Cov kev ua lej ua pov thawj li cas cov kws qhia ntawv tuaj yeem siv tau?
Nplooj 5: Cov Lus Pom Zoo
Txawm li cas los xij lwm lub tswv yim ua pov thawj los pab cov tub ntxhais kawm kawm paub txog lej lej thiab daws teeb meem yog siv cov duab sawv cev. Ntau tshaj li ib daim duab lossis cov lus piav qhia ntxaws, qhov pom kev sawv cev-feem ntau hu ua a schematic sawv cev or schematic daim duab -yog ib qho kev piav qhia tseeb ntawm ib qho teeb meem qhov lej thiab kev sib raug zoo. Lub hom phiaj ntawm qhov kev pom no yog xav txog tus tub ntxhais kawm txoj kev nkag siab txog qhov teeb meem thiab pab nws daws nws kom raug. Piv txwv li, nyob rau hauv daim duab rau sab xis, ib tug me nyuam kawm ntawv tab tom siv qhov pom kev sawv cev - ntawm no, daim ntawv qhia ncuav qab zib - kom kawm txog cov feem sib npaug. Txawm hais tias cov kws qhia ntawv siv lub tswv yim no hauv cov qib kawm thaum ntxov los pab cov tub ntxhais kawm paub txog lej qhov tseeb, cov tub ntxhais kawm uas muaj kev tsis taus ntawm kev kawm lej thiab teeb meem feem ntau tsis txuas ntxiv siv lawv tus kheej los daws teeb meem.
Tshawb Fawb Qhia
- Cov tub ntxhais kawm ntawv uas siv qhov pom tseeb qhov tseeb yog rau lub sij hawm ntau dua los daws cov teeb meem lej kom raug dua li cov tub ntxhais kawm uas tsis siv lawv. Txawm li cas los xij, cov tub ntxhais kawm uas siv qhov pom kev tsis raug cai tsis tshua muaj peev xwm daws tau cov teeb meem ua lej kom raug ntau dua li cov uas tsis siv qhov pom kev sawv cev txhua.
(Boonen, van Wesel, Jolles, & van der Schoot, 2014) - Cov tub ntxhais kawm ntawv uas muaj kev xiam oob qhab (LD) feem ntau tsis tsim cov duab pom tseeb lossis siv cov tswv yim los daws cov teeb meem. Kev cob qhia cov tub ntxhais kawm kom siv lub ntsej muag sawv cev los daws cov teeb meem ntawm lo lus tau ua rau muaj kev txhim kho ntau yam hauv kev ua lej rau cov tub ntxhais kawm tsis taus.
(van Garderen, Scheuermann, & Jackson, 2012; van Garderen, Scheuermann, & Poch, 2014) - Cov tub ntxhais kawm ntawv uas siv cov duab sawv cev los daws cov teeb meem ntawm lo lus muaj feem yuav daws cov teeb meem kom raug. Qhov no yeej ib txwm muaj tseeb rau cov tub ntxhais kawm uas muaj LD, tau txais txiaj ntsig tsawg, lossis tau txais qhov nruab nrab.
(Krawec, 2014)
Cov duab sawv cev yog hloov tau; lawv tuaj yeem siv thoob plaws qib thiab hom teeb meem lej. Lawv tuaj yeem siv los ntawm cov kws qhia ntawv los qhia qhov tseeb lej thiab los ntawm cov tub ntxhais kawm kom kawm cov ntsiab lus lej. Cov duab sawv cev tuaj yeem siv ntau hom ntawv. Nyem rau ntawm qhov txuas hauv qab no txhawm rau saib qee qhov pom kev sawv cev feem ntau siv los ntawm cov kws qhia ntawv thiab cov tub ntxhais kawm.
Qhov kev coj ua no zoo li cas?
High-Leverage Practice (HLP)
- HLB 15: Muab kev txhawb nqa scaffolded
CCSSM: Cov qauv rau kev xyaum lej
- MP1: Ua siab ntev rau cov teeb meem thiab ua siab ntev daws lawv.
Lus txhais: Ib txoj kab ncaj nraim uas qhia qhov kev txiav txim ntawm thiab kev sib raug zoo ntawm tus lej.
Kev Siv Ntau: ntxiv, rho tawm, suav
Lus txhais: Ib qho bar muab faib ua cov duab plaub uas yog sawv cev kom muaj nuj nqis sau tseg hauv qhov teeb meem.
Kev Siv Ntau: Ntxiv, feem, proportions, ratios
Lus txhais: Cov duab kos yooj yim ntawm cov pob zeb lossis cov khoom tiag (xws li, marbles, tsheb thauj khoom).
