42 _
s o 5-2011DmjvaHpc
—— JS<,.\Y SAY
Sir dung bieu diin trifc quan
trong day hgc mon Toan tieu hoc I
TRAN THUY NGA
Vien Khoa hoe Giao due Viet Nam
T
rong day hgc mon Toan a tieu hgc cac dang bieu dien true quan nhu: tranh anh, hinh ve, sa do, mo hinh, bieu bang ... giu mgt vai tro dang ke.Bieu dien true quan dugc xem nhu cong cu nham bieu thi mgt each true quan doi tugng toan hgc va nhiing dau hieu ban chat cua doi tugng toan hgc, dong thofi giup HS the hien.
giai thich nhiing suy nghT "trong dau" ve cac doi tugng toan hgc trim tugng (Arcavi, 2003;
Trin Vui, 2009).
Viec sir dung bieu dien true quan se gop phan ho trg HS trong qua trinh hinh thanh kiln thiic, kl nang toan hgc, dong thai tao diem tua tu duy trong qua trinh di tu cu the den trim tugng va ngugc lai.
O bai bao nay. chiing toi xin neu len mgt vai tac dung chu yeu cua cac dang bieu dien true quan va bien phap nang cao hieu qua su dung cac dang bieu dien true quan trong qua trinh day hgc toan a tieu hgc .
I. Tac dung cua cac dang bieu dien true quan
l.Bieu thi doi tucing todn hpc cii the; bieu thi khdi niem, quan he, tinh chdt todn hpc.
Vi du 1: Bieu tugng "goc vuong, goc khong vuong" (SGK toan 3) dugc giai thieu thong qua hinh anh cua kim gia va kim phiit tren mat dong ho.
a.Goc:
•to
•9 II 12 I
7 6 5
' llfZi \
•10 . 2-:
•9 <fc» 3-f .V 4 . i
. 7 6 5 j
; II iz 1
^ '10 -^ 2
•>,
7 6 5 Hai kim dong tio a moi liinhi ve tao tiianh goc.
b.Goc vuong, goc khong vuong A
B N D
Vi du 2: Cac khdi niem hinh hgc nhu diim, doan thang, duong thing, hinh vuong, hinh tron, hinh tam giac,... dugc giai thieu bing
hinh ve, ching han: Duang thing (SGK Toan 2.
trang 73).
DmjvaHpc SOS-2011
43
B B
Dogn thing AB
Oiro-ng thang AB
A B C
Ba diem A, B, C cung nam tren mot du'cyng thSng.
A, B, C la ba diem thing hang.
Hinh 2
Vi du 3: Hinh ve bieu thi quan he "nhiiu hon, it hon" va quan he "Ion hon, be hon" (SGK Toan 1, trang 6, 17):
' ' ' ' 1 ; !
'^--
Hinh3 2. Ho tru IIS trong qud trinh tir duy, suy nghi gidi quyet vdn di.
Hinh anil thu nhan bang thj giac co tac dung ho trg HS rat nhieu trong qua trinh hinh thanh kien thuc, kT nang toan hoc, dong thoi la diem tua cho qua trinh tu duy va ghi nho (kl ca ghi nho co chii djnh va khong chii dinh).
Vi du 1: Khi thanh lap cac bang tinh hoac hinh thanh cac kT thuat tinh cong, trir, nhan, chia a cac lop 1, 2 can co hinh ve di kem cac cong thuc tinh vi
1 < 2 :t be hon nai
dieu nay khong chi giup i IS hinh thanh ma con giup cac em ghi nhd de dang cac cong thiic tinh. Ghi nhd bang thj giac ia kieu ghi nhd pho bien va de tai hien.
Doi vdi HS, hinh ve nhieu khi co tac dung djnh hudng tu duy mgt each r5 ret. Chang han: vdi hinii ve "chim bay den" (SGK Toan I, tr 50). HS de nhan thay phai lam tinh cong; hinh vc "chim ba\ di"
(SGK Toan 1. tr 56), HS nhan lha\ phai lam tinh
trii....
