TO CHlTC DAY HOC TOAN d TIEU HOC THEO HirVNG KHAI THAC CAC YEU TO THVC T I I N P H A M THI HAI C H A U '''' 1 Giao due Toan hgc theo hudng thuc t i ln (Realistic Mathematics Education) tu lau da dupc nhi[.]
Trang 1TO CHlTC DAY HOC TOAN d TIEU HOC
P H A M THI HAI C H A U '
1 Giao due Toan hgc theo hudng thuc t i l n
(Realistic Mathematics Education) tu lau da dupc
nhieu nudc co nen giao due tien tien tren the gicfi
quan tam.Day la iithuyetdayva hpc toan dupc dua
ra va phat trien a Vien Freudenthal thupc Truang
Dai hpc Utrecht (Ha Lan) tu" nhung nam i 970, sau
do dupc tiep noi va phat trien 6 nhieu nudc khae
nhu: Anh.Du-c.Dan Mach,Tay Ban Nha, MT, Nhat
Ban, Malaysia, (1; tr 1 -2) Nhung nam gan day, a
cac nudc nay, viec dua thuc t i i n vao hoat dpng day
hpc (DH) tiJcac bac pho thong den dai hoc da dupc
thunghiem va dat nhieu ketqua khaquan.Haiquan
diem chinh cua giao due Toan hpc theo hudng thuc
t i l n , dupc Vien Freudenthal dua ra la: 1) Toan hgc
phai dupc gan ket vdi the glcrt thuc tien; 2} Toan hpc
nen dupc xem nhu la hoat dpng thuc tien cua con
ngudi (2; tr 3)
Ljch sii cho thay, Toan hgcco nguon goc tu'tfie
gidi tiiuc tien, chinh suphat trien cua thuc tien da thuc
day suphattrien cua eae npi dung toan hoc, lam nay
sinh, pliat trien va hoan thien cac li thuyet toan hpc
Ngupc lai, toan hpc xam nhap vao thuc tiln va thuc
day thuc tiln phat trien.Tuy nhien, cung chfnh do su
phattrien mgnh meva nhanh chong cua thuc tiln lam
cho toan hpc khdng theo kjp, chung da dan bi keo ra
va tach rdi vdi thuc tiln
0 Viet Nam hien nay, trong qua trinh DH toan
phothdng dang thieu vang bong dang cua yeu tothuc
tien Giao vien (GV) phan Idn la day theo khuon mau
cdsan trong sach giao khoa, hpc sinh (HS)thuc hien
cac hoat dpng hpc tap theo nhftig each thuc may
mdc, rap khudn, xa rdi vdi cupc song Chinh vi vay,
giao due pho thong Viet Nam da va dang dao tao ra
nhung the he HS chi biet van dung tri thuc de giai
quyetcac VOT demang tinh li'thuyetnhung lai rat lung
tung trong viec xuli cac tinh huong thuc tiln, De dap
ung muc tieu, nhiem vu doi mdi can ban, toan dien
giao dye phottidng giai doan sau 2015 "ren luyen ki
nang van dung kien thdc vio tht/c tiin", "tang cudng
cac hoat ddng trai nghiem thuc te'{3), thi viec dua
38 Tap chi Giao due so 360
thuc tien vao quatrinh DH toan cho HS phothdng ndi chung va H S tieu hpe ndi rieng la nhiem vu can thiet va cap bach hien nay
2 DH toan or tieu hpc XYseo h u d n g thuc tien
Trong qua trinh DH,GV td'chuc dieu kiiien qua trinh tu to chirc, tu dieu khien cua ngudi hoc nham thuc hien nhiJng nhiem vu hpc tap Quatrinh DH gom
