NANG LV̂ C SUY LUAN THONG KE CUA HOC SINH TRUNG HOC CO SO NGUYEN THI PHUONG CHI Trudng Dai hpc Suphgm Dgi hpc Hui Tom t3t Muc dich cua bai bao la thong qua khung danh gia cua cac ngMen cdu ve suy lugn[.]
Trang 1NGUYEN THI PHUONG CHI Trudng Dai hpc Suphgm - Dgi hpc Hui
Tom t3t: Muc dich cua bai bao la thong qua khung danh gia cua cac ngMen cdu ve suy lugn thong ke de danh gia ndng luc suy luan thing ke ciia hoc sinh tmng hpc co sd Chiing tdi dung mot vi du su dung khung danh gia nay
de danh gia ndng luc suy luan thong ke cua hoc smh trung hoc co sd
Tu khoa: suy luan thong ke, bieu dien du lieu, bilu dl thing ke
I.M6DAU
Tren the gidi cd rdt nhilu nha giao due quan tam din suy lugn thdng ke, ttong do [3], [4], [5] va [6] dd md ta suy Man thdng kg nhu la mdt mue dich bao quat ttong giao due thdng ke, hay [10] da ghi nhdn "suy luan la mgt ITnh vuc ca bdn cua thdng ke" (tt 3) [9] da phat trien mgt khung danh gid cho phep md ta cac dac trung ciia M duy thdng ke Ben canh do, cac dinh nghTa ve bigt dgc thdng ke, suy luan thong ke va M duy thdng ke khdng dugc phan biet rd rang, viec sd dyng qua lai gida cac tbuat ngir gdn nhu dugc chdp nhdn Trong bai bao nay, chung tdi su dung khung danh gid dugc trinh bay ttong [9] dg phdn tich suy luan thdng kg cua hgc sinh trung bgc ca sd Kha nang danh gid cdc
sd ligu, chiing cit vd cac Myen bd dya tten tap dd ligu la nhihig Id ndng quan trgng ma bdt ky bgc sinh nao cimg nen cd, digu dd giup cdc em phdn iing lai vdi cac thdng tm dinh lugng ttong the gidi xung quanh mgt each diing dan va thdng minh
Trong chuang trinh toan bdc trung hgc ca sd d nude ta Men nay chi trinh bdy nhihig khai niem ca ban ve thdng ke, bai tap khdng da dgng, hgc sinh chi Iam mgt each may mdc, khdng giup ich dugc nMlu cho hgc sinh ttong viec phat tiien suy luan thdng ke Hon nOa, hien nay gido vien cung khong cd mgt khung co sd ndo dg ddnh gid ndng lyc suy Man thdng ke cua bgc sinh Viec phat trien mgt khudn khd cho cac dac digm suy Man thong ke giup cho giao vien cd ca sd danh gia nang lyc cua hgc sinh M dd dieu chinh viec dgy va bgc dugc cbiing tdi quan tdm trinh bay tiong bai bdo nay
2 TONG QUAN VAN DE NGHIEN CUXJ
Cac chuang trinh nghien cdu [7], [8] va [9] da tao ngn mdt khung dgc trung cho sy phdt trien suy lugn thdng kg cua bgc sinh tigu hgc va trung hgc ca sd lir mdt gdc nhin toan dien ban Dieu nay phu hgp vdi md hinh phat trien chung cua [1], hg cho rdng suy luan cua hgc sinh cd the dugc md ta phat trien tten muc do phan dnh sy tbay ddi ttong do phuc tgp ttong suy lugn cua cac em Td gdc dg ly thuylt nay, [7], [8] va [9] md ta suy lugn thdng kg cua hgc sinh bang bdn qua trinh chinh sau:
Mo td dit li^u
Qua ttinh nay gdm vigc dgc ro rang cdc du Ueu thd (chua qua xu li), dd ligu ttong cdc bdng sd lieu, bieu do tiidng kg, hay cdc bilu diln bdng dd thi Cd thi xem "viec dgc du Tap chi Khoa h9C v^ Giao due, Trucmg Dai hpc Su pham Hug
Trang 2lieu" nhu giai dogn dau cua viec pMgn dich va phan tich dir Ueu Kha ndng dgc nhiing hiln thi cua du heu trd thanh co sd cho viec bdt ddu tao ra cac dy doan vd tim ra cac xu hudng Hai qua trinh sau Ugn quan den viec md ta du lieu: (a) chi ra nhimg nhdn thuc ve
