SA DUNG LIEN TlTfiNG TRDNG QDA TRINH KHAM PHA TRI THUll Mill CHD HDC SINH QUA DAY HDC HINH HOG TliS V O X U A N IVIAI" Ngay nhdn bdi 29/03/2016; ngdy sua chua 14/04/2016; ngdy duyit ddng 19/04/2016 Ab[.]
Trang 1SA DUNG LIEN TlTfiNG TRDNG QDA TRINH KHAM PHA TRI THUll Mill
CHD HDC SINH QUA DAY HDC HINH HOG
TliS V O X U A N IVIAI"
Ngay nhdn bdi: 29/03/2016; ngdy sua chua: 14/04/2016; ngdy duyit ddng: 19/04/2016
Abstract: Currently, problem-solving method has been applied by teachers in teaching mathemat-ics al high school, encouraging students to engage in mental activities (imagining, expressing, conjec-turing and convincing) to promote understanding and get knoioledge In this article, we propose a process of organizing cognitive activity to apply imagination for teaching geometry at high school in order to improve mathematics learning quality
Keywords: Imagination, discover neu) knowledge, teaching geometry
trpng cua tam li hpc, nhieu quan diem cua thuyet
naydadupcvandungtrongquatrinhdayhpc
Theo li thuyet nay, su nhd Igi mot s u vat, hien tuong
nao do dan tdi sunhcf laisuvat, hien \\sm^ khac ggi la
Sen tudng Lien tudng giup cho chu the nhan tlit>c
thay dugc moiquanhegiiJa cac doituong nhan thu'c
v6i nhau, giup ngudi lioc l<et no! dugc tri thuc, kinh
nghiem da biet vdi tri thurc mdi, la n^n tang de ngudi
hgc CO thekhamphadugc tri thirc mdi trong qua trinh
nlian thiJrc Theo Dao Tam thi "Viec phat hien ra cai
m,di la ket qua cua quatrinh chuyen di cac lien tudng,
chuyen di cac nguyen tac, thai do da c6 vao cac tinh
huong khac nhau "[1;tr41] Bai vietnay hudng den
lam ro vai tro lien tudng trong mo hinh day hgc kham
pha cua Jerome Bruner, de xuait quy trinh to chu'c
hoatddng nhan thu'c su'dijng lien tudng trong qua
trinh ktiam pha tri thiJc mdi va cu the hda trong day
hgc hinh hgc dtrudng phothdng
1 Lien tudng trong mo hinh day hgc kham
phacuaJeromeBruner
Quan diem day hgc kham phacua J Bainerdugc
decap den bdi hai yeu to trong mo hinh day hgc nay
cua dng: mot la, cau true toi uu cua nhan thuc CO 3 dac
tinh quan trgng: tinh tiet kiem; kha nang san sinh ra
cai mdi va siirc manh cua cau taic; hai la, hanh dgng
tim toi, kham pha cua hgc sinh (HS) Kha nang san
sinh ra cai mdiva SLTC manh cua cau tmc la kha nang
tim ra dugc sU kien mdi, hieu bi^t sau va rgng hon
nhOng thdng tin da cho, kha nang van dung kien thuc
da hgc ducjc vao viec giaiquyfetcac tinh huong rienq
Theo Biurier, "cd hai loai iing dung cau tnic: chuyen
di cac m di Hen luang, cac kinang da Mp thu duoc sang cac lien tudng, kTnang gan gidng vdi no va chuyen dicac nguyen tac, cac Mi do died vao cac tinh hudng khac nhau - loai chuyen dl nay chinh la
trgng tam cua qua trinh day hgc, do lasumdrongva dao sau khdng ngimg kien thuc theo nhijng y tudng, nguyen tSc tong quat va co ban" [2; tr 61 ] Nhu vay, quan diem day hoc kham pha nay cung nhan djnh lien tudng va chuyen di cac moi lien t u ^ g trong qua trinh day hgc chinh lamdttrong nhung thanh toquan trpng trong mo hinh kham pha tri thuc mdi cho chu the nhan thiic
Theo Dao Tam [1; 42-43], nang liJC chuyen di
chik nang hanh dong nhd chuyen diiien tudng cac
do/7t/£ffjg'cJa/?oa/donfir la m gt tron g cac thanh to cua nang luc kham pha tim tdi kien thuc Nang luc nay dugc xem xet dua tren quan diem cua li thuyet hoat ddng, thuyetlien tudng va cac thanh tocua sodocau true kham pha nhu da de cap d tren Viec boi dudng nang luc nay gdp phan phattrien, md rdng kien thiic
