SU^ DUNG MO HINH AO THAO TAC BlTOC TRONG DAY HQC KHAI NIEM HAM SO 6 LOfP 10 NGUYEN THI HONG CHUYEN Tnrang THPTBdc Yen Thanh Nghi An Tom tat Mpt trong nhirag giai phap ung dung cong nghe thong tin tron[.]
SU^ DUNG MO HINH A O T H A O TAC BlTOC TRONG DAY HQC KHAI N I E M HAM SO LOfP 10 NGUYEN THI HONG CHUYEN Tnrang THPTBdc Yen Thanh Nghi An Tom tat: Mpt nhirag giai phap ung dung cong nghe thong tin day hpc toan hien la thilt ka va sir dung mo hinh ao thao tac dugc (MHATTD) Xu huong dang dugc nhi^u nha giao due trong, ngoai nude quan tam va da dat dupe nhung cong nhdt dinh day hpc toan Muc dich ciia bai bao nhkm lam sang to han nhiJng h6 trg tich cue ciia MHATTD day hpc toan hpc d trudng ph6 thong qua viec day khai niem ham so, Tir khoa: Virtual manipulatives QUAN NIEM \'E MO HINH AO THAO TAC Dl/OC Cd kha nhieu quan niem vk MHATTD, de phii hgp vdi nghien cuu cua bai bao chiing toi sii dung dinh nghia cua Patricia Moyer, Johima Bolya and Mark Spikell [5]: MHATTD la moi su biiu dien true quan tren man hinh may tinh hoac tren website cua ddi tuong dgng ma no hoc 16 nhung ca hoi cho nguai hoc kien tao tri thuc toan Hien nay, tran mang internet cd hai loai mo hinh ao dgng va tinh Cac md hinh ao tTnh la nhung hinh anh, hinh ve co dinh, biau dien ciia dung vat ly cu tha su dung Idp hgc ma hpc sinh (HS) khong tha thao tac (nhu trugt, lat, xoay ) len chiing nhu sii dung d6 diing vat ly cu the Vdi cac md hinh ao dong, HS cd tha xay dung y nghia theo each ciia riang hg bang each sir dung may tinh de dieu khien cac ddi tugng tren man binh nhu lat, trugt, xoay Cac md hinh ao dgng dugc gpi la MHATTD N H I T N G H O T R O TICH CI/C CUA MO HINH AO THAO TAC DUOC TRONG DAY HOC TOAN a) MHA TTB ho tra HS quan sat, khdm phd, kien tao tri thuc Cac ly thuyet ve giao due gan day thiic day phat trien cua sir hieu biat khai niem bon la day hpc cac quy trinh, ghi nhd cac su kien va cong thuc Ly thuyet kian tao cho rang HS hpc tot nhat cac em dugc dat mot mdi trudng hpc tap cd tinh xa hoi tich cue, d dd cac em cd dieu kien va kha nang de kian tao su hieu biat cua rieng minh (Tran Vui, [4]) Viec hpc tap ciia HS se hieu qua ban giao vien (GV) su dung nhieu chien luge giang day, la su kat hgp cua cac hoat dgng nghe, nhin va lam Mot phuong phap bien de giiip HS quan sat, kham pha, kiln tao tri thuc mdi cho ban than minh la su dung cac MHATTD Vdi tinh nang cua nhung phan mem dgng, cho phep tao md hinh true quan, ho trg HS quan sat so sanh de nit dugc nhung "thdng tin ben trong" chua dung chiing MHATTD tao mdi trudng khao sat toan Khi dugc thao tac tren cac rod Tap chi Khoa hoc va Giao due, Tniong Dai hoc Su pham Hu^ ISSN 1859-1612, S6 01(29)/20I4:tt.16-23 su DUNG MO HINH AO THAO TAC DUOC hinh, HS chii dgng hon viec du doan, kham pha, nhan biat dugc cac dac trung, cac trang thai trung gian va mdi quan he cua cac ddi tugng toan hoc tir HS co tha kian tao tri thuc cho ban than minh b) MHATTD giup HS co su hieu Met sau sac han vi cac khai niSm toan hgc Nhiau nghien ciiii cho thSy HS cung cd thi phat trien