cdc ddc tinh Min thi, va (b) xac dinh dan vi cua cac gia tri dQ Ueu
To chirc die lieu
Qua trinb nay gom viec sdp xep, phan loai hay hgp nhdt dd lieu thdnh mdt dang tdm tdt Ciing nhu kha ndng md ta cac Men thi cua dd Ueu, kha ndng td ebuc du lieu la hgt sue
quan ttgng cho viec bgc each phdn tich va pMen dicb du lieu Viec sap xgp dd lieu vao
cac cum hay cac nhdm cd thg lam sdng td cac quy ludt hay cdc xu hudng ttong dit Ueu Cac sd do tam va do phdn tan la huu ich ttong viec tao ra nhihig so sanh giifa cac tap dir lieu Ba qua trinh sau ndi dgn viec td chuc du Ueu: (a) phan nhdm du Ueu, (b) tdm tdt du lieu vg tdm va (c) md ta su phdn tan ciia dd lieu
Trinh bdy dd" liiu
Qua tiinh nay Uen quan din viec hign thj du Ueu dgng bieu do [2] cho rdng cam gidc bigu dd cdn den ttong viec trinh bay dd lieu "bao gdm viec xem xet cai gi tham gia trong viec dyng cac bieu dd nhu la cac cdng cy cau tnic du lieu va quan ttgng ban, cai
gi la sy lya chgn tdi uu cho mgt bieu dd trong tinh hudng dua ra" Trinh bdy du Ueu, gidng hai qua trinh trudc, la rat quan trgng ttong pban ti'ch va pMen dich dii Ueu Kieu Mgn thi dugc diing va each du Ueu dugc trinh bay se quyet dinh viec dua ra cac xu hudng va cac dy bao Ciing nhu vdy, nhihig hien tbi dit lieu khac nhau cd the truyen tai nhung y Mdng khac nhau vl cimg mgt dd lieu Hai qua trinh sau la ca sd cho trinb bay dif Ueu: (a) boan tbanb hay dyng mdt bien thi cho tap hgp d& lieu dugc dua ra va (b) danh gid tac dung cua cac hien thi du lieu ttong viec trinh bay dd heu
Phan tich vd ly giai dit liiu
Qua trinh nay la cdt loi ciia suy ludn thdng ke, bao gdm viec nhgn ra cac quy lugt vd cac
xu hu&ng ttong dd ligu, dua ra nhihig kit lugn va du bdo M bigu diln dd lieu bang bieu
dd thdng ke Nd kep hgp chat che hai qua trinh: (a) viec dgc M du Ueu va (b) viec dgc vugt ra khdi du lieu Qua trinh trudc lien quan din viec su dyng cac td chuc toan hgc de phdi hgp, ket bgp \ a so sanh dir lieu; qua trinh sau ddi bdi hgc sinh dua ra cac ket ludn
va dy bdo tir dd lieu bang viec khai thdc cac bilu dd thdng tin Men cd, dilu khdng dugc ndi den mdt each ro rang ttong dd Ueu
Lien quan din cac cdp dd suy lugn tiidng ke, [7], [8] vd [9] dd dua ra khung suy ludn thdng ke dgc tnmg cbo suy lugn cua hgc sinh qua bon cdp dd: cap dg 1 (mang tinh chu quan (idiosyncratic)), cdp do 2 (chuygn ddi (transitional)), cdp do 3 (dinh lugng), cap do
4 (pban tich)
Cdp dp 1
Suy lugn cua hgc sinh d cdp do nay hgn hep vd ludn bi rang budc Viec suy lugn mang tinh chu quan, theo each rigng cua minh ma khdng quan tam den du Ugu Hgc sinh cd
Trang 3cdp dd tru&c cdu tnic (prestructural)
Cap dp 2
Hgc sinh bdt dJtu nhan ra tdm quan trgng cua suy Man ve sd lugng nhung mdu thudn ttong vi^c su dung suy ludn nhu vay Suy ludn cua hgc sinh d cdp dd nay thudng chi tap trung vdo mgt khia cgnh ciia vdn de Trong md hinh cua Biggs va CoUis, ddy la cdp do
mgt cdu true (unistrucMral)
C6pdg3
