1. Bayanin Gabaɗaya na Aikin

Wannan aikin yana ba da shawara game da aiwatar da Wurin Ƙirƙira na STEAM don sake farfado da hanyoyin koyarwa da koyo na lissafi, tare da fifiko musamman akan jiyometry, ga ɗaliban aji na biyu na sakandare. Wannan yunƙurin amsa kai tsaye ne ga gazawar da aka gano a cikin ƙwarewar lissafi a tsakanin waɗanda suka kammala karatu, da nufin yin amfani da koyo mai haɗa kai da hannu don inganta sakamakon ilimi da ci gaban fahimi.

Shugaban Aikin: Luis Adrián Martínez Pérez
Alaƙa: Colegio Ceyca / Jami'ar Ƙasa ta Mexico (UNAM)
Lambar Tuntuɓar: lmartinez@edu.prp.ceyca.com, lamp@comunidad.unam.mx

2. Layin Bincike

Aikin ya shiga cikin layin bincike na "Koyo da Cimma Buri a Kimiyya da Fasaha." Yana mai da hankali kan ƙirƙirar hanyoyin koyarwa don rage gibin da ke tsakanin ilimin ka'ida da aikace-aikace, musamman a fannonin STEM.

3. Tushen Ka'idoji

Shawarar ta dogara ne akan sanin muhimmiyar rawar da lissafi ke takawa a tunanin kimiyya, ɗan adam, da fasaha, da kuma rayuwar yau da kullum.

3.1 Muhimmancin Lissafi da Tsarin Tsari

Takardar ta fara da sanannen kalaman Plato, "Kada wanda ba shi da ilimin jiyometry ya shiga," kuma ta ambaci Marjorie Senechal game da yaduwa da muhimmancin tsarin tsari. Tana jayayya cewa ikon gane, fassara, da ƙirƙirar tsarin tsari yana da mahimmanci don shiga cikin duniyar. Wannan ya kafa tushen falsafa da fahimi don ba da fifiko ga jiyometry da tunani na sarari.

3.2 Matsalar Ilimi ta Ƙasa

Shawarar ta gano matsala mai mahimmanci ta ƙasa: gazawa mai yawa a cikin ilimin lissafi da ƙwarewar waɗanda suka kammala sakandare, kamar yadda sakamakon tantancewa na ƙasa (PLANEA) da na duniya (PISA) suka nuna. Marubucin ya yi iƙirarin cewa wannan rashi yana cutar da ci gaban tunani, sana'a, da na sirri na ɗalibai a nan gaba. An sanya Wurin Ƙirƙira na STEAM a cikin Babban Aikin Ilimi na Ƙungiyar Kimiyya na cibiyar a matsayin amsa mai ƙarfi ga wannan matsala.

Mahimman Bayanan da aka Ambata

  • Ambaton sakamakon PLANEA (2015-2017) da PISA (2015-2016) na Mexico.
  • Bincike na cikin gida na sakamakon PLANEA da Kwalejin Kwalejin a Colegio Ceyca.
  • Bincike na tarihi kan gyare-gyaren ilimin lissafi daga shekarun 1960-1980.

3.3 Ragewar Jiyometry a cikin Manhajoji

Babban jigon shawarar shine cewa babban dalilin matsalar lissafi shine rage rawar jiyometry a cikin manhajojin makaranta bayan gyare-gyare daga shekarun 1960 zuwa 1980. Marubucin, tare da goyan bayan shaidar da aka rubuta da kwarewar koyarwa, ya yi iƙirarin cewa wannan warewa ya haifar da rashin fahimtar lissafi gabaɗaya kuma saboda haka ya haifar da ƙarancin aikin ilimi.

4. Fahimtar Cibiya & Ra'ayi na Mai Bincike

Fahimtar Cibiya

Wannan shawara ba kawai game da ƙara na'urar buga 3D a cikin aji ba ce; harbe-harbe ce da aka yi niyya a kan aibi na tsarin a cikin ilimin koyar da lissafi. Babban fahimtar shine cewa rabe-raben manhajojin lissafi na zamani, musamman warewar jiyometry, ya yanke muhimmiyar alaƙa tsakanin ra'ayoyin lissafi da haƙiƙanin sarari. An yi la'akari da wurin ƙirƙira ba a matsayin filin wasan fasaha ba, amma a matsayin kayan aikin sake daidaita fahimi, ta yin amfani da gini na zahiri da ƙira don sake gina tushen tunani na sarari wanda ke goyan bayan tunanin lissafi da kimiyya mai zurfi.

