Vim li cas lawv kawm hauv Ixayees siv phau ntawv qub Soviet?

2024 Tus sau: Seth Attwood | [email protected]. Kawg hloov kho: 2023-12-16 16:06

Nyob rau hauv thaum ntxov 30s ntawm lub xyoo pua xeem, lub ntiaj teb no cov phau ntawv zoo tshaj plaws nyob rau hauv kev ua lej ntawm "tseem ceeb" "pre-revolutionary" Kiselev, rov qab mus rau cov me nyuam socialist, instantly tsa cov kev txawj ntse zoo thiab txhim kho lawv lub hlwb. Thiab tsuas yog nyob rau hauv 70s puas tau cov neeg Yudais hloov "zoo heev" rau "phem".

Academician V. I. Arnold

Kev hu rau "rov qab mus rau Kiselev" tau nrov rau 30 xyoo. Nws tshwm sim tam sim ntawd tom qab kev hloov kho-70, uas tau tshem tawm cov phau ntawv zoo heev los ntawm lub tsev kawm ntawv thiab pib ua cov txheej txheem kev loj hlob degradation ntawm kev kawm … Vim li cas qhov kev thov no tsis txo qis?

Qee tus neeg piav qhov no los ntawm "nostalgia" [1, p. 5]. Qhov tsis tsim nyog ntawm qhov kev piav qhia no yog qhov tseeb yog tias peb nco qab tias thawj tus uas, rov qab rau xyoo 1980, ntawm txoj kev tshiab ntawm kev hloov kho, hu kom rov qab mus rau cov kev paub dhau los thiab cov phau ntawv ntawm Lavxias teb sab tsev kawm ntawv, yog Academician L. S. Pontryagin. Tom qab kev txheeb xyuas cov phau ntawv tshiab, nws ntseeg siab, siv cov piv txwv, piav qhia vim li cas qhov no yuav tsum ua [2, p. 99-112] ib.

Vim tias txhua phau ntawv tshiab yog tsom rau Kev Tshawb Fawb, lossis theej, ntawm pseudoscience thiab tsis quav ntsej cov Tub Kawm Ntawv, kev xav ntawm nws txoj kev xav, uas cov phau ntawv qub paub yuav ua li cas coj mus rau hauv tus account. Nws yog qhov tseeb ntawm "siab theoretical theem" ntawm cov phau ntawv niaj hnub no uas yog lub hauv paus ua rau muaj kev puas tsuaj loj hauv kev qhia thiab kev paub zoo. Qhov laj thawj no tau siv tau rau ntau tshaj peb caug xyoo, tsis tso cai los kho qhov xwm txheej.

Niaj hnub no, kwv yees li 20% ntawm cov tub ntxhais kawm txawj lej (geometry - 1%) [3, p. 14], [4, ib. 63] ib. Hauv xyoo 1940s (txoj cai tom qab tsov rog!) 80% ntawm cov menyuam kawm ntawv uas kawm "raws li Kiselev" tau paub txog txhua ntu ntawm lej.[3, p. 14] ib. Puas yog qhov no tsis yog kev sib cav rau kev xa rov qab rau menyuam yaus?

Nyob rau xyoo 1980, qhov kev thov rov hais dua no tsis quav ntsej los ntawm kev saib xyuas haujlwm (M. A. Prokofiev) raws li cov ntsiab lus hais tias "cov phau ntawv tshiab yuav tsum tau txhim kho." Niaj hnub no peb pom tias 40 xyoo ntawm "zoo meej" phau ntawv phem tsis tau tsim cov zoo. Thiab lawv yug tsis tau.

Ib phau ntawv kawm zoo tsis yog "sau" hauv ib lossis ob xyoos los ntawm kev txiav txim ntawm txoj haujlwm lossis rau kev sib tw. Nws yuav tsis "sau" txawm tias thaum muaj kaum xyoo. Nws yog tsim los ntawm ib tug kws qhia txuj ci xyaum ua ke nrog cov tub ntxhais kawm thoob plaws hauv lawv lub neej pedagogical (thiab tsis yog los ntawm tus xibfwb qhia lej lossis tus kws qhia ntawv ntawm lub rooj sau ntawv).

Pedagogical txuj ci tsis tshua muaj - ntau tsawg dua li kev ua lej nws tus kheej (muaj ntau tus lej zoo, tsuas muaj ob peb tus sau phau ntawv zoo). Cov cuab yeej tseem ceeb ntawm pedagogical txuj ci yog lub peev xwm ua siab ntev rau cov tub ntxhais kawm, uas tso cai rau koj kom nkag siab qhov tseeb ntawm nws txoj kev xav thiab qhov ua rau muaj kev nyuaj siab. Tsuas yog nyob rau hauv qhov xwm txheej no tuaj yeem pom cov kev daws teeb meem raug. Thiab lawv tseem yuav tsum tau kuaj xyuas, kho thiab coj mus rau qhov tshwm sim los ntawm kev ua haujlwm ntev ntev - ua tib zoo saib xyuas, pedantic kev soj ntsuam ntawm ntau qhov yuam kev ntawm cov tub ntxhais kawm, lawv cov kev xav zoo.