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< / • - •
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X - 1 - Hinh 4
44
so 5-2011 DmjvdHl?C_ _ . ^ ^ ^S',At SAY
Ngoai ra, biiu dien trirc quan co thi giiip HS tim HS co thi dua vao hinh anh true quan de tra ldi ngay ngay kit qua ciia bai toan mgt each true giac, ma kit qua bai toan la "Hoa an nhiiu banh hon Mai"
khong can phai thuc hien mot chuoi cac thao tac tinh
toan, nhieu khi kha phiic tap. ^ , ^^
Vi du 2: Bai toan: "Mai an — chiec banh, Hoa ~-' — _ J _ - 8
an — cai banh do. Hoi ai an nhieu banh hon?", SGK
J . -i
toan 4, trang 122 Hinh 5
Vi du 3: Bai toan: "Vira ga vua cho, co tit ca 6 con, 20 chan chan. Hoi co bao nhieu ga. bao nhieu cho?'
^
>^-r-
/'""\"^.-<- /
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Hinh 6 HS CO the giai bai toan bang each ve 6 hinh bieu thi cac con vat. Neu moi con 4 chan thi thiia 4 chan.
Vay CO 2 con ga va 4 con cho.
Can chu y la, moi HS co sd thich, phong each hoc tap rieng. Nhieu HS co the de dang ghi nhd va sir dung cac cong thuc, con so. ki hieu toan hoc truu tuong de giai quyet cac bai toan. Nhung ciing co nhung hoc sinh viec ghi nhd va tu duy luon dira tren nhung hinh anh true quan gan vdi van de can giai quyet, chinh vi vay cac em se thuan lgi hon khi giai quyet bai toan bang each dua vao cac hinh anh, so do, mo hinh hon la cac cong thiic, ki hieu triiu tuong.
3. Dong vai tro trung gian trong qud trinh tir (luy tir cu the den triiu tupng vd tir triru tupng ve cu the
Viec hinh thanh mot khai niem toan hgc nao do d tieu hgc thudng dien ra theo hai dang ngugc nhau.
Dang thii nhat. di tu cu the den triiu tugng va dang thii hai di tii triru tugng ve cu the. Bieu dien trirc quan thirdng dong vai tro trung gian trong qua trinh tu duy tir cu the den triiu tugng va ngugc lai. HS bat dau hoat dgng vdi cac doi tugng cu the de thiet lap sir hieu biet thong qua kinh nghiem vdi cac hoat dgng: cam, nam, sap xep, di chuyen,...Sau do cac em md rgng va dao sau sir hieu biet cua minh thong qua cac bieu dien true quan nhu hinh ve, so do, mo hinh cua cac doi tugng cu the. Cudi cung. HS chuyen den cap do triru tugng ciia sir hieu, sir dung thanh thao cac con so, ki hieu, phep toan.
Vi du: De hinh thanh khai niem phep cong cd the to chirc cho HS tien hanh cac hoat dgng: - Sii dung vat that hoac tinh hudng that. Ching han: Em co 3 cai keo, me cho them 2 cai keo. em duoc 5 cai keo.
Hinh 7
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45
- Sir dung hinh ve vdi cac chim trdn giiip HS hinh thanh biiu tugng vl phep cong:
Hinh 8
Su dung cac chu so va ki hieu phep tinh de ghi lai phep cong:
3 - H 2 = 5
II. Bien phap nang cao hieu qua sir dung cac dang bieu dien true quan trong qua trinh day hoc toan 0' tieu hoc
Bien phdp I. To chuc cho HS Idm quen vdi cdc dang bieu dien true quan khac nhau khi bieu thi cdc did tupng todn hpc hope ddu hieu bdn chdt cua doi tupng todn hpc
Chang han de dien ta khai niem so tu nhien hoac phan so. cd the cho HS lam quen vdi cac dang bieu dien khac nhau, thong qua viec su dung mo hinh, hinh anh minh hoa cac doi tupng vat chat (vat that) cu the khac nhau.
