IIIBBBSBBS TlfTUdHG TOAN HOC HIEN DAI TRONG N A I DUNG S 6 TIT NHIEN M D N TOAN L0P1 TS TrJn Ngoc Bfch Tru&ng Dgi hpc Suphgm DH Thdi Nguyin SUMMARY Thinking of elementary students are intuitive, specl[.]
Trang 1IIIBBBSBBS
TlfTUdHG TOAN HOC HIEN DAI
TRONG N A I D U N G S 6 TIT NHIEN M D N TOAN L0P1
TS.TrJn Ngoc Bfch
Tru&ng Dgi hpc Suphgm - DH Thdi Nguyin SUMMARY
Thinking of elementary students are intuitive, speclfical Moreover the language of primary school students are not rich Thus, elementary math used visual Images, approached appropriately with psychological age However, in the visual images are implicit Ideas of modern mathematic The Paper research modem mathematical ideas that have implicit ideas in the concept of nature nimiber, compare two natural numbers, forming the addition, subtraction in math class 1
Keywords: Elementary education, elementary math, arithmetic
Ngdy n/tffn bdl: 6/9/2015; Ngdy duyft bdi: 28/9/2015
1 D$t vin dl
Nfi dung So hpc trong radn Todn d Tieu hpc
bao gIm s6 ty nhien, phan so vd so thfp phdn Trong
dd kiln thflc vl so ty nhien dupc cung cip cho hpc
smh (HS) tfl Idp 1 cho din hit kl 1 cfla Idp 4 Mpt
hong nhflng ddc dilm ciu triu: nfi dung cfla mdn
Todn & Tilu hpc dd Id "Hf thong cdc kiln thflc cfla
mdn Todn d tilu hgc dugc chgn lpe vd sdp xip nhdm
qudn trift tu tudng cfla todn hpc hifn dgi vfla chfl ^
din d$c dilm phdt Uiln tam li Ifla tuli"[3] Trong bdi
vilt chflng tdi phdn tfch tu tudng todn hpc hifn dgi
in tdng trong nfi dung s l ty nhien cfla Todn ldp 1 dl
cd cdi nhin sdu sic hem trong qud trlnh gidng dgy d
tilu hgc
2 Nhihig van de cor sd
a) Tpp hgp tuang duang
- Cho hai tfp hgp A vd B Tgp hpp A tuong
duong vdi tfp hpp B neu cd mpt song dnh tfl tgp hgp
A din tfp hpp B[l]
- Hai tfp hgp A vd B la tuong duong vdi nhau
khi vd chi khi lyc lugng cfla hai tgp hpp ndy bing
nhau
b) Tpp hgp hUu hgn
- Mft tfp hgp khdng hrong duong vdi bit kl mft
bf phfn thyc sy ndo cfla nd dugc ggi Id mft tgp hpp
hihi hgn Vf dy I) Tfp rong Id mft tfp hgp hihi hgn
Thft vfy, vl tgp rong khdng chfla mft bp phfn thyc
sy ndo nSn nd khdng hrong duong vdi bit ki mft bf
phfn thyc sy nao cfla nd, nen theo djnh nghTa, rSng
Id mgt tfp hpp hihi hgn
2) Tfp hpp A = {a} Id tgp hgp hflu hgn, vi {a}
chl cd mft tfp con thyc sy Id tfp rong, md tap rong
khdng tuong duong vdi {a}
c) Khdl nlim sd t\r nhien sd tg nhlin liin sau
- Bdn s6 cfla rapt tfp hgp hihi hgn dupc ggi Id
mft sl ty nhiSn Cdc so ty nhiSn lap thdnh raft tfp hgp Tgp hpp cac so ty nhifn ki hifu la N
Ta cd a e N => tin tgi tfp hgp httu hgn A, card
A = a
Vf dy 0 Id mpt so ty nhlSn vl 0 = card 0 , 0 Id tgp hgp hihi hgn
1 Id s l ty nhien vi 1 = card {x}, {x} Id tfp hihi hgn