Qhov no yog li cas, rau ntau tshaj plaub caug xyoo (thawj tsab nyob rau hauv 1884), tus kws qhia ntawv ntawm lub Voronezh tiag lub tsev kawm ntawv A. P. Kiselev tsim nws zoo kawg nkaus, tshwj xeeb cov phau ntawv. Nws lub hom phiaj siab tshaj plaws yog kev nkag siab ntawm cov ncauj lus los ntawm cov tub ntxhais kawm. Thiab nws paub tias lub hom phiaj no ua tiav li cas. Yog li ntawd nws thiaj yooj yim kawm los ntawm nws phau ntawv.

AP Kiselev tau hais txog nws cov ntsiab lus qhia luv luv: “Tus sau … thawj zaug tau teeb tsa nws tus kheej lub hom phiaj kom ua tiav peb yam zoo ntawm phau ntawv kawm zoo:

qhov tseeb (!) hauv kev tsim thiab tsim cov ntsiab lus, simplicity (!) nyob rau hauv kev xav thiab

conciseness (!) nyob rau hauv qhov kev nthuav qhia [5, p. 3].

Qhov sib sib zog nqus pedagogical qhov tseem ceeb ntawm cov lus no yog qee qhov poob qab lawv qhov yooj yim. Tab sis cov lus yooj yooj yim no muaj nqis ntau txhiab phau ntawv niaj hnub no. Cia peb xav txog nws.

Cov kws sau ntawv niaj hnub no, ua raws li cov lus qhia ntawm A. N. Kolmogorov, siv zog "kom nruj dua (vim li cas? - IK) los ntawm lub ntsiab lus ntawm kev xav, kev tsim tsev kawm ntawv hauv kev ua lej" [6, p. 98] ib. Kiselev tsis quav ntsej txog "kev nruj", tab sis hais txog qhov tseeb (!) ntawm cov qauv tsim, uas ua kom lawv txoj kev nkag siab raug, tsim nyog rau kev tshawb fawb. Qhov tseeb yog qhov sib xws nrog lub ntsiab lus. Qhov kev tsis sib haum xeeb "kev nruj" ua rau kev ncua deb ntawm lub ntsiab lus thiab, thaum kawg, ua kom nws puas tsuaj.

Kiselev tsis txawm siv lo lus "logic" thiab tsis hais txog "cov ntaub ntawv pov thawj" uas zoo li muaj nyob hauv lej, tab sis ntawm "kev xav yooj yim". Nyob rau hauv lawv, nyob rau hauv cov "kev xav", ntawm chav kawm, muaj logic, tab sis nws occupies ib tug subordinate txoj hauj lwm thiab pab lub hom phiaj pedagogical - kev txawj ntse thiab persuasiveness (!)kev xav rau tus menyuam kawm ntawv (tsis yog rau tus kws qhia ntawv).

Thaum kawg, conciseness. Thov nco ntsoov - tsis yog brevity, tab sis conciseness! Yuav ua li cas maj mam Andrei Petrovich hnov lub ntsiab lus zais cia ntawm cov lus! Brevity presupposes contraction, pov tseg ib yam dab tsi, tej zaum tseem ceeb. Compression yog lossless compression. Tsuas yog dab tsi yog superfluous yog txiav tawm - distracting, clogging, cuam tshuam nrog concentration ntawm lub ntsiab lus. Lub hom phiaj ntawm brevity yog kom txo ntim. Lub hom phiaj ntawm conciseness yog purity ntawm essence! Qhov kev qhuas no rau Kiselev tau ua suab nrov ntawm lub rooj sib tham "Kev Ua lej thiab Lub Koom Haum" (Dubna) hauv xyoo 2000: "Dab tsi huv!"