cd cac khau: Xac dinh va nhan dien van de can giai quyet, hinh thanh y thUc doi vtS nhiem vu hgc tap; to chLTc, dieu khien viee finh hpi tri thdc mdi; tochUc, dieu khien viec cung CO tri thut; tochUc, dieu khien viec ren luyen kTnang, klxao; td'ehu'c,dilu khien vific kiem tra, danh gia ket qua hpe tap va ket quaciia timg budc ndi tren tron,g quatrinh DH D e d a m bao tinh thuc tien trong DH loan thi tat cacac thanti to ndi tren cua qug trinh DH toan deu phai gan vdi thuc tien, Toan hpc lamdn hpc cdtinh truu tupng cao, trong khi HS tieu hpc cdn han che ve suphat trien cua ti/ duy, ngon ngu, tri nhd De qua trinh DH toan dtieu hgc cd hieu qua, dong tiidi dap ung yeu cau ddl mdi giao due trong giai doan hien nay, G V can phai tiep
can va thuc hien tinh than Giao due toan ftpctheo
hudn^tiiuc tiln, cu the la: long ghep tritiidc toan vdi tiiuEtienxayraxungquanhHS,tao dieu kien cho cac
em hoatdpng tiiic tiep tren cac dodung DH true quan, trai nghiem vdi nhung tinh huong cdthe xay ra trong eugc song (nhOngtinh huong nay cd thela tinh huong thuc, cung cd thela tinh huong md hlnh dupc GV xay dung nen) Viec khai thac cac yeu to thuc tiln can dupc long ghep vao qua ti'inh DH, giup cho viec hoc toan cua HS trdnen nhe nhang, sinh dpng, hap dan
va hieu qua hdn; dong tiidigiup cac em bietvan dung tri thdc toan vao giaiquyet mpt so van de, tinh huong don gian nay sinh trong cupc song
S.Thifctr^ng DH toan d t i ^ u hpc theo hudng khai thac yeii to'thiic t i l n
3.1 Tht/0 trang DH toan atieu hgc theo hudng khai thac yeu io thuc tiin
* Khoa Giao di|c -TniSng Sai hgc Vinh
Trang 2phuong phap tmc quan duoc xem la phuong phap
chu dao Do dae diem nhan thdc cOa HS tieu hoc cd
tinh tn/c quan cao nen phucmg phap tmc quan (vdi
cac vat that, tranh anh, mo hinh, so do, ) d u p c s u
dung de mo ta cac d a ft;ang toan cung nhu de hinh
thanh vacung co tri thuc mdi Tuy nhien, hau het viec
tiiao tae tren do dung tmc quan 6Mc ttiuc hien bdi
GV,HS th udng quan sat, itdupc tn/c tiep thao ^ e vdi
chung.Vithe,vlec sudung phuong phap tmc quan
chua thuc suhieu qua
Ben canh do, de cung co &i thuc va ren luyen kT
nang, kT xao, GV thudng s u dung he 8i6ng bai tap
trongsach giao khoavatailieutham khao Phan k^
cac bai toan ed ldi van a tieu hpc cd npi dung gan vdi
thuc tiln, tuy nhien, HS thudng giai chung ttieo cac
phuong phap giai, cac thuat toan ed s i n chd it khi cac
em d u « ; tiep xuc va xii li eae tinh huong d i i n ra ti-ong
cupc song thue Cdn cac bai tap toan khae, hau het
dupc HS giaiquyetttieo each sudung cac edng ttiuc
