c. Nang lire la khd nang bien Tri thdnh Hdnh tire la biet dimg vdn tri thirc
2.7.7. Tam quan trgng cda day hgc gidi tod na trudng pho thong
Mot trong nhiJng muc tieu cdt loi cua qud trinh day hpc d nhd trudng phd
thdng hien nay Id bdi dudng phdt trien nang lire tu duy lQ{Interlligence
Quotient) vd nang lire cam nhan EQ{Emotion Quotient) cho hpc sinh thdng
qua day cdc mdn hoe.
Todn hpc duac coi la mdn hpc ed vai trd hang ddu trong bdi dudng phdt trien tri tue eho hpc sinh. Trong day hpc todn d bac hpc phd thdng, gidi todn la mdt npi dung quan trpng gan chat vdi cdc kien thiic, ky nang todn hpc trong chuomg trinh d timg Idp, timg cap. Thuc te day hpc toan ta thdy, bai tap toan dupe sii dung vdi nhieu y nghla khac nhau. Mot bai tap cd the dung tao tien de xudt phat, gpi dong ca nghien ciiu hoac tham gia vao lam viec vdi npi dung mdi, tham gia vao ciing cd luyen tap hoac kiem tra ddnh gia ke't qud hpc tap cua hpc sinh.
Vdi sir phan tieh tren, rd rdng mdi bai tap dat d thdi diem khde nhau cua qua trinh day hpc toan deu chiia dung mot each tudng minh hay an tang cac chiic nang, gid tri khac nhau. Chiing ta cd the ndi rdng: "to chiic hieu qua viec day hpc gidi toan cd vai trd quyet dinh nang cao hieu qud chdt luang day hpc toan" bdi cdc y nghla sau day:
- Hoat ddng gidi todn giiip hpc sinh cung cd, van dung cdc kien thiie todn hpc vd ren luyen ky nang. Day la ca hpi tdt nhat de tu duy ciia cdc em dupe phdt trien va bpc 16 kha nang sang tao nhd qua trmh dem nhiing tri thiic Todn hpc da duac trang bi vao gidi cdc bai todn cung nhu gidi quyet cac van de trong cupc sdng thuc tien lien quan tdi todn hpc, Hoat ddng tri tue nay da gdp phan
ren luyen cac em y chi vugt khd, diic tinh can than, ehu ddo, lam viec ed kl hoaeh, thdi quen xet doan ed can cii, ludn biet tu kilm tra kit qua cdng viec cua minh v.v...
- Viec giai toan cdn gdp phan quan trpng trong gido due tinh cdm eua hpc
f
sinh ddi vdi mdn hoc, bdi thdng qua gidi todn cdc em mdi nhan ra ve dep cua todn hpc ciing nhimg iing dung cua nd trong ddi sdng thue tien vd khoa hpc.
- Thdng qua boat ddng gidi todn eiia hpc sinh, gido vien de ddng phdt hien
f f \ ,
nhiing uu diem hoac thieu sdt ciia cdc em ve kien thiic, ky nang, tu duy todn hoc; tir dd cd bien phdt giiip cdc em phdt huy hoac khac phuc nhirng thieu sdt eiia minh.
Tuy nhien, de phdt huy vai trd eiia day hpc gidi todn, dieu dd cdn phdi tinh den phuang phap, tinh den nghe thuat giang day eiia ngudi thdy. Ngudi thdy phdi bie't khai thae triet de cdc phuang dien cd the cd cua bai todn, giiip cac em hiing thii, say me vdi hoat ddng tim tdi, khdm phd trong gidi todn, tir dd tao
nen loi suy nghi kieu cdu tnic da tuyen trong tu duy hien dai eua hpc sinh. Mudn vay, tnrdc he't ngudi Thay phdi cd nhirng hieu bie't diing ddn ve ca sd ly luan cua viec day hpc gidi toan. Co sd dau tien cdng trinh mudn de cap den la
cdc quan niem ve gidi todn vd day hpc gidi todn.
2.7.2. Quan niem ve gidi todn vd dgy hgc gidi todn
6 trudng pho thdng, day hpc gidi toan la npi dung quan trpng trong day hpc toan. Hoat dong gidi toan la boat dong khong he xa la ddi vdi chiing ta, nhung khdng phdi mdi ai da timg gidi todn hoac tham chi dang day todn deu cd cung mot cdu trd Idi eho cdc cau hdi sau day: Bai Todn la gi ? The nao la giai todn? The nao la day hpc giai toan ?, Diem khac nhau ca ban ciia hai qud trinh giai todn va day hpc giai toan la gi?