So ty nhien Iiln sau: Gid sfl a, b Id hai sl t^r nhien, khi dd b la so Hen sau a nlu tin tgi cdc tgp hgp huu hgn A, B saochoa = cardA, b = cardB vdAc
B, B \ A Id mft tfp hgp don tfl (hay card (B\A) = 1)
Vf dy 1 Id s6 liln sau s6 0 Thft vfy, ta cd a = card 0 , 1 = card {x} vd 0 c {x}, {x} \ 0 = {x} Id tfp dem tfl
d) Phep cgng phep tru hai sd tir nhien
- Djnh nghTa phep cfng; Cho a, b Id hai sl ty
nhiSn Khi dd tin tgl hai tfp hgp huu hgn A, B sao cho a = card A, b = card B, A n B = 0 Ta cd a + b
= card (A u B)
- Dinh nghTa phep trfl hai s l ty nhiSn Cho hai sl
ty nhien a vd b vdi a ^ b Khi dd ton tgi so ty nhifn c sao cho a + c = b So c dugc ggi Id hifu cfla b vd, ki hifu c = b - a
3 Tu tudng todn hgc hifn dgi in timg trong nfi dung s6 ty nhien cfla Todn Idp 1
3.1 Tu tu&ng todn hpc hipn dgi thi hipn trong npi dun^ hlnh thdnh khdi nipm si t^ nhiin a) Y hfdng luang duang trong Todn ldp I
Y tudng tuong duong Uong todn Tilu hgc dupc
thl hifn qua bdi "Bdng nhau Dau =" [2] trong sdch
gido khoa (SGK) Todn 1 SGK Todn I dua ra cdc bflc tranh:
Trang 2ba bing bfl
Bflc Uanh thfl nhit vS ba con huou vd ba byi
cd Moi con huou dupc nli vdi mft byi cd bdng mft
dogn thing, nhu vfy Id dd ngim thilt Ifp mft song
dnh tfl tfp hpp nhttng con hucm din tgp hpp nhihig
byi cd Do dd cd thl hilu ta dugc tfp hgp nhfhig con
huou Id tuong duong vdi tfp h ^ nhfhig byi cd Tfl
nhfhig hinh dnh tryc quan gin giii vdi cufc sing
hdng ngdy, SGK Todn 1 dd tdng mflc dp trim tugng
hon bdng cdch sfl dyng nhihig chim Udn ldm hlnh
dnh tryc quan Khi dd ta ciing cd tfp hpp nhflng cham
trdn ben trdi id tuong duong vdi tfp hpp nhttng chim
trdn ben phdi Hai tfp hgp Id tuong duong vdi nhau
thl chflng ed cflng lyc lugng nfn lye lugng cfla tfp
hgp nhflng chim trdn bSn trdi bdng lyc Iugng cfla tfp
hgp nhQng chim trdn bSn phdi vd bdng 3 hay 3 = 3
Bflc tranh thfl hai vS b6n chile coc, Uong mSi
chile c6c cd bd mft chile thia Bflc tranh ndy cibig
ngim thilt lfp quan hf tuong img 1 - 1 hay chinh id
thiet Ifp mgt song dnh tfl tfp hgp nhQng chile clc
din ^ hgp nhftng chile thia Nhu vfy ta cd tfp hpp
nhQng chile clc Id tuong duong vdi tgp hpp nhQng
Chile tfiia Sau dd, SGK sfl dyng cdc hinh vudng dl
tdng mflc df trflu tugng vd gin vdi todn hpc Nhin
vdo hlnh vS ta thiy mSi hlnh vudng mdu xanh duge
nli tuong flng vdi mft hlnh vudng mdu trdng vd sy
tuong flng ndy Id I - I Do dd cd mft so sdnh tfl tfp
hgp nhihig hlnh vudng mdu xanh din tfp hgp nhftng
hlnh vudng mdu h ^ nSn hai tfp hgp ndy Id tuong
duong vdi nhau VI vfy lyc lugng cfla tfp hgp nhttng
hinh vudng mdu xanh bfing lyc lugng cfla tfp hgp
nhftng hlnh vudng mdu trdng vd bflng 4 hay ta cd 4
= 4
b) Tpip hgp hOu hgn thi hipn trong todn Tliu hgc
