Please ensure Javascript is enabled for purposes of website accessibility Leqephe la 1: Bohlokoa ba Thuto ea Mathematics ea Boemo bo Phahameng
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  • Taelo ea Mathematics ea Boemo bo Phahameng: Seo Matichere a Lokelang ho se Tseba
hlahisitse phephetso
Mehopolo ea Pele
Maikutlo le Lisebelisoa

Litaelo tsa boleng bo holimo tsa lipalo ke eng, hona hobaneng li le bohlokoa?

  • 1: Bohlokoa ba Thuto ea Lipalo ea Boemo bo Phahameng
  • 2: Kharikhulamo ea Lipalo e Thehiloeng Maemong
  • 3: Litloaelo tsa Mathematics tse Thehiloeng Bopaking

Ke mekhoa efe ea lipalo e thehiloeng bopaking eo matichere a ka e sebelisang?

  • 4: Taelo e Hlakileng, e Hlophisitsoeng
  • 5: Boemeli ba Pono
  • 6: Taelo ea Schema
  • 7: Metacognitive Strategies
  • 8: Mekhoa e Atlehang ea ka Tlelaseng

Resources

  • 9: Litšupiso, Lisebelisoa tse Eketsehileng, le Likoloto
Phethela
Tlhahlobo
Fana ka Maikutlo

Litaelo tsa boleng bo holimo tsa lipalo ke eng, hona hobaneng li le bohlokoa?

Leqephe la 1: Bohlokoa ba Thuto ea Mathematics ea Boemo bo Phahameng

li-calculator le li-graph le lichateE 'ngoe ea lithuto tsa mantlha tsa thuto United States le lefats'eng lohle, lipalo ke senotlolo sa mesebetsi ea rona ea letsatsi le letsatsi le mekhoa e tloaelehileng, lintho tse kang ho reka, ho banka, ho pheha le ho lokisa mahae. Ho feta moo, sechabeng sa kajeno se itšetlehileng haholo ka theknoloji, mesebetsi e ntseng e eketseha e hloka tsebo e itseng ea lipalo le saense. Baithuti ba hlokang tsebo le litsebo tse lekaneng tsa lipalo ba na le monyetla oa ho fumana litholoana tse mpe ha e se e le batho ba baholo, ho kenyeletsoa menyetla e fokolang ea mesebetsi e nang le morero le menyetla e fokotsehileng ea ho ikemela moruong. Ka lebaka la lintlha tsena, ho bohlokoa hore baithuti ba qale ho nts'etsapele mehopolo le litsebo tsa lipalo ba sa le banyenyane. Ka bomalimabe, liphuputso tse entsoeng ho tloha lilemong tsa bo-1970 li bontšitse hore liithuti tsa United States ha li sebetse hantle litlhahlobong tsa lipalo joaloka lithaka tsa tsona linaheng tse ling.

Lipontšo tsa Lipatlisiso

Liphuputso, tse kang tse ka tlaase mona, li hlahisitse matšoenyeho mabapi le ho lekana ha thuto ea lipalo United States.

