THAM S8 DO KHO CUA CAU HOI VA THAM SO NANG LUC CUA CON NGUOI T R Q N G L I T t i U Y E T L T N G D A P E A U tt&l
O ThS. TRAN THI C A M THO*
1. Li thuyet ung dap cau hoi va dudng cong dgc trung (DCDT) cau hoi
a) Ba mo hinh cua Thuyet ung dap cau hoi (IRT) Li thuyet ung dap cau hoi (CH) xay dung cac mo hinh toan de xu li du lieu trdc nghiem khdch quan dua tren viec nghien cuu mgi cap tuang tdc nguyen td «Thi sinh - CH" khi trien khai moi hoqt ddng trdc nghiem khdch quan. Mdi thf sinh (TS) dung trudc mot CH se ung ddp nhu the ndo, dieu dd phu thudc vdo ndng luc tiem dn cua TS vd cdc ddc trung cua CH. Hdnh vi ung ddp ndy dugc md ta bdng mdt ham dgc trung CH cho biet xdc sudt trd Idi dung CH tuy theo tuang quan cua ndng luc TS vd cdc tham sd dqc trung cho CH. Hien nay, cd ba md hinh phd bien nhdt trong IRT: Mo hinh mot tham so (md hinh Rasch) chf xet den dd khd cua CH, mo hinh hai tham so cd xet den dd phdn biet cua CH vd md hinh ba tham so xet them muc dd doan md cua TS khi trd Idi CH.
Ndm 1960, nhd todn hoc Dan Mach, Gerorg Rasch dd dua ra md hinh ung dap cau hoi de md td mdi tuang tdc nguyen td giua mdt TS vdi mdt CH. De xem xet mdi quan he giua TS vd CH;
dd'i vdi TS, Rasch chon tham so ndng luc; ddi vdi CH, Rasch chf chon mdt tham sd lien quan den dd khd (khdng xet den dd phdn biet). Ta dugc cdng thuc cua ham dgc trung CH mot tham so theo mo hinh Rasch:
P(e) =
Tuy nhien, nhu dd biet, trong trdc nghiem cd dien, ngudi ta cdn su dung mdt tham sd quan trqng thu hai dqc trung cho CH Id do phan biet.
Tu dd, nhieu nhd nghien cuu dd dua them mdt tham sd thu hai lien quan den dd phdn biet bdng each nhdn them mdt tham sd a trudc dqi luqng (9 - b) d sd mu cua ham e. Ket qua thu duqc bieu
hai tham so. Ham dqc trung CH hai tham sd vd ham dqc trung CH theo md hinh Rasch cd cung dang thuc, chi khdc nhau d gid tri tham sd a (ddi vdi md hinh Rasch a = 1). Cdc ham cd dang nhu vdy dugc ggi Id ham logistic, Id logi ham dan gian cd rdt nhieu thudn Igi trong bien ddi todn hgc.
Trong thuc te trien khai trdc nghiem, chung ta deu biet, ddi khi mdt TS cd ndng luc bdng khdng nhung do doan md tra Idi hu hog mdt CH nen anh ta vdn cd mdt xdc xud't tra Idi dung CH. Tu thuc te dd, ngudi ta cd the dua them tham sd c phdn dnh hien tugng doan md vdo ham dgc trung CH dd chinh Id md hinh ba tham sd, ket qua se ddn den bieu thuc: P(0) = c + (1-f)-
\+e
thuc: P(9) =
b) Duang cong dgc trung cau hoi
Neu cho gid trj cua 0 bien ddi lien tyc tren true sd, chung ta thu duqc mdt do thj duqc goi Id DCDT CH (item characteristic curver- ICC). DCDT cua mdt CH (hay dd thj dqc tfnh CH) chfnh Id dudng hdi quy giua xdc sudt giai dung CH dd dd'i vdi ndng lyc cua TS. DCDT cua CH the hien kha ndng gidi dung CH cua TS, nd di len tu tu theo dd tdng trudng cua ndng lyc TS, bien dd di len dugc bieu thj bdng ham sd, bieu thuc cua ham so cd sy khdc nhau tuy theo sy khdc nhau cua ca sd Thuyet ung ddp vd dudng cong cua cdc ham sd khdc nhau dd cung khdng gidng nhau.