Khi hlnh tiidnh cho HS cdc s6 1, 2, 3, 4 5 (cdn
gpi Id cdc s6 tryc gidc) till SGK Todn 1 dd sfl dyng cdc
tfp hqi hftu hgn, Cy thl, khi hlnh tiidnh eho HS sl 1,
SGK da sfl dyng bflc hanh cd mft bgn gdi Qua bflc
tranh ndy cd thl hilu ddy Id tgp hpp don tfl, rad tgp hpp don tfl thi chi cd mft tgp con thyc sy Id tfp r5ng vd tfp r§ng thi khdng tuong duong vdi tap hpp don tfl Do dd t ^ hpp cd mpt phan tfl Id t ^ hpp huu han
Tuong tu nhu vay khi hinh tiidnh cho HS sd 2, SGK dua ra bflc Uanh cd 2 bgn ngdm Idling djnh ddy la tfp hgp hflu hgn Tfp hpp nay cd hai tfp con thyc sy Id tgp rdng vd tfp hpp don tfl, nhung hai tgp con thyc sy khdng tuong duong vdi tfp hgp cd 2 phin tfl
c) vdn di khdi nipm sd tyr nhien vd sd tg nhlin lien sau trong todn Tieu hgc
Cdc s l ty nhiSn 1,2,3,4,5 dupc gidi thifu cho
HS ldp I qua hai bdi
"Cdc s6 1, 2, 3" vd
"Cdc s6 1,2, 3,4, 5"
[2] SGK Todn 1 dd sfl dyng cde tfp hgp tuong duong, nghTa
Id cdc tfp hpp cd
cflng bdn s6 dk hlnh
tiidnh cho HS bilu tupng ban diu vl s6
ty nhifn Chflng lign, SGK Todn 1 dd sfl dyng cdc tfp hpp cd mft phan tfl nhu 1 con chim, I bgn gai, I chim trdn, 1 con tinh khi hinh thdnh bilu tupng ve
s l 1; tfp hpp cd hai phin tfl nhu 2 con mfo, 2 bgn, 2 chim trdn, 2 con tinh dl hhih tiidnh sd 2; tfp hpp cd
3 phin tfl nhu 3 bdng hoa, 3 bgn, 3 chim trdn, 3 con tlnh dl hhih tiidnh bilu tupng sd 3 cho HS
v i n dl so ty nhtSn Iiln sau dupc sfl dyng khi hlnh thdnh bilu tugng ban diu vl s6 ty nhien cho HS tilu hgc khi gidi thifu s l 6,7,8,9 Chdng hgn, hvng bdi "Sl 6", SGK dua ra bflc tranh ed 5 bgn dang choi,
1 bgn chgy din Id 6 bgn; cd 5 chim Udn thSm I chim trdn Id 6 chim tr&n Tfl dd hlnh thdnh cho HS bilu tugng ban diu vl s l 6 Qua dd ngim gidi thifu cho
HS s6 6 Id sl dflng liln sau s l S TUong ty nhu vfy vdi cdc so 7,8,9
3.2 Tu tu&ng toin hpc hipn dfil thi hipn & npi dung so sdnh hai sS tgr nhiin
v i n dl so sdnh so ty nhiSn h'ong todn Tilu hpc till hifn rd ti-ong bdi "Bf hem Diu <", "Ldn hon Diu
Trang 3
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M
cd sy tuong tflng 1 - 1 gifla hai tfp hgp ndy, nghla Id,
chl cd thl ghSp 1 chile d td d tfp hgp ben trai voi 1
chile d td d tfp hpp bfn phdi thl khi dd tgp hgp ben
phdi sg thfla 1 chile d td Qua dd ngim gidi thifu cd
mft don dnh tfl tgp hpp cac d td d ben Udi din tfp hpp
cdc d td & bSn phdi hay tgp hpp cdc d to d ben trdi
Id tuong ducmg vdi mft bg phfn tgp hgp cdc d td d
bSn phdi Nhu vfy, theo djnh nghTa vl quan hf thfl ty
trSn tfp hpp sl ty nhifn ta cd mpt bS hon hai Tuong
ty nhu vfy vdi hiic Uanh thfl hai ta cd hai bi hon ba
Bdi "Ldn hon Diu >" [2] SGK dua ra hai bflc
tranh, mli bflc tranh in chflra 2 tfp hpp md sl lupng
cdc phin tfl cfla hai tfp hpp ndy Id khdc nhau Khi dd
