Tu lieu tham khao So SO nam 2013 PHAT HUY TINH TICH ClTC VA SANG TAO CUA HQC SINH TRONG MOI TRITONG KHAO SAT TOAN NGUYEN THI DUVeN'''' T6M TAT Khdo sdt todn Id mgt liip egn dgy hge ldy hge sinh ldm Irung[.]
Trang 1Tu- lieu tham khao
PHAT HUY TINH TICH ClTC VA SANG TAO CUA HQC SINH
TRONG MOI TRITONG KHAO SAT TOAN
NGUYEN THI DUVeN' T6M TAT
Khdo sdt todn Id mgt liip egn dgy hge ldy hge sinh ldm Irung Idm Tiep can ndy dd
vd dang dugc nghien ciiu vd dp dgng trong cdc Ihue hdnh dgy hge de ddi mdi viic hoc lodn eua hge sinh Bdi viil ndy trinh bdy tdc dgng ciia liip can khdo sdt lodn den tinh lich cue vd sdng Igo cita hoc sinh Irong qud trinh hge todn cita cde em dga tren mdi nghien cim dinh tinh ve tiep cdn ndy
Tir khoa: khao sat loan, quy trinh khao sat loan, mdi trudng khio sat toin
ABSTRACT
Promoting students' being active and creative
in mathematical investigation environment
Mathematical investigation is a student-centered teaching approach This approach has been being studied and applied to teaching practices lo innovate students' mathematics learning This paper presents Ihe impact of mathematical investigation approach on students' being active and creative during their mathematical learning process from a qualitative research on this approach
Keywords: Mathematical investigation, mathematical investigation process,
mathematical investigation environment
I Md dau
Phat huy tinh tieh eye va sang tao
eiia hpe sinh trong qua trinh hpc toan li
mdt trong nhitng yeu ciu cap thiit ciia
nln giio dye nudc ta trong giai doan hien
nay nham dap iing yeu cau ddi mdi viec
day hpc toan trong nha tnrdng phd thdng
va theo kip xu hudng tiln bp trong giio
dye toin fren thi gidi Mac dii chuong
trinh toan da duac ddi mdi hucing din
viec phit frien tu duy toan hpc eho hpc
sinh, tuy nhien viec hpc toan cua mdt bp
phan cac em hpc sinh van chua dim bao
dupe ylu td tich cue vi sing tao [2]
Nghien eiiu cua tic gii niy ehi ra ring
hau het hpc sinh, ke ca cac hpc sinh cd
TiiS Trudng D^i hpc Su pham Hue
nang khieu toan chi dupe giao nhitng bii toan mang tinh quy trinh la ehu yeu Cac
em it cd ca hpi khim phi nhiing bii toin mang tinh thieh thuc, yeu eau kha nang giii quyet eac van de thyc tien va cie loai hinh tu duy bac cao Vi the hau hit hpc sinh it cd himg thu vdi eac gid hpc toin cua minh Trong luc dd, nhieu nghien cim da chi ra rang hpc sinh th|t sy bj cudn hilt vio mpt gid hpc toin neu cac
em dupe hpc toin trong mdt mdi trudng ehua dung nhieu ylu td thach thuc va kich thieh tri td md, tudng tupng cua cic
em [4] Nhilu tilp can day hpc da dupe
dl xuat dl tim kiem cic mdi trudng hpc tap tuang tac nhim thiic diy vipe hpc toan ciia hpc sinh nhu: tilp can hdi-tim, giii quyet vin dl, khio sat toin Trong
Trang 2dd, khao sat toan dugc xem la tiep can
day hge cd the mang lai nhieu co hgi cho
hge sinh hoc toan mdt each tich cue va
sang tao Tiep can dgy hoc nay da va
dang thu hut su quan tam, nghien ciiu ciia
cac nha giao due tren the gidi nham tim
kilm each thiic de cai tien viec hoc toan
ciia hge sinh va phat trien nang luc toan
hoc cho cac em Tuy nhien, d nudc ta
ti£p can nay van chua dugc quan tam
nghien ciiu va ap dung mdt each rdng rai
vao thuc tien day hge d trudng phd