Kev Siv Ntau: suav, ntxiv, rho tawm, sib faib, faib
Lus txhais: Cov duab kos uas qhia txog cov ntaub ntawv siv kab, duab, thiab xim.
Kev Siv Ntau: muab piv cov lej, txheeb cais, piv txwv, algebra
Lus txhais: Visual uas pab cov tub ntxhais kawm nco qab thiab teeb tsa cov ntaub ntawv, nrog rau kev piav qhia txog kev sib raug zoo ntawm cov tswv yim (xws li, lo lus webs, rooj, Venn daim duab).
Kev Siv Ntau: algebra, geometry
| Triangles | ||
|---|---|---|
| Vaj Huam Sib Luag | - txhua sab yog tib qhov ntev - tag nrho cov kaum sab xis 60 ° |
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| isosceles | - ob sab yog tib qhov ntev - ob lub kaum sab xis yog tib yam |
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| scalene | - tsis muaj ob sab yog tib qhov ntev - tsis muaj cov ces kaum zoo ib yam |
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| txoj cai | - ib lub kaum sab xis yog 90 ° (lub kaum sab xis) - ntxeev sab ntawm lub kaum sab xis yog sab ntev (hypotenuse) |
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| obtus | - ib lub kaum sab xis ntau dua 90 ° |  |
| mob | - Tag nrho cov kaum sab xis yog tsawg dua 90 ° |  |
Ua ntej lawv tuaj yeem daws tau cov teeb meem, txawm li cas los xij, cov tub ntxhais kawm yuav tsum xub paub seb hom kev pom kev pom dab tsi los tsim thiab siv rau cov teeb meem lej. Qee cov tub ntxhais kawm-tshwj xeeb, cov tub ntxhais kawm tau txais txiaj ntsig zoo, cov tub ntxhais kawm muaj txiaj ntsig-ua qhov no tau txais, qhov lwm tus yuav tsum tau qhia meej meej li cas. Qhov no yog qhov tshwj xeeb tshaj yog rau cov tub ntxhais kawm uas tawm tsam nrog kev ua lej thiab cov neeg muaj kev tsis taus kawm lej. Yog tsis muaj kev qhia meej, kev qhia txog kev tsim thiab siv cov duab sawv cev, cov tub ntxhais kawm no feem ntau tsim cov duab sawv cev uas tsis sib xws lossis muaj cov ntaub ntawv tsis raug lossis ib feem. Xav txog cov piv txwv hauv qab no.
Elementary Piv txwv
Mrs. Aldridge hais kom nws cov tub ntxhais kawm qib ib ntxiv 2 + 4 los ntawm kev kos cov dots.
Talia kos cov hauv qab no:
Colby kos cov hauv qab no: 
Daim ntawv ceeb toom tias Talia tau txais cov lus teb raug. Txawm li cas los xij, vim tias Colby rub nws cov dots hauv kev ua haujlwm tsis zoo, nws tsis suav tag nrho lawv thiab yog li tuaj txog ntawm qhov tsis raug.
Piv txwv Tsev Kawm Ntawv Phaj Siab
Mr. Huang hais kom nws cov tub kawm los daws cov teeb meem hauv qab no:
Lub flagpole yuav tsum tau hloov. Lub tsev kawm ntawv xav hloov nws nrog tus ncej loj. Thaum Juan sawv 11 taw ntawm lub hauv paus ntawm tus ncej, lub kaum sab xis ntawm qhov siab ntawm Juan ko taw mus rau sab saum toj ntawm tus ncej yog 70 degrees. Tus ncej siab npaum li cas?
Sib piv cov duab kos hauv qab no tsim los ntawm Brody thiab Zoe los sawv cev rau qhov teeb meem no. Daim ntawv ceeb toom tias Brody kos tus sawv cev raug thiab siv lub tswv yim kom raug. Hauv qhov sib piv, Zoe kos ib daim duab nrog cov ntaub ntawv muaj tseeb. Lub 11 yog nyob rau hauv qhov tseeb, tab sis lub 70 ° tsis yog. Raws li qhov tshwm sim ntawm nws tus sawv cev tsis raug, Zoe tsis tuaj yeem txav mus tom ntej thiab daws qhov teeb meem. Txawm li cas los xij, muab qhov tseeb sawv cev tsim los ntawm lwm tus neeg, Zoe feem ntau yuav daws qhov teeb meem kom raug.
