I d NGHItNCAU-
REN LOYEN CHO NGO0I HOC CAC HINH THUfC CHOYEN DOI NGON NGO DllN DAT BAI TOAN NHAM DOI D O S N G NANG LOC PHAT HIEN GIAI PHAP GIAI QOYET VAN DE
1. Dat van d l
Trong day hpe (DH) Toin, cd nhung vin de trong trang thai ban d i u , ngfldi hpc khd phat hifn ra giii phip gill quyft van d l (GQVD). chuyen doi ngdn ngfl (CONN) la mdt trong nhflng djnh hfldng giup ngudi hpc tim gill phip GQVD. Tuy nhifn, vifc hieu ngdn ngfl dien dat v i lya chpn ngdn n g f l d i dien dat lai bai toan vdi ngfldi hpe l i m d t v a n d l .
Vifc ren luyfn cho ngfldi hpc biet mdt sd hlnh thflc CDNN dien dat bii t o i n se giup hp tim tdi, phit hiln nhflng kiln thfle mdi liln quan den chii d l trong nhflng tinh hudng hpe t i p ; lim tang khi nang lifn tfldng, nhin nhin vin d f dfldi nhifu gdc do. Wee sfl dyng d c loai ngdn ngfl khic nhau trong td chfle DH d c kiln thiic Toin hpe khong chi giflp rfn luyfn cho ngfldi hpc nang luc (NL) difn dat ma cdn khai thic tiem ning phong philj cfla cie phflong phap toan hpc d moi loat ngdn ngfl.
Hoat ddng nay bdi dfldng cho ngfldi hoe NL phit hifn giii phap GQVO.
2. Ngon ngCva ngdn nguTToln hpc Ngon ngfl II h | thdng nhung i m , tfl, kf hifu va quy tic kft hop dflng de giao tifp, tu duy. Theo L.X. Vugdtxki,
"...Ngdn ngfl eung nhfl cle h f thdng tin hifu khac, thoat d i u 11 phfldng tifn giao luii, tren ed sd dd, trd thinh cdng cu cua tu duy v i sy dilu chinh hanh vi mpt cieh cd chfl djnh..." [11. Ngdn ngfl cd vai trd quan trpng trong tat e l eic qui trinh t i m If ciia eon ngfldi, die bift la qui trinh nhan thfle.
Xet dgdc dd thdng dung va chuyen mdn, ngdn ngfl gdm hat loai: Ngdn ngflthdng thfldng v l ngdn ngfl khoa hoc. Ngdn ngfl thdng thudng l i ngon ngfl dUpe dung trong giao tiep thdng thudng, thilu trau ehudt, ft gin vdi chuan mye hay nguyfn t i c Ngdn ngfl khoa hpe l i ngdn ngfl dflpc chpn Ipc, gin liln vdi nhflng ehuan mflc nguyen tic, sfl dyng trong nhung van bin khoa hpc. O l difn dat mdt vin de, ngdn ngfl bao gdm ngfl nghia (ndi dung) va efl phip (hinh thflc difn dat).
Ngdn ngfl t o i n hpe theo nghTa hep la ngdn ngfl dflpe xly dung tren he thfing cae thuit ngfl v i cic ki hifu t o i n hpe. Ngdn ngfl toin hpc theo nghTa rdng bao him ngfin n^fl toin hpc theo nghTa hep v i hlnh vf, mo hinh, bilu do, dfi thj,... cd tfnh chit quy Ude nhlm diln dat cic npi dung t o i n hpe chinh xic, logic v i ngan gon.
Ngdn ngfl toan hpc ed dac diem bilu dat ngin gon, logic, ddn trj v i khdng mang sic t h i i bilu cim. Ngdn ngfl toan hpc sfl dyng trong nha trfldng phii d i p flng dupe d e yfu d u ngin gpn, chinh xic, de hieu va phCi hpp vdi \(Sa tudi ngudi hpe.
3. Chuyin doi ngon nguT dien dat bli toan nhlm phit hien giii phip giii quylt van de
CONN trong DH Toan, ngflcri day cho ngfldi hpc thiy dflpc quan hf cua d c loai ngdn ngfl trong Toin hpc. Qua dd, ngfldi day cd cp sd d l hfldng dan v l rfn luyfn cho ngfldi hpc biet Ifla chpn each difn dat mdt npi
TS. PHAN ANH TAI Trudng Bai hoc Sii Gin
dung t o i n hpe theo hfldng cd lpi eho vifc GQVO. Ngudi hoc phii hiiu ngfl nghTa va efl p h i p difn dat van de;
bift CDNN v i dien dat lai v i n de; sfl dyng cie thao tac tfl duy v i k i t h ^ vdl cic hoat ddng ktiae de phit hifn giii phap GQVO.