thdng Vi the, can tien hanh nhieu nghien
Cliu hudng den viec tim hieu tac dgng cua
tiep can khao sat toan len qua trinh hoc
toan ciia hoc sinh nh4m phat huy tinh tich
cue va sang tao cua cac em trong qua
trinh hge toan
Phuong phap nghien ciiu chinh
dugc Sli dung trong nghien ciiu nay la
phuang phap dinh tinh Hai hoat ddng
chinh trong nghien ciiu nay la quan sat
hpc sinh khi cac em hge tap trong mdi
trudng khao sat toan va phdng vdn cac
em trudc va sau cac tiet hoc dd Thanh
phan tham gia vao nghien ciiu nay gdm
cac hge sinh cua nhirng lap chgn ban tu
nhien 11 A,,11 A, va 12 A, d mdt trudng
trung hoc phd thdng viing ngoai d thanh
pho Hul Cdng cu ciia nghien ciiu nay la
cac tinh hudng khao sat toan va bang cau
hdi phdng \kn hoc sinh De thu thap du
lieu eho nghien ciiu nay, cac cugc phdng
van ban d^u se dugc thuc hien nham tim
hieu v6 mdi trudng hge toan hang ngay
cua hge sinh Tilp den, cac quan sat va
ghi chu \h cac chii diem du dinh thiic day
tinh tich cue va sang tao ciia hoc sinh se
dugc thuc hien khi cac em lam viec trong mdi trudng khao sat toan Sau do, cac cugc phdng vdn hge sinh se dugc tiln hanh nham tim hieu tac ddng ciia moi trudng khao sat toan len viec hge toan ciia cac em Du lieu thu dugc tu nghien Cliu nay se dugc phan tich mdt each djnh tinh Giai doan dau tien trong qua trinh phan tich dii lieu Men quan den viec viet
ra cac ghi nhd tir viec xem lai cac bang ghi hinh va ghi am cung nhu dgc lai cac ghi chii dugc thuc hien khi quan sat va phdng van hoc sinh Nhiing ghi nhd nay
la cac md ta tdm tat ve thdng tin thu dugc tir cac bang ghi am va cac ghi chii va dugc sir dung nhu nhung thdng tin ban dau de tim hieu ve ca hdi hge tap da nay sinh giiia cac hge sinh tham gia vao nghien ciiu nay khi cac em lam vi?c trong mdi trudng khao sat toan Viec ma hda do- lieu se dua tren nhihig ghi nhd nay va dugc thuc hien bang each diing cac tir
khda ia dgt cdu hoi, dua ra cdc y tudng
vd cde gid thuyei, thu thgp vd xir li dir lieu, dua ra cdc kit ludn vd cdc tong qudt hoa, sir dung suy lugn quy ngp vd suy lugn ngogi suy Nhung tir khda nay la
nhiing thuat ngu Men quan den cac thanh
td trong quy trinh khao sat toan ma hge sinh se tiln hanh khi cac em hge tap trong mdi trudng day hge liy khao sat Iam trung tam Chiing cung la nhihig thanh td cd mdi lien he mat thiet vdi tinh tich cue va sang tao cua hge sinh trong qua trinh hge toan Mgt tiep can diln giai
se dugc sii dung trong khi phan tich dit lieu dl riit ra nhtmg kit luan tir nhiing thdng tin thu dugc
Trang 3Tu" li§u tham khao
2 Phat huy tinh tich circ va sang tao
cua hpc sinh trong moi trirdng khao
sat toan
2.1 Quy trtnh khdo sdt todn
Khao sat toan la mgt tiep can day
hoc da dugc cac nha giao due tren thi
gidi quan tam nghien ciiu va ap dung vao
thuc tiln day hoc tir nhung nam 1970
Tuy nhien, hien nay cac nha giao due van
chua tim dugc su thdng nhat trong quan
niem vS thuat ngii nay Mgt sd nha giao
due ling hg quan dilm cho rang khao sat
toan la tilp can md [3, 7] Hg eho ring
khao sat toan la qua trinh hge sinh kham
pha cac bai toan md bang each tiep can tir
nhilu con dudng khac nhau nhSm dua
din nhilu y tudng toan va nhilu ldi giai
khac nhau Ndi each khac, khao sat toan
la qua trinh hge sinh tien hanh kham pha