Tsarin Ma'ana

Hujjar ta bi wata maƙasudi, sarkar dalili da sakamako: 1) Maki na gwajin ƙasa (PLANEA/PISA) sun bayyana rikicin lissafi. 2) Binciken tushen ya nuna gyare-gyaren manhaja waɗanda suka rage jiyometry. 3) Ragewar jiyometry yana raunana tunanin sarari da fahimtar tsari/siffa. 4) Wannan rashi yana hana aiki a cikin STEM. 5) Saboda haka, sake gabatar da jiyometry ta hanyar haɗin kai na STEAM mai hannu (wurin ƙirƙira) shine madaidaicin shiga tsakani na gyara. Gudun daga gano matsala zuwa takamaiman mafita mai goyan bayan ka'ida yana bayyana kuma yana da kariya.

Ƙarfi & Aibobi

Ƙarfi: Babban ƙarfin shawarar shine daidaiton bincike. Maimakon ba da shawara a fili don "ƙarin fasaha," ta gano takamaiman rauni na tarihi-ilimi (asara na jiyometry) kuma ta ba da takamaiman magani. Haɗa shiga tsakani da ka'idar fahimtar sarari, kamar yadda aka bincika a cikin ayyuka kamar "Tunani, Sauri da Sannu" na Daniel Kahneman game da tunanin Tsarin 1/Tsarin 2, ko bincike daga Hukumar Kimiyya ta Ƙasa game da koyo na sarari, zai ƙarfafa wannan ƙarin. Mayar da hankali kan ƙungiyar ɗalibai da aka ayyana (aji na biyu na sakandare) shima yana sa ya zama mai iya aiki.

Aibi Mai Muhimmanci: Shawarar ta yi shiru a fili game da hanyar tantancewa. Za a auna nasara ta yaya? Gwaje-gwajen tunanin sarari kafin/bayan (misali, Gwaje-gwajen Juyawa na Hankali)? Binciken kwatancen maki na jarrabawar jiyometry? Tantancewar ingancin shigar ɗalibai da rikitarwar aikin? Ba tare da ingantaccen tsarin tantancewa da aka riga aka ayyana ba, aikin yana fuskantar haɗarin zama wani yunƙuri mai kyakkyawar niyya amma ba a tabbatar da shi ba. Ambaton binciken cikin gida na kwalejin fari ne, amma ba shirin ba.

Fahimta Mai Aiki

1. Fara da Ma'auni Kafin: Kafin cikakken fitarwa, gudanar da gwaji mai sarrafawa tare da ƙungiyar sarrafawa bayyananne. Ma'auni na farko: haɓaka a cikin daidaitaccen warware matsalolin jiyometry. Ma'auni na biyu: ra'ayoyin ɗalibai da malamai, ƙimar kammala aikin.
2. Haɗa Manhaja, Ba Warewa ba: Wurin ƙirƙira bai kamata ya zama tsibiri ba. Ƙirƙiri takamaiman sassa na darasi waɗanda ke haɗa ayyukan ƙirƙira (misali, gina murhun rana mai siffar parabola) kai tsaye zuwa ra'ayoyin algebra da lissafi, ƙirƙirar madauki na amsa tsakanin zahiri da rabe-rabe.
3. Malami a matsayin Mai Ƙira, Ba Kwararre ba: Ci gaban ƙwararru yana da mahimmanci. Horon ya kamata ya mayar da hankali kan ƙirar ilimin koyarwa—yadda ake ƙirƙira ayyukan da ke haifar da takamaiman tunanin jiyometry—ba kawai yadda ake sarrafa na'urorin yanka laser ba. Yi amfani da tsarin kamar TPACK (Ilimin Fasaha na Ilimin Koyarwa da Abubuwan Ciki).
4. Neman Tabbatarwa na Waje: Haɗa kai da sashin ilimi ko ilimin halayyar ɗan adam na jami'ar gida don gudanar da bincike na yau da kullun. Wannan yana haifar da bayanan da za a iya bugawa kuma yana ɗaga aikin daga yunƙurin makaranta zuwa gudummawar binciken ilimi.

