DOI NET VE NGON NGU^ TOAN HOC Q TtiS TRAN N G Q C B ICH '''' Ngfin ngO ( N N | sii dyng frong gidng dqy, hqc ldp vd nghifin ciiu fr>dn hqc bao gdm ngfin ngu tg nhifin (NNTN) vd ngfin ngi? todn hqe (NNTH)[.]
DOI NET VE NGON NGU^ TOAN HOC Q TtiS TRAN N G Q C B I C H ' N gfin ngO ( N N | sii dyng frong gidng dqy, hqc ldp vd nghifin ciiu fr>dn hqc bao gdm ngfin ngu tg nhifin (NNTN) vd ngfin ngi? todn hqe (NNTH) NNTH duqe nghlSn ciiu hi gii)a thdp nifin cua t h l kl XX Cdc nghifin ciiu v l NNTH xudt hl^n n h l l u d A n h , Ue, mdt sd nude d chdu Au, chdu A vd Bde MT Vi0t N a m , mdt sd nhd nghifin eiiu nhu Phqm Vdn Hodn, NguySn G i a Cde, Trdn Thiic Trinh, Hd ST Hd, d d d l edp d i n vdn d l NNTH; cdc tdc gtd nhu NguySn Vdn Thudn, Nguyin Huu Hdu, d d cdng b d m§t sd bdl v l l t mong Hnh chuyfin khdo v l vd'n de NNTH frong dqy hqc todn d frudng p h d thdng frfin ede hap chf cd uy h'n ehif cdi, ki h/ alphabetic, cde phip todn vd quan h$ duge diing todn hgc C d c yfi'u Id' c o b d n c u a n g d n ngijr todn hqc Gid frl, b l l n , hdm vd b l l u thiic Id nhirng y i u ldcobdncOaNNTH(dl - Gid ti (values) Id n l n tdng eo sd di xdy dyng NNTH Cdc b l l u thiic frjdn hqc d i u duqc h30 ihdnh h i gid trj, tham chieu hi gtd frj Khi d d , gid fri duqc h l l u Id so cuo m$t dql luqng hoy sd duqc thoy t h l bdng mdt kf h i f u - Hdng sd'cOng cd nghlo Id gid trj nhimg nd cd t h l Id m f t b i l n vdi gid frj khdng ddl mqt khodng thdi glan hodc mqt sd md Ghian n i f m v l ngdn n g u todn hqc hinh todn hqc Nhllu nhd nghlen eiiu gido dye quan nifim Todn - Bidn (vorlables) Id mot dqi luqng cd gid trj hqc cOng Id mqt N N Cde tdc gid Phqm Vdn Hodn, b l l n ddi frong qud trinh duqc xet Id sy k i t hop N g u ) ^ Glo Cdc, TrSn Thue Trinh quon nifim: Todn glCra tfin vd gid trj, Id chu duqe sii dyng d l dqf hoc hidu theo mdt nghta ndo dd Id m$t tht/ NN dd difin cho cdc dd'i tuqng lodn hqc mdtdnhOng Hnh hudng c^) thi ndy sinh tnxig nghiin - Hdm (funcHon) Id bien md gid trj cua nd cdu Idioa hgc hay hogt ddng tht/c filn cOa duqc xdc djnh dd bifi't gid trj eOa m f t hay /od/ ngudi (1) Cdn LDlone Miller cho rdng, Todn nhieu bien khdc Hdm cdn duqc eol Id mdt gid trj hge Id mdf NN bag gdm cdc bleu tugng de dien phy thuqc vdo gid frj khdc Cdc gid frj md gid trj dgt chinh xdc Ididl ni$m ca bdn cua todn hgc (2) Clio hdm phy thuqc duqc gqi Id ddl sd (hoy bifi'n Theo O'Halloran, Todn hgc Id m^t /i# thdng cdc ki sd') cuo hdm Mol dd'l sd xdc djnh nhd't mdt hliu da dgng, gdm ede biiu h/gng, NN vd htnh gid frj cuo hdm Hdm cd t h l cd ddi sd hodc khdng dnh trgc quan {3) cd dd'i sd Hdm khdng cd dd'i sd se bj hqn c h i M d l sd nhd nghifin ciiu khdc cung cd quan tfnh ling dyng vi nd ludn cho gid frj gidng nhou d ni$m ve NNTH nhu sou: NNTH tht/e chdt Id nhOng mqi thdi diem Thdng thudng, mql hdm cd m f t gi ngt/dl hgc phdl hgc dd ndl vi ^ tt/dng