D l CONN dien dat b l i t o i n , ngudi hpe phil biet hudng biln ddi van de, nhin thiy mdi lifn hf gifla cai da cho vdi cai phii tim hay d i phii chflng minh va moi lien h f gifla d c y l u t6 dd vdi tri thflc da bilt. Ddng thdi ngfldi hpc thay dflpc mdi lien hf gifla bli toin can gilt vdi bai toin ed lifn quan; dfla v l bii toan tfldng tfl da e6 each gill. Vdi ngdn ngfl dien dat mdi, vife phit hifn cacti giai bai toin thuan ldi hdn, ddi khi phit hifn dflpe cieh gill "hay", each gill ddn gtln.
Nhflng bai tdIn cua mdn TdIn hay eae mdn hpc khae cd lifn quan t o i n hpc hay d e bai toin thUe tien co ndi dung ehfla dUng nhieu kiln thfle dan kit vdl nhau eo t h i dien dat theo ngdn ngfl niy ho|c ngdn ngfl khic NL CDNN gilip ngUdi hpe ed dupe sU Iinh hoat khi lim toan cung nhfl d c h tiep can bai toln.Tiiy thude ndi dung bai toin, cd mdt so hinh thfle CDNN sau: CONN trong ciing mdt phin mdnToln; CDNN gifla cie phin mdn Toin vdi nhau; CONN cua mdn hpc khae v l ngdn ngfl toin hoc;
CDNN thflc t l v l ngdn ngfl toan hpc (ddi vdi cie bii toin lien quan d i n Toin hpc).
Qui trinh CONN de tim d c h giii bii toin dupe thiic hifn nhu sau:Tfl ngdn ngfl bai t o i n ban diu, nh§n biet dau hieu toan hpc d l chuyen ve ngdn ngfl mdi thich hdp vdi li thuyet toan hpe; Gill bai toan trong khudn khd d a li thuylt t o i n hpe theo ngdn ngfl mdi; Chuyen kft qui Idi gill v l ngdn ngfl efla bai toan ban dau.
4. Mdt sdvidii chuyen doi ngdn ngCiTdiin dat bii toin
4. T, Chuyen ddi ngon ngd trong cung mgt phan mdn Todn
Quan tam eic doi tupng quan hf trong bli toan dupe xem xet eai dat trong d c md hinh khic nhau;
ngudi day hudng d i n ngudi hoe theo eac hudng khac nhau trong cflng mdt phin mon Toin. Tfl dd, phin tfch bii t o i n de tim cieh gilL
ViduiCho hinh l i p phflOng ABCD.A,B,C,D,. Gpi G l i trpng tam cua tam giie BDA . Chflng minh ring ba ^ I m A, G,C, thing hang (Hlnh 1). A, n.
Thdng thfldng, sfl dung ngon ngfl hinh hoc tdng hpp se ed d e cich giii: Chflng ^iZ minh A, G, C, thude giao tuyen ctia hai m i t phing phin b i f t Chflng minh hinh chifu efla ba d i l m A, G, C, theo hai phflcmg khae nhau dfu cd Inh la d c d i l m j thing hing;...
Viec phit hien d e each
12*KH0AHqCGlA0DMC
. NGHIEN CUU 1 ^
giii niy khong ddn giin. Tfl dfl kien hinh l i p phflOng ABCD.A,B,C,D, v i d i u hifu nh|n b i l t d l CONN efla b i i toan, ta dinh hfldng dflpc cic d c h gill sau:
- Chuyen b l i toan sang ngdn ngfl vecto: Dat
^ = a, ^ = b, A X ; = E . Khi dd, A, G, C, thing hing khi va chl khi AG = kAC,, xac dinh k. Khai trien cic veaa
AG, AC, qua 3 vectd khdng ddng phing a, b, c; tinh
- Chuyen sang ngdn ngfl tpa dp: Chpn he tpa dd sao cho .4(0.0.0), S(l,o,0), £>(0,1,0), ^(0,0,1); tint! tpa dp cfla trpng t i m G. Chflng td ring tpa dd ctia G thda man phflong trinh dfldng thing AC,.
4.2. Chuyin ddi ngdn ngd gi&a cdc phdn mdn Todn vdi nhau
Trong mdt sd bai t o i n thupc mdt phan mdn Toin, neu chi sfldyng kiln thflc cfla phin mdnToln do thi vifc tim d c h glli khd khin hoac nfu tim dflpe cich giii thi Idi gill phfle tap vl npi dung ehfla nhflng y l u to thupc kifn thflc cfla phin mdn Toin khic (dang t i l m an). Van d l )i vlfc phit hifn duac nhflng dau hifu trong ndi dung b i i t o i n thude kien thfle eiia phan mdn Toan khic nhlm gilip ngfldi hpc biet CDNN difn dat Hen tfldng din cic kiln thflc cin sfl dyng d l giii toin. Ngfldi day hudng d i n eho ngfldi hpc hlnh thinh nhflng suy nghi, ren luyfn nhflng kT nang CDNN trong gill toin; CDNN gifla eic phin mdn Toan: Hinh hpc, Dai sd. Gill tieh,... vdi nhau.
