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SDNG MY TNH TRONG GING DYV NH GI CHT LNG HC TP
Phm Huy inVin Ton hc (Vin Khoa hc v Cng nghVit Nam)
Nguyn Quang MinhVin Ton hc (Vin Khoa hc v Cng nghVit Nam)
Nguyn Vn SinhTrng Cao ng Sphm Hng Yn
1 Phn mm v my tnh l cng chtrc lc
1.1 Phn mm v my tnh khng lm gim vai tr ngi thy, m chhtr cho thyPhn mm l cng chtrthy trnh by cc minh ha vi cht lng cao, gim bt c
thi gian lm nhng cng vic th cng, vn vt, d nhm ln (v hnh, tnh ton trung
gian,...) c iu kin i su vo bn cht ton hcca bi ging. Di y l mt sminh
ha cho iu ny. Hai chc chn lm v dl: Dy sv gii hn ca dy s, Hm s
v gii hn ca hm s. R rng chng c ci my no c ththay thy ni cho hc sinh hiu
vbn cht hai khi nim ny. Ngc li, nu khng c my, thy cng kh m minh ha
cho hc sinh hiu c khi nim ny n ni n chn.1.1.1 Dy sv gii hn dy s
1.1.1.1 Minh ha dy v gii hn ca dy
Minh ha dy sbng lnh vdy im pointplot. Th dta minh ha 20 phn tu ca
dy s bng lnh:
> with(plots):
pointplot([seq([n,sin(n)/(n+1)],n=1..20)],symbol=cross);
1.1.1.2 Minh ha dy hi t(v0)
=un
( )sin n
+n 1
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Mun xem xt tnh hi tca dy ta vnhiu im hn, th dta v100 im ca dys bng lnh:
>pointplot([seq([n,sin(n)/(n+1)],n=1..100)],symbol=cross);
Xem thm mt khc ui
>pointplot([seq([n,sin(n)/(n+1)],n=1..200)],symbol=cross,color=red);
C thxem tip nhiu khc ui khc na, v ta lun thy rng khc ui cng vsau thcng gn trc honh, cho nn dy hi t. Thc tl nhvy
> limit(sin(n)/(n+1),n=infinity);
1.1.1.3 Dy khng hi t(v0)
Xem xt dy s
>pointplot([seq([n,sin(n)+cos(n)],n=1..100)],symbol=cross);
>pointplot([seq([n,sin(n)+cos(n)],n=1..150)],symbol=cross);
0
=an
+( )sin n ( )cos n
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>pointplot([seq([n,sin(n)+cos(n)],n=1..200)],symbol=cross);
Mi khc ui u lun cha nhng phn t"v tchc", cho nn dy khng hi t. C th
chng minh iu ny mt cch cht chbng nh ngha.
1.1.1.4 Nhng dy sphc tp
C nhng dy khng dg bit c n c hi thay khng. V d
Hy thxem my biu din cc phn tca n ra sao:
>pointplot([seq([n,(abs(sin(n)+1/n))^(n/ln(n+1))],n=1..500)],symbol=cross);
>pointplot([seq([n,(abs(sin(n)+1/n))^(n/ln(n+1))],n=1..1000)],symbol=cross);
=un
+( )sin n1
n
n
( )ln +n 1
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>pointplot([seq([n,(abs(sin(n)+1/n))^(n/ln(n+1))],
n=500..800)],symbol=cross);
>pointplot([seq([n,(abs(sin(n)+1/n))^(n/ln(n+1))],
n=800..1000)],symbol=cross);
Qua y ta c thhnh dung c l dy khng hi t.
Mt v dkhc, n gin hn nhng cng khng tm thng
>pointplot([seq([n,(abs(sin(n)+1/n))^sqrt(n)],n=1..1000)],symbol=cross);
=vn
+( )sin n1
n
n
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>pointplot([seq([n,(abs(sin(n)+1/n))^sqrt(n)],n=1000..2000)],symbol=cross);
>pointplot([seq([n,(abs(sin(n)+1/n))^sqrt(n)],
n=2000..3000)],symbol=cross);
1.1.2 Hm sv gii hn hm s
Cch dy c: Ly vic vthl ci ch t ti (rt nng n, qu ti, v phi thc tin v
lp hm c thkho st v vthl rt t i).
Cch dy mi: Ly thlm khi im (nhnhng, dhiu v khthi trong giai on hin
nay, v thca mi hm u vc bng my).
1.1.2.1 Tnh gi trv vth
Hy thvmt thm cc loi mo mc, kthut kho st u thy ngn,
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nh:
Vi my tnh, ddng tnh gi trca hm sti (bao nhiu im ty thch), th d:
Ngoi ra, ddng thy rng khi th . Ty ddng suy ra thnhsau
thca hm s cng ddng vc bng cch trn
1.1.2.2 ng dng ca th
+ Cho thy c tng minh cc thuc tnh ca hm s.
+ Phng php gii phng trnh vn nng (mnh hn clnh Solve ca Maple).
1.1.2.3 Gii hn hm s
Mt trong nhng vn nan gii ca ngi gio vin ph thng l phi lm cho hc sinh
"cm nhn" c bn cht ca gii hn (m khng cn phi i vo phn tch chi li theo nh
sin(cos )( )
cos(sin )
xf x
x=
k f
0 0.841471 0.84507
2 0.85450
3 0.86536
4 0.86954
5 0.85451
6 0.80340
7 0.69763
8 0.52360
9 0.28294
10k= 0f =
( ) ctg(cos(tg(sin )))g x x=
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ngha). Vi Maple, ta c thcho hc sinh "nhn thy" bn cht vn . Vi lnh sau, hc sinhsnhn thy (trong Maple) qu trnh tin ti gii hn ca hm khi tin v
0:
>picts:=[seq(plot([x*sin(1/x)*piecewise(x
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R rng, nu chvi mt hnh vminh hony, hc sinh kh m hnh dung c rng khi
ly phn hoch mn th tng din tch mhnh chnht ln nhn li c thtrng vi
din tch ca hnh thang cong (xc nh bi hm s). Mun thy c iu ny ta cn a ra
mt dy hnh vminh hothhin rng qu trnh xp xhnh thang cong (bng tp cc hnh
chnht "mnh mai") t chnh xc cng cao khi phn hoch cng mn. My tnh l cng
cl tng cho ta thc hin iu ny. Bng cch ly brng phn hoch bc sau bng nabc trc, chcn qua 3 bc ta c c kt quhon ho:
>middlebox(sin(x^2+x-1)-cos(x^2-x+1)+3,x=-3..3,30);
middlebox(sin(x^2+x-1)-cos(x^2-x+1)+3,x=-3..3,60);
middlebox(sin(x^2+x-1)-cos(x^2-x+1)+3,x=-3..3,120);
Mun cho thuyt phc hn, ta cn phi a ra hng lot v dkhc. Nu khng c my tr
gip th ta kh m thc hin iu ny, nhng vi my th thc l n gin.