  • Ka 2015, Lenaneo la Tlhahlobo ea Liithuti Tsa Machaba (PISA) le ile la bapisa tsebo ea lipalo—ke hore, bokhoni ba ho hlalosa, ho sebelisa le ho hlalosa thuto ea lipalo maemong a sa tšoaneng—ea liithuti tsa lilemo tse 15 tsa United States le tsa linaheng tse ling tse tsoetseng pele indastering. Ho tsoa linaheng tse 69, United States e boemong ba bo36.
    (Kastberg, Chan, & Murray, 2016)
  • Ka 2015, Trends in International Mathematics and Science Study (TIMSS) e bontšitse hore liithuti tsa sehlopha sa borobeli United States li atlehile ho feta tsebo ea lipalo ke liithuti tsa Singapore, Rephabliki ea Korea, Chaena, Japane, Kazakhstan, Russia Federation, Canada le Ireland.
    (Provasnik, Malley, Stephens, Landeros, Perkins, & Tang, 2016)
  • Selemo se seng le se seng, National Assessment of Educational Progress (NAEP) e fana ka liteko tsa katleho ea lipalo ho liithuti tsa sehlopha sa 4, sa borobeli le sa bo8 United States. Tshebetso ya baithuti e bontsha tekanyo eo ba fumaneng tsebo le bokgoni bo lebeletsweng boemong ba mophato wa bona. Liphetho li arotsoe ka e 'ngoe ea maemo a mane: Ka tlase ho Motheo (boitseanape bo bonyenyane), Motheo (boitsebelo bo itseng), Tsebo (boqhetseke), le E tsoetseng pele (ho feta ho ipabola). Liphetho tsa 12 tsa sehlopha sa 2022 le 4 li bonts'itsoe lethathamong le ka tlase. Lintlha tsa sehlopha sa 8 li tsoa 12 hobane tlhahlobo ha ea ka ea fuoa baahi bana ka 2019.

    (https://www.nationsreportcard.gov)

Tlhaloso

Kerafo ena e bonts'a liphetho tsa tlhahlobo ea katleho ea lipalo ea 2022 National Assessment of Educational Progress (NAEP) bakeng sa sehlopha sa 4 le sa borobeli le lintlha tsa 8 tsa sehlopha sa 2019. Tafole e arotsoe ka litšiea tse tharo—e ’ngoe bakeng sa liphetho tsa sehlopha sa bone, e ’ngoe bakeng sa liphetho tsa sehlopha sa borobeli, ’me ea ho qetela bakeng sa liphetho tsa sehlopha sa 12—’me kholomo ka ’ngoe e arotsoe ka mela e ’meli. Mola o ka holimo o ngotsoe “Students Proficient & Advanced,” ha o ka tlaase o ngotsoe “Students Basic & Below Basic.”

Liphetho tsa liteko li hlahisoa bakeng sa mekhahlelo e meraro ea ba etsang liteko: "Liithuti Tsohle," "Baithuti ba nang le Bokooa," le "English Learners (ELs)." Li-bar "All Students" li na le 'mala oa aqua. Libara tsa "Baithuti ba nang le Bokooa" ke perekisi. Qetellong, maballo a "Baithuti ba Senyesemane" a mosehla.

Kholomong ea sehlopha sa 4, "Baithuti Bohle" ba 36% ho Proficient & Advanced range le 64% ho Basic & Below Basic range. "Baithuti ba nang le Bokooa" ke 16% ho Proficient & Advanced le 84% ho Basic & Ka tlase. Ka mokhoa o ts'oanang, "Baithuti ba Senyesemane" ba 14% ho Proficient & Advanced le 86% ho Basic & Below.

Kholomong ea sehlopha sa borobeli, "Baithuti Bohle" ba 8% ho Proficient & Advanced range le 26% ho Basic & Below Basic range. "Baithuti ba nang le Bokooa" ke 74% ho Tsebo & Advanced le 7% ho Basic & Ka tlase. Qetellong, "Baithuti ba Senyesemane" ke 93% ho Proficient & Advanced le 4% ho Basic & Below.

Kholomong ea sehlopha sa 12, "Baithuti Bohle" ba 24% ho Proficient & Advanced range le 76% ho Basic & Below Basic range. "Baithuti ba nang le Bokooa" ke 7% ho Tsebo & Advanced le 93% ho Basic & Ka tlase. Qetellong, "Baithuti ba Senyesemane" ke 3% ho Tsebo & Advanced le 97% ho Basic & Ka tlase..

Lintlha Tsee li Bontša Eng?