Qhov zoo kawg li Voronezh mathematician Yu. V. Pokorny, "mob ntawm lub tsev kawm ntawv", pom tias cov txheej txheem architecture ntawm Kiselev cov phau ntawv yog feem ntau raws li txoj cai ntawm lub hlwb thiab caj ces thiab cov ntaub ntawv ntawm kev loj hlob ntawm cov tub ntxhais txawj ntse (Piaget-Vygotsky), nce mus rau Aristotle's " ntaiv ntawm tus ntsuj plig daim ntawv". "Muaj (hauv Kiselev phau ntawv geometry - IK), yog tias leej twg nco qab, pib qhov kev nthuav qhia yog tsom rau kev xav sensorimotor (peb yuav superimpose, txij li ntu lossis lub kaum ntse ntse sib npaug, lwm qhov kawg lossis sab nraud coincide, thiab lwm yam)…

Tom qab ntawd cov kev ua haujlwm tawm tswv yim ntawm kev ua, muab qhov pib (raws li Vygotsky thiab Piaget) geometric intuition, los ntawm kev sib txuas ua rau muaj peev xwm ntawm kev kwv yees (kev pom, aha-kev paub). Nyob rau tib lub sijhawm, kev sib cav nyob rau hauv daim ntawv ntawm syllogisms yog loj hlob. Axioms tshwm sim tsuas yog thaum kawg ntawm lub planimetry, tom qab ntawd qhov kev txiav txim siab nruj dua tuaj yeem ua tau. Nws tsis yog rau tsis muaj dab tsi uas yav dhau los nws yog qhov tseeb geometry raws li Kiselev uas instilled nyob rau hauv cov me nyuam kawm ntawv cov kev txawj ntawm formal logic kev xav. Thiab nws ua tau zoo heev [7, p. 81–82].

Nov yog lwm qhov zais cia ntawm Kiselev lub zog pedagogical zoo! Nws tsis tsuas yog kev puas siab puas ntsws kom raug nthuav tawm txhua lub ntsiab lus, tab sis tsim nws cov phau ntawv kawm (los ntawm cov qib junior mus rau cov qib laus) thiab xaiv txoj hauv kev raws li cov hnub nyoog tshwj xeeb ntawm kev xav thiab kev nkag siab ntawm cov menyuam yaus, maj mam thiab loj hlob lawv. Lub siab tshaj plaws ntawm pedagogical xav, nkag tsis tau mus rau niaj hnub certified methodologists thiab ua tiav phau ntawv sau ntawv.

Thiab tam sim no kuv xav qhia ib qho kev xav ntawm tus kheej. Thaum qhia qhov kev xav ntawm qhov yuav tshwm sim hauv tsev kawm qib siab technical, kuv ib txwm muaj kev tsis xis nyob thaum piav qhia rau cov tub ntxhais kawm txog cov ntsiab lus thiab cov qauv ntawm combinatorics. Cov tub ntxhais kawm tsis nkag siab cov lus xaus, lawv tsis meej pem hauv kev xaiv cov qauv rau kev sib txuas, qhov chaw, thiab kev hloov pauv. Tau ntev nws tsis tuaj yeem qhia meej, txog thaum lub tswv yim tig mus rau Kiselev rau kev pab cuam - Kuv nco qab tias tom tsev kawm ntawv cov lus nug no tsis ua rau muaj kev nyuaj siab thiab tseem nthuav. Tam sim no ntu no tau raug muab pov tseg ntawm cov ntaub ntawv kawm theem nrab - hauv txoj kev no Ministry of Education tau sim daws qhov teeb meem ntawm overload, uas nws tsim nws tus kheej.

Yog li, tom qab nyeem Kiselev qhov kev nthuav qhia, Kuv xav tsis thoob thaum kuv pom hauv nws txoj kev daws teeb meem tshwj xeeb, uas ntev ntev tsis ua haujlwm rau kuv. Kev sib txuas zoo siab ntawm lub sijhawm thiab tus ntsuj plig tau tshwm sim - nws tau pom tias AP Kiselev paub txog kuv qhov teeb meem, xav txog nws thiab daws nws ntev dhau los! Cov kev daws teeb meem muaj nyob rau hauv ib tug nruab nrab concretization thiab puas siab puas ntsws tsim cov kab lus, thaum lawv tsis tsuas yog qhia txog lub essence, tab sis coj mus rau hauv tus account tus tub ntxhais kawm txoj kev qhia ntawm kev xav thiab coj nws. Thiab nws yog ib qho tsim nyog yuav tau raug kev txom nyem ntau npaum li cas nyob rau hauv lub sij hawm ntev kev daws teeb meem ntawm ib tug methodological teeb meem nyob rau hauv thiaj li yuav txaus siab rau cov kos duab ntawm AP Kiselev. Heev inconspicuous, heev hloov maj mam thiab tsis tshua muaj pedagogical art. Tsis tshua muaj! Cov kws qhia ntawv niaj hnub no thiab cov kws sau phau ntawv coj mus muag yuav tsum pib tshawb fawb cov phau ntawv ntawm tus kws qhia gymnasium A. P. Kiselev.

