Tran Ngpc Bfch Tap chi KHOA HOC & CONG NGH$ 135(05): 75-
VAI N E T T I N H H I N H N G H I E N ClTU VAN DE N G O N N O C T O A N H O C TrSn Ng9C Bfch Trudng Dai hge Suphgm - DH Thai Nguyen TOM T A T
Tren the gidi da co rat nhieu nghien ciru \k m6i quan he giua ngon ngu su dung h^ng ng^y vdi ngon ngii toin hpc, nhCJng khd khan vl ngon ngir mi HS thucmg gSp phai trong hoc toan, van dl ngon ngOtoin hpc trong chucmg trinh mon Toan d mpt so nude tren the gioi... O Viet Nam da co mpt so nha nghien ciiu quan tam din van dl ngon ngit toan hpc va viec su dung ngon ngir todn hpc trong nhi trucmg phi thong. Bai viit t6ng quan tinh hinh nghien ciru van de ngon ngii toan hpc trSn the gidi va Viet Nam vdi mong muon ggi ra nh0ng djnh hudng nghien ciiu dl ngay cing co nhieu han nhOng ket qui nghien ciru ve ngon ngiJ toan hoc va vi^c sir dung ngOn ngit toin hpc trong thuc tien day hpc,...
Tii khda: ngdn ngU, ngon ngd^ todn hoc, d<^ hoc, day hoc mon Todn. gido due hoc loan hge.
DAT VAN DE
Trong day hpc mdn Toan, van de ren luyen kha nang sir dyng chinh xac ngdn ngii' toan hpc (NNTH) cho hoc sinh (HS) chiem mdt vi tri rat quan trpng bdi "toan hpc hieu theo nghTa nao dd la mpt thii ngdn ngir de md ta nhirng tinh huong cu the nay sinh trong nghien cii'u khoa hpc hoac trong hoat dpng thyc tien ciia loai ngudi"[5]. "Day hpc toan xet ve mat nao dd la day hpc mot ngdn ngii, mpt ngdn ngii dac biet, cd tac dung to Idn trong viec diln ta cac su ki?n, cac phuang phap trong cac ITnh vuc rat khac nhau ciia khoa hpc va hoat dpng thuc tien" [I].
Tren thi gidi dS cd rat nhilu nha nghien ciiu quan tam din vSn de NNTH va su can thiet cua NNTH trong giang d&y va hpc tap toan. (IJ Viet Nam cd da cd mpt so cdng trinh nghien Cliu de d p den khia canh NNTH va van de NNTH trong d^y hpc mdn Toan d tru'dng pho thdng.
NOI DUNG
Tong quan tinh hinh nghien cihi van de ngon ngir toan hpc
Tren the gi&i
NNTH ddng gdp dang ke vao viec hge tap toan ciia HS. NSm 1952, Hickerson da nghien Cliu y nghTa cua cac ki hieu so hpc dugc hinh
Tel: 0904 321939. Email. bichtranspin@gmail com
thanh trong gid hpc toan cua HS. Tuy nhien nghien ciiu nay khdng dugc quan tam ma den tan nhimg nam 1970 thi NNTH mdi bat d4u dugc nghien ciru mot each cd he thdng trong moi quan he vdi NNTN. Chang hiin, Waywood (1986) da nghien ciru nhirng anh hudng cua NNTH den HS trung hpc ca sd bang each ghi nhat ki vao cuoi mdi tiet hpc toan trong suot thdi gian bdn nam. Nghien ciru ciia Stigler va Baranes (1988) ve viec su dung NNTH ciia HS tieu hpc d Trung Qude, Nhat Ban, Han Qude va My. Nghien ciiu cua Sullivan va Clarke (1991) ve nang cao chat lugng sii dung cau hdi trong ldp hpc toan de HS ti'ch cue tham gia, tren co sd dd phat trien NNTH [14].
Martin Hughes (1986) da nghien ciiu nhung khd khan ve mat NNTH ma cu the la cac ki hieu sd hpc trong viec hpc tap toan ciia HS [13].