Brody
Zoe
Manipulatives
Qee cov tub ntxhais kawm yuav tsis muaj peev xwm nkag siab txog kev txawj lej thiab cov ntsiab lus siv tsuas yog hom kev pom kev pom tau sau tseg hauv cov lus saum toj no. Cov menyuam yaus thiab cov tub ntxhais kawm uas tawm tsam nrog kev ua lej feem ntau xav tau ntau hom kev pom kev sawv cev hu ua manipulatives. Cov pob zeb, cov khoom siv tes ua thiab cov khoom siv - piv txwv li, abacus lossis npib - pab cov tub ntxhais kawm los sawv cev rau lub tswv yim lej uas lawv tab tom sim kawm lossis qhov teeb meem uas lawv tab tom sim daws. Manipulatives tuaj yeem pab cov tub ntxhais kawm tsim lub tswv yim nkag siab txog lej. (Rau lub hom phiaj ntawm no module, lub sij hawm cov khoom ua vaj tse hais txog manipulatives thiab lub sij hawm cov duab sawv cev hais txog schematic daim duab.)
Nws yog ib qho tseem ceeb uas tus kws qhia ntawv qhia meej txog kev sib txuas ntawm cov khoom vaj khoom tsev thiab lub tswv yim paub daws teeb uas tau qhia. Lub hom phiaj yog kom tus menyuam kawm ntawv thiaj li nkag siab txog cov ntsiab lus thiab cov txheej txheem yam tsis muaj kev siv dag zog. Rau cov tub ntxhais kawm theem nrab uas tawm tsam nrog kev ua lej, cov kws qhia ntawv yuav tsum qhia qhov paub daws teeb meem nrog rau cov ntsiab lus los yog qhov muag pom thiab ua kom muaj kev sib txuas ntawm lawv.
Ib qho kev txav los ntawm cov khoom siv los yog cov duab sawv cev rau kev siv cov kev sib npaug sib npaug tuaj yeem nyuaj rau qee cov tub ntxhais kawm. Ib tus kws qhia tswv yim tuaj yeem siv los pab cov tub ntxhais kawm hloov pauv ntawm cov khoom vaj tse, cov duab sawv cev, thiab kev sib npaug ntawm kev paub daws teeb meem yog Concrete-Representational-Abstract (CRA) moj khaum.
Qhob-Representational-Abstract Framework
Lub hauv paus ntsiab lus ntawm Concrete-Representational-Abstract (CRA) pab cov tub ntxhais kawm kom nkag siab txog lub tswv yim ntawm kev ua lej, tsis yog ua kom tiav cov algorithm (xws li 2 + 4, 2x + y = 27). Kev sib txuas cov khoom vaj huam sib luag lossis cov duab sawv cev rau qhov kev sib npaug ntawm kev paub daws teeb yog ib txoj hauv kev los ua kom tus menyuam nkag siab. Cov yam ntxwv ntawm lub moj khaum yog:
- Qhob -Cov tub ntxhais kawm sib cuam tshuam thiab tswj cov khoom peb-dimensional, piv txwv li cov vuas algebra lossis lwm yam algebra manipulatives nrog cov sawv cev ntawm qhov sib txawv thiab cov chav nyob.
- Sawv cev - Cov tub ntxhais kawm siv cov duab kos duab ob sab los sawv cev rau cov teeb meem. Cov duab no yuav raug qhia rau lawv los ntawm tus kws qhia, lossis los ntawm cov ntaub ntawv kawm siv hauv chav kawm, lossis cov tub ntxhais kawm tuaj yeem kos lawv tus kheej sawv cev ntawm qhov teeb meem.
- Abstract - Cov tub ntxhais kawm daws teeb meem nrog cov lej, cim, thiab cov lus yam tsis muaj kev pab cuam los yog sawv cev.
CRA muaj txiaj ntsig zoo thoob plaws txhua qib hnub nyoog thiab tuaj yeem pab cov tub ntxhais kawm hauv kev kawm cov ntsiab lus, txheej txheem, thiab kev siv. Thaum siv txhua yam, cov kws qhia ntawv yuav tsum siv cov lus qhia meej, ua kom muaj kev qhia zoo thiab txuas ntxiv saib xyuas cov tub ntxhais kawm ua haujlwm los soj ntsuam lawv txoj kev nkag siab, nug lawv cov lus nug txog lawv txoj kev xav thiab muab kev qhia meej raws li xav tau. Kev ua yeeb yam thiab kev sawv cev yuav tsum muaj kev cuam tshuam txog cov txheej txheem tiag tiag ntawm kev daws qhov teeb meem kom cov tub ntxhais kawm tuaj yeem nthuav dav cov txheej txheem los daws qhov kev ua tsis tiav. Cov duab hauv qab no qhia txog txhua yam ntawm cov khoom no.