da d u o ; ITnh ha mptcach may mdc, rap khuon.Chinh
vivaycactiithuctoanducchinhttianh,ghinhdkh6ng
ben vung va HS eung khong bietvan dung nhirng tri
thdc loan da duac hpc vao viec giai quyet cac van de
xay ra h^ong eugc song ttiuc tiln
Nhuvay, cothe ttiay rang hien nay GVtieu hpc
chua ttiuc sukhai ttiac cac yeu tottiuc tiin vao qua
trlnh OH toan eua minh Ton tai nay v i mpt so li do
sau: - Npi dung chuang trjnh, sach giao khoa duac
xay dung ehua thuc s u g^n lien vdi tiUc tien; - Thdi
gian quy djnh cua cac tiet hgc cung anh hudng den
kha nang sang tao cua G V; - G V gap nhieu khd khan
trong viec tim kiem va xay dung tinh huong tiiUC tien
de g i n vdi tri ttiiit toan hpc can day;-Trinh dp eua
nhieu G V tieu hpc hien nay chua dap dng duac yeu
eau DH khaithac cac yeu tothuc tien
32 Dinh hudng tang cudng ktiai thac cac
yeu to thtic tiin trong DH toan atieu hgc:
- Siia doi, bo'sung ngi dung chuang trinh, sach
giao khoa mon foandtieu hpe hien hanhttieohudng
tang eudng gan cac tri t i d e toan vdi ttiuc tien Dieu
nay gdp phan dap ung muc tieu giup HS biet van
dung ki§'n ttiuc toan hpc vao ttii/c tiln va phat frien
nang luctiiuchfflih.phuhgpvdixuttieDHtfieo hudng
tiep can nang lue tix)ng tucmg lai gan
- Thudng xuyen to' chijfc cac hoat dpng giup GV
tieu hpc nang cao kha nang khai ttiac cac yeu to ttiuc
tiln vao DH toan, nhu: d u gid, ttiao luan, hpi nghj,
tap huan, ;
ttiuc tiln, GV phai quan sat cac tinh hudng ttiUc tien
da dien ra nhu ttienao frong cuoe swig xung quanh Viec quan sat va phan tich kT cae tinh huong xay ra xungquanhgiupGV tim ra dtrpc van de toan hgc cd lien quan den tiiuc tien xay ra Nhd dd, cd ttie long ghep tinh huong dd vao ngi dung toan hge va xay dungyeutd'ttiuctilnvao hoatdgng DHeuaminh cho phuhppvaehinh xac
- Da dang hda hinh ttiuc DH toan cho HS tieu hpc G V phai biet to' chue cae hoat dpng DH theo hudng khaittiacttiucti^dnhieu hinh ttiuc khac nhau
Dethuc h\en dupc djnh hudng ndi fren, budc dau
chungjdi de xua't mgt so hinh tiiuc tang cudng tinh ttiuctien frong DH toan dtieu hpc nhusau:
3.2.1 Khaithac cac yeu tothuc tien trong to chdc
DH hinh Mnh kiin thdc mdi.DoivdiHSiiuhQccac
kien ttiuc toan hpc phai dupc hinh tiianh b i n g eon
dudng nhan tiiuc "tdtn/c quan sinh ddng den tuduy tniu tugnd', vi ttie khai ttiae eae yeu to thue tiln ket
hpp vdicac phuong phap DH khac nhau se giup HS dedang tiep nhan kiai ttidc mdi va ghi nhdchung mpt each lau ben Cd tiie tang cudng yeu to tti Uc tien vao npi dung day kien thuc md^ de HS d i hieu, dong ttidi cac em ttiay dupc tam quan ti-gng cua kien ttiiic duac hgc doivdi cupc sd'ng