Suy luan cua bgc sinh la ludn dinh lugng ttong dd hg cd the xac dinh cac y Mdng toan hgc cua vdn dl vd khdng bi phdn tam hodc bi nhdm ldn cac khia cgnh lien quan Tuy nMen, hgc sinh d cdp do nay khdng hgp nhdt Igi cac y Mdng toan hgc khi giai quylt van
de [1] xem day la cdp dO da cdu true
C6pdp4
Suy Man cua hgc sinh dya ttgn viec hgp nhdt cac kMa cgnh ciia mdt vdn de thanh mdt
cdu tnic cd y nghTa Day la nhimg gi ma [1] ggi la cap do quan he
3 CAC PHU'ONG PHAP NGHIEN COU
Chung tdi tiln hanh ngMgn cuu dudi dgng ly thuylt, tii dd dua ra mdt bang chi tilt khung ddnh gia suy Man tiiong kg Ben canh dd, chung tdi dua ra mdt bai kiem tta gdm
3 bai toan, tiln banh khdo sdt 155 em hgc smh ldp 7 va 8 cua tmdng Trung hgc ca sd Nguyen Du, thanh phd Hui dg xem phdn dng cua hgc sinh nhu thi ndo Do sy hgn chg cua bai bao, chung tdi chi ttich ra day mgt bai todn dl phdn tich mmh hga cho danh gia suy lugn tiidng kg Bdi toan nhu sau:
Hai dd thi dudi day Min thi thdng tin vl chuyin luu dien the gidi cua cac ca sT Madonna, Lady Gaga, Linkm Park, Eminem Tbeo em, ai cd cbuyen luu diln thanh cdng nhdt? Giai thich cdu tta ldi ciia em?
5dbu6i bilu diln tdng so tiln kilm du^c
111 I^L I I I
Ddp dn: Madonna
Cap dp
Cap dp 1
Cdp d? 2
Cau trd ldi dy kiin
Lady Gaga vi do dai 2 cpt cong lai dai nhdt
Eminem vi sd buoi bieu diln khong nhieu so vdi nhiing ngudi khac nhung so tien
Trang 4Cap dp 3 Madonna \i l> le giua so tien kiem dugc va buoi bieu dien la 3:1 trong khi nhitag ngudi khac la 5:13, 8:5, 8:3
Cap dp 4 Madonna vi thu nhap trong moi buoi bieu dien ciia cd ia nhieu nhdt 3 trieu do la, con nhimg ngudi khac la khoang 0,38 trieu do la, 1,6 trieu dd la va khoang 2.18 trieu do la
Phdn tich tru&c thuc nghiim: Bai toan lien quan dgn cdu hdi "thi nao la cbuyen luu
diln thanh cdng ban?" Cd thg la nhieu budi bieu dien ban hay kilm dugc nhilu tien hon, sd budi bigu diln it ma tign kilm dugc nMeu, ciing cd the la nhimg quan Mem sai lam nhu tdng sd budi va sd tign kiem dugc nMeu ban Mdi ngudi sg cd mdt quan diem
va h le rieng de bien hg cho >' kien cua minh Cau hot nay ddi bdi bgc sinh dgc va higu dugc bieu dd, tu dd so sanh pban tich va Uen ket cac y tudng cung nhu ngu canh de tim
ra mgt suy ludn va nit ra kgt ludn hgp ly, vdi luu > rang suy Man dua ra la Madonna thanh cdng nhdt Do dd, bai toan dugc xep vao mdc dO cao
4 KET QUA NGHIEN CUU
Ket qua cy the dugc ihdng kg nhu sau:
C a p do
Cap do 1
Cap do 2
Cap do 3
Cap do 4
S6 p h a n t r a m hoc sinh d a t tirng cSp do
25.13%
62.54%
- :
12.33%
Ddy Id bdi toan d mirc do cao Trong bai toan nay, tat ca bgc sinh deu tra ldi chd khdng
de trdng Dieu nay cho thdy cac em khd tMch thu vdi nhiing dgng bai toan nhu thg nay hoac cimg cd the tinb budng trong bdi khd gan vdi nhiing mdi quan tam cua cac em trong cudc sdng Cac em d cap do 1 deu tra ldi diing nhu du kien cua chung tdi nhung khdng em nao giai tMch nhu dy kien Trong trudng hgp nay cac em khdng kit hgp hai bigu do ma cM xet theo y kien chu quan ve viec thg nao la "chuygn luu diln thanh cdng" nhu bai Iam sau:
C-^AillCi-Ciai, ^ Lccrl!
