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J O U I ( N A I ( ) I '''' S C I I N C I ; ( ) I I I N U E l diiealional Sei 2012, Vol 17, No 9, pp 40 45 M()T SO Y KIKN vfe REN LUYKN NANG LlTC TU DUY VE SO CHO HOC SINH Tli?U H O C C h u C a m T h d Tr[.]
JOUI(NAI.()I'.SCII-:NCI;()I-IINUE l-diiealional Sei 2012, Vol .17, No 9, pp 40-45 M()T SO Y KIKN vfe REN LUYKN NANG LlTC TU DUY VE SO C H O HOC SINH Tli?U H O C Chu Cam Thd Truimg Dai hpc Supham Hd Noi R-mail; camtho@hnue.edu.vn Tom tat, Bai bao de xual nhflng phUOng phap giup hpc sinh lieu ht)c ren luyen "IU ve sd" tren co sci y thtic dune lam quan trpng cua "IU vc sd" vice hoc Toan va thi'eh nghi vdi ddi sdng cua mdi eon ngfldi Til khoa: Tfl ve so, day loan d lieu hpc, phUPng phap day hpc mdn Toan, each bieu dien gia tri eua sd, the due eho tri lue Md dau Nhiing nam gan day, ed nhieu hpe gia Iren tren the gidi da dung thufit ngii "tU ve sd" (djcb Iheo tU khda Tieng Anh "number sense" [2]) Cac lai lieu phd bien Uen internet [4] cd khai quat nhiing each bieu chung nhat ve "Number sense" nhu sau;" la sfl hieu biet true quan ciia cac sd, dp ldn, cac mdi quan he giufa cac sd giiia sd va cac doi tflpng toan bpc khae nhu tbS nao" Trong [2] Gersten va Chard da ban tdi khai niem tfl ve sd, hai dng nban manh den kha nang linh hoat cila tinh loan vdi cac sd, y nghia cua nhiing eon sd, kha nang tinh nha'm va su tUdng ting cua sd vdi Ihuc tii^n, kha nang toan hpc hda tinh hudng thuc tidn Trong cac nghien cflu ciia Berch (1998), Bruer (1997), Case (1998), Gersten va Chard (2001) va mdt sd tac gia khac cho thay, khdng cfin thiet phai cd mdt dinh nghia chinb xac "tU vd sd" la gi, vi doi vdi tre nhd, sU UUc quan la cdng cu hieu qua nhat giup chiing hieu va biet ap dung kien thflc vao thitc liln hpc tap Day cUng chinh la nguyen nhfin dfin den giao vien, nhiing chuyen ^ia ve phUdng phap giang day mdn Toan hau nhif khdng quan tfim dkn nghien cflu mdt each day dii ve ndi ham va phUPng phap day hpc de ren luyen "tfl ve so" cho hpc sinh Cung eac nghien ciiu cho thay, hpc sinh cd nang lUc "tu ve so" tdt se de dang di chuyen giiia the gidi toan hpc, cac sd, cac bieu thflc sd va the gidi thuc ciia so lupng, hp cd the de dang tim thay quy luat theo each ciia rieng hp tien hanh cac hoat ddng lien quan den so, hp cd cam giac tdt vl s6, r^t cd ich Udc lupng va gidi quyet cac van de ddi hdi sU linh hoat, Cudi cung, ho cd die d l dang tim thky nhiing thudc tinh chung, su logic cua mdt van de ma khdng c4n lam bat ki mdt tinh toan nao NhU vfiy, cd the ndi, "tU ve so" la mpt nang luc cfin ren luyen qua Uinh hpc Toan, nd khdng chi cd ich viec hpc Toan ma cdn cd vai trd quan 40 Mdt sd y kien ve ren luyen ndng life hf vi so eho hge tinh lieu hgc trpng ddi sdng cua ngudi NgUdc lai, nhflng nghien cflu ircn cung chi rang, cdn nhieu hpc sinh hpc loan nhflng cd nang lUc thich ngbi vdi ddi sdng chfla tdt, mdt phan nguyen nhan la hp cd chfla cd nang luc "tu ve sd" Lot O Viet Nam, nhflng nghien cflu vc "tfl vc sd" chUa nhicu Trong cac tai lieu vc phUdng phap giang day loan lieu hpc ngUdi la cdn chUa chi gianh gidi gifla cac phan mdn Toan hpc, chUa dinh linh dinh lUpng rd nel vc "tu ve sd" Trong cac khudn khd nghien cflu ciia minh biii bao khdng cd y dinh dUa mdl djnh nghia chinh xac "lU vl sd", khdng iranh luan vc cac ndi dung khoa hpc Toan hpc lien quan, ma cbi tap trung de xuat nhflng each thflc dc giup ren luyen "tU ve sd" cho