su hieu biet ve cac khai niem phuc tap hon su dung MHATTD Cac md hinh co thi tao cong cu minh hga vdi nhiJng hinh anh song dgng, va dac biet him ich cho cac HS viec kian tao tri thuc nen gdp phan quan trong viec hieu sau s§c khai niem toan hpc Kha nang ket hgp nhieu bieu dian mot mdi trudng ao cho phep HS thao tac va thay doi cac ddi tugng, do tang kha nang tham dd da phat trien cac khai niem va kiem tra cac gia thuyet Viec su dung ed hieu qua MHATTD cd the giiip HS kat ndi y tudng va tich hgp cac kian thuc ciia minh da dat dugc su hieu biat sau sac ve khai niem toan hpc c) MHATTD tao moi tru&ng co van de nham ho tree hieu qua qua trinh giai quyet vande Hien nay, xu hudng doi mdi chuong trinh toan thdng, nang luc giai quyet van de (GQVD) va cac ki nang tu bac cao rat dugc eac nha giao due chii Cac MHATTD dugc thiat ka bang phSn mem GSP cd the tao moi trudng cd van dS Van de d day cd the xuit phat tir y tudng thiet ke ciia GV mong mudn dat cho HS hoac sinh qua trinh HS tuong tac vdi mo hinh Vdi tinh nang ca boat, than thien ciia MHATTD nd cho phep HS thao tac, quan sat, kham pha, thiet lap nen tang kien thirc, lam eho HS cam thay tu tin vdi each tiep can mot md hinh toan hgc va cac em cd the du doan cong thdc, de xuat nhihig y tudng qua trinh GQVD d) MHA TTD ho tra HSphdt trien kha nang tu toan hgc Viec hgc toan la mot qua trinh sang tao chir khong phai tiep thu mot thuc the kien thuc sin cd Do nhiem vu cua ngudi GV la md rpng tri tue ciia HS chu khong phai la lam d^y tri tue eiia cac em bang each truyan thu tri thuc da ed (Tran Vui, 2008, [4]) Da phat trien tu cho HS ngudi GV c5n phai tao mdi trudng hpc tap co y nghia ddi vdi cac em MHATTD gdp phan tao mdi trudng ma HS cd the ITnh hdi kien thu^c bSng chinh boat dgng thuc hanh ciia minh, d dd cae em co the ren luyen va phat trien tu thong qua cac hoat dgng tri tue nhu: quan sat, du doan, phan tich, so sanh, tong hgp, khai quat hda, trim tugng hda, lat ngugc van de 81/ DUNG MHATTD TRONG DAY HOC KHAI NIEM HAM SO L P 10 Ham s6 la mpt khai niem cd tinh triru tugng cao va dong vai trd trung tam chuong trinh toan d nha trudng phd thdng Do lam cho HS hieu khai niem ham so la dieu het sue can thiet cho vi|c hgc tot cac n6i dimg lien quan Qua khao sat mpt so GV va HS d mot so trudng trung hpc thdng tran dia ban Hue chiing tdi nhan thay rang: hau hat cac em hiau rat mo ho ve khai niem ham so, khong n5m dugc quy tac "tuong ung", thuat ngir "vdi mdi" va dac biet la cau tnic hdi cua hai dieu kien khai niem ham so: NGUYEN THI HONG CHUYEN - Vdi moi phan tu x&Ddhu tdn tai mot phan tu tuong irag - Vdi moi phSn tit xED phkn tu tuong img f(x)ER f{x)E^R la n h k Muc tieu: - Hieu khai niem ham sd, tap xac dinh ciia ham so, dd thi ciia ham sd; - Biat each tim tap xac dinh cua cac ham sd don gian Y tu&ng thiit ki: Thilt ke md hinh ho trg HS khao sat toan: Khao sat moi lien he giira chu vi (hoac dien tich) va canh goc vuong cua mot tam giac vudng can nham hinh khai niem ham sd - Bat dSu vdi Custom\ hethugon] Ihetruc - L5y d\kmA{-6;\) Chgn