Rheta N Rubenstein (2009) nghien cii'u vl ki hieu toan hpc va nhan thay ki hieu la mdt yeu td quan trpng cua NNTH trong hpc tap mdn Toan d mpi cap hpc. Ki hieu la cdng cu bieu dien cac quan he va giai quyet van de toan hoc. Tren:co sd dd tac gia de xuat mot sd giai phap hd trg GV khac phuc khd khan ciia HS trong hoc tap toan ve phuang dien cu phap va ngii nghTa ciia NNTH [16],
Charlene Leaderhouse (2007) da nghien ciiu ve NNTH va su hiiu bilt NNTH ciia HS Idp 6 trong hpc tap Hinh hge. Tren ca sd dd, tac 75
Tran Ngpc Bich Tap chi KHOA HOC & CONG NGHS 135(05): 75- gia nhan thay kha nang hieu, sir dung chinh
xac cac thuat ngii toan hpc se hd trg rat nhieu cho sir hiiu biet vl khai niem toan hoc va trong hpc tap HS can cd dugc nhirng co hdi thao luan y tudng, thuc hanh sir dung NNTH [7].
Diane L. Mille (1993) nghien cim ve vai trd ciia NNTH trong phat trien cac khai niem toan hpc va su ket ndi ciia ngdn ngu' khi tieng Anh la ngdn ngu" thir hai ciia ngudi hpc [9].
Eula Ewing Monroe va Robert Panchyshyn (1995) nghien cuu ve van de tir vung cua NNTH va neu len su can thiet ve tir vung cua NNTH trong phat trien cac khai niem toan hpc [10].
Cung nghien ciru ve van de tir vung cua NNTH, David Chard (2003) xay dung ke hoach phat trien tir vung trong hpc tap toan va nhan thay NNTh la phuong tien rk quan trpng giiip HS phat triln cac khai niem mdi.
HS hge tap toan tdt nhSt bang each sd dung NNTHva sir hiiu biet ve NNTH dl ren luyen kT nang ndi, viet trong dien dat khai niem toan hge [8].
Mat khac, mpt sd nha nghien ciru giao due da quan tam din v4n de NNTH trong chuang trinh mdn Toan cua mot sd nude. Chang han, Mihaela Singer (2007) da nghien ciru vin dk NNTH trong chuang trinh giao due pho thong mdn Toan cua Rumani. Trong nghien ciiu tac gia khang dinh "Giao tilp biing NNTH" la mdt trong bdn muc tieu giao due mdn Toan, dugc thuc hien bat dau tir ldp 1 cho din ldp cudi ciing ciia giao due phd thdng. Ngdn ngu la phuang tien de bilu dat tri thiic toan hpc, do do viec giup cho HS "cd kien thiic va kT nang sOr dung cac khai niem toan hge" cung ddng nghTa vdi viec hinh thanh, su dung NNTH mpt each chinh xac. rd rang. Ddng thdi NNTH cdn la cdng cu, phuang tien dl HS su dung trong khi giai quyet vkn dl va ap dung toan hpc vao thuc tiln. Birgit Pepin (2007) nghien ciru chuang trinh giang day quoc gia cua nude Anh ve NNTH. Tac gia nhan thiy ngay tir cap liiu hpc (KSl va KS2) Chuang trinh da chii y din van dl ngdn ngff 76
ndi chung va NNTH ndi ri§ng. CJ giai d o ^ dau (KSl), HS sii dung diing ngdn^ ngir, ki hieu, tir vung trong hpc t^p mdn Toan; sij dung ndi, viet dimg ngdn ngff thdng thudng va sau do la NNTH. Giai doan sau (KS2) HS giao tilp bang NNTH bao gdm ca viec str dung chinh xac NNTH. Ben canh do cac tac gia da nghien ciiu khia canh ngdn ngu" va giao tiep, trong dd cd de cap den NNTH, trong Chuang trinh mdn Toan ciia mpt sd nude nhir Sigmund Ongstad (2007) nghien cim vl Chucmg trinh giao due mgn Toan ciia Nauy, Brian Hudson va Peter Nystrdm (2007) nghien Cliu Chuong trinh mdn Toan ciia Thuy Dien,...
Hon nii'a, ngdn ngii la phuang tien ciia giao tiep nen Sullivan.P va Ciarke.D (1991), Dean.PG (1982), Torbe.M va Shuard.H (1982) da nghien ciiu ve van de giao tiep bang NNTH trong bgc tap mdn Toan ciia HS.