cac bai toan cd mue dich, quy trinh va ldi
giai mang tinh chat md Trong khi dd,
mdt sd nha giao due khac lai dua ra quan niem khac ve cdng viec khao sat toan [5, 9] Trong nghien ciiu ve qua trinh nhan thirc ciia hge sinh khi cac em hoc tap trong mdi trudng khao sat toan, hai tac gia Yeo va Yeap cho rang khao s^t toan
la qua trinh hoc sinh kham pha cac bai toan bang nhirng thao tac nhu dac biet hda, phdng doan, kiem chung va tdng quat hda Vi khao sat toan dirge xem xet tren gdc dd la mot quy trinh nhan thiic nen nd khdng bd hep vao cae bai toan md
ma cd the tich hgp vao cac bai toan ddng Tir hai quan diem neu tren, cd the xem khao sat toan la qua trinh hge sinh tim tdi, giai quyet cac tinh hudng toan hge phiic tap thdng qua cac hoat ddng nhu nghi van, thii nghidm, kiem chimg, khai quat hda va phan anh Mgt quy trinh khao sat toan gdm cac buac theo sa dd sau:
Dat cau hdi
gia thin-et
/"
Phan anil,
da J ill gia
^
^4 Thu thap liir heu
tnu kiem idi giai
t/
Ket hiiin
tdng quat hda
Hinh 1 Quy trinh khdo sdi lodn
Budc diu tien frong qui trinh khio
sat toin lien quan din viee tim hilu tinh
hudng ban diu dl dat ra cic cau hdi, tim
kiem cie myc dich dl khim phi, xay
dyng eac gia thuylt bing cic hoat ddng
thye nghipm toan nhu dac biet hda, doin
va thu, tim kilm quy luat Budc tilp
theo lien quan din cic boat ddng nhu thu thap dit lieu, tim phucmg in dl giii quylt van de, kilm chimg hay bic bd cac gia thuylt Budc kl tilp lien quan din viec nit ra cic ket lujn va tdng quit hda Bude cudi cung trong quy trinh nay lien quan din cac hoat dpng nhu thao luan,
Trang 4Nguyen Thj Duyin
danh gia ve cac phucmg an giai quylt vin
dl, md rdng cac ket qua tim kilm dugc
d^t ra cac cau hdi de tiln hanh nhung
kham pha xa han Qua trinh khao sat toan
khdng dimg lai d budc nay ma vSn tilp
tuc vdi nhiing chu trinh tilp theo Cac
budc trong quy trinh khao sat toan khdng
dua ra cac chi din cu the cho viec kham
pha cac tinh hudng ri^ng le ma chi cung
cip cac ggi y mang tinh dinh hudng dl
kich thich ngudi hge theo dudi cac nghi
van cua minh trong qua trinh kham pha
kien thiic
2.2 Moi trudng day hpc ldy khdo sdt todn ldm trung tdm
Mdi trudng day hoc liy khao sat toan lam trung tam la mdi trudng su pham ed dae trung the hien d viec hge sinh tiln hanh cac hoat ddng khao sat toan khi eac em giai quylt cac nhiem vu hoc tap dugc yeu cau Cd bdn ylu to ciu thanh nen mdi trudng day hge liy khao sat toan lam trung tam: tinh hudng khao sat, khao sat toan, hoc sinh, giao vien theo sa dd sau:
Hinh 2 Moi trudng dgy hpe ldy khdo sdt ldm trung tdm
IChi hoc t$p trong moi trudng khao
sat toan, hge sinh bj cudn hiit vao cac tinh
hudng khao sat ddi hdi cac em phai dat
cac cau hdi, dua ra cac gia thuySt, thu
thap dii lieu va tien hanh nghien ciiu
Kiln thiic toan se dugc chilm linh bdi
nhiing hge sinh tich ci^c tham gia vao qua
trinh khao sat toan de tim kilm cau tra ldi
cho nhCing cau hdi ciia minh Van de ca
ban nhat trong qua trinh khao sat toan
khdng phai la viec hge sinh dua ra dugc
cau tra ldi diing ma viec cac em dat ra
dugc cac cau hdi va tim kiem eho minh