Vidu 1: De hinh ttianh tinh chi'tgiao hoin cua
p / ? ^ n/jandldp 4, GVedttieehoHS hoat ddng ttieo nhdm hoac canhan tiong ti'nh huong sau:; G V chuan
bi cho HS mpt sd'md hinh cay xanh, chang han 28 cay; - Cho HS ttong cay vao mpt khu vudn hinh chi? nhat sao cho cac cay dhang ngang hay hang dpe phai gidng ttiang vdi nhau; - Yeu cau H S tinh t a i g so cay trong frong vudn ma khdng can bude vao khu vudn
Du kien HSseduara cac phuong
an tra tdi nhu sau:-Di dpc
^eochieuda cua khu
vuon, 6h\
daac cd 7
cay, di dpc theo chieu rpng vudn,daTidugc^ca4hang,nhuvay so cay la: 7x4 = 28 (cay); - Di dgc ttieo chieu rdng ciia idiu vudn.dan dupc c64 cay.dldgcttieo chieudavuon,dan dugc t ^ ca 7 tiang, nhu vay so cay la: 4x7 = 28 (cay); -Hudng dan HS dua ra k^luan: Socaycdthetinh la
Tap chi Gido due so 360 39
Trang 3GV kha quat hdatinh huong fren;"/Vei/i'?eoc/7^
dii khu vmid&n duac a cay va Mo chieu rdng khu
vudn dim dugc b cay thi tmg so cay tmng khu vudn
labaonhieu?'; *
Giup HS neu dupc: So cay cd ttie tinh duac la
axbhoacbxa;
- HS ket luan axb = bxa
-GVgidittiieutinhchatgiaohoancua phep nhan
3.2.2 KhaiMc cac yeu tothuc fien tmng to chih
ff7M7/7an/i,/uye/)(^.Cac hoat dpng ttiuc haih, luyen
tap chiem mot ttidi luang kha ldn frong chuong trinh
DH toan tieu hoc, nd xuat hien frong cac tiet day bai
mdi, cae tiet luyen tap, luyen tap chung, dn tap dudi
dang cac bai tap Nhiem vu chu yeu cua day ttiuc
hanh, luyen tap la eung co cactri ttiue ma HS mdi
chiem ITnh dupc Viec dua ttiuc tien vao npi dung toan
mama HS can phai ttiuc hanh, luyen tap se giup cae
em d i h i n h dung vade dang giai quyet cac nhiem vu
dupc giao khi duac hoat dwig vdi do diing true quan
trong eae tinh huo'ng cu ttie gan gui vdi ddi sd'ng cua
cac em
Khigiai cac bai tap trong saeh giao khoa,HSttiudng
chuydoi cac dif lieu v a ^ sd'cua baitoan, chdtti udng
khong de y de'n yeu to ttiuc tien xuat hien trong do
Dieu nay, mpt phan do GV cdn chua chu trpng den
viec hudng cac em g i n kien ttidc da hpc vao cac hoat
dgngfrongcudcsong.ben canh dd,GVfriudng hudng
cac em giaquyetbaitap mptcach ttiudpng ttieo djnh
hudng s i n cd Dieu dd lam HS hoatdpng mptcach
thu dpng va khdng hieu dupc y nghTa cua tri tiidc da
duoc hpc dd'i vdi cupc song h i n g ngay
Khi dua cae bai tap ed ye'u tottiuc tien de H S ttiuc
hanh, luyen tap.GV can xay dung cac tinh huong ttiat
gan gui vdi eae em, cho cac em hoat dpng fren do
dung true quan (cdttie la vat tiiat hoac mohinh) Tuy
vao npidung cua bai tap,GV cdttiecho HS ttiiiC hien
nhiemvgttieonhdmhoaccanhan.yeucauHSdua
ra eae phuong an giai quyet ba\tap Viee de cho HS