AM Abramov (ib tug ntawm kev hloov kho-70 - nws, raws li nws nkag [8, p. 13], koom nyob rau hauv kev sau ntawv "Geometry" Kolmogorov) ncaj ncees lees tias tsuas yog tom qab ntau xyoo ntawm kev kawm thiab tshuaj xyuas Kiselev cov phau ntawv pib nkag siab me ntsis. zais pedagogical "kev zais cia" ntawm cov phau ntawv no thiab "qhov tob tshaj plaws pedagogical kab lis kev cai" ntawm lawv tus sau, uas nws cov phau ntawv yog ib tug "lub teb chaws cov khoom muaj nqis" (!) ntawm Russia [8, p. 12-13] ib.

Thiab tsis tsuas yog Russia, - tag nrho lub sij hawm no nyob rau hauv Israeli tsev kawm ntawv lawv tau siv Kiselev cov phau ntawv kawm tsis muaj complexes. Qhov tseeb no tau lees paub los ntawm tus thawj coj ntawm lub tsev Pushkin, Academician N. Skatov: "Tam sim no ntau thiab ntau tus kws tshaj lij tau sib cav tias, kev sim, cov neeg Ixayees ntse tau qhia algebra raws li peb phau ntawv qhia Kiselev." [9, p. 75] ib.

Peb muaj obstacles los txog txhua lub sijhawm. Lub ntsiab lus sib cav: "Kiselev yog outdated." Tab sis qhov ntawd txhais li cas?

Hauv kev tshawb fawb, lo lus "tso tseg" yog siv rau kev xav, kev poob lossis tsis tiav uas yog tsim los ntawm lawv txoj kev loj hlob ntxiv. Yuav ua li cas yog "obsolete" rau Kiselev? Pythagorean theorem lossis lwm yam los ntawm cov ntsiab lus ntawm nws phau ntawv? Tej zaum, nyob rau hauv lub era ntawm lub tshuab xam zauv high-ceev, cov cai rau kev ua nrog cov lej uas niaj hnub kawm tiav high school tsis paub (tsis tuaj yeem ntxiv cov feem) yog qhov qub?

Rau qee qhov laj thawj, peb tus lej zoo tshaj plaws niaj hnub no, Academician V. I. Arnold tsis xav txog Kiselev "tso tseg". Obviously, nyob rau hauv nws phau ntawv kawm tsis muaj dab tsi tsis ncaj ncees lawm, tsis scientific nyob rau hauv lub niaj hnub kev xav. Tab sis muaj lub siab tshaj plaws pedagogical thiab methodological kab lis kev cai thiab conscientiousness uas tau ploj mus los ntawm peb pedagogy thiab uas peb yuav tsis mus txog dua. Tsis txhob!

Lo lus "obsolete" tsuas yog sly txais toscov yam ntxwv ntawm modernizers ntawm txhua lub sijhawm. Cov txheej txheem uas cuam tshuam rau subconscious. Tsis muaj ib yam dab tsi uas muaj nuj nqis tiag tiag yuav ploj mus - nws nyob mus ib txhis. Thiab nws yuav tsis muaj peev xwm "tshem nws tawm ntawm lub zog ntawm kev niaj hnub," ib yam li RAPP modernizers ntawm Lavxias teb sab kab lis kev cai tsis tau tswj kom muab pov tseg lub "tso tseg" Pushkin nyob rau hauv lub xyoo 1920. Kiselev yuav tsis tau dhau los, thiab Kiselev yuav tsis nco qab lawm.

Lwm qhov kev sib cav: qhov rov qab ua tsis tau vim qhov kev hloov pauv hauv qhov kev pab cuam thiab kev sib koom ua ke ntawm trigonometry nrog geometry [10, p. 5]. Qhov kev sib cav tsis ntseeg - qhov kev pab cuam tuaj yeem hloov tau dua, thiab trigonometry tuaj yeem raug txiav tawm ntawm cov duab geometry thiab, qhov tseem ceeb tshaj, los ntawm algebra. Ntxiv mus, qhov no "kev sib txuas" (nrog rau kev sib txuas ntawm algebra nrog kev tsom xam) yog lwm qhov yuam kev loj ntawm cov neeg hloov kho-70, nws ua txhaum txoj cai tseem ceeb ntawm txoj cai - nyuaj rau kev sib cais, tsis txuas.