Cac nha nghien ciru da khSng djnh khdng co NNTH se khdng cd qua trinh giao tiep trong ldp hoc toan va toan hpc khdng the dien ra.
Ngoai ra cdn rat nhieu nha nghien cii'u quan tam din vin de NNTH va anh hudng ciia NNTH trong hpc t§p mdn Toan ciia HS nhir Marilyn Bums (2004), Raymond Duval (2005), Robert Laurence Baleer (2011), Chad Larson (2007),...
Dac biet, trong nhirng nam gan day, Hiep hpi Chau Au vl nghien ciiu Giao due Toan hpc (CERME) da thanh lap ra cac Tiiu ban nghien ciru nhirng vin de khac nhau, trong d6 cd mpt tieu ban chuyen nghien ciru vl vSn dl Ngdn ngir va Toan hpc. Trong CERME 4 (2005) da trinh bay cac kit qua nghien ciiu vl Ngdn ngu va Toan hge cua cac tac gia nhir Raymol Duval va cpng su, Jenni Back, Valeria, ...[15].
Mdt chuang trinh cd tinh toan ciu (hien nay da cd tren 65 nude va lanh thd tham gia, trong dd cd Viet Nam) gpi la chuang trinh PISA, khao sat giao due duy nhit chi chuyen danh gia vl nang lire phd thdng d dp tuoi 15 vdi 3 ndi dung: Dpc hiiu, toan hpc, khoa hpc. Danh gia hieu bilt cua HS ve nang luc toan hpc
Tran Ngpc Bich Tap chi KHOA HOC & CONG NGHE 135(05): 75- theo 3 cap dp (ghi nhd, tai hien; ket ndi va
tich hgp; khai quat hda, toan hpc hda) vdi 7 kT nang: tu duy va lap luan toan hpc; giao tiep toan hpc; md hinh hda toan hpc; dat va giai quyet van de; bieu diln; sir dung ki hieu, ngdn ngii' va cac phep tinh hinh thirc; sii dyng phuang tien va cdng cy. Cac cap dp va kT nang toan hpc ciia HS theo PISA diu rit quan tam tdi cac ylu td NNTH.
6 Viet Nam
(j Viet Nam, van de NNTH cung da dugc nghien ciiu va van dyng vao thuc tien giang day d cac khia canh khac nhau nhung nhin chung mdi chi la nhii'ng nghien ciru so luge ban dau. Sau day la mgt sd ket qua nghien ciiu lien quan den NNTH va viec van dung NNTH trong day hpc mdn Toan d trudng phd thdng.
Cac nha nghien cuu Ph^m Van Hoan, Nguyin Gia Cdc, Tran Thiic Trinh (1981) khang dinh
"the hien diing dan mdi quan h? giira npi dung tu tudng toan hge va hinh thirc NNTH la mpt CO sd phuang phap luan quan trpng cua giao dye toan hpc". Cac tac gia trinh bay ba diem khac biet giQ-a NNTN va NNTH: thir nhat, trong NNTH mpt dau chLi sd, chii cai, dau phep tinh hay dau quan he bieu thi dieu ma NNTN phai diing din tir hay mdt ket hgp tir mdi bilu thi dugc, dieu dd Iam cho NNTH gpn gang han so vdi NNTN; thii' hai mdi ki hieu toan hge hay mdi ket hgp cac ki hieu deu cd mdt nghTa duy nhat, dieu dd Iam cho NNTH cd kha nang dien dat chinh xac tu tudng toan hpc han hin NNTN; thir ba NNTH cd dimg den ngdn ngS bien dieu dd cho phep NNTH rSt thich hgp de khai quat dien dat cac quy luat chung: nhitng hinh thiic tuy cd ngi dung khac nhau nhung ciing dugc dien dat nhu nhau [5].
Tac gia Ha ST Ho (1990) da trinh bay mdt sd dac diem ciia NNTH. Cu thi: NNTH chu ylu la ngdn ngit sii dung ki hieu; NNTH khdng phai la ngdn ngii' "Idi ndi" ma chii yeu la ngdn ngii' "viit"; NNTH vira chat che vira uyen chuyin [3].