Vi du 1: S6 23 co the bieu dien dudi cac dang:
" v >./ >.f y-f >^ "w
^ >.rf > > %v l ^ -W
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Ch uc D on vi
Hinh 9 Vl du 2: Phan so — cd the bieu dien dudi cac dang: , 2
3
o o o
Hinh 10
Bien plidp 2. Khuyen khich IIS sd dung cdc chit cua nd. Cac hoat ddng to miu, ve, eit, dan...cd biSu diSn true quan tir tiii hien, gidi thich nhirng the ho trg HS the hien each hieu cua cac em ve mpt suy ng/if "trong ddu" vi cdc ddi tupng todn hpc khai niem hoac quan he toan hpc nao dd.
triru tirang Vidu 1: C» ldp 2. moi HS cd the luachgn mpt Khi HS chii dpng tg thi hien mpt khai niem each td miu vao mgt sd d vuong de bieu thi phep hoac quan he toan hpc cac em se hiiu sau sic ban nhan tuong iing
46
s o 5-2011DmjvaHpc
— .JsCAY SAY
rucng tilu hoc '.yj. 5AM i ^p.-^
Hovaten:*;.;;, 'H*!....r..J...
PHieU HOC TAP
Vi du 2: HS ldp 4 tir bieu diln phan so
Hp va ten: •f
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Trtrb-ng tl^u hoc fe.ui-.i'.'<i'V'- Lcrp:J.£
Hp vA i^n:.iJ^tuij^ii...'Ui.tJ.'..
P H I 6 U HQC T A P
Hinh 11
Hp va iea/b/u^ehy^.'^if^n. .€vM-4i.
ore
00 0
Hinh 12
Vi du 3: Ve mot hinh chiJ nhat roi to mau vao — hinh chir nhat do 3
Bieu phdp 3. Sir dung cong nghe thong dn ho trp Vi du: Khi hgc vl Hinh hop chii nhat (ldp 5), cdc bieu dien trice quan. cac biiu dien phong phii va sinh dgng cua hinh hop
May tinh cung cip nhiiu dang biiu diln toan chu- nhat tren may tinh giiip HS cd biiu tugng vl hpc phong phu. hip din giup GV va HS de dang hinh hop chiJ nhat va phat hien ra cac dac diim vl khai thac sii dung. Va cung cho phep ngudi dung cd <l'"h, canh, mat cua hinh hop chiJ nhat. Chang han, thi chu\ln ddi giua cac dang biiu diln trirc quan dl HS nhan biit dac diim cac mat ciia hinh hop chii hiiu khai niem hon. nhat thdng qua cac biiu diln:
Hinh hop chu nhat c6 6 mat: hai mat day va bon mat ben deu la cac hinh chii nhat.
DmjvaHpc
JsCAY SAY
SO5-2011
_ 4 7
Mat 1 bing mat 2 Mat 3 bang mat 5 Mat 4 bang mat 6
Hinh 13
- HS cd thi thuc hien xoay, lat, ddng md, thay ddi kich thudc cac hinh hop chii nhat dl qiian sat kT cac mat ciia hinh hop chu nhat:
/
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Hinh 14
- D I tim cdng thuc tfnh the tich hinh hop chir nhat, HS tim sd hinh lap phuong Icm^ xep vao diy hop bing cac thao tac tren may tinh:
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z:
/
A I 4 I'
j A /
Hinh 15 III. Mot s6 luu y khi sir dung cac bieu dien true quan trong day hoc mon toan tieu hoc
I. Biiu dien trirc quan cdng dan gidn cdng tot NIU hinh anh minh hpa cang ric roi thi viec phat hien ra moi quan he co ban cang khd khan them, ma khd khan dd la vd ich niu khdng ndi la cd hai. NIU sir phong phu vl ban than vat lieu true quan phan nao de
gay hiing thii, thi cai hiing ihii ben ngoai a\ lai dl lam mat hiing thii nghien ciiu ban chat ben trong. Vi the, don gian cd nghTa la hinh anii minh hpa phai the hien dugc nhQng thupc tinii va mdi lien he co ban nhat cua kiln thiic toan hpc, nhCfng cai thii }cu cd thi lupc bd bdt.