Trong cac giao trinh cu ve phuang phdp day hpc todn, cac tdc gid hau nhu khong dua ra dinh nghla ve nhimg khai niem nay, Tuy nhien, qua dieu tra,
khao sdt, so sanh tai lieu, dam thoai true tie'p vdi gido vien gidng day todn, sinh vien su pham toan va bpc sinh pho thdng, chiing tdi thdy cd mot sd quan niem khac nhau sau day:
Quan niem ve bdi todn
a) Quan niem ve bdi todn ciia mot sdnhd khoa hgc
L Astobar: chia bai todn thanh bdi toan chiing minh vd bai todn tim tdi, - Bai todn chiing minh menh de A tir gid thiet B la su ddi hdi mot day huu ban cdc menh de A,, A2, A3...A„ thoa man dieu kien:
i. Menh de eudi ciing A^ cua day chinh la menh de A.
ii. Mdi menh de Aj cua day hoac la tien de, hoac Id dinh ly hoac Id dupe nit ra tir nhiJng menh de diing trude nd nhd mot quy tdc suy luan 16 gic, - Bdi Todn tim tdi la ddi hdi tim mien diing eua hdm menh de
2. Nha todn hpc Gpolya cho rdng: Bdi toan dat ra sir cdn thie't phai tim kie'm mot each cd y thiic phuang tien thich hap de dat duac muc dich trong thdy ro rang nhung khong dat ngay dupe,
3. G.S. Fanghanel khdng dinh: Bdi todn la sir ddi hdi hanh dong trong dd quy dinh: ddi tuang ciia hanh dong, muc dich ciia hanh dong, cac dieu kien cua hdnh dong.
4. G.S. Rubinstem lai quan niem: " Ve bdn chat, mot bai toan la sir phdt
trien bang Idi ciia mot van de".
5. T.S. Trdn Van Vu6ng va Vu Dire Mai (Trudng DHSP Ha Npi II) quan niem mot each cu the ban:
Bai todn la sir ddi hdi dat duac mdt muc dich nao dd. Muc dich neu trong
bai toan cd the la tap hap bat ky (cua cdc sd, cdc hinh, cdc bieu thdc.) su
diing ddn hoac sai lam eiia mot hoac nhieu ket luan. Bai todn dupe phdt bieu
chuyen mdn dd. Vdi each hieu nay, bai todn se ddng nghla vdi de todn, bai tap, cSu hdi, vdn de, nhiem vu...
6. T.S. Ha SI Ho lai cho rdng, ed sir khac biet giira bai tap va bai toan, giiia bai tap va vdn de. Cd bai tap khdng la vdn de ma chi yeu cdu hanh dong. Bai tap la bai toan da xir ly v^ mat su pham.
b. Mdt sdquan niem khde:
Theo nghla rong, bdi todn la bdt cii vdn de nao cua khoa hpc hay cupc
sdng cd vdn de dang dat ra cdn dupe giai quyet. Vdi quan niem nay, vdn de trat tu an toan giao thdng d cac thdnh phd ldn cung dupe coi la bai todn.
Theo nghla hep ban, bdi todn la van de nao dd ciia khoa hpc hay cupc sdng
cd vdn de dang dat ra cdn duac gidi quyet bdng kien thiic vd phuang phdp cua Toan hpc.
Vi du: Cae bai toan sd hpc, hinh hpc, dai sd vd cd nhirng bai tap trong sach gido khoa vat ly, hod hpc deu dupe coi la bai toan.
(^ phuang dien cue hep, cdn cd quan niem cho rdng: Bdi todn la bai tap
trong sach gido khoa toan.
Tir nhirng quan niem tren, chiing ta cd the rut ra bdn chdt chung cua mot
bdi todn khi dua tren ca sa cua tu duy cdu true dd Id: mdi bai todn deu phdi
cd ba thanh td ca ban:
- Dii kien ciia bdi toan( cdi da cho)
- An sd ( cdi phdi tim)
- Dieu kien cua bai toan {mdi quan he giita cdc difkien vdi dn sd)
Quan niem vegidi todn vd dgy hgc gidi todn
Cung nhu khai niem ve bai todn, qua dieu tra khdo sat chiing tdi thay: cd nhieu y kien khac nhau xung quanh khai niem gidi toan va day hpc giai toan,
hgc gidi todn la day cho hpc sinh tim ra dap sd cua bdi toan. Vdi quan niem
nay qua trinh day hpc giai todn da chii trpng den ddp sd cu the eiia bai todn.