tiJsuy nghTva ndi len y ti/dng eua minh se giup HS
hinh ttianh va phatttien nhieu nang luc c a i ttiiet nhu:
nang luc phan tich, nang lue phat hien va giai quyet
van de, nang lue suy luan bgie, nang luc suy doan,
G V khdng nen cung nhac yeu eau HS phai di tiieo
phUPngan maGV dadukien,macan khuyen khich
HS tutim tdi, kham phadedua ra each giaiquyetcua
minh Mdi tinh hudng ed ttie giai quyet ttieo nhieu
eachkhacnhau
w/OOd Idp 2, yeu cau HS giai bEU toan " ^ n c d 0 viSn
bi Ha cd 6 viin bL Hdi An va Ha cd tatca bao nhieu vien bi?" Vdi bai toan nay, G V da chuan bj do diing
fruc quan gom nhdm 8 vien bi eua An va 6 vien bi cua
Ha de HS ttiao tae tren fren do dting DH
HS cd the dua ra nhieu phuang an giai quyet nhu sau:
- Phuang an 1; Dat vien bi dau tien cua Ha sang
n h a n 8 vien bi cua An, dd la vien bi ttiu 9; dat vien bi ttiu 2 eua Ha sang nhdm bi cua An, dd la vien ttiu 10; ednhuthe'chodenvien cuoi Cling cua Haduac dat sang se ia vien ttid 14 Ket qua: cd 14 vien bi
- Phuang an 2 Tach 2 vien bi cua Ha sang nhdm
8vienbicuaAn,tadupc10vien;epng10viennayvcii
4 vien cdn lai cua Ha, ket qua dupc 14 vien bi (thdng thudng HS se de lam phep tinh hPn khi dua ve td'ng trdn chuc)
- Phuang an 3: Tach 6 vien bi cua An ra cgng
vdi 6 vien bi cua Ha, dupe td'ng la 12 vign; 12 vien nay cdng vdi 2 vien dang cdn cua An, duac td'ng 14 vien bi
3.2.3 KhaiMc cac yeu ^'ffiiA: bin ^ngtd'chiic cac hoatdgng ngo$ikhda To ehdc cac hoat dpng
ngoai khda cho HS tieu hpc la hinh ttidc DH phii hpp khi GV cd dung y khai ttiac ttiue tiln vao fri ttiiic toan Thdngqua cac hoatdgng dd.HS sedupc ti-a nghidm ttiuc su, se tiiay dupc hinh anh cua cac tri ttiirc toan xuat hien mpi luc, mpi nai xung quanh cac em Qua
dd HS hieu dupe y nghTa cua viec hgc toan dd'i vdi cudc song h i n g ngay
De viec khai ttiac thue tien trong hoatdpng ngo^i khda ed hieu qua, G V can phai dua HS vao cac tinh hudng ttiuc tiln phu hpp HS tieu hpc la doi tupng CO kinh nghiem song va hieu biet cdn ngheo nan, vilhe nhirng linh huong dua vao to' chdc hoat ddng ein phai gan gui, d l hieu ma cae em thudng tiiajr frorjg cupc song xung quanh ed the lien quan den ban
40 Tap chi Gido due so 360
Trang 4Ben canh do, biet lua chpn tinh huong ttiu vj se kieh
thich hdng thu cua fre, Idi cudn tre vao hoat dpng
hoc tap, lam cho quattinh hgc cua HS dat hieu qua
cao Ngoai ra, van de ttiuc te dua ra cho HS phai
mang tinh md pham, chda dung cae yeu to tieh cue
trong eugc sdng
Vidu 3: Cho HS k5p 5 quan sat cai cong ben
dudng va yeu cau cac em giai tiiich: Tai sao ttidng
ttiudng nap cong la hinh frdn ma khong phai la hinh
vudng?