mdt muc dich de kham pha tinh hudng ban dau Khi tien hanh qua trinh khao sat toan, eac em se dat ra cho minh cac cau hdi cd dang nhu nhirng van de nao dugc dat ra trong tinh hudng nay, dieu gi se xay ra neu ta xem xet phan nay hay phan kia ciia tinh hudng, nhiing chiln luge giai quylt vin dl nao se dugc sir dung, nhtmg phucmg an glal quyet van de nao cd the chap nhan, phuang an nao la tdi uu Cac em ciing sir dung hai kieu suy luan dac trung khi kham pha toan dd la suy luan quy nap va suy luan ngoai suy Neu
Trang 5Tu" li§u tham khao
nhu suy luan-quy nap dupe xem la qui
trinh suy l u ^ nhim dua din ket qui tdng
quit tu hOn ban cic kit qua tuong ty tit
mdt sd trudng hpp dat biet thi suy l u ^
ngoai suy li qua trinh suy luan nham tim
kiem hoac xay dyng mpt gia thuyet phii
hpp nhat de giii thich cho nhiing gi quan
sat dupe [1] Mac du khdng cd gi dam
bio gia thuyet tren li dung nhtmg cic
kieu suy luan nay cd the mang den sy
sing tao khi hpc toan
Vai frd cua ngudi giio vien la cung
cap cho hpc sinh cae tinh hudng khao sit
toan mang tinh van de eao vi chira dyng
nhieu co hpi cho hpc sinh khim pha kien
thirc toan Giao vien li ngudi dua ra cac
chi dan mang tinh dinh hucing khi that sy
can thiet de trp giup hpc sinh lim sing td
eae nghi van nham giup eac em theo dudi
nhirng kham phi xa hon trong qui trinh
khio sat toan
2.3 Dgc trung cua Ilnh hudng khdo
sdt todn
Cic tinh hudng khao sit hop li va
ldi cudn la yeu td co bin nham dam bao
thinh cdng cua mdt gid hpc toan trong
mdi trucmg day bpc liy khio sat lim
trung tam [6] Cic tic gii niy cung chi ra
rang xay dyng mdt mdi trudng thiic diy
viec hpe vdi nbieu ca hdi dl hpc sinh
tranh luan va phin anh li cin thiit nhung
chua du nlu tinh hudng khio sat khdng
dii thach thiic vi thilu tinh kich thieh qua
trinh khim phi toan eiia hpe sinh Vay
mpt tinh budng khio sit toan phai dim
bao nhdng ylu td gi dl cd thi thue diy
viec khim phi toin eua hpc sinh nhim
phit huy tdi da tinh tich eye nhan thirc
cua cac em? Mdt tinh hudng khio sit
toin duoc xem li ed tinh thiie day viee kham pha toin cua hpc sinh neu nd tich hop dupe mpt sd dac trung sau: Kieh thich hpc sinh dat ra cac nghi van va cac gii thuyet trong qua trinh kham pha kien thirc Tir dd, cic em tich cyc thu thap, xir li cic dd lieu de tim ra cau tra ldi cho nhitng nghi van cua chinh minh, khang dinh hay bac bd nhihig gii thuyet da dupe dua ra, tim kiem eic quy luat hoac di din cac tdng quit hda, tilp tuc de xuat nhung cau hdi hay nhiing gii thuyet mdi de theo dudi nhirng khim phi xahan
Mang lai nhieu ca hdi de hpc sinh phat huy tri tudng tuang vi phit trien thdi quen suy nghT mdt each sang tao Mdt khi hpc sinh cd the tiep can tinh hudng hpc tap dudi nhieu gdc dp, dat ra dupe nhieu nghi van vi gii thuyet khic nhau de md rdng tinh hudng khao sit ban dau thi cac em cd nhieu ca hdi de phat huy thdi quen suy nghT mpt cich phan ki
vi nang luc sing tao cua bin than Ddi hdi hpc sinh phai tich hop mdt each sing tao cic kiln thitc va kT nang khdng ehi cua mdn toin ma cua cic mdn hpc khac Hpc sinh cd co hdi sir dung cic kien thire vi kl nang lien mdn theo each thyc tl nhat khi khim phi kiln thuc toan hpc Dieu do cd nghTa li each thirc mi hpc sinh suy nghT de giii quyet eic nhiem vu hpc tap phai gan gidng vdi cich mi cac
em suy nghT khi ddi mat vdi tinh hudng tuong ty trong eudc song hang ngay Vira dem lai himg khdi cho hpc sinh nhung vira du thich thiie dl kich thich cae hpc sinh theo dudi nhimg thic mac, nghi vin cua minh trong qua trinh
