co tri thftc, kT ndng, kT xao trong nhftng khau khdc nhau ciia qua Irinh dgy hpc...
- Phat trien ndng lye tri tup; ren luyen nhftng hoal dpng lu duy, hinh thdnh nhftng phdm chat tri tue.
Vdi y nghTa dd bdi tap toan la phuong tipn de danh gia muc dg, ket qua day hpc, khd ndng Idm viec ddc lap va trinh dp phat trien TD ciia HS.
Tuy nhien, khdng phai bai tap ndo cung khai thdc de the hien dugc day du chuc nang cd the cd ciia nd, ma cd the nhdm vdo mgt hay nhieu dyng y tren. O day ta se di sau vao viec day hgc giai bai tap loan vdi dung y khai thac nham ren luypn va phat trien TD cho cac em.
Vi dy: Mo phong viec ren luyen va phat trien d HS tu duy loan hgc thdng qua viec khai thdc nhftng hogt ddng dua tren cac nguyen tdc phdt trien TD,
Bai toan 1. Tinh long
^ 1 1 1 1
S = — + — + — -\-... + — 1.2 2.3 3.4 1945.1946 Nhan xet. Ddy la bai todn ve day so viet theo qui lugt, ddi hdi HS phai cd mgt thao tdc TD tinh te; dd la phai suy nghT, phdn doan, tim tdi sang tgo de tach dugc cac sd hang cua mgt tdng thanh nhftng hipu hogc tdng sao cho long da cho cd the thu gpn thdnh mdt tdng co it sd hgng va cd thi tinh dugc. Nhftng each tach ay se ren luyen cho HS nhdn xef, phan dodn, thu nghipm.
*) Tim each gidi bai loan bang khai thdc chuoi cdu hdi
(1) Tdng ndy cd the tinh dugc bdng vipc van dung kien thue ve phep cdng phan sd khong?
(2) Hay nhan xet mau sd ciia cac sd hang trong tdng cd dac diem gi chung?
Ho Thj Mai Phuang Tgp chi KHOA HQC & C 6 N G N G H $ 94(06): 43-48 (3) Da gdp nhftng phep tinh ndo cho ta kit
qua nhu sau khdng?
I 2.3- ho$c
2 3 1 3.4.
n 1 n{n +
n + l 1)
(4) Vgy de tinh tong tren bdy tlm lien hp gifta cau hdi (2) vd cau hdi (3). Cho bill dp dyng phep bicn doi ndo se cd hipu qud ? Nhu vgy, bdng khai thdc can hdi giiip HS hieu thau, nim viing kiln thuc ve phep cgng cdc phan so, bing kinh nghipm, suy dodn vd tudng tugng HS c6 dugc Idi giai bdi todn.
Nhgn thay
i-_L-l_l
2 ~ 1 . 2 " l 2 ;
_L = 3-2 1 1
2.3 2.3 ~ 2 3 '
J_=i_i.
3.4 3 4''"'' 1 1 1 1945.1946
Vay, 1.2 2.3
1945 1 - + —
3.4 1946
1 1945.1946
__1_J^ l l l_l_ _l 1_
~ 1 2 2 3 3 4 ••• 1945 T946
^1^ 1 _ 1 9 4 5 1 1946 ~ 1946
(5) TIT Idi giai bai toan tren co the khai th^c dirge cac bai toan tuang t\i khong?
*) Khai thac lai giai bai toan theo hucmg phan ti'ch tinh chat d§c thii cua mau so cua cac so hang trong tong. Bang phe phan, tich luy kinh nghifm, ghi nha, HS phan tich, khai thac bai toan theo huong sang tao bai toan moi.