Classical kev qhia "raws li Kiselev" presupposed txoj kev kawm ntawm trigonometric functions thiab lub apparatus ntawm lawv transformation nyob rau hauv daim ntawv ntawm ib tug cais kev qhuab qhia nyob rau hauv lub X qib, thiab thaum kawg - daim ntawv thov kev kawm rau cov kev daws ntawm daim duab peb sab thiab cov kev daws. ntawm cov teeb meem stereometric. Cov ntsiab lus tom kawg tau ua tiav zoo kawg nkaus ua haujlwm los ntawm ib ntu ntawm cov dej num sib xws. Qhov teeb meem stereometric "hauv geometry nrog kev siv trigonometry" yog qhov yuav tsum tau ua ntawm qhov kev xeem zaum kawg rau daim ntawv pov thawj ntawm kev loj hlob. Cov tub ntxhais kawm ua tau zoo nrog cov haujlwm no. Hnub no? Cov neeg thov MSU tsis tuaj yeem daws qhov teeb meem yooj yim planimetric!

Thaum kawg, lwm qhov kev sib cav - "Kiselev muaj yuam kev" (Prof. N. Kh. Rozov). Kuv xav paub qhov twg? Nws hloov tawm - omissions ntawm logical cov kauj ruam hauv cov pov thawj.

Tab sis cov no tsis yog qhov yuam kev, cov no yog kev txhob txwm tshaj tawm, pedagogically justified omissions uas pab kev nkag siab. Qhov no yog ib tug classic methodological txoj cai ntawm Lavxias teb sab pedagogy: "ib tug yuav tsum tsis txhob sim tam sim ntawd ntawm ib tug nruj me ntsis cov ntsiab lus ntawm qhov no los yog qhov tseeb lej. Rau lub tsev kawm ntawv," lub ntsiab lus leaps los ntawm intuition "yog heev txaus, muab qhov tsim nyog nkag tau mus rau cov ntaub ntawv kawm" (los ntawm kev hais lus ntawm tus kws qhia txuj ci tseem ceeb D. Mordukhai-Boltovsky ntawm Lub Rooj Sib Tham Thib Ob All-Lavxias teb sab ntawm Cov Xib Fwb ntawm Kev Ua lej hauv xyoo 1913).

Modernizers-70 tau hloov lub hauv paus ntsiab lus no nrog rau kev tawm tsam pedagogical pseudoscientific hauv paus ntsiab lus ntawm "nrhiav" kev nthuav qhia. Nws yog tus uas rhuav tshem cov txheej txheem, ua rau muaj kev nkag siab yuam kev thiab kev qias neeg ntawm cov tub ntxhais kawm rau lej … Cia kuv muab ib qho piv txwv ntawm pedagogical deformities uas lub ntsiab cai no coj.

Nco ntsoov tus qub Novocherkassk xib fwb V. K. Sovaylenko. "Lub yim hli ntuj 25, 1977, lub rooj sib tham ntawm lub UMS ntawm lub USSR MP, nyob rau hauv uas Academician AN Kolmogorov soj ntsuam cov phau ntawv lej los ntawm qib 4 txog rau qib 10 thiab xaus kev xeem ntawm txhua phau ntawv nrog cov kab lus: "Tom qab qee qhov kev kho, qhov no. yuav yog ib phau ntawv zoo heev, thiab yog tias koj nkag siab lo lus nug no kom raug, ces koj yuav pom zoo cov phau ntawv no." Ib tug xib fwb los ntawm Kazan uas nyob rau ntawm lub rooj sib tham hais nrog tu siab rau cov zaum ntawm lawv: "Qhov no yog tsim nyog, ib tug ntse heev nyob rau hauv lub rooj sib tham. lej yog ib tug layman nyob rau hauv pedagogy. Nws tsis to taub qhov ntawd cov no tsis yog phau ntawv, tab sis freaksthiab nws qhuas lawv.”

Tus kws qhia ntawv Moscow Weizman tau hais hauv kev sib cav: "Kuv yuav nyeem lub ntsiab lus ntawm polyhedron los ntawm phau ntawv geometry tam sim no." Kolmogorov, tom qab mloog lub ntsiab lus, hais tias: "Txoj cai, tag nrho cov cai!" Tus kws qhia ntawv teb nws: "Kev tshawb fawb, txhua yam yog qhov tseeb, tab sis nyob rau hauv cov kev xav ntawm pedagogical, nws yog blatant illiteracy. Cov ntsiab lus no yog luam nyob rau hauv bold, uas txhais tau hais tias nws yog tsim nyog los cim, thiab nws yuav siv sij hawm ib nrab ib nplooj ntawv? Thaum nyob rau hauv Kiselev. Cov ntsiab lus no tau muab rau lub convex polyhedron thiab siv tsawg dua ob kab, qhov no yog ob qho tib si scientific thiab pedagogically raug."