Tac gia Hoang Chiing (1994) nghien ciru ve NNTH va viec sCi' dung NNTH trong SGK Toan cip 2. Theo tac gia thi cac thuat ngii-, ki hieu toan hpc dugc hinh thanh va phat trien trong qua trinh hinh thanh. phat trien ciia cac khai niem toan hpc va phuang phap giai cac bai toan; Mdt thuat ngir, mpt kl hieu phan anh ciing mdt khai niem, cd the dugc djnh nghTa theo nhieu each tuang duang nhau. Tac gia luu y khi dimg cac ki hieu toan hpc can phan biet: nhung ki hieu phai diing nguyen ven, khdng thay ddi; nhii'ng kl hieu nen dimg (tuy cd the thay bang ki hieu khac) vi da quen thupc vdi nhieu ngudi; nhung ki hieu cd the tiiy y chpn. Theo tac gia qua trinh phat trien toan hpc ludn ddi hdi phai md rpng, thay ddi mpt khai niem, keo theo viec md rdng, thay ddi each hieu ddi vdi mdt thuat ngii-, mdt ki hieu; Trong toan hpc cd the diing cac ki hieu khac nhau de chi ciing mdt ddi tugng nhung khdng dugc diing mdt ki hieu de chi hai ddi tugng khac nhau trong ciing mot van de [I].
Cac tac gia Ha ST Hd, Do Dinh Hoan, Dd Trung Hieu (1998) da de cap den van de NNTH trong tai lieu Phuang phap day hoc Toan (tap 1). Theo cac tac gia, viec xay dung mdt ngdn ngu" khac phuc dupc cac nhugc diem cua NNTN (thudng dai Idi khien khd nam mdt lire dupc nhieu y, phy thudc vao nhiing yeu td cam xiic lien quan den y, gay ra tinh trang hieu khdng thdng nhat, gay khd khan suy luan chinh xac, ..) va thich hgp vdi viec dien dat npi dung toan hpc la can thiet.
Dd la NNTH. Trong toan hpc, cac ki hieu dugc sap xep theo nhirng "quy tac ngii phap"
thanh bieu thirc hay cdng thirc dien dat cac ddi tugng hay menh de toan hpc. Trong NNTH cung cd nhung "tir ddng nghTa" nhu trong NNT7<, dd la nhirng ki hieu khac nhau nhung chi cimg mdt ddi tugng [4].
Nguyin Van Thuan (2004) da de xuat cac bien phap su pham nham phat trien tu duy logic va sir dung NNTH chinh xac cho HS trung hpc phd thdng trong day hoc Dai sd [6].
Cdn Nguyen Hiiu Hau (2011) da de xuat cac 77
Tran Ngoc Bich Tap chi KHOA HOC & CONG NGHE 135(05): 75-81 bien phap de phat triln NNTH cho HS trong
qua trinh day hpc Toan d trung hoc phd thdng va ren luyen cho HS kha nang van dung kien thiic toan hpc vao cac bai toan thuc tien [2].
Cac tac gia Dao Tam, Nguyen Van Lpc, Dinh Tan Phudc cung da van dung tiep can ngdn ngir trong day hpc mdn Toan d trudng Trung hoc phd thdng, khai thac cac phuang phap khac nhau trong giai toan, thiet lap qui trinh cdng nghe day hpc.
Pham Gia Diic da khai quat vai trd thao tac day hpc ngdn ngir ki hieu hinh ve trong day hpc hinh hoc cap Trung hpc co sd; Biii Huy Ngpc coi trgng viec ren luyen ngdn ngO' trong day hge toan d Trung hpc ca sd nhu mdt each thirc de tang cudng cho HS kha nang iing dung toan hge trong day hpc mdn Toan d Trung hge ca sd; Le Van Hdng van dung quan diem ngdn ngii trong each tiep can bieu thirc dai sd de hoan thien ndi dung va phuang phap day hpc chii de nay d trung hpc ca sd, mdi day tac gia da nghien ciru van de "Hd trp chat lupng day hpc mdn Toan d trudng pho thong theo hudng tiep can ngdn ngii".