4B
SO 5-20112. Bieu dien true quan phdi ddng cdu vdi quan he todn hpc cdn the hien vd ddng cdu vdi hoat dpng tri tue dien ra trong ddu dc hpc sinh
GV can phan tich kT nhung yeu td trong npi dung toan hpc can the hien va nhung mdi quan he giua nhung yeu td ay. Tu dd, cd the thiet ke cac bieu dien true quan the hien dugc day du cac yeu td va cac mdi quan he ay. Nen su dung cac bieu dien true quan theo cac hudng nhu sau:
- Su dung true quan de hieu ban chat cua ddi tupng toan hpc can ITnh hpi.
- Su dung true quan nhu la mpt phuong tien hd trg giup cho viec ITnh hpi cac tri thiic khai quat. Thuc day HS tim kiem nguyen nhan, li le thuc su hay ngudn gdc ciia mpt quan he toan hpc nao do.
3. Trdnh cdc dn tupng sai khi sir dung cdc bieu dien true quan
Chiing ta thay lpi ich thiet thuc ciia tranh anh, hinh ve la dap ngay vao giac quan hpc sinh, gay nhung an tupng manh me, ddi khi khdng can li le phien phiic. Chang han, khi treo hai biic tranh, bue tranh thii nhat cd 5 con chim, biic tranh thu hai cd 3 con chim, thi HS nhan ngay ra 5 nhieu hon 3 ma khdng cd nhu cau phai "chiing minh" hay li giai tai sao; tuy nhien han che la d chd HS khd nhan ra dupe mdi quan he toan hpc bi che dau bdi vat cu the kia.
Hon nua, khi su dung nhung hinh anh true quan trong day hpc mdn Toan tieu hpc van dc thudng gap nhat la HS thudng hinh dung theo mpt md hinh cd san va trong trang thai tTnh tai.
Vi vay, trong day hgc GV can khuyen khich HS the hien sir hieu biet cua minh thdng qua cac bieu dien toan hpc, thuc hanh chuyen dich giua cac loai bieu dien khac nhau tu dd nhan ra cac mdi quan he toan hpc trong trang thai van dpng.
IV.Ket luan
Bieu dien true quan cd vai trd rat quan trgng trong day hpc mdn Toan d tieu hpc. Tuy nhien, cung can phai luu y rang ddi khi trirc quan chi bieu dien dugc mgt khia canh ciia ddi tugng hoac quan he toan hpc ma khdng lam bpc Id dugc ban chat cua chiing.
Ndi each khac, hinh anh true quan cd the lam cho tre cd in tupng sai va dan ehung "nhay cdc" ngay den nhung ket luan ma khdng dua ra dugc nhung lap luan hgp li de cd dugc cac ket luan do. Vi the, khdng chi
nen dira vao true quan de vdi vang khai quat hda, ma nen td chiic cac hoat dgng sii dung true quan nhu mgt cdng cu thiic diy HS suy nghT tim tdi, lap luan kham pha ban chit ciia cac khai niem va cac quan he toan h g c
Tai lieu tham khao:
1. Dd Dinh Hoan (chii bien) (2007), Todn 1,2,3,4,5. Nha xuat ban Giao due.
2. George Malaty (2006), "The Role of Visualization iu Mathematics Ediiccition:
Can visualization Promote the Causal Thinking? ".
3. M.I. Moro; A.M. Puskalo. Nhimg vdn de cdp thiet trong PPDH Todn a truang lieu hoc. Matxcova. NXB Sir pham, 1977 4. Arcavi, A., The role of visual
representalions in the learning of matheinalics. Educational Studies in Mathematics 52: pp.215-241, Kluwer Academic Publishers, Printed in the Netherlands, 2003
5. Tadao Nakahara, Development of Malhemalical Thinking through
Representation: Utilizing Represenlalional Systems, Progress report of the APEC project "Collaborative studies on Innovations for teaching and Learning Mathematics in Different Cultures (II) - Lesson Study focusing on Mathematical Communication", December 2007, University of Tsukuba, Japan, 2007. . 6. Tran Vui (2009), Xu hicdng kit hap
nhieu bieu dien khac nhau mot cdch hieu qud trong dgy vd hoc todn. Tap chi Khoa hoa hgc giao due.