Txog Koj Cov Ntaub Ntawv
Ib qho kev cog lus zoo rau kev txav cov tub ntxhais kawm theem nrab uas muaj teeb meem kev ua lej lossis kev xiam oob qhab los ntawm kev siv cov manipulatives thiab pom cov duab sawv cev rau qhov kev sib npaug tsis meej sai yog CRA-I cov tswv yim. Hauv qhov kev hloov kho no ntawm CRA, tus kws qhia ntawv ib txhij nthuav tawm cov ntsiab lus uas siv cov khoom ua vaj tse, pom cov duab sawv cev ntawm cov khoom vaj tse, thiab kev sib npaug ntawm kev paub daws teeb. Cov kev tshawb fawb tau pom tias lub moj khaum no muaj txiaj ntsig zoo rau kev qhia algebra rau cov tub ntxhais kawm ntawv no (Strickland & Maccini, 2012; Strickland & Maccini, 2013; Strickland, 2017).
Kim Paulsen tham txog cov txiaj ntsig ntawm kev siv dag zog thiab ntau yam uas yuav tsum nco ntsoov thaum siv lawv (lub sijhawm: 2:35).
Kim Paulsen, Ed
Associate Professor, Kev Kawm Tshwj Xeeb
Vanderbilt University
Cov ntawv sau: Kim Paulsen, EdD
Manipulatives yog ib txoj hauv kev zoo los pab cov menyuam nkag siab txog kev xav. Kev siv manipulatives tiag tiag pab cov tub ntxhais kawm pom qhov kev xav, thiab nws nyem me ntsis ntxiv nrog lawv. Qee yam, txawm li cas los xij, uas peb yuav tsum nco ntsoov thaum peb siv cov khoom siv dag zog yog qhov tseem ceeb uas yuav tsum tau muab sijhawm me ntsis rau cov tub ntxhais kawm dawb thaum koj siv tus tshiab manipulative kom lawv tuaj yeem tshawb nrog lawv. Peb yuav tsum muaj cov cai tshwj xeeb rau kev siv cov khoom siv dag zog, uas lawv tsis yog cov khoom ua si, tias lawv yog cov ntaub ntawv kawm tiag tiag, thiab cov tub ntxhais kawm tuaj tos lawv li cas, lawv tso lawv li cas, sijhawm siv lawv, thiab xyuas kom lawv tsis txhob cuam tshuam thaum peb tab tom ua qhov kev nthuav qhia ntawm zaj lus qhia. Ib qho tseem ceeb yog tias peb tsis xav kom cov tub ntxhais kawm ntawv cim cov algorithm lossis cov txheej txheem thaum lawv tab tom siv cov khoom siv. Nws tsuas yog pab lawv nkag siab txog kev xav. Qhov ntawd tsis tau txhais hais tias cov menyuam yaus yuav nkag siab txog lub tswv yim lossis muaj peev xwm ua tus choj ntawm kev siv cov pob zeb ua rau lawv tuaj yeem daws cov teeb meem. Rau qee cov menyuam yaus, nws nyuaj rau kev siv cov khoom siv. Qhov ntawd tsis yog lawv kawm li cas, thiab yog li peb tsis xav yuam cov menyuam yaus yuav tsum tau siv cov khoom siv dag zog yog tias nws tsis yog ib yam uas yuav pab tau rau lawv. Yog li ntawd, peb yuav tsum nco ntsoov tias manipulatives yog ib txoj hauv kev los xav txog kev qhia lej.
Kuv xav tias ib feem ntawm vim li cas qee tus kws qhia ntawv tsis siv lawv yog vim nws siv sijhawm ntau, siv ntau lub koom haum, thiab lawv kuj xav tias cov tub ntxhais kawm tau txais kev cia siab dhau los ntawm kev siv cov khoom siv. Ib txoj hauv kev xav txog kev siv manipulatives yog tias koj ua ob peb zaj lus qhia thaum koj tab tom qhia ib lub tswv yim tshiab, thiab tom qab ntawd tshem tawm kom cov tub ntxhais kawm tuaj yeem ua qhov kev suav ntawm nws xwb. Nws yog qhov tseeb peb tsis tuaj yeem taug kev nyob ib puag ncig lub neej nrog kev ua haujlwm ntawm peb txhais tes. Thiab kuv xav tias ib qho ntawm cov laj thawj uas ntau lub tsev kawm ntawv lossis cov kws qhia ntawv tsis siv cov khoom siv yog vim lawv kim heev. Thiab yog li ntawd nws yuav pab tau heev yog tias tag nrho cov kws qhia ntawv hauv tsev kawm tuaj yeem muab cov peev txheej thiab muaj chav ua haujlwm uas cov kws qhia tuaj yeem mus xyuas cov kev siv dag zog kom tsis txhob kim. Cov kws qhia ntawv yuav tsum paub siv lawv li cas, thiab qhov ntawd yuav siv sij hawm ntau heev.