Song quan di^m khac lai cho thdy: Gidi todn la trinh bay dupe Idi giai cua
bai toan da cho; cdn day bpc gidi toan la giiip bpc sinh biet trinh bay Idi bai
toan dd. Vdi quan diiva nay, ngudi thdy da rdt chii trpng den viec day hpc sinh
"mdu loi gidi' cua cac dang todn.
Nghien cuu hai quan niem tren, ehiing ta thdy cdc quan niem dd deu cd mdt sd han che' nhdt dinh vi chua ehi ra dupe mat tich cue, chu d6ng sang tao
cua hpc sinh thong qua boat dong gidi toan. Tir ca sd dd, chung toi cd the de
xudt mot quan niem rieng ve gidi todn vd dgy hgc gidi todn:
Giai toan la mot hogt dgng tri tue tich cue cua chu //z/nhdm tim ra each
gidi quye't nhirng yeu cdu ddi hdi ciia bai toan va trinh bay dupe Idi gidi bai todn mot each phii hap vdi cdp hpc. Cdn day hoc giai toan la boat ddng tri tue cua ngudi thdy nhdm dieu khien trd tu gidi dupe bai todn mot each sang tao.
Day hpc gidi toan theo quan diem tren khong chi cdn den nhirng kien thiic ngudi hpc da dupe trang bi ma ddi hdi mot n6 lire tich cue, tu luc trong tu duy cung vdi kha nang sang tao vd kinh nghiem da dupe tich luy eiia cdc em tir viec gidi cac bai toan trude dd. Cdn phdi luu y rdng, de ren luyen nang lire vd tao hiing thii trong giai toan, bpc sinh nen tu minh tim ra Idi gidi bai toan hoac nhd Thdy gpi y de tu gidi quyet; dimg bao gid voi vang xem tnrdc Idi gidi bdi
todn. Cdn ngudi thdy, mudn co dupe sir chii dong, virng tin trong day hpc gidi
todn, ngudi Thdy phdi tham gia vao qua trinh gidi todn vd hieu dupe sau sde Idi gidi bdi toan.
Qua phan tich tren, chiing ta cang thay ro; viec hieu diing khai niem giai
toan vd day hpc gidi toan cd y nghla quan trpng de gdp phdn nang cao hieu qua eua gid day dong thdi giiip chiing ta nhan ra diem khac nhau eiia hai qua
Giai toan Day hpc gidi todn • Ngudi giai tu tim ra hudng
gidi quye't cho bai toan.
• Hoat d6ng gidi todn diln ra dpc lap
• Ngudi day dieu khien ngudi hpc tu tim ra hudng gidi quye't cua bdi todn,
• Hoat dong trong day bpc gidi todn mang hudng tap the.
2.7.5. Cdc budc trong dgy hgc gidi todn
Vdo nam 1950, GPdlia dua ra tien trinh bdn budc gidi toan song song vdi
nhimg thdnh tim ciia cdc nhd tam ly hpc da de cap den trong boat ddng nhan
f y t
thuc tim kiem ehan ly. Dieu dd dupe the hien qua bdng so sdnh sau day: Nhd tam ly hpc
1.Chuan bi( preparation)
2.Ap li(ineubation)
3.Bimg sang(inspiration)
4,Kiem ehiing(verification)
r
G.Pdli dua ra bdn budc trong gidi todn
1. Tim hieu dau bdi toan{understand
theproblem)
1
2. Ke hoaeh gidi( devise a plan)
3.Thue hien ke hoach gidi(carry out the plan)
4,Kiem tra(verification)
2.2. Tac dong tuong hd giiia hoat ddng giai toan voi ren luyen, boi du-ong,
phat trien nang luc tu duy cua hpc sinh
2.2.1.Ndng luc tu duy cdn thiet trong timg buac cua hogt dgng gidi todn
Budc 1: Tim hieu ddu bai todn
Tim hieu ddu bai todn la viec lam tnrdc tien trong qua trinh day hpc giai toan. Mudn hpc sinh tu minh gidi quyet dupe nhirng yeu cau ddi hdi ciia bai toan ngudi giao vien cdn phdi lam cho hpc sinh ndm dupe y nghla npi dung cua bdi todn, xdc dinh dupe yeu td ca bdn ciia bdi todn ddng thdi biet the hien bai toan dudi mot hinh thiic ngdn gpn de hieu. Cd nhieu each de tim hieu ddu bdi toan va chiing ta cung thdy rdng: mdi bai toan cu the dat d mdi cap hpc
khac nhau se co nhiing each tim hieu d^u bai khac nhau. Thong thucmg de tim hi^u dSu bai toan, ngudi ThSy c^n phai biet hudng hoc sinh tdi cac cau hoi: