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[.]
NANG LV^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 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 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 [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 thdng ke Ben canh do, cac dinh nghTa ve bigt dgc thdng ke, suy luan thong ke va M 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 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 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 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 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 phan dnh sy tbay ddi ttong 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 gdm vigc dgc ro rang cdc du Ueu thd (chua qua xu li), dd ligu ttong cdc bdng sd lieu, bieu 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 ISSN 1859-I6I2,S6 04(28)/2013:tr 125-131 NGU'YEN THI PHirONG CHI lieu" nhu giai dogn dau cua viec pMgn dich va phan tich dir Ueu Kha ndng dgc nhiing hiln thi cua du heu trd co sd cho viec bdt ddu tao cac dy doan vd tim cac xu hudng Hai qua trinh sau Ugn quan den viec md ta du lieu: (a) chi 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 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 tam va phdn tan la huu ich ttong viec tao 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 Uen quan din viec hign thj du Ueu dgng bieu [2] cho rdng cam gidc bigu dd cdn den ttong viec trinh bay dd lieu "bao gdm viec xem xet cai gi tham gia 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 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 cac xu hudng va cac dy bao Ciing nhu vdy, nhihig hien tbi dit lieu khac cd the truyen tai nhung y Mdng khac 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 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 la cdt loi ciia suy ludn thdng ke, bao gdm viec nhgn cac quy lugt vd cac xu hu&ng ttong dd ligu, dua 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 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 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 khung suy ludn thdng ke dgc tnmg cbo suy lugn cua hgc sinh qua bon cdp dd: cap dg (mang tinh chu quan (idiosyncratic)), cdp (chuygn ddi (transitional)), cdp (dinh lugng), cap (pban tich) Cdp dp Suy lugn cua hgc sinh d cdp 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 the bi phan tdm hoac hi nham ldn bdi cac khia canh cua van de Muc Mang iing vdi NANG LUC SUY LUAN THONG KE CUA HQC SINH TRUNG HOC CO SO cdp dd tru&c cdu tnic (prestructural) Cap dp Hgc sinh bdt dJtu nhan 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 thudng chi tap trung vdo mgt khia cgnh ciia vdn de Trong md hinh cua Biggs va CoUis, ddy la cdp 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 khdng hgp nhdt Igi cac y Mdng toan hgc 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 mdt cdu tnic cd y nghTa Day la nhimg gi ma [1] ggi la cap quan he CAC PHU'ONG PHAP NGHIEN COU Chung tdi tiln hanh ngMgn cuu dudi dgng ly thuylt, tii dd dua mdt bang chi tilt khung ddnh gia suy Man tiiong kg Ben canh dd, chung tdi dua mdt bai kiem tta gdm bai toan, tiln banh khdo sdt 155 em hgc smh ldp va cua tmdng Trung hgc ca sd Nguyen Du, phd Hui dg xem phdn dng cua hgc sinh nhu thi ndo Do sy hgn chg cua bai bao, chung tdi chi ttich 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, cd cbuyen luu diln 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 Cdp d? Cau trd ldi dy kiin Lady Gaga vi dai cpt cong lai dai nhdt Eminem vi sd buoi bieu diln khong nhieu so vdi nhiing ngudi khac nhung so tien kiem duac nhieu nhat NGUYEN THI PHUONG CH! Cap dp Cap dp Madonna \i l> le giua so tien kiem dugc va buoi bieu dien la 3:1 nhitag ngudi khac la 5:13, 8:5, 8:3 Madonna vi thu nhap moi buoi bieu dien ciia cd ia nhieu nhdt trieu la, nhimg ngudi khac la khoang 0,38 trieu la, 1,6 trieu dd la va khoang 2.18 trieu la Phdn tich tru&c thuc nghiim: Bai toan lien quan dgn cdu hdi "thi nao la cbuyen luu diln 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 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 mgt suy ludn va nit kgt ludn hgp ly, vdi luu > rang suy Man dua la Madonna cdng nhdt Do dd, bai toan dugc xep vao mdc dO cao KET QUA NGHIEN CUU Ket qua cy the dugc ihdng kg nhu sau: Cap Cap Cap Cap Cap S6 p h a n t r a m hoc sinh d a t tirng cSp 25.13% 62.54% 12.33% : Ddy Id bdi toan d mirc cao Trong bai toan nay, tat ca bgc sinh deu tra ldi chd khdng de trdng Dieu cho thdy cac em khd tMch thu vdi nhiing dgng bai toan nhu thg hoac cimg cd the tinb budng bdi khd gan vdi nhiing mdi quan tam cua cac em cudc sdng Cac em d cap deu tra ldi diing nhu du kien cua chung tdi nhung khdng em nao giai tMch nhu dy kien Trong trudng hgp cac em khdng kit hgp hai bigu ma cM xet theo y kien chu quan ve viec thg nao la "chuygn luu diln cdng" nhu bai Iam sau: C-^AillCi-Ciai, ^ Lccrl! i L., A.