Các quan niệm về chướng ngại trong dạy học toán ở phổ thông

TRONG DAY HOC TOAN 6 PHO THONG

O PGS. TS. LE VA N TI^N" - ThS. TRAN AN H DUNG "

Ht^n noy, khdf nl|m chudng ngpi (CM)

thudng xu£ft hi$n trdn cdc tpp chi khoa hpc

vd ht>ng cdc cdng h'lnh ngnidn cuu todn

hpc. if Vi^t Nam, chung to cOngbdt gQp m^t s^

quan ni|m khdc nhau v l khdi ni^m ndy. Qua

phdn tfch, so sdnh cdc vl dy, bdi vilt gidi thi^u

noi quon ni^m v l CN dd Id chudng ngpi thfch

nghi (CNTN) vd CN iheo quan dilm DidacKc todn.

1 . Chirdng ngpi thich nghi

Khdi nl|m CN gdn liln vdi khdf ni|m thich

nghi trong ldm If hpc phdt sinh cua J.Pioget. Hopt

d^ng thfat nghi thi hl^n qua hoi hopt d^ng ddng

hda vd dliu ffng. Khf chO thi dp khdch thi vdo

c^u h^e nhdn thtk dd cd thi dd Id sy ddng hda.

Hoat ddng dlllu Ong dfin ra ngupc Ipf: chO thi

dilu ehinh Ipl cd'u true nhpn thi>c dd cd cho phij

hpp v6f khdch thi d l nh^n thuc dupc khdch thi.

Ddng hda vd dliu ung Id hai hopt d$ng trdI

nguoc nhau, nhung Ipl £m xen khdng the tdch

rdi. Trong hopt d^ng ddng hda luon cd hopt d^ng

dilu ung vd ngupc k;if.

Du6i ddy, chOng to s3 Kip cdn khdi nf$m

CNTN qua vf dy sou:

Vf dg 1: Cho x vd y Id cdc sd' thvc duong

thay ddi vd ihda man h^ thuc: x' + y^ - 1. Tim

gid h"! nhd nhdt (GTNN) vd gid h-j \dn nhrft (GTIN)

2(x^+6xy)

l + 2xy + 2y^ '

Thvc tiln dpy hpc cho thdy, nlu hpc sinh (HS)

cua bllu thuc P =

bfin ddi P v l dpng P

3 + 2xVI-x'-2x'

vd liln hdnh khdo sdl hdm sd Hx) xdc djnh bdl

bllu thuc d v l phdi (phuong phdp HS dd quen

lhu$c), HS s§ g$p khd khdn khi Hnh dpo hdm vd

lim nghidm cua phuong hlnh P(x) - 0. Nl u HS

khdo sdt hdm sd 'm-^i^l"', »dl ' = " ihl bdl

todn sd don gidn hon.

Nguyin nhdn djn din thdl bpi ciia HS xudt

phdt h> khd khdn tfnh dpo hdm ciJa m$t hdm si

phi>c Ipp vd khd khdn khi biin 66l bllu thi}c hai

Diln v l bllu thuc m^t blln cda dn php I, md

vl|c Knh dpo hdm vd Hm nghifm Pit) - 0 si di

ddng hon.

Cdc khd khdn ndy dupc gpf Id CN. CN Ihl hl«n

qua nhOng khd khdn khi HS v ^ dvng kiln ihiic ^

hpc vdo cdc Hnh hudng mdi. Trong vfc^ /,cdlhl

hllu CN Id khd khdn md HS g<ip phdi khi ihvc

h l ^ cdc hopt d^ng ding hda vd dilu ung dH «M

m^t khdch ihl mdi Id bi£i ihuc hai bl ^ sllhoyvl

m$t biin X (vl^ Hm GTIN vd GTNN cuo m^l bilu

thuc dd quen ihu ^ vdl HS lip 12|. Cv ihl, hopi

d ^ g ding hda vd dilu Ong diin ra khi HS blln

ddi P v l dpng mfl blln x (ho<ic biin I), sou d6

khdo sdt hdm sd f|x|, ho$c 1^1).

Tdm Igi, bdn chd't cua CN theo quan dlim

ndy chfnh la nhOng khd khdn Irong vlic thfch

nghi vdl mil mdi Irudng md d dd, khdch thi

Kndng cdn Id d6l luqrtg quen lhuic;CH ndy dupc

gpi Id CNTN. M$t hong nhOng gidi phdp hOu

hi|u khdc phvc CNTN Id bd sung kiln riiih: cho

HS. Chdng hgn, rin luy ^ cho HS cdch v^n dvng .

kiln ihOc vdo cdc Hnh nudng mdi, cdch nhin m ^

ddi lupng, mfl vd'n d l dudn nhilu gdc d$ khdc

nhou,...

2. C N iFong DldocHc todn

Chiing Idi lilp c^n khdi nifm CN Irong

DldocHc lodn iheo hudng phdl cdo Phdp, bdl ddu

h> vi ^ phdn Hch hai vf dv sou ddy;

Vf dv 2: Trln m<^t phdng h;a d$ 0 » cho

dudng cong (C), A vd B Id hai dilm thudc dudng

cong nhu hlnh v8 [hinh /).

bllt blln doi P v l dpng «i . , i , didu a v l *TnlMiCMlS«i(>lwi1niim(TP.HCMWili

y' y ••TrMltTlirrclnoiilllM|IMVM,Mi|llai

W lap clii Slao due so 285 w i • utmaj