Bai toan (BT) I.I. Tinh tong
o _ 1 I 1 1
Hudng din (HD): BJng sir huy dpng kiSn thirc v^ kinh nghiem tir Idi gidi bai toin 1 HS tien hinh qui I? ve quen bang vi?c nh?n thay:
1.2.3 2U.2 2.3J
Ho4n toJn bang TD tuang tv, HS tinh dugc tong
2{23 49.50J 7350
BTI.2. Tinh long
1 1 1 1
L2.3.4 2.3.4.5 3.4.5.6 47.48.49.50 HD. Tft kinh nghipm TD qua vipc tlm Idi giai hai bdi toan tren HS dl dang nhgn thiy
I \f I \ \ 1.2.3.4 3U.2.3 23AJ
Tim dugc tdng
j ^ r I 1 \ \ 8.49.50-1 3 U - 2 . 3 4 8 . 4 9 . 5 0 ; 3 48.49.50
*) De xuit bai todn tuong tv trong trudng hgp tdng qudt hon.
Phan tich d$c diem cua bdi todn neu tdng cac so hgng cua tdng S len ta cd the tinh dugc tdng S dya vao each khai thac cac cau hdi nhu tren khdng? Ta cd bdi toan tuong tv trong trudng hgp tong qudt, rgng ban nhu sau:
BT 1.3. Tinh
s=
1 11.2 2.3 BT 1.4. Tinh
P= : +— b
1 3.4
b 1 1945.1946
+...H
1 n(n+l) b
1.2.3 2.3.4 3 . 4 . 5 ^ " 48.49.50
a(a+6) (a+bXa+7b) [a+(n-l)6][a+nii]
BTI .5. Tinh
1 1 1 5 = + + + ...+
1.2.3 2.3.4 3.4.5
48.49.50 «(n+lXn+2) 1 1
Hi Thj Mai Phucmg Tgp chi KHOA HQC & CONG NGHg 94(06): 43 - BT 1.6. Tinh
1 1
1.2.3.4 2.3.4.5 3.4.5.6 47.48.49.50 1
{n-\)n{n + \){n + 2)
*) De xuat bdi toan mdi; Tft each giai vd ket qud cud bai toan, ta nhgn thay neu tdng cdc so hgng cua tdng S len thi cdch gidl bdi toan van tuong ty. Van de mdi dgt ra la khi tim dugc tinh qui luat cua mau so trong cdc so hgng cua tdng S thi ta tinh dugc tdng S, tft do de xudt bdi toan mdi nhdm tao ra chum bai tgp van dyng, cung cd kiln thftc vl cac phep todn tren phan so ve day cdc phan so viet theo qui lugt.
Dieu ndy khdng chi ren luypn cho HS kT ndng tim loi giai va tich luy kinh nghiem trong gidi todn, kien thftc thudng xuyen dugc ciing cd vd luyen tap gdp phdn phdt trien TD cho HS.
BT 1.7. Cho bilu thuc 1 1+1
3
1 1
1 1993006 Mau so ciia cac so hang co dang
1 1 1 + — -t
1 1
Voi " ' »-' Chimg minh S > 1001.
HD. Vai kinh nghiem TD qua cac bai toan tren HS se suy nghT de nhan biet bai toan qua nhihig cau hoi dan dat.
(1) M5u s6 cua mdi s6 hang dugc viet theo qui luat nao? Lieu co the qui mau ve truong hgp bai toan I dugc khong?
Ta thay:
u,=l;
U2 = 2 + U i = 2 + 1 = 3 uj = 3 + U2 = 3 + 3 = 2.3 m = 4 + U) = 4 + 2.3 = 2.5 Us = 5 + U4 = 5 + 2.5 = 3.5 U6 = 6 + Us = 6 + 3.5=3.7
(2) Hay tim cac bien doi them chut niia de tim ra qui lu^t cua cac mau
Taco
_1___2_ i _ ^ _ ? _ . 1 2
«j 1.2' «2 2 . 3 ' ' w„ «(tt + l) (3) bang kinh nghiem trong liri giai cac bai toan tren hay qui bai toan ve bai toan quen thupc da biet