Van de NNTH d tieu hpc, da cd nhieu tac gia quan tam va nghien ciiu kha sau sac, nhu: Vii Qude Chung, Dd Trung Hieu, Dd Dinh Hoan da neu quan niem tdng quan va nhiing dinh hudng can thiet ve day hge NNTH cho HS tieu hoc; Pham Thanh Tam da danh rieng cho thao tac ngdn ngU ki hieu mdt vai trd dang ke trong qui trinh day hpc Toan d tieu hpc bat dau tir thao tac tren dd vat ket hgp vdi ngdn ngir (ldi ndi) den md hinh, sa do va ki hieu toan hpc. Tran Ngpc Bi'ch (2013) da de xuat nhirng hien phap giiip HS cac ldp dau cap tieu hpc sir dung hieu qua NNTH. Mdi day. Thai Huy Vinh da cdng bd ket qua nghien ciiu ve ren kT nang sii dung NNTH trong day hpc mdn Toan ldp 4, Idp 5 cho HS. Ket qua nghien ciiu cCia Tran Ngpc Bich va Thai Huy Vinh da gdp phan hoan thien he thdng kit qua nghien ciiu ve NNTH trong day hpc mdn Toan d tieu hoc.
Nhu vay, tren the gidi, van dk NNTH, vai trd va nhirng anh hudng cua NNTH din qua trinh
hpc tap ciia HS da dugc nhilu nha nghien cini quan tam. 0 Viet Nam, NNTH budc dau ^ dugc dl cap den nhung chua cd tac gia va cdng trinh khoa hpc nao nghien ciiru sau va toan dien van dl nay vl ly lu^n, thuc tien.
Ntivng van de chua diroc de cap nghien cihi Tren thi gidi da cd rat nhieu nghien ciiu ve NNTH trong hpc tap toan ciia HS phd thdng.
Tuy nhien cdn mpt vai vin de sau chua dugc de cap nghien ciru. Cu the
- Mdt CO sd ly thuyet chung nhat ve NNTH - T90 mdi trudng hpc tap thuan tiSn cho vi§c phat trien va ciing cd lien ket giiia cac ho^t ddng trong cudc sdng hang ngay vdi NNTH de giiip cho cac kien thiic toan hoc dugc lini giii lau dai. Cac lien ket nay giup ngudi hpc cd the giai quyet van de mdt each sang tao.
0 Viet Nam, van dk NNTH chua thuc sir nhan dugc sir quan tam cua cac nha khoa hpc.
Cd rit it cac cdng trinh nghien ciiu ve su phat triln NNTH ciia HS phd thdng trong hoc tap toan. Chiing tdi dua ra mgt sd van de chua dugc de cap nghien ciiu nhu sau:
- Van de ngdn ngU trong chucmg trinh Toan hpc phd thdng. Cac yeu td NNTH sir dung trong sach giao khoa Toan va nhirng de xuat cho chuang trinh giao due phd thdng sau nam 2015.
- Sy hieu biet, miic do van dyng NNTH cua giao vien trong day hge mdn Toan d trudng phd thdng hien nay va nhirng bien phap gop phan nang cao nang luc sir dung NNTH trong day hpc.
- Nang luc giao tiep bang NNTH ciia giao vien va HS trong cac gid hpc toan d nha trudng phd thdng.
- Can thiet phai cd mdt sd bien phap giup HS phat trien NNTH, gdp phan nang cao ket qua hoc tap mdn Toan cho HS. Ching han, nang cao vdn tir vung toan hpc, giiip HS dpc, viet va ndi toan de hieu, khac sau cac khai niem, djnh li, djph nghTa,... trong toan hge.
- Su chuyen tiep NNTH gi&a cac cip hpc pho thdng trong day hpc mdn Toan hien nay cin
TrSn Ngpc Bich T?p chi KHOA HOC & CONG NGHE 135(05): 75-80 dugc quan tam. Nghien ciiu djnh hudng din
vi?c khai thac vdn NNTH da cd ciia HS dk tir dd ren luyen, phat triln kT nang sir dyng NNTH trong hpc tap mdn Toan.
KET LUAN
Van de NNTH can dugc quan tam nhilu han niia trong giang day, hpc tap va nghien ciru.
Do do nhirng ket qua nghien ciiu dugc tong quan d tren sS la tiln dl, la ca sd cho viec nghien ciiu NNTH trong giai do^n tilp theo.