Cd -^.C^.-JtlK^ j»LiV £iCiA3 MJt\aJA Ct^^
JfUiiii
Da sd cac em dgt dugc cdp do 2 Day la mdt van de mdi ddi vdi bgc sinh trung bgc ca
sd d nude ta Viec so sanh giiia bai bieu do cd lg kMen hgc sinh liing tiing rdt nMlu
.^»fl._^luiL.ik J L - bcflu :k :SiDij A^\t QQ lid c£ t.tu»i.av- yk £Ji«
pMLk .C£i(w ^d.L.4A',.„^jxi;iiiQi ^^ >ia;i-v c«i:t qim.„c.ar
"Lhuiiij iil„-ki^ k.si^ rttC- JaL-nfiictt o-tiCiL C^-JL]
Trang 5diâ—qW- -L^ AZ.-.Sb-ỵh.-s.^ ,-.-^ , J ,-: ; „ ^
^j^-~ £;nM.f.;./i:L -i:ii3 ct- i» -^iZ'-.-.:.'L-'^ ^4.- C-í;^ iị \xZiUC.:X Íi
Khdng cd hgc sinh nao dgt dugc cdp dg 3 Cap do 4 cung chi cMlm ban 1/10 sd lugng cac em tham gia ttong nghien cuu naỵ Dieu nay cho thdy, kbd nang suy ludn cua cac
em chua phat huy dugc ttong nhihig tnrdng hgp cdn phan ticb, ly giai va dua ra nhdn xet Chung tdi cho rdng, đy la mOt kgt qua do qua trinh dgy va hgc M?n nay chi chu trgng cac quy trinh tinh todn ma xem nh? nang lyc suy lugn ciia hgc sinh, gido vien khdng quan tam nMeu den cbucmg thdng kg, hgc sinh lai hpc qud thu đng Qua nhihig bai lam cua bgc sinh dgt dugc cdp do 4 chung tdi tMgt nghT, nlu dugc day vd hgc diing each, viec suy luan cua bgc sinh se dugc phat buy rat ldn Sau day la mgt bai lam dgt dugc cap do 4:
^iLuC-iifl , WBicvJix Lị- d j i i ^ tuu itijị ri,^Ậ L^ ,,.jkixị^ Ut ;
t»(M uJụ &aaạ , -.U^^ !P.ajk - i^ Eam:fạ ^jacị ^vaị ^iUJ Aim ML
dtiSi ịio«j 3Ufuim jjinu Wo(k-atiị.^.ju:' Jị :iuu( M^ s.uor ;;;), (yjvi30«ạ_.iCụ_.J:.uij^ift Lu, .diaị :fcw:Xr.tj3i^- -«J:ii/_
5 KET LUAN
Khung danh gid nay gdn chat che vai cac md hinh phdt trign chung dugc md ta bdi [1]
Mdc du khung đnh gia nay cd nam cdp do nhirag qua nMgu nghien ciiu, phan ticb đ Ugu ciia hgc sinh cho thdy chi cd bdn cdp do cua suy lugn thdng kg
Hgc sinh d cdp dg ! su dung đnh gia chu quan ttong vỉc thyc bien nMem vy thdng kg tap tnmg vdo cac Min thi Widng hgn quan hoac cac y Mdng theo tinh hudng kM tign hanh giai quylt cac vdn dl ve thdng kẹ Hgc sinh d cap do nay chu ygu dua vao thi giac ttong viec dp dyng suy ludn thdng kẹ
Trong ngMen cdu nay, bgc sinh d cdp dg 2 da tinh todn khdng hodn toan hgp ly vd suy lugn chu ylu dya tten du lieụ Diln hinb cua hgc sinh cap do nay la khdng nhdt quan ttong viec su dung thdng tin dinh lugng trong ung dyng thdng kg
Trong ngMgn cuu nay, khdng cd bgc sinh d cap do 3
Hgc sinh d cap dg 4 dua ra cdu tra ldi chinh xac vd thuylt phyc dya ttgn ca hai mat dinh lugng va tinh budng ciia dir Ueu khi suy ludn va so sanh du lỉụ
Trang 6- Ddu tign, hau bet cdc hgc sinh ttong nghien cuu nay da miln cuang td chuc du: lieu
- Thd hai, hgc sinh cd khd khdn ttong viec so sanh hai bd du lif u
Tu nhung kit qua ma hgc sinh da thi hien a bg de kigm tia, chimg tdi nban thdy rang da
sd hpc sinh diu cd kha nang tdt ttong viec dgc dir lieu tten cac bieu do, ddng thdi mgt
sd hgc sinh cung xu ly Mong ddi tdt cac du Ueu bang each so sanh bay su dyng cac phep toan thich hgp vdi tinh hudng dugc dat ra Chii yeu hpc sinh dgt dugc cap do 1 va
2, cdp do 4 cd so lugng hgc sinh dgt dugc it, dilu nay cho thdy kha ndng suy Man thdng