thilt lfp dugc raft dem dnh tfl tfp hgp bSn phdi din
tfp hgp bfn trdi Dya vdo quan hf thfl ty tren tgp hpp
s6 ty nhiSn ta ed hai ldn hon rapt, ba ldn hon hai
3.3 Tu tu&ng todn hpc hipn dgi thi hipn trong
nptdungphip cpng,phip trksSt^nhiin
a) vdn de hinh thdnh khdi nipm phep cgng
Khdi nifm ban diu vl phSp cfng dugc gidl thifu
eho HS Tilu hgc trong SGK Todn 1 tiidng qua hinh
dnh tryc quan Chdng hgn, trong bai "Phep cgng
trong phgm vi 3" [2], khi hinh thdnh cho hpc sinh
phfp tinh 2 + 1 = 3 thi Todn 1 dfl sfl dyng hlnh dnh
tivc quan Id mft bflc tranh vS cdc xe d td Bflc tranh
ngim chuyin tdi npi dung todn hpc: cd hai tfp hgp
khdng giao nhau, tfp hgp
ben Udi ed 2 phin tfl, tap
hgp ben phdi cd 1 phdn tfl;
hgp cfla hai tfp hpp ndy Id
mft tfp hgp cd 3 phin tfl
Do dd tiieo djnh n^Ta phfp
c p n g t h i t a c d 2 + l = 3 T f l
hinh dnh tryc quan la d td
gin gui vdi cufc song cua
HSthlTodn 1 dS trim tupng
bda hem khi dua ra hinh dnh
bilu dl Ven minh hpa cho
•d'm
^
4^
9<d
phep cpng 2 + 1 = 3 Hinh anh minh hpa cfla bieu dl Ven cflng ngim bieu thj npi dung djnh nghTa phep cgng hai so ty nhiSn
b) Vdn de hinh thdnh khdi nlim phep trir
Khdi nifm phep tru Uong SGK Todn
I dugc xdy dyng uSn
CO sd xet phin bfl cua mft tfp hgp doi vdi tfp con cfla nd
Chdng hgn, bdi "Phep trfl Uong phgm vi 5"
[2] hinh thdnh cho hgc sinh cdc phfp trfl trong phgm vi S thdng qua hlnh dnh tryc quan dl HS ty phdt hifn ra cdc phfp
tinh d bflc tranh thfl nhit: Cd 5 qud d trfn canh, c61
qud ryng xulng Hdi cdn miy qud & tren cdnh? Nhdm hlnh thdnh cho hgc sinh ph6p tinh 5 - 1 = 4 Tuong
ty vdi cdc bflc tranh edn lg! hlnh thdnh eho hpc sinh cdc phSp tinh 5 - 2 = 3, 5 - 3 = 2 , 5 - 4 = 1 Sau df SGK gidi thifu bilu do Ven minh hpa cho phep tinh
5 - 1 = 4; 5 - 4 = 1 Khi nhin vdo bilu dl Ven ndy thi hpc sinh cQng sS dpc dupc ph6p tinh cfng 1+4 = 5 hofc 4 + 1 = 5 Qua dd HS thiy phep trfl la phSp tlnh ngupc cfla phfp cfng
4 Kit lufn Trong dgy hpc mdn Todn d Tilu hpc ddi hfi ngu&i gido vien (GV) phdi hilu dflng vd hilu sdu sSc dupc tu tudng todn hpc hifn dgi in tdng trong cdcflf i dung Thdng qua vifc hieu dupc bdn chit todn hgc hifn dgi trong toan tilu hpc sS giup GV chuyin tdi dugc chinh xdc npi dung todn hpc Tfl dd GV c6 thl chfl dfng, linh hogt, sdng tgo trong vifc dilu chinh npi dung dgy hpe phfl hpp vdi doi tupng HS, thyc tl cfla nhd Uudng, dja phuong
Tdi lifu tbam khdo
1 Bf Giao dye vd Ddo tgo - Dy dn phdt trien
gido viSn Tilu hpc (2007), Cdc tpp hgp sd NXB D^ii
hpc Su phgm - NXB Giflo dye
2 Bf Giao dye vfl Ddo tgo (2010) Todn I NXB
Gido dye
3 Do Trung Hifu, Do Dinh Hoan, Vfl Duong Thyy, Vu Quic Chung(l999)./'Ai/o7)^;jA(ip(/<iK/;flc
mdn Todn & ItSu hpc NXB Gido dye