Teko ea NAEP e etselitsoe hore baithuti ba ithutileng tsebo le litsebo tse nkoang e le tsa bohlokoa bakeng sa boemo ba bona ba mophato ba fumane lintlha bonyane boemong ba "Boitsebelo". Leha ho le joalo, lintlha tsa NAEP li bontša hore boholo ba liithuti li sebetsa maemong a "Below Basic" le "Basic", e leng se bontšang bokhoni bo fokolang kapa bo fokolang. 'Me, ehlile, khaello ena ea bokhoni e ka baka litšitiso tse ncha maemong a latelang a mophato, moo kutloisiso ea mantlha ea mehopolo le lits'ebetso tsa lipalo e hlokahalang bakeng sa katleho. Baithuti ba sa tsebeng tsebo ea motheo ea lipalo lihlopheng tsa pele ba ka 'na ba salla morao haholo ha ba ntse ba tsoela pele sekolong.

Ka sena sohle kelellong, sheba hape data e tafoleng e ka holimo. Hlokomela hore baithuti ba bangata ba sehlopha sa 4 (60%) ha ba so ka ba tseba tsebo le mahlale a lipalo a lebelletsoeng, peresente e kholo le ho feta (75%) bakeng sa baithuti ba sehlopheng sa 12. 'Me liphello li mpe le ho feta bakeng sa liithuti tse nang le bokooa hammoho le tsa Senyesemane sa Senyesemane (ELs).

Sepheo sa mojule ona ke ho hlahloba hore na ke hobaneng ha baithuti ba bang ba sokola thutong ea lipalo le hore na ke mehato efe eo matichere a ka e nkang ho fa baithuti ba bona monyetla o ntlafalitsoeng haholo oa ho atleha ka phaposing ea borutelo.

Nahana ka Sena

Lilemong tsa morao tjena, ho hatelloa haholo k'holejeng- le ho itokisetsa mosebetsi ho entse hore ho be le litekanyetso tse phahameng tsa tsebo ea lipalo ea liithuti, hammoho le litlhoko tse matla tsa ho fumana mangolo. Le hoja nakong e fetileng liithuti tsa sekolo se phahameng liprofinseng tse ngata li ne li hlokoa ho qeta Algebra 1 pele li qeta, liithuti tseo hangata li tlameha ho qeta Algebra 1, Geometry, le Algebra II. Hape, nahana ka lintlha tsa NAEP tse hlahisitsoeng ka holimo 'me u nahane ka palo ea liithuti tse tla sokola ho fihlela litlhoko tsena tse ncha.

Hobaneng ha Baithuti ba Bang ba Loana Haholoanyane ka Math?

Baithuti ba nang le Bokooa ba ho Ithuta

Ha ho bapisoa le palo ea batho ka kakaretso, palo e nyenyane haholo ea liithuti tse nang le bokooa e bontša tsebo ea lipalo. Leha moithuti e mong le e mong a ikhethile, baithuti ba nang le a bokooa ba ho ithuta lipalo (MLD) ba tloaetse ho bonts'a litšobotsi life kapa life tse amang ts'ebetso ea bona ea lipalo, ho kenyelletsa:

x

bokooa ba ho ithuta lipalo (MLD)

lenaane-foko

  • Bothata ba ho sebetsa litaba
  • Bothata ba ho lemoha tlhahisoleseding e nepahetseng mathateng a lipalo, haholo-holo mathateng a mantsoe
  • Bothata ba ho fetolela litaba ho polelo ea lipalo kapa equation
  • Bothata ba ho boloka tlhokomelo
  • Bothata ba ho khetha leano le sebetsang la ho rarolla mathata
  • Tsebo e fosahetseng ea ho beha mabaka le ho rarolla mathata
  • Ho sebetsana le bothata ntle le ho etsa bonnete ba hore mehato eohle e phethiloe kapa hore karabo ea utloahala
  • Likhaello likarolong tsa lintlha tsa lipalo le tsebo ea ho bala
  • Mathata a ho hopola le mantsoe
  • Bothata ba ho rarolla mathata a mehato e mengata
  • Bokhoni bo fokolang ba pono / sebaka sa boemeli
  • Bothata ba ho bala ka lipalo
  • Bothata ba ho utloisisa puo, kapa pokello ea mantsoe, ea lipalo
  • Bothata ba ho utloisisa likhopolo tsa lipalo le hore na likhopolo li amana joang le mekhoa
  • Matšoenyeho a lipalo
  • Ho ithuta ho hloka thuso—ke hore, ho ba le tšusumetso e fokolang, ho ba moithuti ea sa etse letho, le ho bolela hore katleho le ho hlōleha ho amana le lintho tse ka ntle, tse sa laoleheng (mohlala, mahlohonolo)