ke cua hgc sinh trung hpc ca sd nhin chung vdn cdn mgt sd ban chg Tuy nhien, day la mpt bai toan khdng quen thudc vdi hgc smh do do kgt qud dgt dugc cbo thay nhung nang luc dang cdn tiem dn ve suy Man thdng ke ttong bgc sinh vdn rat ldn Neu bigt
each khai thdc vk cd su hd ttg hgp ly td giao vien cung nhu chuong ttinh giang dgy tbi
sg la tiln de thuc day cac em tien xa ttong each suy Man, giiip cac em ty tm, cd nhiJng phdn ung thdng minh ttong cudc sdng va ttong cdng viec sau nay
TAI LiEU THAM KHAO
[1] Biggs, J B., & CoUis, K F (1991) Multimodal leaming and intelligent behavior In
H Rowe (Ed.), Intelligence: Reconceptualizafion and measurement (pp 57-76)
Hillsdale, NJ- Erlbaum
[2] Friel, S N., Curcio, F R., & Bright, O W (2001) Making sense of graphs: Critical
factors influencing comprehension and instmctional imphcations Journal for Research in Mathematics Education, Vol 31, pp 124-158
[3] Gai, I & Garfield, J (Eds.) (1997) The Assessment Challenge in Slalislics Education
Amsterdam: lOS Press
[4] Garfield, J., & Ben-Zvi, D (2004), Research on statistical literacy, reasoning, and thmking: Issues, challenges, and unplications In J Garfield & D Ben_Zvi (Eds.),
The Challenge of Developing Statistical Literacy, Reasoning and Thinking
Dordrecht Kluer Academic Pubhshers
[5] Garfiled, J & Chance, B (2000) Assessment in statistics education: Issues and
challenges Mathematics Thanking and Leaming, 2, 99-125
[6] Garfield, J., & Gal, I (1999) Teaching and assessing statistical reasoning In L Stiff
& F R Curcio (Eds), Developing mathemalical reasoning in grades K-12 Reston,
VA: National Council of Teachers of Mathematics
[7] Jones, G A , Langrall, C.W., Thornton, C A,, Mooney, E S.,Wares, A., Jones, M R., Perry, B., Putt, I.J., & Nisbet, S (2001) Using students' statistical thinking to
inform instruction Joumal of Mathematical Behavior, 20, 109-144
[8] Jones, G A., Thornton, C A., Langrall, C W., Mooney, E S., Perry, B., & Putt, I J
(2000) A framework for characterizing sMdents' statistical thinking Mathematics Thinking and Leaming, 2, 269-307
[9] Mooney, E S (2002) A framework for characterizing middle school students'
statistical thinking Mathematical Thinking and Leaming, 4, 23-63
[10] Pratt, D., & Ainley, J (2008) Mttoductmg the special issue on informal inferential
reasoning Slalislics Education Research Joumal, 7(2), 3-4 Retrieved from
http://www.stat.auckland.ac.nz/_iase/serj/SERJ7(2) Pratt Ainley.pdf
Trang 7Title: STATISTICAL REASONING CAPABILITY OF LOWER SECONDARY SCHOOL STUDENTS
Abstract: The purpose of the report is based on the existing research on statistical reasoning to assessment the described statistical reasoning capability of secondary school students We use
an example of using die assessment fl-amework was developed to assess die capacity of statistical inference secondary school students
Keywords: statistical reasoning, performance data, statistical charts
ThS NGUYEN THI PHUONG CHI
DT: 0122 452 5773, Email: phuongchil90386@gmail.com