todn sd c d dinh cdc dd'i sd nhung khdng d6ng frong hgc (4) N t ^ cd t h l dupc hleu Id mdl h f thdng Id'l cd cde frudng h c ^ Thii tg cOo ede dd'l sd xud't cdc thudt ngi/, kf h i f u todn hqc chu y i u d dqng hlen frong hdm rd't quan trqng vi gid frj cuo hdm N N v l l l Cdc kt hifiu ndy cd tinh chdt quy ude d l (x; y) frong mdt so trudng hqp se khdc gid frj dien dqt ndi dung todn hqc, ddm bdo tfnh logic, hdm (y; x) Trong thyc hdnh, cdch b l l u thj: hdm (, et/mft>vd cdc quy tde ket hgp h i f u ngdn gqn hem Bleu luqng d y y ^ atOng ddng Idm phuang tiin didlBn dgt n^l dung cho len hdm dupc viet giiia ^ _^^math'fcSinhgc mgt edeh logic, ehinh xdc, rd rdng Bleu hqn ((tdng' dupc t h e y t b ^ M gdm hinh dnh, hinh ve, sa dS hodc md hinh cda ddi tugng a/ the Ki hliu gdm chu sd Tap chi Glao due so (k* i • n/aon) ^-^ *n»aGHOiltKti&kP^' ^, B Id mft dnh xq thl dnh xq nguqc cOo f Id: f •': B - > A Nhu v$y, Hnh hf thdng frong NNTH khdng chf t h l hifn d ndl dung md cdn d hlnh thiic Khi tdch cdc tii, cym hi frong NNTH ro Ididl hf thdng thl nghTa cOa chung sfi mdt di Dijc h-ung ct)a N N T H NNTH mong ddy du dijc trung ciia mft N N khoo hqc nhu: tfnh don frj, tfnh hf thdng, Hnh qudc t l vd Hnh tniu h/qng r/iii ba, NNTH cd tfnh qudc t l N l u nhu NNTN ( N N Vift} chi mong tfnh dja phuong, h'nh dfin tfc thl NNTH Iql mong Hnh qudc Mf cd v l hlnh thi/c vd ngi? nghTa Ddy Id mdl ddc frung quon Thu nhd't, NNTH ed Hnh don frj, cd nghla Id trqng d l pjidn bift NNTH vdi N N T N vd N N ciJa mdl hi, cym hi ho^Jc kf hifu ehl cd mft nghTo cdc ngdnh khoa hqc khdc Nhd cd tfnh qudc l l nhdt, frong mql vdn cdnh khdc nhou thl nghTa md cdc chuyfin gla todn hqc d cdc qude gla khdc cuo nd vfin khdng thoy ddl Tinh don frj ciia NNTH nhou vfin cd t h l frao ddi vd cCing gldl quylt cdc dd Idm nfin sy khde bift giao N N T N vd NNTH vdn d l todn hqc Trong N N T N , mft hi cd i h l ed nhilu nghTa (hifn Thu tu, NNTH cd h'nh friiu tuqng Tfnh trin) h/qng nghTo) cdn frong NNTH, mdi hi chi cd h/png Clio NNTH thl hifn d ngCr nghTa cija cdc kf mqt nghTa xdc djnh nhdt Chdng hqn, hi hifu, thudt ngCrtodnhqc Cd nhihig hi hong N h ^ Keqnh" frong NNTH dupc hllu Id doqn ldm thdnh mong ^ nghTa khdc vdi nhiing N N st} dyng gioo phdn cua mdl dudng gdp khijc hay mft da gidc Hip hdng ngdy nhu: cqnh hinh torn gidc, cqnh hlnh thoi, cqnh Ngodl ro, NNTH khdng mang sdc thdi tu Kr hinh binh hdnh, Tii «cqnh" N N T N cd rd't bllu cdm Ddy cung Id mft frong nhOng ddc frung nhieu nghTa, chdng hqn: dudng rio cua mqt v^t, khdc bift vdi N N T N Cy t h l , N N T N ihudng sii cqnh bdn, cqnh ghl Trong NNTH, ede hi, kf dyng dql hi nhdn xung, nhung frong Nt^HH dqi hifiu, thudt ngir Id dem nghTa nfin ndl dung ludn hi nhdn xung khdng xudt hifn vd cdc hi chi cd duqc dien dqt chfnh xdc, ngdn gqn vd rd rdng nhdi mqt nghTa nfin khdng xdy hlfin tuqng Tht/hal, NNTH cd Hnh hf thdng Mdl