Diane Bryant, ea etsang liphuputso mabapi le mehato ea lipalo bakeng sa liithuti tse nang le LD, o hlalosa hore na ke hobane'ng ha liithuti tse nang le bokooa ba ho ithuta lipalo le ba nang le bothata ba lipalo hangata li kopantsoe hammoho ho etsa lipatlisiso sebakeng sena (nako: 1:00).

Diane Pedrotty Bryant, PhD
Motsamaisi oa Morero, Setsi sa Mathematics bakeng sa Bokooa ba ho Ithuta le Mathata
Univesithi ea Texas e Austin

/wp-content/uploads/module_media/math_media/audio/math_p01_db.mp3

tlaleho

Diane Bryant

Sengoloa: Diane Pedrotty Bryant, PhD

Baithuti ba nang le bothata ba thuto ea lipalo le ba fumanoeng ba e-na le bokooa ba ho ithuta lipalo ba arolelana litšobotsi tse tšoanang. Ka mohlala, lihlopha tse peli tsa liithuti li ka 'na tsa e-ba le bothata ka se bitsoang moelelo oa palo, ho utloisisa lipalo le moelelo oa lipalo le ho bala ka sebele. Ho rarolla mathata ke karolo e 'ngoe. Kahoo ke nahana hore lena ke lebaka le leng leo ka lona lihlopha tsena tse peli li atisang ho kenyelletsoa lithutong. Lebaka le leng le amana le ho etsa bonnete ba hore u na le boholo bo lekaneng ba sampuli e le hore u ka sheba liphello tsa phekolo ea mekhoa e ka 'nang ea fetoha mekhoa e thehiloeng bopaking. Ka hona, ho tloaelehile ho bona liithuti tse peli tse nang le mathata a lipalo le liithuti tse nang le bokooa ba ho ithuta lipalo li kenyelelitsoe sampuling.

Baithuti ba Senyesemane

EL le bona ba na le bothata ba lipalo, le hoja mathata a bona a ka bakoa ke mathata a puo. Ho bohlokoa hore matichere a utloisise hore lipalo ha li na lipalo feela; e kenyelletsa palo e kholo ea mantsoe a ikhethileng a amanang le litaba. Ha matichere a buisana ka mekhoa le likhopolo tsa lipalo, hangata a li sebelisa puo ya thuto, e entsoeng ka pokello ea mantsoe a tobaneng le litaba—ka mohlala, mantsoe a kang ntlha, lekanya, 'me kakaretso- pokello ea mantsoe e nang le meelelo e mengata - mohlala, tafoleng—le dibopeho tse rarahaneng tsa puo. Kahoo, ha ho makatse hore ebe li-ELL tse ngata li sokola ho rarolla mathata a lipalo a mantsoe.

x

puo ya thuto

lenaane-foko

Matichere a ka Etsa'ng?

Ho kopanya mabone a mabone a nang le Kharikhulamo e Thehiloeng ho Maemo ka lehlakoreng le leng le Litloaelo tse Thehiloeng ho Bopaki ka ho le leng. Mmoho ba theha Taelo ya Mathematics ya Boemo bo Phahameng.

