Vận dụng nguyên tắc "Đảo ngược" của Altshuller trong dạy học giải toán ở trường phổ thông

VAN DUNG NGUYEN TAG lA O NGirUC" CUA ALTSHULLER

TRONG DAY HOC GIAI TOAN Oi TRU'dNG PHO THONG

Q ThS. THAI THI H6N G LAM"

Trong dpy hpc Todn, glal todn Id mdt hop!

ddng chu ylu vd quon hpng cdo hq>c sinh

(HS). Vd'n dl ddt ro Id vdi m^l bdl todn,

ldm thi ndo d l Hm dupe phucmg phdp gidi, ddc

bl|t Id phucmg phdp hoy, ddc ddo. Nguydn tdc

«E)do ngupc" Td m^t hong nhiJng thu thudt cd thi

glup hpc sinh (HS) khdc phyc tfnh >' ldm If, llnh

hopt vd sdng tpo hon hong cdch h/ duy d l Hm Idl

gidi bdt Iodn. Bdi vilt dl cdp vi^c v^n dyng

nguyfin tdc «E)do ngupc* (nguyfin tdc thu mudi

ba hong 40 nguyfin tdc sdng tpo eua Allshuller)

vdo vl ^ tim cdch gidl cdc bdl tdp todn trong

day hpc Todn (chu de kiln thuc vl phucmg hinh

(fTl, bdt PT, bd't dfing thuc hong Dpi si 10).

1. Nguyfin tdc «Ddo ngupc'

Khi vdn dpng nguyfin tdc «Ddo ngupc' h'ong

qud hinh gidl todn, thoy vi thpc hl^n yfiu cdu cuo

bdl todn, chung to ddo ngupc vdn d l vd thi/c

hl|n ede yfiu edu ngirpc Ipl.

Hl|n thpc khdeh quon boo gdm m$t s^ m^t

dd'l ldp (khdc nhou, ngupc nhou, lopl hv vd bu

hv nhau,. ..).Vi^ xem xit nhilu mdt cua mdl v^n

d l nhdm tdng h'nh boo qudt, loan dl|n, ddy du,

cd thi glup HS linh hopt hong suy nghTvd hong

cdch gidl quylt vdn dl. Sp ddo ngupc v^n d l sS

phd vd 1^1 tu duy thdng thudng vd phdt h-lln dupe

h/ duy sdng hpo cho ngudi hpc.

2. Mdt si cdch thuc vQn dpng nguyfin ttfc

«Ddo ngupc' hong gidl Iodn

7; Niu gidl bdl todn cho trud>c (bdl Iodn

thudn) gip khd khdn vdl nhldu tnidng hqp,

ta nghT din vl$c xdt bdl todn gidn ttip (bdl

todn ngugc) cd thi It trudng hqip, it rdc ril

han. Trong hopt d$ng gidl todn, niu bdl Iodn

da eho khd phuc h?p, ngudi gidl h>dn cdn llnh

hopt chuyin nudng suy nghi, cd ihl nghT din vt|c

xit bdl todn ngupc. Chdng ta cung nfin xem xit

khd ndng gtdt bdl Iodn ngupc hong nhihig dllu

kl|n, tinh huffng cp thi, chong hpn nnu vdl nhOng

bdl todn llln quon din ttm dllu ki|n cuo tham so

d l b^ PT hodc h| ?\ cd nght|m, vd nghlfim.

Vi dv: Tim dllu kl$n cua thom s^ m d l bat PT

sou ed nghl|m

mx^ + (m+l)x-7a0(l |

Nlu gtdt bdl todn ndy hpc tllp tht HS phdl

xfit khd nhllu hvdng hpp phdc tpp. GV cd thi

hudng dSn HS ehtiywi hudng song gidl bdl todn:

«Tim m di bit PT: mx'+ (2m + l)x -7i0(2)

vd nghldm". LOc ndy, GV cd thi hudng dfin HS

phdt bllu bdl todn n>di theo hinh thdc khde: m^l

bd't ddng thuc F(x) ^ 0 vd nghi|m cd nghTo Id

khdng tin hsl x d l f(x) £ 0, dllu ndy hiong duong

vdt f(x) < 0 vdt V;c € J? - Ddy Id bdl todn 00 bdn

de^ivdlHSk^lO.

2) Thay Hi vol Ird cOa cdc yiu li trong

bdl Iodn

VI dv: Gtdt FT: x* - 2mx= + x + m' - m = 0

(m Id thom s^. Vdt P\ ndy, nlu HS gidl theo

cdch thdng thudng (Knh x theo m) tht sfi gdp khd

khdn vt day Id FT bdc 4 dn X khdng od dpng ddc

bl|t, cung khdng nhdm dupe nghl|m. GJuon sdt

PT, ta d l ddng nhdn hiy bdc cda x khd tdn md

bdc cOo m ehl Id 2, nhu v^y, ta si xfit PT dd cho

nhu Id PT bdc 2 d£fl vdi dn m. Khi dd, ta tfnh dupe

m =» x^ + X, hodc m • ;^ - X + 1, dfly Id nhOng PT

bde hat dn x ehdo thom sd m, HS dS bilt cdch

gidl. Tuy nhlfin, GV cdn quon ldm din vi$e rfin

luy|n Knh llnh hopt, Ifnh sdng h ^ cho HS.

3) Si} dgng phuong phdp suy ngupv ft> kit

qud. Mdt bdl todn iht/dng gdm hal phdn: Phdn

gid Ihlit vd phdn kit ludn. Di gidi mdl bdl todn,

hvdc hit, ta edn phdn tfch gid ihllt, sou dd huy

ddng kt ^ thde dd bllt (dfnh nghTo, ^nh If, quy

tdc...), h>ng budc suy ludn, tfnh h>dn din kht tim

dupe kit qud. NghTo Id dl h> «cdl da bilt' dl

cu6\ cOng thu dupe «cdl cdn Hm ho ^ cdn chung

minh'. Od Id phfip tdng hpp (phfip suy xudt). Tuy

nhlfin, hong nopt d^ng gidl h>dn, nlu HS thilu

sv djnh hudng ddng ddn, sou mdt ii phfip bl ^

dll, iadl todn h4 nfin phOc h?p hon, ddi kht Ipl hd

'TnMiflfib^c Villi

Tap chi Slao due so 29 0 (h a • T/aom