diem-4, su dung Graphs Define Origin - Dung phep tinh tiln de xac djnh cac diem (2;0), (3;0), (4;0), (5;0) tren he true mdi nay, ta dugc doan thang AM - l i y dilm C thay d6i tren AM Dung tam giac vudng can ABC canh ^ C va td mau cho nd - Chon C rowko Measure-^ Abscissa(x),ta duac dai c a n h ^ C cua tam giac tren, dat Cantix - Trd va tpa cu bang each chpn O va thuc hien Mark Coordinate System ' Dung chuc nang Graph -* Plot Point xuat hien bang Plot Point, dung diam cd hoimh Canhx tren true hoanh, dat ten x - Su dung Number-> Calculate va nhap bieu thuc chu vi C = (y/l + 2)* x (hoac dien tich = —* x''2, dat chuvi (hoacDientich) - Chpn lan lugt Canhx, Chuvi (hoac Dientich), ap dung Graph\ plot as (x,y), dat dilm la_v - T p cac niit chuyln dong tren timg doan [0;1], [1;2], [2,3], [3,4], [4;5] tren d o a n ^ M Chang ban dich cbuyin C tren doan [0;1], chgn C, (1;0) ap dung Edit^ Action^ Buttons -* Movement, dat ten Move - Chpn 15n lugt Canhx, Chuvi (hoac Dientich), vao Number^ Kich cac niit Move de lap bang s6 lieu Tabulate dl lap bang - Chon ISn lugt x, y ap dung Display -^ Trace dl tao vlt cho x va y Sau hoan md hinh dgng, gidu di nhiing ddi tugng khong can thilt su" DUNG MO HINH AO THAO TAC DUOC Hinh Cac mo hinh dong ve ham so dicac thiet ke Hinh Cac vet chi thi cua so duac khao sat Chiing tdi khao sat tren mpt nhom gdm HS cd nang luc khac eiia lap 10 A2 ban KHTN d trudng THPT Bac Yen Thanh Su danh gia dua vao kit qua thi ky thi tuyen sinh vao Idp 10 va nhan xet cua GV toan giang day d Idp dd Tien hanh day thuc nghiem vdi quy trinh nghian cuu bai hpc da quan sat HS thao tac tren cac MHATTD bang each cir mot GV giang day la ngudi thudng giang day cac em HS nham dam bao khdng tu nhien ciia lop hgc Trong dd mot so GV khac se quan sat bai hpc mpt each ky luong, chii y nhung gi ma GV va HS dang trinh bay Quan sat qua trinh HS tuong tac tran MHATTD, trao ddi cua HS vdi ban hpc, qua trinh HS suy nghl va giai quyat cac nhiem vu hgc tap nham thu thap dQ lieu cho qua trinh phan tich Trong qua trinh len lap, chung toi tian hanh chia HS cac nhom nhd, mpt niia sd nhdm nhan nhiem vu tha hien qua bai toan: "Cho tam giac vudng can ABC canh x Khao sat mdi lien he giiia chu vi va canh x cua tam giac do.", nira sd nhdm cdn lai vdi nhiem vu: "Cho tam giac vudng can ABC eanh x Khao sat mdi lien he giiia dien tich va canh x ciia tam giac dd." Viec sii dung nhiing MHATTD dugc thilt ke d tren co the tiln hanh theo quy trinh sau: NGU1EN THI HONG CHUYEN Bu&c 1: GVgiai thieu vi MHATTD va giao nhiem vu cho HS GV gidi thieu ve cac MHATTD d hmh 1, hinh Giao nhiem vu tuong Cmg cho cac nhdm thi hien qua bai toan sau day: "Cho tam giac vudng can ABC canh x Khao sat mdi hen he giira chu vi (hoac dien tich) va canh x ciia tam giac dd." HS tien hanh thao tac tran man hinh bang each kich vao cac niit Reset, Move 1, Move hoac keo re dilm C tren doan thing AM va quan sat bang ben canh de tim mdi lien he giira chu vi (hoac dien tich) va canh cua tam giac ABC x thay ddi Bu&c 2: HS tuong tac vai MHATTD di thuc