1.2.1.2 Qu trnh tin ti gii hn ca tng Riemann
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Mt vn kh khn l lm sao hc sinh cm nhn c rng tng Riemann c th"tin
dn" ti din tch hnh thang cong (khi phn hoch mn dn)
> hamso:= t*sin(t^2-t+1)/(t^2+1)-cos(t^2+t-1):picts := [seq(middlebox(hamso,t=-3..3,30+3*i), i=1..50)]:display(picts, insequence=true);
1.2.2 Tch phn xc nh tnh kh hay d?
Trc y, v khng c my, thy v tr khng th tnh c tch phn xc nh theo nh
ngha (qua tng Riemann), cho nn cha ra nh ngha ri quay sang tm nguyn hm.
By gitnh th i khc, vi my tnh th vic tnh tch phn xc nh cng bnh thng
nhvic "khai cn mt s"> Int(sin(x)/x,x=1..2);
> evalf(");
Nhvy, nu c my tnh th vic tnh tch phn (xc nh) l v cng n gin, kci vicc hm m ta khng thno tm c nguyn hm (nhtrn chng hn).
1.2.3 Nhng cu hi t ra
1.2.3.1 Vic no kh hn: tm nguyn hm hay tnh tch phn xc nh?
My tnh tm nguyn hmcng gii nhta:
> Int(x*sin(x),x);
> value(");
d
1
2
( )sin x
xx
.6593299064
dx ( )sin x x
( )sin x x ( )cos x
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V cta ln my cng phi chu "b tay" khi gp phi nhng bi "khng c trong sch gio
khoa", nhdi y?
> int(sin(x)/(x+sqrt(x)),x);
> value(");
Nhvy, vi hm ny khng thtm c nguyn hm(di dng mt biu thc hin). Tuy
nhin ta vn ddng tnh ctch phn xc nhca n trn mi on
> Int(sin(x)/(x+sqrt(x)),x=0..1);
> evalf(");
Tm li, vic tm nguyn hmkh hn hn vic tnh tch phn xc nh.
1.2.3.2 Tnh tch phn xc nh bng nguyn hm?Hay tm nguyn hm thng qua tch phn xc nh ?
Ta bit rng nguyn hmca hm s l tn ti, nhng khng thbiu din
c qua cc hm sta bit:
> int(sin(x)/(x+sqrt(x)),x);
Tuy nhin, nh l cbn ca php tnh tch phn cho ta thy rng n biu din c di
dng tch phn xc nhvi cn l bin s. Tht vy, n l mt hm F(x) xc nh nhsau:
> F(x):=int(sin(t)/(t+sqrt(t)),t=0..x);
Chng trnh tnh ton cho ta bit mi thng tin vhm ny, y v phong ph nhbt
kmt hm quen thuc no khc. Th dta c thbo my cho xem gi trca hm ti bt k
im no, hoc hn th, ta c thbo my vcho ta thca hm trn mt on bt k
>with(plots):plot(F(x),x=0..10);
d
( )sin x
+x x x
d
( )sin x
+x xx
d
0
1
( )sin x
+x xx
.3615792078
=( )fx( )sin x
+x x
:=( )F x d
0
x
( )sin t
+t tt
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1.2.3.3 C nn u tqu nhiu thi gian cho vic tm nguyn hm ?
Nhvy ta c chng kin mt skin c tnh bn cht l: Trong trng hp tng qut
th tch phn xc nh chnh l cng c tnh nguyn hm, ch khng phi l ngc li
(nh lu nay nhiu ngi nhm tng v dn mi sc lc cho vic tnh nguyn hm thng
qua cc loi mo mc, tiu xo,...). Cho nn ci ng hc l khi nim tch phn xc nh (theo
ng bn cht ca n), v bit sdng my tnh n, chkhng phi l hc my ci "mo"tnh nguyn hm.
R rng hc khi nim tch phn xc nh v bit dng my tnh l n gin v hu ch
hn rt nhiu so vi vic "nhi nht" cc loi tiu xo tnh nguyn hm.
1.3 Phn mm htrnh hng dy v hc kin thc cbno Bi tp ton kh khng cn l con ngo p v vic hc ton khng cn l gnh
nng cho hc sinh bnh thng.
o Vic hc ton i vo bn cht: hc vn ha ton, m khng phi hc mo mc v tiuxo lm bi tp ton.
o Ci ti cho hc sinh c gim nh, nhtng c ti cho thy!!!
2 Xy dng gii php nh gi cht lng dy v hc2.1 ngha v Mc chVic i ph vi thi chin nay tiu tn khng bit bao nhiu sc lc, tin ti ca ton x
hi v trn thc tang tr thnh mt ci gnh ngy cng nng. Thc trng ny khin
khng t ngi cho rng n lc phi xa s nhng kthi. Xt cho ng, thi l mt binphp nh gi cht lng gio dc o to, hay ni nm na th l mt thc o trnh
hc sinh. R rng, y l mt vic khng ththiu v mi cquan sdng lao ng u cn
bit trnh ca ngi mnh tuyn dng. Mt vai tr hin nhin na ca cc k thi l thc
y ngi hc tch cc hn trong hc tp. Thc thin nay nc ta cho thy nu khng c
vic kim tra, thi cth phn ln hc sinh i hc nhi m cua bng githng y. y l
cha ni n lp ngi i hc khng phi v ly kin thc m chct kim c mnh bng,
chng ch,... leo thang danh vng. (ng tic l nhng ngi ny ang y ry trong x
h
i ta, v c lchnh h
ang lm ch
t cc h
c
ng, t
o ra s
c p v
nhu c
u gi
to cho
ngnh gio dc). Thit ngh, nu loi bc nhu cu hc rm th ngnh gio dc nc ta s
vt vhn rt nhiu. Ai c thgnh vc trch nhim ny, nu khng phi l nhng kthi?