Dac biet, cin cd nhiing kit qua nghien ciru Iy luan chung nhat vl NNTH, vai trd ciia NNTH trong thuc tiln, ... Mat khac, vdi yeu ciu phat trien chuong trinh, sach giao khoa sau nam 2015 theo djnh hudng ddi mdi can ban, toan di?n giao dye dao t?o thi viec tilp can ngdn ng& ndi chung va NNTH ndi rieng trong day hpc d trudng phd thdng, sy kl thira va phat triln NNTH giua cac cip hpc cin tilp tuc dugc quan tam, nghien cuu.
TAI LIEU THAM K H A O 1. Hoang Chiing (1994), Mgl .sd vdn di vi gidng dgy ngdn ngit vd ki hifu todn hge a truang phd thdng cdp 2, Bp Giio due va Dao tao, Vy Gido vien. Ha Npi,
2. Nguyin HOu H^u (2011), Tap luyen cho hoc smh phdt Irlin ngdn ngii- todn hge trong qud trinh dgy hge Todn, Tap chi Giio due, so 253.
3. Ha ST H6 (1990), Nhung vdn di co bdn ciia phuongphdp dgy hge cdp 1, Nxb Gido due.
4 Ha ST Hi, D6 Trung Hieu, Do Dinh Hoan (1998), Phuang phdp dgy hpc Todn, Nxb Giao dye
5. Pham Van Hoan, Nguyen Gia Coc, Tran Thiic Trinh (1981), Gido due hge mdn Todn.^'Hxb Giao due.
6. Nguyin Van Thugn (2004), Gdp phdn phdi trien ndng luc lu duy Idgic vd sir dung chinh xdc ngon ngir todn hoc eho hoc sinh ddu cdp Trung hoc phd thdng trong dgy hoc Dgi sd, Luan an Tien sT khoa hpc Giao due, Dai hpc Vinh.
7. Clare Lee (2006), Language for learning Mathematics Assessment for learning in Practice, Open University Preess.
8. David Chard (2003), Vocabulary strategies for the Mathematics classroom, Houghton Mifflin Math.
9. Diane L. Miller (1993), Making the connection wilh language. The Arithmelie Teacher, Researching Library, pg 311.
10. Eula Ewing Monroe, Robert Panchyshyn (1995), Vocabulary considerations for teaching Mathematics childhood Education; 72, 2, Pro Quest Education Journals pg 80
11. Ken Winogard, Karen M. Higgins (1994), Writing, reading and talking mathematics: One interdiscipl, (In) The reading teacher. Research Library, pg 310.
12. Madeline Kovarik, Building Mathematics Vocabulary,
In www.cimt Plymouth ac uk/joumal/kovarik.pdf 13. Martin Hughes (1986), Children and number, Blackwell Publishing,
14 Nerida F. Ellerton, M.A. Clement (1991), Mathematics in language A review of language factor in Malhemalies learning, Deakin
University.
15. Ray mond Duval et. al. (2005), Language and Mathematics, CERME 4.
16. Rheta N. Rubenstein (2009), Mathematical symbolization: Challenges across levels, in:
http/tsg.kme 1 l.org/document/get/853
Tran Ngpc Bich Tsip chi KHOA HOC & CONG NGHE 135(05): 75 - SUMMARY
OVERVIEW OF THE RESEARCHING SITUATION ABOUT MATHEMATICAL LANGUAGE PROBLEM
Tran Ngoc Bich*
College of Education - TS i There are a lot of researchs in the worid on the relationship between everyday language and mathematical language, difficulties in language that smdents often encounter in math, mathematical language problems in mathematics program in some countries in the world ... . There were some researchers in Vietnam interested in mathematical language problems and the mathematical language useing in secondary schools. This paper is an overview of research of mathematical language problems in Vietnam and the world to expect a suggesting of researching directions for more than results of research on mathematical language, application of mathematical language in teaching practice
Keywords: language, mathematical language, leaching, teaching Maths, mathematical education
Ngiiy nhdn bdi:25/l 1/2014; Ngdy phan biin. 15/12/2014; Ngdy duyet dang: 31/5/2015 Phan bien klioa hoc: TS. Le Thi Thu Huang - Tru&ng Dgi hoc Suphgm • DHTN
Tel. 0904 321939, Email: biclitransptn@gmail com