hien nhiem vu hoc tap Trong qua trinh quan sat HS tuong tac vdi MHATTD, GV cd the dua mot sd ggi y nhu sau: - Tim cong thirc tinh chu vi (hoac dien tich) tam giac ABC theo x? - Chu vi (hoac dien tich) cua tam giac thay ddi nhu tha nao dai canh x thay ddi? - Chu vi (hoac dien tich) cua tam giac ABC cho d bang ben duge tinh theo quy luat nao? Bu&c 3: Thao luan va nit ket luan GV to ehue eho HS thao luan va nit kat luan: Cong thiic tinh chu vi (hoac dien tich) tam giac vudng can ABC\a C = fV2 + | x ( h o a c = —x^) GV cd the ggi y mot sd cau hoi nhu sau: - Trong bai toan nay, canh x nhan gia tri tran tap hgp nao? - Vdi moi gia tri ciia x a tren thi ton tai mky gia tri cua chu vi (hoac dien tich)? Va gia tri CO nhat khong? - Quy tac/dat tuong ling moi sd X E [ ; ] vdi mot va chi mpt sdC = (>/2 + 2W(hoac = —X') la mpt ham sd xac djnh tran [0;5] Tap [0;5] gpi la tap xac dinh, x gpi la biln sd hay doi sd cua ham so / Mpt each tdng quat em hay cho bilt quy tac f nhu thi nao ggi la mpt ham so xac dinh tren tap D? Luu y: GV cd the sii dung MHATTD d tren dl hinh khai niem v l dd thi cua ham sd Sau hinh khai niem va dd thi ciia ham sd, GV cd thi \iy nhieu vi du va phan vi du da dang toan hgc va ddi sing dl giiip HS hilu sau sSc vl khai niem Sau day la vi du su dung MHATTD giiip HS hilu sau sac khai niem ham so s u DUNG MO HINH AO THAO TAC DUOC Quy tic nao la ham so? Quy tic n^o khong la ham so? Vi sao? Hinh Cac mo hinh ve quy lac ham so Trong cac dudng sau thi dudng nao la thi eua mot ham sd Khi hay xac dinh tap xac dinh eda ham s6 do? J Hinh Xac dinh thi cua mgt ham so Ddi vdi MHATTD minh hga d hinh 4, GV cd the td chuc cho HS thao luan nhu sau: Chang ban, ddi vdi quy tac/: - Vdi mdi phan tii xE^A tdn tai hay khdng mot phSn hi tuong ung /(xJGi?? -Vdi moi phan di xEA phan hi tuong ling la /(x)GJ?duynhSt khdng? Sau HS xem xet quy tac tren, GV co the dua cau hoi sau day nhiim chdt lai van de: NGUYEN THI HONG CHUYEN - Nhu vay, mot quy tac / tir tap hgp D vao tap R thda man nhirDg dilu kien gi t h i / la mpt ham sd? Tir dd hudng din HS nit cau tnic hdi ciia hai dieu kien dinh nghia ciia ham sd, va nlu quy tac nao dd vi pham mpt hai dieu kien tren thi nd khong phai la ham sd nham giiip HS hilu sau sac khai TRAO DOI VA KET LUAN Trong qua trinh nghian ciru, thuc nghiem day hpc va trao doi vdi mpt so dong nghiep tham gia day thuc nghiem, chung toi nhan thay rang MHATTD dong vai trd quan trpng qua trinh day hgc Toan Ddi vdi GV: MHATTD thiic diy GV dao sau, tun y tudng mdi phuang phap, nang cao su hilu hilt wi kien thuc cua mdn hgc va nhiing kien thuc lien quan d cac mdn hpc khac ciing nhu thuc te eudc song No tao co hdi cho GV xac dinh dilu gi la phii hgp vdi trinh ciia HS, nham lao mdi trudng lam viec tich cue cho cac em Ddng thdi dd la phuong tien true quan sinh dong hd trg GV tha hien y tudng cua mmh qua trinh nghian ciru bai hgc Trong qua trinh day hgc, cac md hinh la cau nli giup GV hieu dugc y tudng ciia HS cac em tuong tac tren md hinh va dua giai quyet van de Tir GV cd the hieu