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Xem ra, cc kthi tn khng c ti tnh g. Chnh nhng ngi khng bit tchc hp l
bin chng thnh ra gnh nng cho ton x hi, thm ch lm cho chng trnn phn
tc dng v ang bkhng t ngi ln n.
C l, vai tr ca cc k thi (nghim tc) l khng thphnh c. Nu nhu
ngi ta c thbc cc kthi tt nghip, tuyn sinh,... th chnh l v ngi ta c cc chkim tra cht lng (mt hnh thc khc ca thi) nghim minh trong sut qu trnh
hc tp ca hc sinh. iu ny cng dhiu nhvic kim tra sc khe u n hng thng
th cho php bqua vic tng kim tra sc khe cui nm. R rng, trong bi cnh nc ta
hin nay, vic duy tr kim tra cht lng thng xuyn (mt cch nghim minh) l kh khn
hn rt nhiu so vi vic chdn cho mt vi kthi. Ai cng bit nn xin im ang honh
hnh mi ni, mi cp hc,... khin cho khng t sng kin ca ngnh gio dc trthnh
v dng. Thhi, trong bi cnh ny m bcvic thi th cht lng gio dc si ti u?
Vic bqua cc kthi chc ththc hin c nu ta c c cchkim tra, nh gi chtlng dy v hc mt cch nghim minh v thng xuyn. Ni dung bi vit ny nhm
cp n vic thit lp mt gii php cho vn nan gii . Khi nim thi y sc
hiu theo ngha rng, tc l mt dp kim tra cht lng ni chung.
2.2 Ni dung nh gi nh hng quyt nh ti ni dung v phng php dyKt qu thi l biu hin u tin ca kt quhc hnh, cho nn ngi ta thng tm nim
"hc m thi" v hqutheo sau l "ci khng thi th khng cn phi hc". Chnh v vy,
nu xc nh ni dung thi c"chch mc tiu" th vic hc hnh cng bi lch hng. iu
ny thhin rt r i vi mn Ton, mt trong 3 mn c xem l trng im hin nay.
Vic xc nh ni dung thi ton trong cc ktuyn sinh lgii mt sbi tp ton khin c
thy v tr x i luyn lm cc bi tp, mt cng vic vn chng vai tr thyu trong
vic dy v hc ton (gip cng ckin thc l thuyt cho chc hn). Ai cng r vic gii
cc bi tp ton chng gip g my trong cng vic ca mnh sau ny (kcnhng ngi lm
ton). Vic gii quyt cc bi ton thc tin khng ththc hin c bng cc mo gii bi
tp hc sinh, m phi dng cc chng trnh tnh ton chuyn dng xy dng trn cscc
phng php ton hc cbn; cn phng php tduy cbn c ch cho ngi ta vlu di
l trong cc chng minh cc nh l kinh in (phn l thuyt), m khng phi t my"mo" lm bi tp. Vn c ngi thch "thi phng" vai tr rn luyn tduy ca vic lm bi
tp, cn nhng ngi lm ton thc sth bit rng vic nhi nht qua mc ci phng php
tduy kiu ny sgy hu quxu cho ngi ta nh l vic "dng thuc qu liu lng".
iu thi l, do quthi gian c hn v ly vic gii bi tp lm mc ch cui cng, ngi
ta cho hc l thuyt mt cch "chiu l" (chhc vt mt scng thc my mc phc vcho
gii bi tp). iu ng ni l chnh kin thc l thuyt mi l iu hc sinh cn phi hc. Kt
quca cch dy v hc phi cbn (ly bi tp lm trng tm) khng chlm hc sinh "rng"
vvn ho ton, m cn lm cho hc sinh ston, hoc mt mi v ton,... R rng, cch hc
ton sai lch hin nay l con ca cung cch nh gi, thi cang c tin hnh. Nu ta
nh hng ni dung thi l cc kin thc l thuyt cbn th chng nhng gip cho thy tr
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dy v hc ng nhng thcn thit cho mnh trong tng lai, m cn ngn nga c nn
dy v hc thm trn lan, bi v hc sinh xc nh c phm vi cn phihc. (Ta bit rng l
thuyt c thgi gn trong vng mt quyn sch gio khoa mng, cn cc bi tp "n theo"
th c thtri khp chng chc cun sch dy, m vn khng ht!!!).
Mt iu cn lu l cung cch thi ctheo kiu "htrcc l luyn" nhhin nay khng ch
gy lng ph ln vnhn lc cho ton x hi, m cn ang lm mt khnng tip cn cc
trng i hc ca nhng hc sinh rt c nng lc nng thn (nht l ngi ngho v ngi
vng su vng xa), v cc em khng c iu kin c "tri qua l luyn" nh cc bn
thnh phhay con em cc gia nh kh gi. Hy nhn li xem bit bao ngi thnh t v ti
gii hm nay xut thn ttng lp ngi ngho ca thi kcha pht sinh cc "l luyn"?
2.3 Phng php nh gi quyt nh tnh cng bng v hiu qu
Khi thi bao qut ton bchng trnh th hc sinh khng th"hc t" theo kiu n may,
cht lng o to sc nng cao. Mun cho thi c thbao qut c chng trnh ththi buc phi di (gm nhiu cu hi). Khi y,phng php trc nghim khch quansl
ph hp, khng chi vi ni dung thi l cc cu hi vkin thc l thuyt cbn m vi c
nhng bi tp i hi suy lun cc kiu (min l ngi ra bit cch). c bit, do vic chm
bi thi thc hin bng my, n c tnh khch quan vt, gim thiu cc sai st gy oan tri,
ngn nga cc khnng tiu cc v tit kim c rt nhiu thi gian, sc lc trong khu
chm bi.