va boi dudng phuong Wiuc kham pha cho HS tren CO sdcac kien thtic dacd Nhuvay, suphat trien nhan thiic cua ngudi hgc tuy thugc vao quatrinhtich luy cac md'i lien tudng, trinh do nhan thiic phu thugc vao so lugng, chat lugng cac moi lien tudng va toe do hoat hda cac lien tudng do Theo tam li hgc lien tudng, cai mdidugc hinh thanh thong qua hoatdgng chuyen di cac lien tudng, viec luyai ^ cho HS hoat dgng chuyen hda cac lien tudng tu dd'i tugng nay sang dd'i tugng khaccdtacdungphattrien nang luctuduydechijthe
* tnidng fiai FiQcfiongTIiap
Tap chi Giao due so 382 55
Trang 2mi3i Vi vay, lien t f l ^ g c6 vai tro nen tang trong qua
trinh phai trien tuduy cua HS cflng nhfl trong qua
trinh i<ham pha tri thflc mdi
2 Su dung lien tudng trong qua trinh kham
pha tri thflc moi cho HS qua day hgc hinh hoc a
trudng pho thong
2.r.BeHStutim toiphathieni<ien_thflc mdi,giao
vien (GV) CO the ggi van de tren eo s6 cae itien thflc
dacg, khoi day cho HS lien tfldng den cac van de co
lien quan Dua tren mgt so quy luat hinh thanh lien
tfldng nhfl: quy luattflong tfl, quy luat tuong phan,
quy luat nhan qua [3], GV djnh hfldng cho HS phat
hien ra cac tinh chatquan trgng tfl do d l dang tim tdi
ra nhflng khai niem, djnh li mdi ma cac tinh chat hay
quan he cua khai niem dd da quen thugc vdi HS Viee
sfldung lien tfldng frong qua trinh to ehflc hoat dgng
nhan thflc de day hgc tri thflc mdi eho HS theo quy
trinh sau day: Budc 1: Khoi day ki flc ciia HS vetinh
huc'ng lien tfldng Sutfc^.'Nhan biet dac diem quan
trgng cija kien thflc da biel 5i/oc3;Thietlap sfltuong
flng giiia kien thuc da bietva kien thflc can day (kien
thflemdi) 6[/Eic4;Dua ra gia thuyet (HS tim tdiva
phat bleu gia thuyet} Budc S.'Rut ra ket luan ve kien
thfle mc* (GV the che hda kien thflc) Budc ft-Van
dung kien thflc mdi
2.2, Van dung quy trinh sfldung lien tfldng trgng
qua trinh to chfle hoat dgng nhan thfle de day hge tri
thflc mdi cho HS qua day hge eac tinh huong dien
hinh trong mdn loandlnrdng phothdng
2S / S I ? dung len tudng nham kham pha cac
tinh chat, quan he mdi cua cac ddituimg Van dung
quy trinh tren de day ngi dung Phuang trinh dudng
thing {Hmh hoc ^2)
'Budc i: Khai day ki OccdaHS ve tinh hudng
lien tudng.Jmng baitmdc, chung ta da thay sutuong
tueiia phflOng trinh td'ng quat cua matphing trong
he tga do khdng gian Oxyz vdi phflOng trinh tong
quat dfldng thang trong he tga do mat phlng Oxy
Xet theo mgt khia canh khac, phflOng trinh tham sc
(PITS) ciia dudng thing trong khdng gian Oxyz eung
edIiSnhevdi PITS ciia dudng thing trong mat phSng
Oxy ma Chung ta da biet nhu the nao?
'Budc2: Nhan bietdac diem quan tmng cua kien
H^iicrfaA/ef NhSc lai kien thuc dabletvephuang trinh
dfldng thang Irong he tga dg Oxy
- Cac yeu td nao can thiet de viet dfloc P I T S ,
phuong trinh ehinh t i c (PICT) eua dfldng thing
trong he tga do O x y ' Va P I T S , P I C T cd dang nhfl
thenao?
561 Tap chi Qiao due so 382
M(i|,;!/||)vacdveetoeh?phflang(VTCP)u = („.ji
PTTSdang: t'.lllt', «^R,(«" + ''>ii)
'Budc3:Thieil$psutuangi}nggiuaki&it«kdi biet va kien thdc can day
- Tuong tfl, de lap dugc P I T S va PTCT cJa
dfldngthingtronghetgaddOxyz,taoiingcan2yeii to: VTCP ciia dfldng thang vatga dgdiem thudc dirohg thang
-Chg dfldng thang (A) di qua diem M{x^;y^;z^)
va eg VTCP « = (a; 6; c) dieu kien can va dtJ dediem
M{x; y; z) thugc (A) khi nag?