Vidu 1: Chflng minh ring: Vu' + a +1 + Va' - a +1 ^ 2 V a e i i
D l y la bai t o i n Oai sd. Qua t r i i nghifm vdi dau hifu nhan b i l t la cac bilu thfle dfldi d i u can ed the nghT dfn vifc tpa dp hda de tim d c h gill b i i toin. Phin tfch hpp li d e b i l u thflc dfldi dau can, biln ddi v l dang tong binh phflong. Khi dd, ngfldi hpc CDNN dai so cfla bii t o i n vf ngon ngfl hinh hpc. Tiep theo, sfl dyng kiln thflc dfi d i i cfla mpt vectd,... Ngfldi hoc djnh hfldng giii bii t o i n nhfl
Phin tieh: o +a + l =
i^^m
ing toa i
Trong mat phSng toa do Oxy, x6t hai vecto:
f 1 J3
Khid6, |5[ = Vo'+o + l ,|v| = V a ' - o + l v j i ; + ; - ( i ; > / 3 ) , | ; + ; | - 2 . BStaSngthOfc |u| + |v| s | i ; + v|
Tuong duong vdi
a + i ^
Dau"=" khi va chi khi 2- = -2= = l o a = 0.
-4 I
4.3. Chuyin dii ngdn ngd eda mon hgc khdc vi ngdn ngd todn hgc
Ngoii vifc CDNN trong ndi bfi mdn Toin d l gill toan, ngudi hpc cd t h i CDNN mdt sd bai t o i n cfla cac mdn hpc khac vf ngdn ngfl t o i n v l sfl dung kiln thflc toan hoc di gill. Gill bii toan cCia d c mdn nhfl Vit li, Hda hoc, Sinh hpc,... khi phit hifn trong ndi dung cd d i u hifu ehfla eic y l u td toan hpc, d c mdi quan h f t o i n hpe.
Cung vdi viec sfl dyng kifn thflc cfla eae mdn hpe do, ngfldi hpe tim each CDNN cua bii toan v l ngdn ngfltoin va sfl dijng kiln thflc Toan hpc di gill. Hoat dpng CDNN giflp ngfldi hpc ren luyfn ki ning flng dyng kiln thfle toan hpc vao gill bli t o i n eua mdn hpe khic, nhilu khi phat hifn dflpc each giii "hay" cho bii t o i n eua cae mdn hpc dd.
Vfdul: Bai toan Vit If: Mdt moi khf If tfldng thflc hifn bien ddi theo quy luit P = Po - a V ' . Tim nhift dd eye dai T^^efla khi.
Trfldc hft ngudi hoc phii hieu kiln thflc v i t li: Quy luat P = Pn - aV- l i su phu thude etia i p suit vio t h i tieh V, trong dd a: Op biln thifn t h i tfch tuong dfldng v&\
mdi ddn vj i p suit thay ddi, gpi l i suat nen ding nhiet.
Bilu dien mdi quan h f gifla cle dai Ifldng v i t If trong b l i toan; ddi vdi khi If tfldng (hay khf xem nhfl khf If tfldng).
Oilu kien l i : Nhift dp ehuan la nhift dp 0°C = 273°K;
Ap suit ehuan P,, = 1 atm = 1,013 x 10^ Pa.
Phfldng trinh trang t h i i khf li tfldng: PV = RT R: Hing sd khf li tfldng, R = 8,31 J/mol."K T la nhiet dp khoi khf d i p suit P, the tfch V Biln ddi: PV = RT
o ( P „ - a V ' ) V = RT (1)
Trong dd, P^,, a, R11 d e hang sfi, V thay doi v l T phij thude V.
Dau hieu toan hpe trong ndi dung bai toin Vit If l i d e y l u tfi bifn thien, yfu td khdng ddi va mdi quan he PV P a , ham.Tllp ttJC biln doi, (1)-J^ T = " ^ = ^ ' V ~ ^ ^
Nhan bilt dUdc dau hifu t o i n hpc trong bai t o i n Vat li, ngfldi hpc CDNN v i t li v l ngdn ngfltoan. Xem T l i ham so cfla bifn sd V, ta ed bii toin: Tim gia trj cflc dai
a P
"^max *^"^ ^^"^ so T = ——V +-^v . Dung dao him, vifc giii bai t o i n niy don giin.
4.4. Chuyin dii ngdn ngd thdc ti ve ngdn ngd todn hgc (doi vdi cdc bdi todn thdc ti liin quan din Todn hge)
cic b i i toan thfle t l lifn quan d i n Toan hpe la cac b i i toan cd ndi dung thye te, difn dat bing ngfin ngfl thdng thfldng. Difu quan trpng la t i p luyen cho ngudi hpc bilt xic djnh dai Iflpng, phit hif ri mdi lifn quan gifla eac dai Iflpng, bilu thi nhflng tinh hudng thyc t l bing
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