Vic chm bi thi bng my cho php sdng nhiubkhc nhau trong cng mt kthi
(min l tng ng nhau vtrnh ). iu ny shn chc rt nhiu tnn gian lntrong thi c, k c tpha th sinh ln nhng ngi t chc, qun l k thi. Ngi ta cng
khng cn phi qu lo vi chuyn "l", v khi thi bao qut cchng trnh hc th l
cng chnhl "lchng trnh". Hn na, do vic sdng rt nhiu khc nhau, vic
lmt chng c ngha l g, v chng ai bit trc mnh bt phi no (cn nu nhl
ht v hc sinh chun bc ht trc khi thi th y chnh l mong mun cao nht ca
ngnh gio dc!!!). Nhvy, vi kiu thi trc nghim khch quan, vic to mi trng lnh
mnh cho mi kthi l khng kh khn, v khi y h tt phi thi tp trung ti mt a im
(thm ch cng khng nht thit phi thi trong cng mt ngy, v khng cn chuyn l).
iu ny khng chgp phn gim bt gnh nng cho cc th sinh vng xa, m cn gii ta
c cnh ch tc trin min (vmi mt) cc thnh phtrung tm mi khi ma thi n.
Tuy nhin, ci c ln nht ca phng php trc nghim khch quan l em li mi trng
trong sch cho cc kthi, lm cho cngi ln ngi trt u thy thoi mi vsnh
gi khch quan v t, v khng lm cho ai nghti chuyn "chy cht", v n cn kh hn l
i thi. Nhng ai tng tri qua cc kthi ngoi ngkiu trc nghim, nhTOEFL, hn
tmnh kim nghim iu ny.
Nu nhc c cc trung tm kho th (khch quan v t), tchc vic thi cv cp chngchmt cch thng nht (trc mt cho hc sinh phthng), th skhc phc c rt nhiu
iu bt cp trong lnh vc ny. Khi y, vic dy thm-hc thm (theo mc ch ring ca
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gio vin) cng stbin i, v cht lng hc tp cui cng ca hc sinh sc nh gi
khng phi bng cc bi kim tra theo chquan ca thy, m bng cc bi thi ca trung
tm kho th. Cc kthi nhvy cng scho chng ta mt thc o chnh xc vcht lng
o to ca tng trng, tng thy.
2.4
Nhng kh khn v trngi trn ng i ti thi clnh mnhVic tchc thi trc nghim i hi schun brt cng phu: cvmt thit lp chng trnhln son tho ni dung cu hi trc nghim. Khu thnht tuy khng d, nhng c thxem l
nm trong tm tay ca cng ngh thng tin Vit Nam; khu thhai tng l d, nhng rt
kh lm c hon ho. Nhng ngi khng o tng th lun thc c rng "ci kh
khng tnhin mt i mn chbin i tdng ny sang dng khc", do kiu thi trc
nghim khch quan em li cho ta bao nhiu thun li trong khu tchc v chm bi th n
cng i hi ta phi ng u vi by nhiu thch thc trong khu son tho ni dung cu
hi. Vic ny khng phi l qu kh, nhng i hi su tcng sc rt ln, vt xa s"o
tng"ca nhiu ngi. N i hi phi huy ng c nng lc hp tc ca mt thrt ng
cc nh gio, nh khoa hc u ngnh. Bng cch ny, vic thi cskhng cn b lthuc
vo chmt vi c nhn (vn tim n khnng ri ro cao), m c htrbi mt tp thln
(trong s "trc trc" ca mt vi c th t c khnng gy nh hng ng kn hot
ng ca chthng). Vic huy ng mt tp thrt ng ngi tham gia son khng h
lm tng nguy cvkhnng "l" (nhcch ra thi thng thng hin nay), m ngc
li "xc sut l" c thxem nhtlnghch vi lng ngi tham gia son . Tm li,
c c h thng thi trc nghim hon ho, vic u t ban u l kh ln. Cho n nay,
phn ln cc trng khng thnh cng trong vic p dng hnh thc thi ny l do khng sc u ttha ng ngay trong giai on u.
Ni nhvy khng c ngha l hnh thc thi trc nghim i hi u tqu nhiu v khng
mang li li ch vmt kinh t. Ngc li, vic u tnghim tc cho mt nm u khng
thtn km hn nhng g m BGio dc v o to ang phi u tcho mt kthi trong
nm, cn cc khon chi ph cho vic bsung v chnh l chng trnh thi trc nghim cho cc
nm sau l rt nhso vi chi ph ban u, v nhvy hiu qukinh tvlu di ca hnh
thc thi trc nghim l iu khng cn phi bn ci.
2.5 Nhng mc tiu hin thcChng ta c ththit lp c mt m hnh thi cvi cc c tnh sau y:
Ni dung thi c nh hng chyu vo cc kin thc cbn. Tng thi c kh
nng bao qut chng trnh trn din rng, c thnh gi trnh kin thc th
sinh mt cch ton din v chnh xc. iu ny sgp phn xo btnn hc t, hc
lch, cc kiu ra thi "nh " v nn "luyn thi trn lan".
C ch chm v sinh thi bng my cho php mi thi sinh lm mt thi ring
(nhng tng ng nhau vkh). Khnng gian ln trong thi c c gim nmc ti thiu. Skhng cn tnn quay cp, bi v cc th sinh vi cc thi khc nhau
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schng c g chung sao chp. Cc loi tnn gian ln ngoi phng thicng khng cn
chng, vi ngi "ngoi cuc" rt kh bit c "th sinh nh mnh" bt phi no
(trong shng vn ) m lm hv tm cch "tun vo". iu ny khng chgim
nhcng vic cho khu tchc thi, m cn htrc lc cho cho chtrng tchc
thi phn tn ti cc a phng, tit kim chi ph cho nhn dn vng su vng xa v
gim ch tch cho cc thnh phln trong ma thi c.
Cng vic chm thitrnn nhnhng, chnh xc, gim thi gian v chi ph. Trn thc t,
chm bi khng cn l vic kh i hi cc chuyn gia gii, m chl cng vic nhp
dliu thng thng ca cc nhn vin thk. Kt quchm thi chnh xc, bi v cc s
sut ca vic nhp liu t hn rt nhiu so vi cc sai st ca vic chm bi th cng
(nhhin nay); ng thi cc ssut vnhp liu (nu c) cng dc pht hin v
xl kp thi, khng cn phi lm cc thtc "phc tra" rm r nhhin nay.