— = - = — -
u, 1 1.2' 1
2.3
-"-1
1 2)U 3j «, '\
1 1
1996.1997 U996 1993006 3986012 1996.1997 U996 1991) (4) Hay tinh tdng S va so sanh tdng S vdi 1001.
Cd the thay dgy hgc giai bai tap todn theo hudng nhu tren do la qua trinh de HS ciing cd kiln thuc tgo ra khd nang suy dodn, tudng tugng, qui Ig ve quen... due rut tich luy kinh nghipm gidi todn gop phin ren luyen vd phdt triin TD, HS se hftng thu hgc hon. Tu duy cua hpc sinh khdng ngftng dugc ndng cao neu trong qud trinh dgy hgc, cac ngi dung dugc xdy dyng va viec giai bai tap gido vien biet khai thdc cdu hdi bang nhftng tinh hudng ggi van de.
Vipc ren luyen vd phat trien TD cho HS la mgt khdu quan trgng trong xu the dgy hpc phdt trien hipn nay. Giao vien dgy todn nen tim tdi de dua ra cac tinh hudng ggi vdn de, ggi cho HS su td md tim hieu, hftng thii hpc tap, vipc tao tinh hudng ggi vin de trong day hpc mon Toan ndi chung giai bdi tap todn ndi rieng ddi hdi ngudi gido vien phdi khong ngftng hgc hdi nang cao tay nghe, trinh do chuyen mdn nghiep vu de tiet dgy c6 nhieu tinh hudng gdy dugc cam xuc va ngac nhien cho HS tft dd tgo cam giac hung phan, hftng thu hgc tgp, lam cho tiet bai tap khong cdn khd khan md diy Iy thu, de HS xem viee gidi bai tap toan Id chdn trdi dl kham phd, la phuong tipn hipu qud gdp phdn tich eye trong ren luypn va phat trien TD.
47
Ho Thj Mai Phuang Tgp chf KHOA HOC & C 6 N G N G H $ 94(06): 43 - 48 T A I LIFU THAM KHAO I'*'- ^^'^^ S'^" ^^°^ *°^"' ^^^^ ^^^ ^''' '"^^ ^°^"
•" THCS 2004, Nxb Gido dye.
[1]. NguySn Bd Kim (2004). Phuang phdp dgy [5], Sdch todn ndng cao vd cdc chuySn dl todn d hpc mdn todn - Nxb Dgi hgc Su phgm Hd N^i, trudng THCS 2003, Nxb Gido dye.
[2], Nguyen Thdi I lo6. (2001), Ren luyen lu duy [6], Nguyen Duy Thudn (2007), Phdi iriin lu duy qua vi^c gidi hai tgp todn, Nxb Gido dye, todn hgc trong hgc sinh, Nxb Dgi hpc Su pham [3], Le Thing Nhit, (2001). Rin luyi/n kT ndng [J]. Trin Thic Trlnh (2003), Tu duy vd hogl dpng gidi loan THCS, Nxb Gido dye, todn hpc, Hd N^i.
SUMMARY
DEVELOPMKNT OF MIDDLK SCHOOL STUDENTS' THINKING THROUGH TEACHING MATH EXERCISES
Ho Thi Mai Phuong' College of Education T^ L' Training and developing thinking for students is an imporlanl task in teaching. Mathematics is a scieniific subjecl which Is so abstract and strict logic that students are required to have scientific and innovative methods of thinking. Mathematics has a great potential and also the best environmeni to train and develop the thinking of students. In the process of teaching mathematics, the teacher not only leaches studenls how lo find a solution, but also give exercises that help them to solve the problem of thinking in many different ways to exploit the problem in many directions.
The activities will promote the training and development of students' thinking.
Key words: Training, development, thinking, learners, ihe teacher
Ngaynhan. 16/01/2012, Ngdy phdn bi4n:26/03/2012. Ngdy duy?l ddng: 12/06/2012
Tel- 0915590027; Email [email protected]