Trang 6Nguyen Thi Duyen
kham pha kien thirc Mdt mat, hge sinh
phai cd hiing thii va thay viec kham pha
linh hudng hge tap la dang lam va cd y
nghTa TLT dd cac em mong mudn tien
hanh viec khao sat va mong mudn thuc
hien thanh cdng cac qua trinh khao sat
Mat khac nidi hge sinh phai nd lire tdi da
de tiep can tinh hudng tiiy theo kha nang
ciia ban than minh Dieu nay ddi hdi linh
hudng hoc tap phai cd nhieu diem bat dau
phu hgp vdi trinh dd khac nhau ciia cac
hoc sinh trong lap hoc
Thiic day qua trinh giao tiep va thao
luan gitra cac hoc sinh trong tdp hoc
Tinh hudng phai mang lai ca hdi de hge sinh giao tiep va tranh luan vdi nhau ve eac y tudng toan hge trong mdt mdi trudng tuong tac d do cae em lam viec mgt each ca nhan va hgp tac, ciing nhau chia se cac y tudng de tien hanh cac khao sat xa ban
Cd the thay rd sir khac biet gitra mgt tinh hudng khao sat toan va mdt nhiem vu hge tap mang tinh tiuyen thdng khi so sanh chiing vdi nhau:
Nhiem vu HQC tap truyen thong
- Cau hdi dugc dat ra bdi giao vien
- T^p trung vao cac hoat dgng ghi nhd
nhan biet va ap dung mang tinh quy
trinh
- Khuyen khich cac hoat dgng nhd lai
va Ihuc hanh
- Tap trung chu yeu vao kien thirc va kT
nang trong mdn toan
- Thieu tinh thuc te va it khi dugc dat
trong vao mdt ngu canh cu the
- Viec md rdng bai toan dugc thuc hien
sau khi giai bai toan ban dau
- Cho phep ngudi hoc sir dung it chien
luge hge tap khi giai quyet van de
• Hge sinh chii )eu lam viec mdt each
ca nhan khi giai quyet cac bai toan
Tinh huong khao sat toan
- Tinh hudng ban dau co the do giao vien hoac hoc sinh dua ra nhiing cau hdi kham pha tinh hudng tiep theo thudng dugc dat ra bdi hge sinh
- Khuyen khich cac hoat ddng kham pha kien thiic bang viec thir nghiem, tien doan dac biet hda tdng quat hda vdi trgng tam la giai quyet van de
- Khuyen khich viec suy nghT, tudng tugng va phan anh
- Mang den cho hge sinh ca hdi sir dung kien thiic \a kT nang lien mdn bang each tich hgp cac tinh hudng thuc te vao mdi trudng khao sat toan
- Mang tinh thue te va dugc dat trong mgt ngir canh nao dd
- Viec md rgng bai toan dugc chiia dung trong tinh hudng ban dau
- Ddi hdi ngudi hoc phai sir dung nhieu chiln luge hge tap khac nhau
- Khuyin khich su hgp tac cua cac hoc sinh vao viec kham pha tinh hudng
Trang 7Tu' lieu tham khao
Mdt quy trinh kha him ich trong
viee giiip giio vien lim quen vdi viec
thiit kl cic cau hdi hieu qui trong day
hpc toan duoc dl xuit bdi Sullivan va
Lilbum [8] se dupe v§n dung de thiet ke
cic tinh hudng khao sit toan Quy trinh
niy gdm ba budc nhu sau:
Budc 1: Nhan ra mpt chil de cin day
Bude 2: Thiet kl mdt cau hdi ddng
vi tim cau tri Idi cho cau hdi dd
Budc 3: Thiit kl tinh hudng khio
sit toin tuong img mi qua trinh kham
phi tinh hudng nay bao him viec tim ra
cau tri ldi cho cau hdi ddng ndi tren
Xet vi dy ve viec thiet ke mpt tinh
hudng khao sat toan:
Budc 1: Chu de bai hpc li sd trung
binh
Budc 2: Cau hdi ddng cd the li:
Biem thi lot nghiep cudi cdp cdc mdn
Todn, Vdn, Li, Sinh, Sir vd Anh vdn cua
bgn An ldn lugt Id 7, 8, 6, 5, 7 vd 9 Biem
trung binh cdc mdn thi lot nghiep cua
bgn An Id bao nhieu?