2.6 Mt sgii php kthutSau hai nm nghin cu, trn cskinh nghim ca nc ngoi kt hp vi c im tnh
hnh thc tin nc ta, cc chuyn gia ca phng Nghin cu Pht trin Phn mm (Vin
Ton hc, Vin Khoa hc v Cng nghVit Nam) xut mt m hnh chng trnh nh gi
cht lngtheo hnh thc trc nghim sau y:
2.6.1 Cc tnh nng cbn ca chng trnh
C thsinh thicho nhiu kthi(khc nhau vni dung v chng trnh);
Trong mi kthic thsinh nhiu thikhc nhau, nhng tng ng nhauvtrinh ,
mi th sinh c mt ring;
Mi thi gm nhiu cu hi, c thqut ton bni dung chng trinh hc;
C modul qun trNgn hng Dliu thicho php nhp thiv thng xuyn chnh
l, nng cp ni dung cc thi;
C modul thng k v nh gi cht lng thi, cho php kim nh li cht lng ca
tng cu hi (sau nhiu ln sdng), htrcho vic chnh l v bsung Ngn hng D
liu thi;
C modul Qun trthi phc vcho thit lp v qun l Danh mcth sinhng kydthi
(chnhng th sinh ng k, c sbo danh, mi c php tham gia kthi). Modul
ny cn qun l cc thng tin lin quan n thi, kt qulm bi, im sthica tng th
sinh.
2.6.2 Ngn hng dliu thi
2.6.2.1 Yu cu vni dung thi
C tnh in hnh v bao qut ton bchng trnh (i hi ngi ra phi c trnh
chuyn mn cao);
C nghthut din t (hi c nhng vn phc tp bng nhng cu n gin);
Mi cu hi c th c nhiu phng n tr li sn th sinh la chn ra phng n
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ng; nhng cng c th c khng c phng n cho sn, m th sinh phi t in
phng n trli ca mnh vo mt trng cho trc;
im ca mi cu hi c cho tng phng n trli, c thnhn cc gi trskhc
nhau (m khng nht thit chc hai gi trnghoc sai), thun tin cho vic phn
loi khnng th sinh.
2.6.2.2 Tchc Ngn hng dliu thi
Cc cu hi c phn loi theo cc chuyn mc (hp ca tt ccc chuyn mc phi
phkn ton bchng trnh);
Mi chuyn mc gm nhiu cu v c phn loi theo mc d- kh (thng chia
thnh 3 mc : d, trung bnh, kh) v c gn thi gian lm bi.
Mi cu hi (thuc mt loi, mt chxc nh) c chbin thnh nhiu phin bn
tng ng nhau (t10 n 50, tunhu cu) v c xp trong cng mt "ngn ko";
Mi phin bn u c gn m, trong bao gm c: M chuyn mc, m phn loi
mc , m cu hi, m phin bn.
2.6.3 Qui trnh sinh thi v chm im
2.6.3.1 Chun bthi cho mt kthi
C 3 bc trong quy trnh chun bcho mt kthi:
Bc 1:Xc nh cc chuyn mccn a vo thi (cn ctheo ni dung chng trnh cn
thi hay kim tra); Vic ny thng p dng cho cc kkim tra nhtrong nm hc
(vmt vi chcthmi dy qua);
Bc 2: Xc nh mc kh cho tng chuyn mc ca kthi (tutheo mc ch ca kthi
v yu cu nm bt kin thc ca tng loi i tng vchuyn mc );
Bc 3: Chn ngu nhin cc "ngn ko" cu hi thi (theo mc kh-d xc nh trong
Bc 2) v n nh thi gian lm bi thithng qua thi gian nh cho tng cu hi;
Nhvy, sau bc chun bta a ra c mt tp hp cc "ngn ko" cu hi thi. Tp cc
ngn ko ny l ngu nhin (ngi chun b thi cng khng th chnh c theo
mnh). ng lu l mi ngn ko gm nhng cu hi c lpnhng tng ng nhau vkh-d. Mt iu cn ch l thi gian lm bi thi c xc nh theo tp hp cu hi c
chn, chkhng phi l c xc nh trc nhta thng lm theo truyn thng (15 pht, 1
gi, hay 3 gi,...). iu ny l hp l hn, v thi gian thi phi phthuc vo ni dung thi c
th, chkhng phi l vo mun chquan ca ta. Tuy nhin, ta ddng iu tit lng cu
hi c c thi gian lm bi xp xnh nh theo thi quen.
Trong thc ttrin khai, bc chun bcho mt kthichnh l bc sinh m xc nh cc
"ngn ko" cu hi (bao gm: M chuyn mc, m phn loi mc , m cu hi, trong hai
m u c chnh theo yu cu, cn m th3 c sinh ngu nhin). Nu thi trn dinrng (gm nhiu a im thi), th bc ny chcn thc hin ti 1 trung tm, sau thng
bo kt qu(thc cht chl mt chui s, nhl mt cha kho) cho tt ccc ni (c thm
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ho nu thy cn thit).
2.6.3.2 Sinh thi cho tng th sinhMi th sinh vo thi sc chng trnh sinh ngu nhin mt thi ring, bng cch ly ngu
nhin mi phng n ttrong tng ngn ko ( c xc nh trong bc chun bcho mt
kthi). Sau khi c sinh, chng trnh scho ra m sca thi(c thly trng vi s
bo danh) v tp m scc phin bn c chn cu thnh .
V cc phin bn ca mi cu hi l tng ng nhau, cho nn cht lng ca mi thi
trong mt kthi (c sinh ngu nhin theo phng php trn) l tng ng nhau.
2.6.3.3 Lm bi v chm im
Nu thi trc tip trn my, th sinh in trc tip cc phng n trli vo cc c sn trn
my, v c bit kt qungay sau khi thi xong. Phiu im thi (vi kt quim ca tng
cu hi) sc in ra cho tng th sinh.