Bdt ludn ham so dugc bieu thj the ndo, ve ca bdn ham sd phai thoa mdn nguyen tdc tiem tien (tdng ddn); tuc Id khi trj so ndng lyc tdng len thi trj sd cua ham sd hodc xdc sudt gidi dung CH khdng the giam di. Trong ung dyng, ngudi sogn CH phai chgn dugc md hinh ham sd xdc ddng de bieu thj DCDTCH. Cdn viec kiem chung ham so dugc chgn cd xdc ddng hay khdng, cd the dung ket qua trdc nghiem thyc te de chung minh. Vi tham so dqc trung chf lien quan tdi ndng lyc cao
\ + e : goi Id ham dgc trung CH * Truong Cao dang sir pham Nghe An
Tap chi Giao due so 2 3 6 (ki a . 4/aoio)
hay thap, con nang lyc cua TS phan bo binh thuang hay thien lech cung khong anh huang tai each dyng duang cong dqc trung, nen xac suat trd lai dung CH cua TS khong bi dnh hudng bdi viec TS do thuoc nhom TS mdu nao. Tinh chat bat bien do Id diem ddc thu cua DCDTCH.
e P{0)
Item 1 p(e)
Item 2 P(0) Item 3 -3 0,014064 0,002599 0,001113 -2,5 0.032295 0,00606 0,002599 -2 0,072426 0,014064 0,00606 -1.5 0,154465 0,032295 0,014064
-1 0,299433 0,072426 0,032295 -0.5 0,5 0,154465 0,072426 0 0,700567 0,299433 0,154465 0,5 0,845535 0,5 0,299433
1 0,927574 0,700567 0,5 1,5 0,967705 0,845535 0,700567
2 0,985936 0,927574 0,845535 2,5 0,99394 0,967705 0.927574 3 0,997401 0,985936 0,967705
V; dy: Vdi 3 CH cd dd khd Idn luqt Id:
- 0,5 ; 0,5 ; 1. Vdi cdc gid tri dd cho cua 6 ta cd cdc gid tri P(0) tinh theo cdng thuc P(9)
a(S M
= ; tuang ung cua tung CH nhu 1 + e
bdng tren. DCDT cua tung CH duqc ve trong Microsoft Excel nhu hinh 1.
C» I 2 ICO ti
Hinh 1
2. Tham so dd khd cua CH vd tham so ndng lyc cua con ngudi trong li thuyet ung ddp cdu hdi
Trong li thuyet trac nghiem cd dien, ngudi ta xdc dinh dd khd dya vdo viec thu nghiem CH trdc nghiem tren cdc ddi tuqng TS phu hqp vd djnh nghTa dp khd p bdng ti sd phdn trdm TS Idm dung CH tren tdng so TS tham gia Idm CH dd. Viec su dyng tri so thdng ke p de do dp khd nhu tren cho ta biet muc do khd de cua cdc CH md
MELBOURNE I Do kho cua cau hoi 1
• H i - 1 •
1
m
I • O H
Hinh 2
khdng can xem xet nqi dung cua chung thupc cac hnh vue khoa hoc khdc nhau. Nhu vdy, do khd cua CH phy thudc vdo mdu TS dung de trac nghiem thu.
Trong li thuyet ung ddp CH, do khd cua CH khong phy thudc vdo mdu TS dung de trdc nghiem thu. Cung nhu ndng lyc cua TS khdng phy thudc vdo CH. Tu nhung cdu trd Idi thu thdp duqc thdng qua bdi trdc nghiem, hai loqi tham sd duqc udc luqng Id: tham so nang luc cua con ngudi -0 vd tham so do kho cua cau hdi-d.
Trong mdt md hinh trd Idi cdu hdi, tham so ndng lyc con ngudi -
(6) vd tham sd dp khd cdu hdi - (§) duqc xdc dinh tren cung mdt phqm vi, n hu hinh 2.