Budc 3: Tinh hudng khao sit toin
tucmg img Ii: Biem irung binh edc mdn
Ihi lot nghiep cuoi cdp Todn, Vdn, Li,
Sinh, Sir vd Anh vdn cita bgn An Id 7
Biem thi mdi mdn cita bgn An Id bao
nhieu?
Rd rang viec khim phi tinh budng
niy se giiip hpc sinh tim ra dupe nhieu
Idi giai khic nhau trpng dd cd ea cau tri
ldi cho cau hdi ddng tucmg img Trong
khi viee tri ldi cau bdi ddng hucing hpe
sinh din viec ap dung kiln thue mang
tinh quy trinh tbi tinh budng khio sit
toan niy se mang lai nhieu ca hpi dl cac
em thyc hinb ve khii niem sd trung binh
nhim hilu sau ban vl khai niem niy
2.4 Tinh tich cifc vd sdng Igo cua hoc sinh trong moi tru&ng khdo sdt lodn
NhOng tinh hudng khio sat toan cd tinh thuc diy viee bpc se mang den hirng khdi eho hpe sinh va kich thieh eic em kien tri tim kilm nhtJng khim phi xa ban Kit qua tir viee quan sit lap hpe da eho thiy nang lye suy luan, dac biet la suy luan quy nap va suy luan ngoai suy dupe phit huy khi cac em kham pha cac tinh hudng khao sit toan Khi tiln hinh cac boat dpng khio sat toin, hpc sinh se diing suy luan quy nap de de xuat cic gia thuylt thdng qua viec tien hanh cae boat ddng dy doan, thir nghiem, tim kilm quy luat, tdng quit hda Cic em se diing suy luan ngoai suy dl dua ra eac gii thuylt phu hpp nhit tir nhirng dit lieu da cd de khim pha tinh hudng ban dau Cd the thay ro dieu niy qua viec phan tich dap img cua hpe sinh khi cac em lim viec vdi tinh hudng sd hinh
Tinh hudng 1 (so hinh) Du dodn sd hgng tdng qudt cua cdc ddy so lam gide hinh vudng, ngU gidc
Tinh hudng niy dupe thiet kl de day tiet ty chpn trong chuang Day sd, cap sd cdng va cap sd nhan, Dai sd vi Giai tich Icip 11 Nang cao Muc tieu cia tilt hpe niy la nham giiip hpc sinh lim quen vdi chien lupc tim kiem quy lu|it, cu the li tim kilm quy luat de du doan ket qua cua mdt sd bai toin frudc day dupe phat bilu dudi dang ehimg minh cic dang thirc d bii Phep quy nap Giio vien
se diing md hinh bieu diln tryc quan tit cie philu hpe tap dl giii thich cho hpc sinh thuat ngu sd hinh Dyng mdt da giic
Trang 8Nguyen Thi Duyen
deu ldi k dinh (k>3) vi canh li 1 dem vj
A la mdt dinh eua da giic dd, thyc hien
cac phep vi ty tim A ti sd 1, 2, , n-1
(n > 2) se thu dupe nhirng da giac diu k
eanh vi ty vdi da giac ban dau Tren cic
canh ciia da giic dd, xuat phit tir dinh A
danh dau eie diem each deu nhau mot
khoing bang don vi Sd cic diem dupe
dinb dau tren tat ca cic mien da giic
dyng dupe gpi la sd k-giac thit n cua day
sd k-giac Tiep din hpc sinh trong Idp dupe phan thinh cic nhdm vi dupe giao cac philu bpc tap cd chita md hinh bilu dien trye quan cua cie sd k-giae dl ty khim phi
Day sd tam giic: Hpc sinh dim sd chim tren mdi hinh bleu diln vi tim ra sd hang thit n cua day sd niy li tdng n so bang dau ciia mdt cap sd cdng cd sd hang dau li 1 vi cdng sai li 1:
1, = 1 t , = l + 2 t, = l + 2 + 3
."