hpc sinh lieu hpc Iren cd sd y thflc dfldc tam quan trpng cua "IU vc sd" vice hpc Toan va thich nghi vdi ddi sdng cua mdi ngUdi Noi dung nghien cii'u 2.1 TiT ve so va cac noi dung day hoc lien quan Trudc hit, bai bao khang dinh tu vl sd dUdc hinh tfl ngudi bill giao lUu vdi the gidi xung quanh va dan hoan chinh giai doan hpc lieu hpc (vdi nhflng ngudi binh UiUdng) Hieu ddn gian Tu ve sd cd the dUpc the hicn qua nhflng nang luc sau: cAu TRUC sP THLTC Ht^N PHEP TINH Hinh I Sd the hien quan he giua tu day so vd cdc npi dung day hgc - Hieu duge hdn chdt so, phdn tich dUtfc cau true eua sd, vi cde thdnh phdn tgo nen long thesd do, vai trd, the hien cda sd, so sdnh giii'a cde sd - Thuc hien dugc phep tinh tren ca sd thdy dutfc vai tro cua sd phep tinh, ed khd ndng tinh nhdm nhQng tinh huong don gidn - Hieu vd van dting dugc ti le tinh todn vd ddi sdng - Lua chgn don vi ludng cd y nghia cho mot tinh huong nhdt dinh - Hi/u dupc y nghia ciia cdc s6 bdng so lieu vd tinh huong thtic te 41 Chu Cam Tho - Co klui ndng ude lifdng vdi cdc cfin w vd tinh huong thue ti Phan (ich dac diem, cau iriic ciia mdn Toan d lieu hpc, chung la cd the thay mdn Toan d iiLii hoc lii mdl mdn ihdng nhal khdng chia phiin mdn Hal nhan la sd hpc, cac npi dung vc dai lfldng cd ban dai so, yen td hinh hpc, gi;ti bai loan cd ldi van dUdc gin bo chill die vdi liai nhrm sd hoc lao sfl ho Up lan Cac kiln thflc, ki nang cua mon Toan dun^ mpt sd khai niem, kT thuat bo trd giup de dang ti'nh toan, udc ItfOng Muc lieu Clia bicn phap la xay dflng mdt sd khai niem ki thuat ddn gian, bo trd cho l i s (hpc sinh) dl dang ihuc hien cac phep linh, Udc Ifldng Cac khai mem kl thuat dudc de xuat phai ihda man nhflng yeu cau nhfl: de dang nam bat nhd trflc quan, khong mau thuan vdi dac diem va cau true ndi dung day hpc, de dang van dung thflc lien (vi the cd the lam thdi bd qua nhflng yeu cau chinh xac vl thuat ngfl) Tren cd sd nghien cflu cac tai lieu day hpc cua mdt sd nfldc tien lien va chfldng trinh day hpc Toan d Viel Nam, bai bao xay dflng mdl sd khai niem, ki thuat sau: Khdi niem "Sd bu " "Sd bu" dfldc hieu quan he gifla hai sd A va B ma long (hoac tich) ciia hai s6 khdng ddi thi sd la sd bu cua so Hai thudc tinh quan trpng cua "so bu" la: Khi mpl sd tang len, thi sd giam xuong va mpt so la so 0, thi so la tong so ([I]) Chang han: sd banh quy da an va so banh quy cdn lai hop la hai "so bu" cua HS cd the van dung khai niem so sanh hai sd (so sanh qua "so bu" ciia nd), tinh nham, chang han: de tinh tdng: 99 + 98 + 97 + 96 + 95 ta se xet cac "so bu" cua 99, 98, 97, 96, 95 quan he "tdng bSng 100" lan Ifldt la 1, 2, 3,4, Khi dd tdng phai tinh la: 100+ 100+ 100+ 100+ IOO-(I + + + + 5) = 485 Kl thudt phdn tieh qua bg phdn De minh hpa ki thuat nay, chung ta xet mot vi du sau day: "Hay thflc hien cac phep tinh sau: ( - : ) va ( - x )" Chung tdi da thay rat nhilu hpc sinh quy ddng cac hdn sd tren roi thflc hien phep tinh theo dung quy lac (da phan ho phai dung den but va giay) Nhung vdi ki thuat ma ehung ta dang ndi den se giup chung ta khdng can den giay, but ma rat dl dang tinh nham Viec dd dUpc tien hanh nhU sau: tach hdn so hai bd phan va nham phep u'nh vdi tflng bp phan, sau dd cdng kit qua lai Ta co the md ta viec thUc hien phep tfnh dd cu the' hdn: (2 : 2) + ( i : 2) = l i va (3 x 2) + ( i x 2) = ^ Ben canh dd, giao vien cung nen dung nhflng thuat ngii ddn gian de bien bai toan nhflng bai 42 Mgt