Nu khng thi trc tip trn my, mi th sinh c my tnh sinh (ngu nhin) mt ringv in ra giy. Th sinh lm bi trn giy thi in sn (nhthng thy cc kthi TOEFL hin
nay). C thin ring thivphiu lm bi, chcn chng c chung mt m thi(nhchung
mt sphch trong cc tgiy thi truyn thng). Khi lm xong bi, th sinh chcn npphiu
lm bi(khng nht thit phi np li thi, v c my lu theo m ). Kt qutphiu
lm bi thic thc nhp vo my tnh bng mt trong 2 cch: nhp liu thng thnghoc
qua my qut tng(c2 phng php u khng i hi nhng chuyn gia c trnh cao,
nhi vi cng tc chm bi hin nay, m chyu cu cc nhn vin thk nhp liu thng
thng). Kt qunhp liu cin ra giy ddng kim nh li khi cn.
Trn csdliu nhp vo, chng trnh cn cvo m thi tm ra m cu hi,m phin
bnri ly ra p n tng ngchm im. im sc lu li vo tp dliu vthng
tin th sinh, cng vi m thi v m cc phin bn cu hi. Kt qucng c in ra di
dng phiu im thi(nhkhi thi trc tip trn my).
2.6.3.4 Nhn xtSo vi cch thi v chm im thcng nhhin nay, phng php trn thhin nhiu u th
vt tri:
Tc chm caohn rt nhiu (thi gian nhp phiu bi lm t hn rt nhiu so vi thigian chm bi bng thcng nhhin nay). Ni chung, thi gian chm bisau mi k
thi khng cn l vn ng quan tmca ngi tchc kthi. Chi ph cho khu chm bi
gim i rt nhiu ln, khng chdo thi gian v cng sc c rt ngn, m vic nhp
liu trong khu chm bi khng i hi cc chuyn gia c trnh cao (nhchm bi
theo kiu thcng hin nay).
Kt quchm thi chnh xc, bi v cc ssut ca vic nhp liu t hn rt nhiu so vi
cc sai st ca vic chm bi thcng (nhhin nay); ng thi cc ssut ny, nu
c, cng c pht hin v x l rt ddng (chcn nhp li d liu cho ng, mkhng cn phi lm cc thtc "phc tra" rm r nhhin nay).
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Khnng gian ln trong thi cc gim thiu. Skhng cn tnn quay cp, bi v 2
th sinh vi 2 khc nhau s chng c g chung sao chp. Ngi "ngoi cuc"
khng thbit c "th sinh nh mnh" bt phi no (trong shng vn ) m
lm hv tm cch "tun vo".
Khnng "on m - n may"trong phng php thi trc nghim ny skhng xy ra, v
trong bi khng phi chl nhng phng n (ng - sai) c sn c th "chn
m", m cn c khnng trng "khung p s" cho th sinh tin vo kt qu
m mnh tm ra.
2.6.4 Cc chc nng htrkhc
2.6.4.1 Qun l Hsth sinh
y l chc nng khng ththiu ca bt cchng trnh thi cno. N cho php:
Thit lp danh mc cc th sinh (vi cc tiu ch thng tin cn thit), thng qua giao
din Web (v c thnhp tbt cni no trn mng, nu c php).
Kim tra t cch th sinh: Ch cc th sinh ng k (c khai bo trong c sd
liu) mi c quyn tham gia thi.
Tng cp nht ni dung thi c(M thi, danh mc cc phin bn cu hi c
sinh, kt quim scho tng cu hi,...) vo Hsth sinh.
2.6.4.2 Qun l v tng cng cht lng Ngn hng thi
Ddng mrng dung lng (thm chthi, thm cu hi v phng n trli);
Giao din cp nht thi thun tin (trn Web); cho php lm vic tmi ni trn mng quc
gia (khi ngi qun trtrao quyn truy nhp); mi nhp c lu vo "vng m" Ban
kim nhxem xt, chcc t tiu chun mi c bsung vo Ngn hng thi.
Tng cng cht lng ngn hng thi bng chc nng Thng k kt quthi qua nhiu giai
on, pht hin ra cc cu hi qu d, hoc qu kh, hoc khng chnh,... loi bhoc
chnh l.
2.7 Cc hnh thc p dng
2.7.1 Cc kkim tra trn din hp
Vi cc kkim tra trn din hp(lng ngi tham dkhng nhiu) th hnh thc thi nhanh
gn nht l lm trc tip trn my. Do bqua c cng on in thiv nhp kt qucho nn
thi gian gim xung rt nhiu. Thi gian cho c3 cng on chcn rt li bng ng thi
gian lm bi thi. Hnh thc ny rt thun tin cho cc mc ch kim tra th im, kim tra
cho,...
2.7.2 Cc kthi trn din rng
Vi cc kthi trn din rng(lng th sinh dthi rt ng) th hnh thc thi trn giy l ph
hp vi hon cnh hin nay, v khng i hi nhiu my tnh (mi hi ng th thi chcn 1
vi ci lm nhim vsinh v in cc thi). Hnh thc ny lm nhng ngi t tip xc vi
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my tnh t tin hn (khng bm nh bi khnng xy ra "sc" m ngi ta khng hiu
c). Vic lm bi trn giy cng m bo tnh xc thc "khng thchi ci c" vkt qu
lm bi ca mi th sinh. Cc th sinh khng thchi ci vcc phng n trli do mnh
chn trn "giy trng mc en".
Lu rng, trnh "qu ti" trong vic sinh qu nhiu trong mt thi gian ngn (vo
thi im thi), khu sinh thi cho cc th sinh hon ton c ththc hin trc mt bc m
khng smt tnh "khch quan v t". Ngi c thm quyn ti mt Hi ng thi c thcho
sinh mt cch ngu nhin(vi sgim st ca ngi c thm quyn, nu cn) mt lng thi
ln (nhiu hn hn lng th sinh tham gia thi ti hi ng ) v cho in ra trc thi
im thi. n khi thi, cc thi sinh chvic chn ngu nhin mt trong (rt nhiu) cc thi
in sn.
2.7.3 Thi kt hp trc nghim v tlun
Hai hnh thc thi trc nghimv tlunkhng phnh ln nhau, m ngc li chng htrv b sung cho nhau. Hnh thc thi trc nghim cho php phn loi nhanh trn din rng,
trong khi hnh thc thi tlun cho php phn loi tinhtrn din hp. Chnh v vy, m hnh
thi hon ho hn c l cho th sinh tri qua hai vng: vng th nht dng hnh thc trc
nghim loi ra nhng th sinh thc skm, vng thhai dng hnh thc thi t lun
phn loi nhng hc sinh thc sgii. R rng, gii php ny l tn km hn so vi thi mt
vng, v vy chnn p dng khi thy tht cn thit.