Day sd hinh vudng: Hoc sinh dem sd cham tren mdi hinh bieu dien va tim ra sd hang thu n eua day sd nay la tdng n sd hang dau ciia mgt cap sd cgng cd sd hang diu la
1 va cdng sai la 2 Mdt sd hge sinh thi phat hien ra quy luat khac, cac em nhan ra sd hang thii n trong day sd nay la sd chinh phuang n":
s, = 1
S, = I
S j = l + 3
s, =2=
s , = l + 3 + 5
s, =3=
s,=l+3 + 5 + 7
s,=4=
^ = l+3 + 5 + 7 + - + ( 2 n - l ) = n' s„ =n"
Day sd ngu giac: Tuang tu hoc sinh tim ra sd hang thii n ciia day sd nay la tdng n
sd hang dau cua mdt cap sd cgng cd sd hang dau la 1 va cdng sai la 3:
p = l + 4 + 7 + 1 0 + - + ( 3 i l - 2 )
= n ( 3 n - l ) / 2
Hge sinh khdng dimg lai d viec tim
kilm sd hang tdng quat ciia cac day sd
tam giac, hinh vudng va ngu giac ma cdn
t\r minh dat cac eau hdi de kham xa han
ve tinh hudng eac sd hinh nay Cac em
thSc mic lieu cd the du doan sd hang
tdng quat cua mdt day sd luc giac va day
sd k-giac vdi k >3 tir tinh hudng nay hay khdng Mdt sd hge sinh da nhin ra dugc
su tuang tu khi tim kilm quy luat du doan sd hang tdng quat ciia day sd tam giac, hinh vudng va ngu giac Cac em
Trang 9Tu' lieu tham khao
nhan thiy t„ la tdng n sd hang dau cua
mdt cip sd cdng cd sd hang dau la 1 vi
cdng sai li 1 din s„ la tdng n sd hang
diu cua mdt cip sd cdng cd sd hang dau
la 1 va cdng sai li 2 vi p„ la tong n sd
hang diu ciia mdt cip sd cdng cd sd hjng diu li 1 va cdng sai li 3 Tit dd cac em dua ra gii thuylt cua minh ve sd hang tdng quit h_, ciia mdt day sd iyc giic:
Cd the ndi hpc sinh da sir dyng kieu
suy luan ngoai suy khi md rdng kham
phi trong tinh hudng niy Tir viec nhan
ra quy luat ddi vdi sd bang tdng quit ciia
day sd tam giic, blnb vudng va ngii giac,
bing cich tucmg tu hpc sinh di den gia
thuylt ve sd hang tdng quit cua day sd
Iyc giac Cac em cung nhan thay sd hang
tdng quit cua day sd tam giac, hinh
vudng, ngii giac vi luc giic deu ed sd
hang dau Ii 1 va edng sai bang sd eanh
eiia cic hinh dd tru di 2 nen cic em ciing
dl xuit mdt gia thuylt vl sd hang tdng quit ciia mdt day sd k-giac vdi k>3 li tdng n sd hang diu cua mdt cip sd cdng
cd sd hang diu la 1 vi cdng sai la k-2 hay u = l ( 2 + (n-l)(k-2))
Mdt sd hpc sinh cdn tiln hinh nhimg khim pha xa hon khi ed gang tim kiem mdi lien he giira cac sd hinh niy Cac em dua ra mpt sd du doin tbu vi khi ed gang tim kiem mdi lien he giira cic sd hinh dya tren bieu dien hinh hpc cua chung:
M;
s = t „ _ i + t „
p„ =n+3t„_|
Co the thay nang luc giao tiep toan
hge bang cac bieu dien bgi eua hoc sinh