hi, cym ddng nghTa nhu frong Nh^TN hi frong NNTH diu cd vj frf xdc djnh; hich cdc Chiic ndng cua N N T H hi, cym hi dd ro khdl hf thdng thi ede hi dd sS Trong dqy hqc todn, gloo Hip Id mdt ehiic mong mdt nghTo khdc Chdng hqn, tii sKch" frong ndng quan frqng Cd rd't nhilu thdng Kn duqe lodn hqc cd nghTa Id «klt qud eua phfip nhdn" nhinig tdch ro vd sii dyng nhu mft tii frong troo ddi giira gido vlfin (GV) vdi t$p t h l \dp, NNTTNI thl nd Iql cd nghTa Id «ddn, gdp hing ft giiia GV vdi HS, glOo hing HS vdi tdp thl \dp, ddng k l " Tuy nhifin, mqt hi giiia cde HS vdi nhou Chdt luqng hqc tqp cOo xudt hifn frong nhllu ngdnh HS cd lien quon d i n chd'l lupng giao Hep vdl nhung cung mft hf GV, bdl glao Nip Id mdt phuong Hfn d l dqt ldl cym hi chi cd mqt nghTa sy hllu bilt v l todn hqc cua HS Torble, M.Shuard V , frong NNTH cd nghTa Id eho rdng, khdng ed N N thi khdng cd qud frinh ^ , ^ c , bdng — ctJa dudng gioo tllp, khdng ed thdng tin trao ddi thi Idp hqc * nhimg hf ihd'ng sfi khdng dlln Dean cung khdng chnh, rd't khd V cd nghla Id «phqm d l diSn dqt cdc y h/dng h:>dn hqc hodn todn bfing '~ra hoi mdt chd't N N T N , vi vdy, HS thudng xuyen phdi gloo Hip ddl din mqt bdng NNTH (l)Ngu>w thOng Dy hn gi&o3pi Day Id Bfin cqnh chiic ndng gioo tifi'p, NNTH cdn ed ehiic ndng tu Thdi vqy, N N chinh Id hinh thue tdn tql, td phuong tifn vdt chd't d l Tap chi Glao due so (ki i • n/aon) bifi'u dqt tu Do d d , ed the col NNTH Id hifin ihyc trye tiep cua h/ h/dng todn hqe Khdng cd kf hlfiu, thudt n g u todn hqc ndo md Iql khong hifi'u h i f n eOa khdl n l f m hodc tu tudng todn hqe Ngupc Iql, khong ed f nghT, l u tudng ndo Iql khdng duqc the h i f n nhd NNTH Chdng hqn, bie'u thiic {d4 : + - x 3), de Hnh duqc g i d trj cuo bifi'u thiic ndy, ngudi hqe phdl t u NNTH cdn Id phuong H f n d l thyc h i f n q u d trinh t u duy, bleu d q t kfi't qud cOa tu Do dd, cd the khdng d j n h , t u Id cdi duqc bifi'u hifin edn NNTH Id sy b l l u h i f n kfi't q u d c u a tu NNTH, ngudi hqc cdn ndm vung cdc quy tdc, kf h i f u , b l l u h/png todn hqc Tdm Iql, NNTH Id phuang tifin d l dien dqt ndl dung todn hqe m f t cdch logic, ngdn gqn vd chfnh xdc NNTH mong ddc trung cuo N N khoo hqc, cd chiic ndng gioo t l l p vd ehiic ndng tu duy; hjy cd n h l l u d i l m khdc b i f t so vdl NNTN nhung NNTH ed mdt phdn N N T N vd khdng phdi td't cd N N T N d i u cd y nghTa todn hqe.Q (1) Ph^m Van Hoin - Nguyfin Cia CO'c - Trdn Thue Trinh Gl^o dye hpc mdn Todn NXB Gido di^c, Mdt khdc, N N cdn Id cdng cy cua h/ duy, H 1981 fryc Hip thom gla vdo qud frinh hinh thdnh v d (2) L Diane Miler Making the connection with language The Arithmetic Teacher; Feb 1993 phdt friln tu NNTH tham gio vdo qud frinh Research Library gidi quyet cdc vd'n d l fr>dn hqc M q l ^ nghT, hr (3) Gong Wengao - Hong Huaqing - Koh Kim Hong tudng todn hqc chi trd nfin ro rdng, chfnh xdc