^^.L^y 10^ JfUiiii Cd -^.C^.-JtlK^ j»LiV £iCiA3 MJt\aJA Ct^^ Da sd cac em dgt dugc cdp Day la mdt van de mdi ddi vdi bgc sinh trung bgc ca sd d nude ta Viec so sanh giiia bai bieu cd lg kMen hgc sinh liing tiing rdt nMlu .^»fl._^luiL.ik J L - bcflu :k :SiDij A^\t pMLk .C£i(w ^d.L.4A',.„^jxi;iiiQi ^^ QQ lid c£ t.tu»i.av- yk £Ji« >ia;i-v c«i:t qim.„c.ar C^-JL] "Lhuiiij iil„-ki^ k.si^ rttC- JaL-nfiictt o-tiCiL NANG H.rc SUY LUAN THONG KE CUA HOC SINH TRL-NG HOC CO SO .dia^—qW- -L^ AZ.-.Sb-y.h.-s.^ ,-.-^ , J ,-: ; „ ^ ^j^-~ £;nM.f.;./i:L -i:ii3 ct- i» -^iZ'-.-.:.'L-'^ ^4.- C-i';^ ii \xZiUC.:X I'i Khdng cd hgc sinh nao dgt dugc cdp dg Cap cung chi cMlm ban 1/10 sd lugng cac em tham gia ttong nghien cuu Dieu cho thdy, kbd nang suy ludn cua cac em chua phat huy dugc ttong nhihig tnrdng hgp cdn phan ticb, ly giai va dua nhdn xet Chung tdi cho rdng, ddy la mOt kgt qua qua trinh dgy va hgc M?n 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 ddng Qua nhihig bai lam cua bgc sinh dgt dugc cdp 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 4: ^iLuC-iifl , WBicvJix Li.- d j i i ^ tuu itiji ri,^A^ L^ ,,.jkixi.^ Ut ; t»(M uJu &aaa , -.U^^ !P.ajk - i^ Eam:fa ^jaci ^vai ^iUJ Aim ML dtiSi i.io«j 3Ufuim jjinu Wo(k-atii ^.ju:' Ji :iuu( M^ s.uor ;;;), (yjvi30«a._.iCu._.J:.uij^ift Lu, .diai :fcw:Xr.tj3i^- -«J:ii/_ KET LUAN Khung danh gid gdn chat che vai cac md hinh phdt trign chung dugc md ta bdi [1] Mdc du khung ddnh gia cd nam cdp nhirag qua nMgu nghien ciiu, phan ticb dd Ugu ciia hgc sinh cho thdy chi cd bdn cdp cua suy lugn thdng kg Hgc sinh d cdp dg ! su dung ddnh gia chu quan ttong vi?c 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 ke Hgc sinh d cap chu ygu dua vao thi giac ttong viec dp dyng suy ludn thdng ke Trong ngMen cdu nay, bgc sinh d cdp dg da tinh todn khdng hodn toan hgp ly vd suy lugn chu ylu dya tten du lieu Diln hinb cua hgc sinh cap la khdng nhdt quan ttong viec su dung thdng tin dinh lugng ung dyng thdng kg Trong ngMgn cuu nay, khdng cd bgc sinh d cap Hgc sinh d cap dg dua cdu tra ldi chinh xac vd thuylt phyc dya ttgn ca hai mat dinh lugng va tinh budng ciia dir Ueu suy ludn va so sanh du li?u Mgt vai khia cgnh cua suy luan thdng ke cdn phai dugc khao sat ky ban: NGUYEN TH! PHUONG CHI - Ddu tign, hau bet cdc hgc sinh ttong nghien cuu 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 Chii yeu hpc sinh dgt dugc cap va 2, cdp cd so lugng hgc sinh dgt dugc it, dilu 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 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 TAI LiEU THAM KHAO [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] 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 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 Gai, I & Garfield, J (Eds.) (1997) The Assessment Challenge in Slalislics Education Amsterdam: lOS Press 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 Garfiled, J & Chance, B (2000) Assessment in statistics education: Issues and challenges Mathematics Thanking and Leaming, 2, 99-125 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 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 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 Mooney, E S (2002) A framework for characterizing middle school students' statistical thinking Mathematical Thinking and Leaming, 4, 23-63 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 NANG LUC SUY LUAN THONG KE CV^A HOC SINH TRUNG HOC CO SO Title: 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 ... LUC SUY LUAN THONG KE CUA HQC SINH TRUNG HOC CO SO cdp dd tru&c cdu tnic (prestructural) Cap dp Hgc sinh bdt dJtu nhan tdm quan trgng cua suy Man ve sd lugng nhung mdu thudn ttong vi^c su dung suy. .. nhu vay Suy ludn cua hgc sinh d cdp dd thudng chi tap trung vdo mgt khia cgnh ciia vdn de Trong md hinh cua Biggs va CoUis, ddy la cdp mgt cdu true (unistrucMral) C6pdg3 Suy luan cua bgc sinh la... khung suy ludn thdng ke dgc tnmg cbo suy lugn cua hgc sinh qua bon cdp dd: cap dg (mang tinh chu quan (idiosyncratic)), cdp (chuygn ddi (transitional)), cdp (dinh lugng), cap (pban tich) Cdp dp Suy