se dugc phat huy khi cac em lam viec
trong mdi trudng khao sat toan Hge sinh
khdng nhiing lam toan vdi cac bieu dien
dai sd ma cac em cdn dung cac bieu dien
hinh hoc nhu mgt phuang tien de tien
hanh qua trinh suy luan ngoai suy nham
tim kiem cac gia thuylt khi tien hanh qua
trinh khao sat toan Ben canh do, viec co gang tim kiem bieu dien bgi trong qua trinh khao sat toan da lam cho tri tudng cua hge sinh phong phii hon Hoc sinh da dua ra dugc mdt sd dang bieu dien khac nhau cua day sd (n') Tir day cac em cung tim ra mdi lien he giiia cac dang bieu dien khac nhau cua da\ sd (nM vdi mo
Trang 10Nguyen Thi Duyen
hinh hinh hpc bieu dien tdng
S =l'+2-+ +n- Cie em da sudung mdi
lien he giiia cic bieu dien hinh bpc dd de
dy doin ket qui cua S, khi nhan thay
Sau dd eae em diing phep chimg minh quy nap de kiem chimg dy doin cua minh
Mdt sd hpc sinh cdn tien hinh nhirng
khim pha xa ban khi cd ging tim kiem
phuong phip tinh tryc tiep S, Cac sd
hang ]-, 2- n- trong tdng nay Iam cic em
lien tudng den viec su dung cic bang dang
thitc dang (l + xf vdi x=0,l,2 , Tuy
nhien khi eic em edng eie hang dang thirc
ve theo ve thi eic sd hang ]-, 2', , n- bi triet tieu nhtmg lai tim ra tdng
S, = ! + 2+ +n Dieu dd Iam eho eie em nghT den viec diing cic hang dang thifc dang tuong ty nhung bac phai cao hem 1 don vi la (i + x)\ Cac em thay x = o i, 2 ,TI vio hang dang thiie dang (i + x)':
3'- (-ttJ)-'- ^'r t ?^ < !'-,}'
-(1*4^ J = ^ fj)i.=- ^ Ij y , *" n
fatjXffl-ltir ruT f ,<( <Y >^^ •^•^iJ
- - ^ - i ( (nifi^-trtlj) WciMji
Mpt SO hpe sinh khdng dimg lai d
viec tim ra tdng s, bing each tuong ty
cic em cho ring cd the diing cic hang
ding thirc dang (i + x)' de tinh tdng
S, = l'+2"+ +11" Rd ring, dy doin eiia
eic em la chinh xac Cd the thiy mdi
trucmg khao sit toan da mang den cbo
hpc sinh nhilu co hpi de khim pha kien
thitc toan Cic em khdng bi gd bd vao
cic phuang phip giii quyet eic bai toan
dupe trinh bay trong sich giao khoa ma
cd ging tim kiem eic con ducmg tiep cin
khae eho rieng minh Cic em ty do di-xuat cic gii thuyet vi theo dudi cic y tudng de tim kiem cho minh nhirng ket qui mdi va thu vi bing eich tiln hinh eie boat ddng ngoai suy, quy nap, tuong
ty, tim kiem quy luat vi tdng quit hda Ben eanh dd, viec khim phi cic tinh budng khio sat md cdn mang den eo hpi eho hpc sinh tim ra cic phuang in giai quylt vin dl phii hpp vdi khi ning ciia bin than minh Cd thi thiy rd dieu niy qua viec phan tich dip img ciia hpc sinh vdi tinb hudng tai khoin tiet kipm