Lwm tus kws qhia ntawv tau hais ib yam hauv lawv cov lus hais. Thaum kawg, A. N. Kolmogorov tau hais tias: "Hmoov tsis zoo, ib yam li yav dhau los, kev thuam tsis tsim nyog txuas ntxiv es tsis yog kev sib tham ua lag luam. Koj tsis txhawb kuv. Tab sis nws tsis muaj teeb meem, txij li thaum kuv tau pom zoo nrog Minister Prokofiev thiab nws txhawb kuv tag nrho." Qhov tseeb no tau hais los ntawm VK Sovailenko hauv tsab ntawv tshaj tawm rau FES hnub tim 25.09.1994.

Lwm nthuav piv txwv ntawm kev hais lus phem ntawm pedagogy los ntawm cov kws lej tshwj xeeb. Ib qho piv txwv uas tau npaj txhij txog qhia ib qho tiag tiag "kev zais cia" ntawm cov phau ntawv Kiselev. Kwv yees li kaum xyoo dhau los kuv tau tuaj ntawm kev qhuab qhia los ntawm peb tus kws lej tseem ceeb. Cov lus qhuab qhia tau mob siab rau lub tsev kawm ntawv lej. Thaum kawg kuv nug tus kws qhia ntawv ib lo lus nug - nws xav li cas txog Kiselev cov phau ntawv? Teb: "Cov phau ntawv yog zoo, tab sis lawv yog outdated." Cov lus teb yog banal, tab sis qhov txuas ntxiv yog qhov nthuav - piv txwv li, tus kws qhia ntawv kos duab koselevsky rau lub cim ntawm kev sib luag ntawm ob lub dav hlau. Nyob rau hauv cov duab no, cov dav hlau khoov sharply nyob rau hauv thiaj li yuav sib tshuam. Thiab kuv xav tias: "Xwb, dab tsi yog daim duab tsis txaus ntseeg! Kos dab tsi ua tsis tau!" Thiab mam li nco dheev kuv kom meej meej nco ntsoov tus thawj daim duab thiab txawm nws txoj hauj lwm ntawm nplooj ntawv (hauv qab-sab laug) nyob rau hauv phau ntawv, uas kuv tau kawm yuav luag plaub caug xyoo dhau los. Thiab kuv tau hnov qhov kev xav ntawm cov leeg nruj uas cuam tshuam nrog kev kos duab, zoo li kuv tau sim yuam kom txuas ob lub dav hlau tsis sib tshuam. Los ntawm nws tus kheej, ib tug meej formulation tshwm sim los ntawm lub cim xeeb: "Yog hais tias ob txoj kab sib tshuam" ntawm tib lub dav hlau yog parallel -.. ", thiab tom qab nws tag nrho cov luv luv pov thawj "los ntawm contradiction."

Kuv xav tsis thoob. Nws hloov tawm hais tias Kiselev imprinted no lub ntsiab lus lej qhov tseeb nyob rau hauv kuv lub siab mus ib txhis (!).

Thaum kawg, ib qho piv txwv ntawm Kiselev's unsurpassed art nyob rau hauv kev sib piv nrog cov neeg sau ntawv niaj hnub. Kuv tuav hauv kuv txhais tes ib phau ntawv rau qib 9 "Algebra-9", luam tawm xyoo 1990. Tus sau - Yu. N. Makarychev thiab K0, thiab los ntawm txoj kev, nws yog cov phau ntawv ntawm Makarychev, raws li zoo raws li Vilenkin, uas hais txog LS Pontryagin ua piv txwv ntawm "tsis zoo, … nyeem tsis tau ntawv" [2, p.. 106] ib. Thawj nplooj ntawv: § 1. "Function. Domain and range of values of a function".

Lub ntsiab lus hais txog lub hom phiaj ntawm kev piav qhia rau cov tub ntxhais kawm peb lub tswv yim kev ua lej sib cuam tshuam. Qhov teeb meem pedagogical no daws tau li cas? Ua ntej, cov ntsiab lus raug muab, tom qab ntawd ntau qhov piv txwv motley abstract, tom qab ntawd ntau qhov kev tawm dag zog uas tsis muaj lub hom phiaj pedagogical rational. Muaj overload thiab abstractness. Qhov kev nthuav qhia yog xya nplooj ntawv ntev. Daim ntawv ntawm kev nthuav qhia, thaum lawv pib los ntawm qhov tsis pom qhov " nruj" cov ntsiab lus, thiab tom qab ntawd "piav" lawv nrog cov piv txwv, yog stencil rau niaj hnub scientific monographs thiab cov khoom.