Incorporating corpus linguistics into content duqc b i l u dqt bdng NNTH, nfi'u khdng, y h/dng teaching: the feasibility of using small corpus in dd se cdn mu mo, chua sdng td Singapore primary Maths teaching, http:// hdl.handle.net/l 0497/182.2005 Cdc binh d i f n nghifin ciiu N N T H Tii vyng Id mqt khfa cqnh quan trqng (4) Clare Lee - Language for Learning Mathematics NNTH Co t h l col: Tdp hgp cdc bli'u tugng, kl Assessment for Learning in Practice Open University hieu, td, ei/m tu dung todn hgc duge ggl Press, 2006 Id tu vgng todn hge Cii phdp (syntax): gidng (3) H^ Si Hd Nhttng v&n di co'bSn cua phuong phtip day vd hpc todn cflip NXB Gido due H 1990 nhu N N , NNTH eung c d cii p h d p rifing Cu (6) Robert Laurence Baber The Language of phdp frong NNTH c d the h i i u Id cdc quy tdc Mathematics Printed in the United Slates of America, kethgp kihieu, tir, ct/m h i thdnh bieu tht/e, cdng 2011 thi/c, minh di, de truyin tdl ngl dung todn (7) Hoing Phe (chCi bifin) TO- di^n Tiing Vi^t NXB hgc vdl chinh x d c cao Chdng hqn, «phdt Dd Ndng - Trung tdm Tie diin hpc, 2010 bifi'u cdng bfing 8" duqc vie't diing eii phdp la: + = Trong N N T H , cde kf hlfiu ddi Tdi li$u tham khdo CO i h l bj d'n dl cdc bieu ihiic N g o d i r a , Mai Ngpe Chilr (chu bifin) - NguySn Thj Ngin Hoa cdc lifin ice't logic «nfi'u t h i " , «khi v d chi k h i " , - D6 Vi$t Hung - Biii Minh Toin Nh?ip mdn ngdn «ean v d d i i " , dupc sii dyng d l ke't ndl cdc y ngtfhpc NXB Gido due H 2007 h/dng hoy khdl n i f m todn hqe nhdm d d m b d o NguySn Thifin Giip (chii bifin) - Do&n Thifin Thuit tfnh ehdt che, chfnh xdc Cdu triic so sdnh «ldn - Nguyfin Minh Thuydt D5n luftn ngfin ngtthpc NXB Gido dtic, a 2005 hem", «nhd hem" cung duqc d u n g d l bifi'u thj Raymond Duval - PierLuigi Ferrari- MaritJohnsen cde quan h f todn hqc Homes - Candia Morgan Language and mathematic, Ngir nghTo (semantics) frong NNTH cd the h i i u CERME 4, 2005 Id ngfiTa cua bliu tugng, kthlfu, thugt ngd, khdl 3Ut^l^ARY nlim, tlin di, dmh ll, tong todn hgc Do Hnh tviathematicai language plays an Important role don frj nen cdc h i , cym h i frong N t ^ H ludn xdc In teaching, learning and researching mathematics dinh v l nghTa, vi t h l , Ididng ed h i f n hjpng d a Therefore, it is necessary to master the theory on nghTa Trong mqt sd trudng hgp, cde ki h i f u , b l l u mathematicallonguage This article presents the funtupng frjdn hqc cd ehiic ndng khdc nhou thuqc damental Issues of this language with a de^re to tDetheoretlcal basis for the process of researching and vdo ngir cdnh Cd t h l cOng mqt h i nhung frong proposlngmefhods to improve the ability to use mathngO cdnh khdc nhou chung se dupe bleu thj dudi ematical language in teaching and learning mathcde dqng khdc nhou Do d d , d l h l l u dupc nghTa ematics in primary schools Tap chi Glao due so (kt i • n/aoia)