- Bid'n dd'i tren toa dp, ta dugc bilu thuc lien hS giua X, y, z va cae yeu tdda cho nhuthe nao?
- HS tra Idi dugc eac cau hdi, tflong flng viS cac kien thflc mdi dugc hinh thanh qua thiet lap sfl lien tudng
* Bade 4: Dua ra gia thuyet Dudng thing (A) di
qua diem M{x,^;y^^;z^) v a c d u = (a;fe;c) VTCPco
* Budc 5: Rut ra ket luan ve kien thdc mdlQH chinh xac hda lai gia thuyet HS dfla ra (xem bang ()
'Budc 6: Van dung kien thtic mdi, Cho HS v§n
dung kien thfle qua giai bai toan sau: "Trong khdng gian toa do Oxyz, eho tfl dien ABCD viS A(0;02), B(3;0;5), C(1 ;1 ;0), D(4;1 ;2) a) Viet PTTS ciia dfldng caotfldidnABCDhatflD;b)Timtgaddhinhchi5'ii
H eiia D iren mat phSng (ABC)" [4; tr 93)
2S.2 Siidung Hen tudng nham kham pha cac menh demdi, dinh ii mdi trong qua trinh nhan Ihik
ciia WS.Tflnhffngmenhde, djnh li da bi§^,nhdnang Iflc lien tfldng ma HS cdthephat hien duoc eac m?nh
de, dinh li mdi cd lien quan den nhflng kien thflc cii Chang han,tablet ring khainidm tam giac trongmal phing va khai niem tfl dien trong khdng gian la haj khai niem tflOng tu nhau, vdi nhflng tinh chat ta da
Trang 3He phJDng ninh <1] dine gi^ \i PTTSciis diKlriQ ir
FTTS, cMnti Qc cda diMng inlng
CnolUBnBIhing ( i ) tTmuailiSm M ( 3 : „ ; y „ ) v a c
VrCP U = ( a ; 6 ) Uleu Hen cin vJ mi n
M{x; J/) e A IS M | | M = tu vay
rs chinh lai: Dija difflng Ihing Irong h6 Ma a& Ony;
(3; = a;^! + at
y = y„+ bt t£R,(a' +b' > 0 )
,9 (A)
ciw mxing mang (A) iii qua diem M(x^^;y^^;Z^^) va cO vri
U = {a;b;c) <KU uen cin vs dO df JW(.i:;j/;z) e (A)
M^^M = tu vay
^ii + at y,, + 6( ( e ft,a' + b' + c' >0 (i)
Zii + c (
HS phLrang m t i (1] d i m goi la PTTS c i l a M n g Ihing ( A )
lam cho HS lien tudng den tfgQJQ^ dolatuongtutrongtu-dien
cac tinh chat dd nhu tiie
nao? OTnhien, khi HS phat
bieu cac menh de mdi vdi
cac tinh chat tuong t u n h u
thechi la nhung dudoan,
nen co the la menh de
dung, hoac sai Vi the, G V
can the hien dugc vai trd
the che hda kien tiiuc de
cac em cd the xac lap viec
hinh thanh tri thuc mdi dd
Cac budc trong quy trinh
tren dugc the hien trong
bangsau:(xem6anp2)
GV xac nhan kien thu'c
dmenhde tuong tu dinh li
Pytago trong tam giac
vudng qua giai bai toan
sau: "Cho hinh tuf di$n
OABC cd ba canh OA, OB, 0 0 doi mdt vudng goc Ket qua nay hoan toan tuong t ; voi djnh li Pytago
v a O ^ = a , O S - 6 , O f 7 = c.GgiHlahinhchieucua trongtamgiacvudngtrongmatphing,
diem Otren (ABC).Tinh dien tich cac tam giac HAB,
NgUrJC lai ni6i phifOng Mnh dang [1) vdl a' i-b' >
ihi la PTTS cua m i l di/dng th^ng iJc dinh iTi qita i
M(aTj,-,yy) vacd VTCP u - {a\b)
Trong tmflrig htjp a ^ 0 , 6 ?* 0 bSng
PTTS, ladiiiK
^ - ^ n _ y - y , ,
a b
HE phuang trmh (2) dUdi: g
Mgi/qc lai in6l phiHlng Idn
dildng thing hoSn loSn xic
( a * 0 , 6 9S
iiaprcrciiaflirtn
each khi} 1 W
Q){t\
Bling ( A ) TCT cila radi
^glroc lai, mdi phiwig Irlnh dang (1) vti a' +b' + c' > 0 d&j la PTTS
ciia mei dieng h i n g i j i : ilinh di qua diem M{x^^\ J/^^; Z ^ J va cC
u = (a; b\ c)
Trong imSng hdp a * 0 ii * 0, C 5* 0 hing ca
- ( a * 0,6 * 0;c5is 0)(!)