Cia peb sib piv qhov kev nthuav qhia ntawm tib lub ntsiab lus los ntawm A. P. Kiselev (Algebra, Part 2. Moscow: Uchpedgiz. 1957). Cov txheej txheem yog thim rov qab. Lub ntsiab lus pib nrog ob qho piv txwv - txhua hnub thiab geometric, cov piv txwv no paub zoo rau cov tub ntxhais kawm. Cov piv txwv tau nthuav tawm nyob rau hauv ib txoj kev uas lawv ib txwm coj mus rau lub ntsiab lus ntawm kev sib txawv, kev sib cav, thiab kev ua haujlwm. Tom qab ntawd, cov lus txhais thiab 4 cov piv txwv ntxiv nrog cov lus piav qhia luv luv, lawv lub hom phiaj yog sim cov tub ntxhais kawm kev nkag siab, ua rau nws ntseeg siab. Cov piv txwv kawg kuj tseem nyob ze rau cov tub ntxhais kawm, lawv raug coj los ntawm geometry thiab tsev kawm ntawv physics. Kev nthuav qhia yuav siv ob (!) nplooj. Tsis muaj overload, tsis muaj abstractness! Ib qho piv txwv ntawm "kev nthuav qhia kev puas siab ntsws", hauv cov lus ntawm F. Klein.

Kev sib piv ntawm cov ntim ntawm cov phau ntawv yog qhov tseem ceeb. Makarychev phau ntawv kawm rau qib 9 muaj 223 nplooj ntawv (tsis suav cov ntaub ntawv keeb kwm thiab cov lus teb). Kiselev phau ntawv kawm muaj 224 nplooj, tab sis yog tsim los rau peb xyoos ntawm kev kawm - rau qib 8-10. Lub ntim tau tripled!

Niaj hnub no, cov neeg hloov kho tsis tu ncua tab tom sim txo qis ntau dhau thiab "tib neeg" kev kawm, ostensibly saib xyuas kev noj qab haus huv ntawm cov menyuam kawm ntawv. Cov lus teb… Qhov tseeb, es tsis txhob ua lej nkag siab, lawv rhuav tshem nws cov ntsiab lus tseem ceeb. Ua ntej, hauv 70s. "tso lub theoretical theem", undermining lub psyche ntawm cov me nyuam, thiab tam sim no "qis" theem no los ntawm lub primitive txoj kev ntawm pov tseg "tsis tsim nyog" seem (logarithms, geometry, thiab lwm yam) thiab txo cov sij hawm qhia.[11, p. 39-44] ib.

Kev rov qab mus rau Kiselev yuav yog tib neeg tiag tiag. Nws yuav ua kom lej nkag siab rau cov menyuam yaus thiab nyiam dua. Thiab muaj ib qho piv txwv rau qhov no nyob rau hauv peb keeb kwm: nyob rau hauv thaum ntxov 30s ntawm lub xeem caug xyoo, lub "tseem ceeb" "pre-revolutionary" Kiselev, rov qab mus rau "socialist" cov me nyuam, instantly tsa qhov zoo ntawm kev paub thiab txhim kho lawv lub hlwb. Thiab tej zaum nws tau pab kom yeej Tsov Rog Loj

Qhov teeb meem tseem ceeb tsis yog kev sib cav, tab sis Cov xeem uas tswj hwm Tsoom Fwv Teb Chaws cov phau ntawv kawm thiab muaj txiaj ntsig ntau ntxiv rau lawv cov khoom kawm … Xws li cov nuj nqis ntawm "kev kawm ntawv pej xeem" uas tsis ntev los no tus thawj tswj hwm ntawm FES G. V. Dorofeev, uas tau muab nws lub npe rau, tej zaum, ib puas phau ntawv kev kawm luam tawm los ntawm "Bustard", L. G. Peterson [12, p. 102-106], I. I. Arginskaya, E. P. Benenson, A. V. Shevkin (saib lub vev xaib "www.shevkin.ru"), thiab lwm yam., thiab lwm yam., piv txwv li, niaj hnub pedagogical masterpiece tsom rau "kev loj hlob" ntawm qib peb.:

"Qhov teeb meem 329. Txhawm rau txiav txim siab txog qhov tseem ceeb ntawm peb txoj kab lus nyuaj, tus tub kawm tau ua cov haujlwm hauv qab no: 320-3, 318 + 507, 169-3, 248: 4, 256 + 248, 231-3, 960-295, 62 + 169, 504: 4, 256 + 62, 126 + 169, 256 + 693. 1. Ua kom tiav tag nrho cov kev qhia uas tau hais tseg. Qhia koj txoj haujlwm txuas ntxiv mus. " [kaum peb].

Tab sis Kiselev yuav rov qab los! Hauv ntau lub nroog muaj cov kws qhia ntawv uas ua haujlwm "raws li Kiselev." Nws cov phau ntawv pib luam tawm. Qhov rov qab los yog tsis pom! Thiab kuv nco ntsoov cov lus: "Lub hnub nyob ntev! Cia qhov tsaus ntuj nkaum!"