2.7.4 Kt hp 2 kthi trong mt ln thi
Vic kt hp 2 kthi(thi tt nghip v thi tuyn sinh i hc) trong mt ln thi c thcthc hin mt cch kh n gin i vi chng trnh ni trn, bi v c thc chn vi
nhiu mc kh-dtutheo nhu cu. Mt thphp n gin l: phn chia thi thnh 2 cm,
cm thnhtgm khong 80% cu hi loi bnh thng (nh gi tiu chun tt nghip) v
cm thhai gm 20% cu hi loi kh hn (nh gi tiu chun vo i hc). Ngi c tt
nghip l ngi t im chun quy nh cho cm th nht (bt lun kt quca cm
thhai ra sao). Ngi vo i hc phi l ngi t im cao c2 cm ca thi. Cch
tuyn sinh ca B(v cc trng) sxc nh khung im chuncho mi cm ca thi (tu
theo tnh hnh cthca tng nm, tng trng, tng vng,...).2.7.5 Trung tm kho th khu vc
Chng trnh trc nghim nu trn c thc sdng lm ht nhncho mt trung tm kho
th khu vc (ca s, phng, trng,...). y l mt cng ccn thit cho vic chun ho cht
lng o to trn quy m rng. N cung cp phng tin thun li cho nhiu loi hnh kim
tra v nh gi cht lng dy v hc mi mc , kcnhng cuc "kim tra cho", kim
tra nh k, tng trng, tng a phng cth,... Kt qunh gi cc thi im, a
im thi khc nhau vn lthng nhtvthtphn loi theo im s(cng nhl im s
thi ting Anh theo TOEFL hin nay khng ph thuc vo vic thi a im no, vo lcno,...). Vi "Trung tm kho th" ny, vic tchc kim tra nh gi cht lng c tin
hnh mt cch n gin v nhnhng: Tmy chca trung tm kho th, ngi ta nh sn
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bkim tra (theo quy trnh chn ni dung thi trnh by trn), v tmi a im
(trong hay ngoi khu vc) c thtruy cp vo thi (trc tip trn my hay gin tip qua giy),
trong cng mt ngy hay trong vng vi ngy (tutheo hon cnh). Kt qukim tra c
bit ngay sau khi thi xong.
Kt quca cc kkim tra tin hnh qua trung tm kho th phn nh mt cch khch quan
cht lng hc tp ca hc sinh mi a phng, cho nn ta c mt "thc o" cng bng
cho vic nh gi cng tc o to tng a phng. Ngoi vai tr lm "trng ti" nh gi
cht lng, trung tm kho th c thto ra mt "hthng m" cho php mi ngi, mi cs
o to c thtruy cp n tnh gi khnng ca mnh.
3 Thc tin trin khai ban u3.1 Xy dng phn mm(Xem m)
3.2 Trin khai thnghim3.2.1 Ci t trn my
Chng ti tin hnh ci t chng trnh bmn i sv hnh hc lp 10 vo my vi phn
mm trc nghim do cc chuyn gia phn mm ti Vin Ton xut. Chng ti lp cc
mc theo cc chng ca sch gio khoa. Trong mi chng li to ra cc mc nhtheo cc
n vkin thc chnh ca chng. Khi to xong chng ti nhp cc cu hi phhp vi h
thng kin thc c ngn hng .
Cch lp cc mc nhvy rt thun tin khi tin hnh kim tra thng xuyn 10-15 phthng ngy, cng nhkim tra sau mt phn kin thc theo chng trnh ca b, m khng s
khi sinh khng ng phn kin thc hc. Vic kim tra c th tin hnh mt cch
thng xuyn nhm to ra khng khhc tp, buc hc sinh phi thng xuyn n luyn
kin thc. iu ny mang li sthun li trong ging dy v hc tp.
Mt khc mi khi kim tra xong ta tin hnh kim nghim nh gi kh, phn
bit v tin cy. T chnh l li phng php dy cho tng bi, bsung v chnh l cc
cu hi theo cc tit dy so snh vi bng trng sm bo tnh hthng, tnh lin mch
ca kin thc.
3.2.2 Trin khai thnghim
3.2.2.1 Cc hnh thc p dng
1) Kim tra nh gi thng xuyn 10-15 pht.
Vi hnh thc ny thng kim tra u gihoc cui ginhm mc ch n li bi c, cng
cbi mi. Hnh thc ny gip hc sinh n tp mt cch thng xuyn, nhnhng, gy hng
th cho cc em trong hc tp v nhc nhcc em chu kh hc bi. Slng cu hi chng
ti la chn l 5 cu trong 2 cu dchim 40% v 2 cu trung bnh chim 40% v 1 cukh chim 20%.
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2) Kim tra nh gi kt quhc tp ca hc sinh vi thi gian 45 pht.
Khi cc em hc xong mt phn vi lng kin thc nht nh. Ta tin hnh kim tra mt tit
(theo phn phi chng trnh ca b). Chng ti da vo mc tiu gio dc ca chcn
kim tra, ln khung thi. Khung thi gm: slng cu hi theo tng n vkin thc,
mc kh, dca tng cu. Nhm nh gi cc mc nhn thc ca hc sinh. Khi ra da vo trnh yu cu ca tng ban, tng lp m to ra cho ph hp. Chng ti thng
to 3 dchim 20%, 9 trung bnh chim 60%, 3 kh chim 20%. Nhng vi lp c lc
hc kh ta c thtng slng trung bnh v kh ln, vi lp km hay nhng ni iu
kin hc cha tt ta c thgim kh xung ph hp vi thc t.
3) Kim tra nh gi kt quca hc sinh sau khi kt thc mt hc k.