Do thi tren day cho thdy, xdc xud't P(9) trd Idi dung
CH chi cd the bien thien giua 0 vd 1 nhu ta thdy tren tung dd. Khi gid tri cua dd khd bdng gid tri cua ndng lyc, luc dd xdc sudt Idm dung CH bdng 0,5. Dieu ndy cd nghTa Id ca may Idm dung CH cung bdng ca may Idm sai cdu dy. O phia tren cua diem md xdc sudt trd Idi dung tqi dd bdng 0,5 thi ndng lyc cua con ngudi Idn han dd khd cua CH vd xdc sudt trd Idi dung thi cao han xdc sudt trd Idi sai. Cung nhu vdy, d ben dudi diem dd, do khd Idn han ndng lyc vd xdc sudt tra Idi sai Idn han xdc sudt trd Idi dung. Theo Magret Wu (Dqi hoc Melbourne - Australia) cdc chuang trinh IRT (Conquest) hdu nhu deu su dyng cdc nguyen tdc sau de danh gid cdc tham so: Neu cac nang lyc cua con ngudi la tham so da biet, khi do se de dang xac dinh dugc do khd cua CH-, bang each kiem tra nhieu nhom ngudi vdi cac cap dd khd nang khdc nhau, tim ra dugc nhdm nao cd khoang 50% so ngudi dua ra dugc cdu trd Idi dung.
Tuong ty nhu vay, neu biet dugc dd khd cua CH, chung ta cung cd the biet dugc cdc diem sd md mdt ngudi gianh dugc tren tdt cd cdc CH dugc sap xep theo dd kho vd dinh dugc nhung linh vyc md ngudi dd se cd cdu trd Idi dung nhieu hon cdu trd Idi sai. Neu khong the biet dugc cd hai tham sd con ngudi va CH thi cdc phdn mem IRT (Conquest, Vitesta) chi cd the danh gid cdc tham sd theo vdng lap. Dau Hen la dua ra nhung phan doan ban ddu cho nhung thong sd CH. Gid su Id cd nhung tham sd CH cy the, khi dd chung ta se Hep tuc udc lugng nhung thdng sd con ngudi. Mot khi cd dugc cdc tham sd con ngudi, thi tiep theo Iqi lay nhung tham
Tap chi Giao due so 2 3 6 (ki 2 • 4720101
so nay de udc lugng tham so CH lan nua. Cu nhu the, vong lap se tiep tuc cho tdi khi nhung tham so nay hoi tu ve nhung gia tri dn dinh.
De kiem tra hpc ki 2 mon Toan lap 9 bao gdm 23 CH trac nghiem nhieu lya chpn vai 4 phuang dn trd Idi thiet ke dua tren cdc tieu chi kl thudt vd ma trdn de kiem tra dd duac xdy dung (do khudn khd ha n che, cdc tieu chi kl thudt, ma trdn de kiem tra vd de kiem tra khdng duac trinh bay trong bdi viet ndy). Qua thu nghiem de kiem tra tren 180 HS tqi trudng THCS Xd Quynh Hung vd tren 203 em HS tqi trudng THCS Quynh Ldm huyen Quynh Luu, tinh Nghe An vdo thdng 5/2008, ket qua thu duqc phdn tich thdng qua phdn mem Conquest, chung ta cd tham sd dd khd b cua 23 CH vd so sanh do khd cua tung CH d hai trudng nhu bang sau:
THCS THCS Quynh Do chenh Cau hoi^ Quynh Hung a Lam b lech ja-bj