Siv:

Nws feem ntau lees paub tias qhov kev paub zoo ntawm kev hloov pauv lej hauv xyoo 1970-1978. ("Reform-70") tau tsim thiab siv los ntawm Academician A. N. Kolmogorov. Nws yog kev dag ntxias. A. N. Kolmogorov tau ua tus saib xyuas ntawm 70 kev hloov kho twb nyob rau theem kawg ntawm nws qhov kev npaj hauv xyoo 1967, peb xyoos ua ntej nws pib. Nws txoj kev koom tes yog exaggerated heev - nws tsuas yog concretized lub zoo-paub kev hloov kho tus cwj pwm (set-theoretic cov ntsiab lus, axioms, generalizing lub tswv yim, nruj, thiab lwm yam) ntawm cov xyoo. Nws txhais tau tias yog "qhov kawg". Nws tau tsis nco qab tias tag nrho cov kev npaj ua haujlwm rau kev hloov kho tau ua tiav rau ntau tshaj 20 xyoo los ntawm ib pawg neeg tsis txaus ntseeg, tsim rov qab rau xyoo 1930, xyoo 1950-1960s. ntxiv dag zog thiab nthuav. Nyob rau hauv lub taub hau ntawm pab neeg nyob rau hauv 1950s. Academician A. I. Markushevich, leej twg conscientiously, persistently thiab ua tau zoo ntawm qhov kev pab cuam tau teev nyob rau hauv lub 1930s. lej: L. G. Shnirelman, L. A. Lyusternik, G. M. Fichtengolt, P. S. Alexandrov, N. F. Chetverukhin, S. L. Sobolev, A. Ya. Khinchin thiab lwm tus [2. S. 55-84] ib. Ua cov kws ua lej txawj ntse heev, lawv tsis paub lub tsev kawm ntawv txhua, tsis muaj kev paub txog kev qhia cov menyuam yaus, tsis paub txog kev xav txog menyuam yaus, thiab yog li ntawd qhov teeb meem ntawm kev nce qib "theem" ntawm kev kawm lej zoo li yooj yim rau lawv, thiab cov kev qhia lawv. thov tsis txhob poob siab. Tsis tas li ntawd xwb, lawv tau tso siab rau lawv tus kheej thiab tsis lees paub cov lus ceeb toom ntawm cov kws qhia paub txog.

Nyob rau hauv 1938, Andrei Petrovich Kiselev hais tias:

Kuv zoo siab tias kuv tau nyob pom cov hnub thaum lej ua cov cuab yeej ntawm cov neeg coob coob. Puas yog nws muaj peev xwm los sib piv cov scanty prints ntawm pre-revolutionary lub sij hawm nrog rau tam sim no. Thiab nws tsis yog xav tsis thoob. Tom qab tag nrho, tag nrho lub teb chaws tab tom kawm tam sim no. Kuv zoo siab tias thaum kuv laus kuv tuaj yeem ua tau zoo rau kuv Niam Loj

Morgulis A. thiab Trostnikov V. "Tus tsim cai lij choj ntawm tsev kawm ntawv lej" // "Science and Life" p.122

Phau ntawv los ntawm Andrey Petrovich Kiselev:

"Systematic course of arithmetic rau cov tsev kawm ntawv theem nrab" (1884) [12];

"Elementary Algebra" (1888) [13];

"Elementary Geometry" (1892-1893) [14];

"Cov khoom ntxiv ntawm algebra" - chav kawm ntawm qib 7 ntawm cov tsev kawm tiag tiag (1893);

"Brief arithmetic for urban schools" (1895);

"Liab algebra rau cov poj niam cov tsev kawm ntawv sau ntawv thiab kev kawm theological" (1896);

“Elementary Physics for Secondary Educational Institutions with Many Exercises and problems” (1902; mus txog 13 tsab) [5];

Physics (ob ntu) (1908);

"Cov Ntsiab Cai ntawm Kev Sib Txawv thiab Kev Ntsuas Ib Leeg" (1908);

"Cov lus qhuab qhia theem pib ntawm cov lus qhuab qhia rau qib 7 ntawm cov tsev kawm ntawv tiag" (1911);

"Cov duab sawv cev ntawm qee lub luag haujlwm suav nrog hauv theem pib algebra" (1911);

"Ntawm cov lus nug ntawm theem pib geometry, uas feem ntau yog daws nrog kev pab ntawm kev txwv" (1916);

Luv luv Algebra (1917);

"Brief arithmetic for city districts" (1918);

Cov lej tsis raug suav hais tias yog cov lej tsis kawg uas tsis yog ntu ntu (1923);

"Cov ntsiab lus ntawm algebra thiab tsom xam" (qhov 1-2, 1930-1931).

Cov phau ntawv muag khoom

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