Mi mn hc u c mt mc tiu nht nh. Kim tra l cng co lng mc t ti ca
mc tiu ny vi su phm tr chnh l: Nh, hiu, vn dng, phn tch, tng hp, nh gi,
o hnh vi ca hc sinh, chng ti cthho theo ba mc ca l d, trung bnh,
kh. Chng ti da theo yu cu ca tng chtrong chng trnh sch gio khoa. Kt hp
vi gio vin trc tip ging dy trong khi, xc nh r trng tm kin thc cn kim tra,
xc nh r trnh ca hc sinh. T nn khung kim tra sao cho hp l v tin hnh
kim tra.
3.2.2.2 Trin khai thc t
Trc khi kim tra chng ti tin hnh tho lun thng nht vi gio vin trong khi, dy
cng bmn xc nh r ni dung kim tra, phm vi ca nhng vn cn a vo bi kim
tra, thi gian kim tra, cc mc tiu cn nh gi, hnh vi cn o ca hc sinh. Ln khung bi
kim tra theo bng trng s chi tit. Th d, kim tra mt tit (45 pht) chng phng
trnh v hphng trnh mn i slp 10, ta c khung bi kim tra sau:
Bng 6: Khung bi kim tra chng phng trnh v hphng trnh.
Ty ta cho my sinh theo khung trn, vi slng l 10 . My ly xc sut trong
ngn hng to c kh dtng ng.
Tchc kim tra: Chng ti tin hnh thi theo hnh thc thi trn giy vi nhm thnghim
l:
Ni dung D TB Kh
1. Phng trnh 2 1
2. Phng trnh bc nht 2 1
3. Phng trnh bc hai 1 3 14. Hphng trnh 3 1
Trng PTTH Lp SH.S tham gia
Trng chuyn ban T.X Hng Yn
A
B
47
50
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Ta tin hnh kim tra bnh thng mi em mt v mt phiu kim tra. Cc em ngi cnh
nhau khc nhau. Sau chng ti tin hnh chm thi trn my.
3.2.3 Phn tch cu hi sau khi chm
Sau khi chm bi trc nghim, chng ti ly th dmt l 30 em tham gia lm bi. Tin
hnh phn tch rt ra bi hc. Chng ti sp xp theo im bi thi tcao xung thp, ly27% bi c im cao nht lp thnh nhm gii (R
H), ly 27% bi c im thp nht lp thnh
nhm km (RL
), scn li l nhm trung bnh (RM
). Tin hnh kim nh cc so v
kh, phn bit ca cc cu hi, ta c bng sau:
Bng 7: Qu trnh phn tch cc cu hi ca bi trc nghim
C 53
Trng chuyn ban Tin L
A
B
C
50
50
50
Tng s 6 300
Cu
hi
s
Cc
phng
n trli
Sngi
chn ca
RH
Sngi
chn ca
RM
Sngi
chn ca
RL
Tng s
ngi
chn
Hiu
nhm
kh v
kmR
H- R
L
phn
bit
DI
kh
FV
59
1
0,16 0,96
2 1 1 -1
3
4* 8 14 7 29 1
B
Tng 8 14 8 30 0
60
1* 8 10 5 23 3
0,34 0,77
2 1 1
3 2 1 3 -1
4 1 1 2 -1
B 1 1 -1
Tng 8 14 8 30 0
67
1 1 1 1 3 0
0,52 0,67
2 1 1 2 -1
3 2 2 4 -24* 7 10 3 20 4
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B 1 1 -1
Tng 8 14 8 30 0
69
1 3 1 4 -1
0,56 0,68
2 1 2 3 -2
3 2 1 3 -1
4* 8 8 4 20 4
B
Tng 8 14 8 30 0
80
1 1 3 3 7 -2
0,78 0,28
2* 6 2 8 6
3 4 1 5 -1
4 1 4 4 9 -3
B 1 1
Tng 8 14 8 30 0
83
1 2 2 4 -2
0,56 0,65
2 1 1 2 -1
3* 8 8 4 20 4
4 3 1 4 -1
B
Tng 8 14 8 30 0
85
1 1 3 3 7 -2
0,56 0,54
2* 7 6 3 16 4
3 3 1 4 -1
4 2 1 3 -1
B
Tng 8 14 8 30 0
88
1 1 4 3 8 -2
0,60 0,54
2 2 2 4 -2
3* 7 7 2 16 5
4 1 1 2 -1
B
Tng 8 14 8 30 0
93
1 1 4 3 8 -2
0,81 0,24
2 3 3
3 1 4 3 8 -2
4* 6 1 7 6
B 2 2 4 -2
Tng 8 14 8 30 0
1 3 2 5 -2
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hin li do dng ttrong cu dn cha tt hay ging dy phn kin thc ny cha k. Nhng
cu hi nhiu hc sinh trli chng tcu hi li cun c nhiu hc sinh l cu tt, xongnu l cu sai nhcu 80
4; 88
1; 93
1th c thcu dn lm cho hc sinh hiu sai, cn xem li,
cn cu ng nh cu 594 th li l qu d. Sau khi rt kinh nghim v nh gi o,
chng ti bsung, chnh l ngn hng .
3.3 Kt lunVic kim tra hc sinh bng phng php trc nghim khch quan gip cho gio vin xc
nh r mc tiu ging dy. Hc sinh lun c nhc nh, rn luyn qua cc hnh thc kim
tra mt cch thng xuyn. Pht huy c tt ccc i tng trong lp tch cc xy dng
bi mt cch sng to theo nhiu cch, nhiu con ng i ti kt qu. Vic tho lun nhng
cu kh, nhng vn cn nghi vn ca bi trc nghim s to mi quan tm gia cc i
tng hc sinh - hc sinh, gia hc sinh - gio vin. T to ra mt khng kh hc tp v
ging dy mi. Vic tho lun cn cung cp cho cgio vin v hc sinh sphn hi vkt
quging dy v hc tp ca mnh.
Thng qua bi trc nghim ca chng trc ta xc nh c chun kin thc cn nm, gip
gio sinh mi ra trng tip cn nhanh chng vi gio trnh.
Kt quo lng nh gi c cgio trnh ging dy, gip gio vin, hc sinh v cc nh
qun l hiu r vnng lc ca mnh hn, gp phn nng cao cht lng o to.
Vic sdng my cn khc phc c nhng bt cp trong thi cm phng tin thcng
khng thkhc phc c. T nng cao cht lng o to, to ra mi trng lnh mnh
trong gio dc.
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