^.1 ^ y - y ,
1 b
M$ phirang Irlnh (2) S\sOz gpi 13 PTCT cila dildng Ihing ( A ) Ngunc lai, mdi phiidng lilnh dang (2) Ah la PTCT cua mgt diJdng Ihing
HBCvaHCA"[5;tr120].Nhanxetvem6ilienhegii?a
binh phuong dien tich cac mat cua tiirdien?
Dinh hudng giai bai toan nay nhusau {hinh 1):
Tacd 5„,|„ = S^j^ij, cosa trong doalagdcgiira hai
mat phing (OAB)va (HAB)
Bitig 2 Cic menh demdihinii tiiani) ntitJiliSn tifdng qua yeu lo tuang tugiQa tam giac trong mat piling
va tii dien trong l(hdng gian
^yJoF la^b' + bV + c'a'
DgdgS„,»'^»,
Tuong t u V < = '
2-J^-2'Ja'b- + b'c- + c
a V + ftV + c V
Qua ket qua ciia bai toan nay, GV cho HS neu
nhan xetve tinh chattrong tudien vudng:
S = S + ^iiiir •*• ^iir I ~ ~Va^fc' + b'c^ + c'a\
Tfl dd, ta cd dSng thflc s ; „ , = s,',,„ + s,;„ + s,;„,
Kien thuc; da biet trono tam giac
Ton lai d i f m cJch deu cic
canft cua tam giSc B i e m n a y clilnh la t ^ duang Iron nni
t i ^ tam gi^c Tan tai diem c^ch deu cac (ffn/i cua tam giac Qiemnay
tiep tam g l i c
Cac di/dng bung luyen cua tam g\Ac dong quy t j t m g t
diem
Cac di/ang cao cCia tam giac
dong quy tai mOt di^m
Binh liPflago trong tam giac vudng Tiang tam g t i c vuang
binti phuang Ud dii canh
huyen b i n g tong binh phuOng
dg d^i cic c^nh goc vu5ng Binh ll Pytago dio- Neu mot
tam gi^c c 6 binh ptiuang m o i canh biing tong binh phifdng hai canh con lai Itii t a m giac
do la Iam qiac vuong
Dmh II ve bSl dSng (ftiic Irong tam giac Trong mpt tam giac
dp dai mot canh nao d6 luun
be hon td'ng d$ d^i tiai canti c6n lai
P h ^ bi£u gia thuyet tUdng t i ; trong t i l d i f n
Tdn tai diem cich iiu cdc mil
c d a t i j i d l ^ n Q i e m n ^ y chinh l i
t a m m i t c l u nci tiep 111 dl^n
T6n tai diem each deu c i c dinh
cua t i l dien Diem n i y chinh l i
t i m m^t c i u ngpai t i p t i l dl^n
C i c duang trong tuyin cua t u
dien d6ng quy tai mOt didm
Cdc di^ng cao cua t u dl^n dcng
quy lai mOl dl^m Trang tU di^n vuong, binh phUdng
di$n lich mat huy^n b i n g tfing
hmh phuang dien tich c i c m ^ vu6ng
NSU mOt t u di?n cd binh phUdng
diSn lich mpt m i t b i n g tdng binh phUOng dien ticli c i c m i t cbn lai
Ihl d d l i U d i g n vuong
Trong mgt M difin, dign tich mgt
m i t n i o dd ludn hi tiOn t6ng dien
tich c i c m t t cCin lai
K i t
l u i n
Sung
fiOng
Sung
Sal
Oijng
Sai
-Tap chi Giao due so 382 57
Trang 42.2.3 Su durig
len tudng nhim
kliam pha cac quy
tic mdi, phuang
phap mditrong qua
trinh tim loi idi giai ,.<
Wtoar!.L.B.itBnxo
nhan djnh ve lien
tfldng trong day
hge:'Tflduy tdt tflc
latfl duy dung d i n
vacd hieu qua, biet thuc hien duoc nhflng lien tudng
khaiquat, nhflng lien tirmig phu hgp vdi bai tgan can
glal" [6; tr42] De phattrien tfl duy^cd hieu qua khdng
ch! ddi hoi ngfldi hgc phai tim hieu nhflng thucc tinh
hay nhiing quan he chung xac djnh eua cac del tuong,
ma cdn phai biet thude tinh nay ta ban chat dd'i vdi