Cac em quan sat va s d dung nhifrig kien tiiuc
toan da b i ^ de giai thich: - Nap cong nang nen lam
hinh frdn de di chuyai b & i g each lan nap cong (dua
vao kien ttiu'e toan hpc: hinh frdn lan dupc); - Khi md
nap c o i g hinh frdn thi de han, khdng bj nghieng ve
mptphia (dua vao kien ttidc: ban kinh hinh tiijn bang
nhau);-Vi cai cong hinh tm nen n i p cong hinh frdn se
dep hon (dua vao kien ttiuc Hai day eua hinh tixi la
hinhtton)
DH toan dtieu hpc ttieo hudng khai ttiac cac ye'u
td'ttiyc tiln laxu hudng DH phii hpp vdi muc tieu giao
dye phottidng frong giai doan sau 2015 Nd giup eho
hoat dpng bpc tap cua H S trd nen tich cue, ttJ giac va
qua frinh DH dat dugc hieu qua cao De ttiUc hien
dupcquafrinh DH toan tieu hpc g i n lien vdi tti uc tiln,
ddi hdi GV phai tich cue hpe t|p va nghien cdu ve cae
van de lien quan, dong ttidi can phai sua doi, bd'sung
npi dung chuong frinh, sach giao khoa toan tieu hpc
hien hanh •
(1) PMRI Team, Introduction to Realistic
Mathe-matics Education, Southeast Asean Minister of
Education Organization, 2010
(2) Zutkardi, How to design Mathmattcs Lessons based
on the Realistic Approach, www.reocities-com/
ratuilma/rme.htlm 2010
(3) Nghj quySl stf 44/NQ-CP vg "Ban hdnh chuong
sd'29-NQ/TW ngdy 04/11/2013 Hdi nghi ldn thii ldm
Ban chdp hdnh trung uang Ichoa XI vi ddi mdi cdn
bdn todn difn gido diic vd ddo tgo, ddp ung yiu cdu
cdng nghifp hda hifn dgi hda trong dieu kifn kinh
ti thi trudng dinh hudng xd hdi chu nghia vd hdi
nhdpqudc ti, m NOi ng^y 09/6/2014
Tki li^u tham khilo
1 D6 Dinh Hoan (chii biCn) T o i n 2, T o d n 4 , T o i n 5
NXB Cido </(ic.H 2007
2 Tritn Vui Giai quyft vSfn dJ thirc te trong dpy hoc
t o i n NXB Dgi hgc Hui, 2014,
Currentfy, teachmg mathematics in school in Viet-nam IS heavily theoretical, away from reality It de-ics achievement of students Enhancing teaching maths towards exploiting the practical realistic ele-ments in primary school makes the teaching process become signiScant and high efficiency
Gipng Aieu tran HiuaL
(Tiep ffieo Irang 32)
nhleu nhat frong nen van hge hien dai Viet Nam Tat nhien trong van hgc, so' lupng khdng bao gid cd y nghTa quyet djnh ca Cai quyet djnh la chat luong.Td Hoai d mdi giai doan sang tae cua minh deu de lai nhi?ngtrarigedttiexem laco chat luong Trong hanh frinh dai d i n g dac ay, dng da tim cho minh mdt con dudng ttiehien rieng, mdt gipng tJeu rieng.mgtphong each nghe ttiuat rieng Ngudi dpc birdc day, hien nay
va mai sau ed le khdng ttie quen dupc nhi^nq ddng gdp ddc dao, dae sac eua Td Hoai doi vdi nen van chuong dan tgc ndi chung va nen van hpc Viet Nam hien dai ndi rieng •
(1) Nguyfin v a n Long (chii bifin) VSn hoc Vi^t Nam
hien dai (tiip n , tii sau Cach mang thang Tam 1945) NXB Dgi hgc suphgm H 2012
(2) U Ba HSn - Tr^n Dinh Sa - NguySn KhSc Phi
Gido due Viii Nam, H 2009
(3) Tfl Hoai C a t biii c h i n ai NXB Hdi Nhd vdn,
H 1992
T a i iieu t h a m khSo
1 Ha Minh Due (chii bifin) Li l u a n v i n hoc NXB
Cido due, H 200.^
2 Phong Lfi (gioi thifiu) Van Thanh (tuy^n chpn) Tfl
Hoai v^ tac gia va t i e pham NXB Cido due, H 2000
3 Nguygn Thj Ai Van Dgc diim nghf thudt lu truyin
vd hdi ki cUa Td Hodi Trudng Dai hpc sir ph^m TP
H6 Chi Minh, 2011
StIMMARY
To Hoai Is one ofthegreat writers of modem lit-erature in Vietnam To Hoai wrote many genres and with any genre To Hoai also achieved successfully
on both sides: the content and art Forte of To Hoai
Is memoir Artistic styles of To Hoai are expressed through memoir genre in terms of space: art space, art period of time, narrative tone, narrative language However, narrative tone Is one of attractive things which make artistic styles of To Hoai when he wrote 'Cat bui chan ai'
Tap chi Giao dye so 360 41