1 -1.69268 -1.67186 0.02082 2 -0.19030 -0.29371 0.10341 3 -0.39005 -0.45259 0.06254 4 -0.42210 -0.46912 0.04702 5 -0.10133 -0 11329 0.01196 6 -1.24510 -0.25666 0.98744 7 -1.87685 1.68742 0.18943 8 -1.21420 -1.16399 0.05021 9 -1.10001 -1.02757 0.07244 10 -0.75798 -0.73866 0.01932 11 0.43993 0.42570 0.01423 12 -0.92729 -0.93047 0.00318 13 0.66304 0.70130 0.03826 14 0.68153 0.70130 0.01977 15 0.66304 0.68263 0.01859 16 0.03064 0.04798 0.01734 17 -0.26569 -0.26305 0.00264 18 -0.23536 -0.27835 0.04301 19 -0.25050 -0.26305 0.01255 20 -0.50434 -0.46912 0.03522 21 1.21231 1.07184 0.14147 22 -0.42210 -0.41994 0.00216 23 0.90410 0.81914 0.09496 Su chenh lech hai dd khd d tren giua hai trudng Id do dnh hudng cua nhieu yeu td, cd 2 yeu to chfnh dnh hudng den diem sd cua HS, dd Id ndng luc cua HS vd dp khd cua CH. Tuy nhien, cdn cd nhung yeu to khdc dnh hudng den diem so cua HS, dd Id cdc yeu to phy gpi Id Facets. Cd 2 loqi yeu td' phy: cdc yeu to lien quan den dqc tfnh CH (nhu viec in de kiem tra vd hinh thuc HS Idm bdi:
HS Idm bdi tren mang so vdi HS Idm bdi tren gid'y,
hinh thuc Idm bdi tu ludn hay trdc nghiem khdch quan); yeu td ngudi cham (sy khd tinh hay de tfnh cua ngudi cham). Day Id cdc yeu td ndm ngodi HS, tuc Id HS khdng lien quan true tiep.
Mot yeu td phy nua lien quan true tiep tdi HS nhu Id gidi tfnh, qudc tjch. Nhu vdy, khi xem xet ndng luc phai tfnh todn cdc yeu td lien quan true tiep den HS nhu Id: gidi tfnh, qudc tich...
3. L/ng dyng de xdy dung ngdn hdng cdu hdi
Thdng qua thu nghiem de kiem tra, chung ta cd the xdc dinh duqc do khd cua cdc CH.
Cdn cu vdo dd khd cua CH, cd the luu tru CH trong ngdn hdng CH mdt each cd he thdng.
Cdc CH se duqc lay ra tu ngdn hdng theo yeu cdu cua bdt ki ki thi ndo vd se Id thudc do chfnh xdc ndng luc cua HS. Neu biet duqc dp khd cua CH, chung ta cung cd the biet duqc cdc diem sd md mdt ngudi gidnh duqc tren tdt cd cdc CH vd dinh duqc nhung tinh vue md ngudi dd se cd cdu tra Idi dung nhieu han cdu trd Idi sai.
Mdt ngdn hdng CH bao gdm cdc CH dd duqc dinh cd ve dd khd, nhung ngudi ra de thi khdc nhau lay tu ngdn hdng CH nhung cung cd mdt myc dfch su dyng vd su dyng cdc CH khdc nhau vdn so sanh ket qua duqc vdi nhau. Cdc chuang trinh ung dyng Thuyet ung ddp cdu hdi ngodi viec djnh cd cho ta cdc tham sd dd khd, dd phdn biet, dd phdng doan... cdn cung cap cho ta nhieu thdng so khdc md can cu vdo dd cd the biet duqc CH ndo tdt, phuang dn ndo cua CH chua tdt de chinh sua. Tu dd, lya chon CH tdt de dua vdo ngdn hdng CH. Neu xdy dung duqc mdt NHCH tdt se giup chung ta ra cdc de thi phu hqp vdi chudn chuang trinh.
Trong trudng hqp khdng the td chuc ki thi cung mdt ngdy, HS vdn cd the duqc so sanh ket qua mdt each cdng bdng neu chung ta Idm cdc de kiem tra khdc nhau. Nhu vdy, xu hudng ve thdnh tfch qua cdc ndm hoc hodn todn cd the duqc danh gid chfnh xdc. •
Tai lieu tham khao
1.Frank B. Baker. Item Response Theory - Parameter Estimation Techniques. Marcel Dekker, 2004.
2. Magret Wu. Tai lieu tap huan cho doan giao due Viet Nam tai Dai hpc Melbourne - Australia, tir 14/11/2009 den 13/12/2009.
Tap chi Giao due so 2 3 6 (k. a . 4/201 o)