E le ho ntlafatsa mosebetsi oa liithuti oa lipalo, likolo tse ngata le litereke li sebelisitse thuto ea lipalo ea boleng bo holimo. Taelo ena e kenyelletsa ts'ebetsong ea bobeli:

  • Kharikhulamo e thehiloeng ho maemo - Likhopolo le litsebo tseo ho lumeloang hore li bohlokoa hore liithuti li ithute
  • Mekhoa e thehiloeng ho bopaki (EBP) - Maano kapa litloaelo tse netefalitsoeng ka lipatlisiso hore li sebetsa hantle bakeng sa ho ruta likhopolo le mekhoa ea lipalo

Lipontšo tsa Lipatlisiso

  • Ha ba fana ka thuto e sebetsang ea lipalo, matichere a ka fokotsa lekhalo la ts'ebetso pakeng tsa baithuti ba kotsing ea bothata ba lipalo le lithaka tsa bona tse tloaelehileng le tse sebetsang hantle.
    (Clarke, Smollkowski, Baker, Fien, Doabler, & Chard, 2011)
  • Baithuti ba nang le bokooa ba ho ithuta ba fumanang thuto e sebetsang ea lipalo ba ka hlaolela litsebo tsa bohlokoa joalo ka ho rarolla mathata le ho beha mabaka, tse hlokahalang ho fihlela tsebo ea lipalo.
    (Gersten, Chard, Jayanthi, Baker, Morphy, & Flojo, 2008; Allsopp, Lovin, & van Ingen, 2017)

mosebetsi oa

Har'a lintlha tseo ka linako tse ling li susumetsang thuto ea lipalo e sebetsang hantle ea boemo bo holimo ke maikutlo le litumelo tsa matichere le liithuti mabapi le thuto ea lipalo ka boeona.

  1. Tobetsa mona ho fumana maikutlo le litumelo tsa hau mabapi le lipalo le ho nahana ka hore na li ka ama thuto ea hau joang.

    Maikutlo le Litumelo Mabapi le Lipalo

    Na lipolelo tse mabapi le bokhoni ba lipalo ka har'a mabokose a ka tlase ke 'Nete kapa Maaka? Bala e 'ngoe le e' ngoe ebe o tobetsa "'Nete" kapa "False" ho fumana karabo.

    Liithuti tse ling li tsoaloa li e-na le bokhoni ba ho etsa lipalo, ha tse ling li se na tsona.
    ditshwaelo

    Bokhoni bo phahameng ba lipalo bo hlalosoa e le bokhoni ba ho etsa lipalo ka nepo.
    ditshwaelo
    Lipalo li hloka monahano o utloahalang le oa boiqapelo.
    ditshwaelo
    Bokhoni ba ho bala bo bohlokoa bakeng sa katleho ea lipalo.
    ditshwaelo
    Sepheo se seholo sa thuto ea lipalo ke ho fumana karabo e nepahetseng.
    ditshwaelo
    Ntle le ho tseba lintlha tsa lipalo, baithuti ba tlameha ho utloisisa lintlha tsa motheo tsa tsebo eo ba ithutang eona.
    ditshwaelo
    Matichere a thuto ea lipalo ha a hloke feela hore a be le tsebo ea lipalo eo a a rutang empa a boetse a lokela ho tseba ho sebelisa mekhoa e sebetsang ea ho ruta.
    ditshwaelo
    Banna ba hloahloa ho lipalo.
    ditshwaelo

    (Koala phanele ena)

  2. Haeba u phethela ketsahalo ena ka tlelaseng, u e-na le sehlopha se senyenyane, kapa u e-na le molekane, buisanang hore na maikutlo le litumelo tsa hau ka thuto ea lipalo li ka amang kapa li se li amme mekhoa ea hau ea ho ruta. Ka mor'a moo, buisanang ka maikutlo a ho ntlafatsa thuto ea hau ea lipalo.

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