nhflng bai toan nao Vi vay, khi HS tiep xuc vdi bai
toan mdi chua biet thuat loan, phfldng phap giai, can
tap luyen cho HS thdi quensfldung lien tfldng eac
quy tac, phflong phap da biet phu hgp vdi de bai de
giai quyet bai toan dd tfl dd tim ra quy tac, phflOng
phap mdi cho bai loan
Xet baitgansau:"Chg dudng thang d
va mat phang ( P ) : i + a + z - 7 = 0 Viet phflOng
trinh iiinh chieu vudng gdc cua dudng thing d len
mat phing (P)" [5; tr 103]
HS da biet each xac dinh tga dghinh chieu vudng
gdc cua mdt diem IVI tren matphang {cdthelhay dbai
lap van dung d v i d u 2 [4; tr 93]: Hinh chieu H cua
liem M tren matp^hang (P) lagiao diem cOa matphang
(P) vdi dfldng thang di qua diem Ivl dd va vudng gdc
mat phang (P) Tflc la i-IS da biet phfl^ong phap giai
nhu sau:-Vietphuong trinh dudng thang Adi qua M
va vudng gdc (P}:-Tim giao diem H cijaAva(P)
Trd lai bai loan tren, dexac djnh hinh ehleu vudng
gdc cua dudng thang d len matphang (P) cdthequy
ve xac djnh hinh chieu vuong gdc ciia diem len mat
phang hay khdng? H S thuc hien lien tudng Iheo quy
luatnhanqua(dudngthing la l<et qua khita biet dugc
hai diem phan biet cua nd hay mgt diem va phfldng
ciia nd) tfl phflong phap da biet phat hien ra hfldng
giai quyetbai toan:
Ket qua mong doi tii HS:
- Trfldng hgp d song song (P); Ggi d' la hinh
chieu vudng gdc cua d len (P), do d song song (P)
58 Tap chi Giao due so 382
xac dinh hinh chieu vudng gdc H cua did'm M len (P) Viet phflOng trinh dudng thang d' qua H va song sgng vdi d
- Trfldng hgp d cat (P) (khong vudng gee): + Lay hai diem A, B bat ki tren d; + Xac dinh hinh chieu vudng gdc A', B' cua A, B len (P);+Viet phuong trinh dudng thing d ' qua hai diem A', B'
Ta biet neu dudng thing d c i t mat phing (P) ^ i
A Ihi hinh chieu vudng gdc ciia dudng thing a cungdiquaA.Dc dd,HScungedthe dfla ra hfldng giai quyetnhflsau(/7/>?/)^:-TimlgaddgiaodiemAciia
d va (P); - Lay diem M bat ki tren d, tim hinh chieu H ciia diem^M tren mat p h i n g (P); • Viet phflOng trinh dudng thing di qua hai diem phan biet A va H Hiai nhien,bai
phing (P)va(Q)ehinhlahinh chieu ciia dudng thang
d len mat phang (P) Tuy nhien, each giai quyet nay khdng can phai sii dung lien tudng qua phfldng phap glal da biet Tfl dd, GV xac nhan cae phflOng phap
HS de xuat, yeu cau HS giai bai toan tren bing cac phflOng phap da tim ra va so sanh ket qua Vdi eac tinh hudng giup HS sfl dung llSn tfldng, tie'n hanh heat ddng tim Idi kien thflc chg ban than trinh bay d tren, bude dau lam sang td dugc vai tro quan trgng ciia lien tudng trong day hgc kham pha kie'n thfle miS Neu HS dflge bgidflang,tap luyen cac hoat dgng sii dung lien tfldng trong hgc tap se tao duge suket ndi giiia kie'n thflc, kinh nghidm datjietvdi viec hinh thanh kie'n thuc mdi, tfldd giup HS khic sau
va he thdng hda duge cac kien thfle vdi nhau, gdp phan nang cao hieu qua day hcc loan
(Xem liep trang 35)