dugc nang luc cua HS cac em tham gia giai quylt van de, kha nang ngon ngir cua hg va tir dd cd nhiing hd trg hieu qua Doi vdi HS: MHATTD cung cap cho HS binh anh true quan sinh dgng, ho trg dSc luc cho cac em tuong tac, tim quy luat kich thich su tim tdi, sang tao qua trinh hinh khai niem toan hgc ciing nhu GQVD Dira vao cac mo hinh true quan HS dl dang hon viec trao doi y tudng cua minh vdi ban hgc, qua dd cac em thi hien dugc thai va tu qua trinh tuong tac Tren day la nhirng tim hieu \t h6 trg ciia MHATTD dugc xay dung bang phdn mim GSP day hgc khai niem ham so Tuy nhien, MHATTD tu nd khdng cd y nghia von CO, diau quan trgng la GV lam cho y nghTa rd rang va giiip HS xay dung cac kit ndi giua cac d6i tugng cu thi va cac bilu dien ma MHATTD dai dien Nlu dugc su dung mpt each hgp ly, nd se cung cap cho HS co hdi kham pha, xay dung su hilu bilt vung chac ve kien thue toan hpc ma cac em dang hoc TAI LIEU THAM KHAO [1] [2] [3] [4] Nguyen Hoai Anh (2008), Day hoc sinh khai niem toan cho hgc sinh cac lap 4, v&i su ho tra ciia phan mem dgy hoc, Luan an tiln si giao due hoc, Vien khoa hoc Giao due Viet Nam, Ha Npi, Tran Vui, Le Quang Hiing (2006), Khdm pha Dai s6 10 vai the Geometer's Sketchpad, NXBGD Tran Vui (Chii bien), Le Quang Hiing (2007), Thiit ki cac mo hinh day hgc toan THPT vai vai The Geometer's Sketchpad, NXBGD Tran Vui, Day va hgc co hieu qua mdn toan theo nhimg xu hitang mai, Tai lieu dung cho hpc vien cao hpc, Hul - 2008 s u DUNG MO HINH AO THAO TAC DUOC [5] Patricia Moyer Johnna Bolya, and Mark Spikell (2002), What are virtual manipulatives? Teaching Children Mathematics, 8(6), ill-Sn (onlme hiip: m\.ncnn.or';'eresourcesaie\v media.asp'?article id=]902) Title: APPLICATION OF VIRTUAL MANIPULATIVE MODEL IN TEACHING OF FUNCTION CONCEPT FOR GRADE 10 Abstract: Development and using of virtual manipulatives is one of the solutions which applies information technology in mathematical teaching method The solution have been achieving certain success in mathematical teaching and are going to take consideration of many educators in Viet Nam and other countries The purpose of this paper is further illustration providing of usefiil supports of virtual manipulatives in mathematical teachmg at high school through practising of fiinction concept Keywords: virtual manipulatives NGUYEN THI HONG CHUYEN Tnidng THPT BSc Yen Thanh, Nghe An DT: 0977 611 625 Email: hongchuyennguyenI7@gmail.com ... HS viec kian tao tri thuc nen gdp phan quan trong viec hieu sau s§c khai niem toan hpc Kha nang ket hgp nhieu bieu dian mot mdi trudng ao cho phep HS thao tac va thay doi cac ddi tugng, do tang... sanh, tong hgp, khai quat hda, trim tugng hda, lat ngugc van de 81/ DUNG MHATTD TRONG DAY HOC KHAI NIEM HAM SO L P 10 Ham s6 la mpt khai niem cd tinh triru tugng cao va dong vai trd trung tam chuong... MO HINH AO THAO TAC DUOC Hinh Cac mo hinh dong ve ham so dicac thiet ke Hinh Cac vet chi thi cua so duac khao sat Chiing tdi khao sat tren mpt nhom gdm HS cd nang luc khac eiia lap 10 A2 ban KHTN