5. Cikakkun Bayanai na Fasaha & Tsarin Lissafi

Shawarar ta ba da shawara a fakaice don tsarin ilimin koyarwa inda ake gano ka'idodin jiyometry kuma a yi amfani da su ta hanyar gini. Yiwuwar aikin fasaha na iya haɗawa da:

  1. Ma'anar Matsala: Ana gabatar da ƙalubale na zahiri (misali, ƙira gada mai takamaiman tazara ta amfani da ƙayyadaddun kayan aiki).
  2. Ƙirar Jiyometry: ɗalibai suna canzawa zuwa ƙirar rabe-rabe. Wannan ya haɗa da amfani da dabarun yanki, girma, da ingancin tsari. Misali, lissafin yankin ɓangaren katako yana da alaƙa da ƙarfinsa: $\sigma = \frac{F}{A}$, inda $\sigma$ ke nuna damuwa, $F$ ƙarfi, kuma $A$ yanki.
  3. Ƙirar Lamba: Ana fassara ƙira zuwa fayilolin lambobi don ƙira (buga 3D, yanka laser). Wannan matakin yana ƙarfafa jiyometry na haɗin kai ($(x, y, z)$ haɗin kai) da canje-canje (fassara, juyawa, sikelin).
  4. Haɗawa ta Jiki & Gwaji: Ana gwada abin da aka gina da ma'auni. Binciken gazawa yana komawa ga gyaran jiyometry da lissafi (misali, "Gadar ta faɗi saboda kusurwoyin truss ɗinmu ba su da inganci, bari mu sake lissafin ta amfani da ka'idodin trigonometric don mafi kyawun kusurwa $\theta$").

Wannan yana haifar da maimaitaccen zagayowar Ƙira-Gini-Gwaji-Koyo wanda ya dogara da aikace-aikacen lissafi.

6. Sakamakon Gwaji & Binciken Bayanai

Lura: Abin da aka bayar na PDF ba ya ƙunshe da sakamakon wurin ƙirƙira da aka ba da shawara, saboda shawara ce ta aikin. Mai zuwa yana bayyana hanyar gwaji da ake niyya da sakamakon da ake tsammani bisa ga manufofin shawarar.

Za a tantance nasarar aikin ta hanyar haɗa hanyoyi:

  • Ma'auni na Ƙididdiga:
    • Maki na tantancewa kafin da bayan akan daidaitattun gwaje-gwajen jiyometry da tunanin sarari (misali, wani ɓangare na abubuwan lissafi na PLANEA da aka mayar da hankali kan jiyometry).
    • Kwatanta makin ƙarshe a cikin darussan lissafi tsakanin ƙungiyar da ke da damar shiga wurin ƙirƙira da ƙungiyar sarrafawa ba tare da shi ba.
    • Binciken rikitarwa da ƙwarewar lissafi na ayyukan ɗalibai akan lokaci (misali, motsawa daga siffofi na 2D zuwa samfuran 3D waɗanda ke buƙatar lissafi don inganta girma).
  • Ma'auni na Inganci:
    • Binciken ɗalibai da tambayoyi da ke tantance canje-canje a halin da ake ciki game da lissafi (rage damuwa, ƙara fahimtar mahimmanci).
    • Abubuwan lura da malamai da mujallu masu tunani waɗanda ke rubuta shigar ɗalibai da halayen warware matsala tare.
    • Binciken fayil ɗin ayyukan ɗalibai don shaidar ƙira mai maimaitawa da aikace-aikacen ra'ayoyin lissafi.

Jadawali da ake tsammani: Jadawali mai sanduna wanda ke kwatanta matsakaicin riba a cikin makin gwajin jiyometry don ƙungiyar shiga tsakani (Wurin Ƙirƙira) da ƙungiyar sarrafawa (Koyarwa na Al'ada). Hasashen, bisa ga dalilin shawarar, zai zama riba mafi girma ga ƙungiyar shiga tsakani.

7. Tsarin Bincike: Nazarin Lamari Ba tare da Lamba ba

Lamari: Aikin "Akwati Mafi Kyau"

Manufar Koyo: Aiwatar da ra'ayoyin yanki na saman, girma, abubuwan da aka samo, da ingantawa don ƙira akwati na zahiri tare da ƙarancin amfani da kayan aiki don takamaiman girma.

Aikace-aikacen Tsarin:

  1. Mahallin & Matsala: "Kamfani yana buƙatar akwati mai siffar siliki don riƙe ruwa mai lita 1. Don rage farashi, suna son yin amfani da mafi ƙarancin adadin kayan aiki (karfe/roba) mai yiwuwa. Ƙirƙiri wannan akwatin."
  2. Rabe-raben Lissafi:
    • Ayyana masu canji: Bari $r$ = radius, $h$ = tsayi. Ƙuntatawar girma: $V = \pi r^2 h = 1000\, cm^3$.
    • Yankin saman (kayan aiki) don ragewa: $A = 2\pi r^2 + 2\pi r h$.
    • Yi amfani da ƙuntatawar girma don bayyana $h$ dangane da $r$: $h = \frac{1000}{\pi r^2}$.
    • Saka cikin dabarar yanki: $A(r) = 2\pi r^2 + \frac{2000}{r}$.
  3. Ingantawa: Nemo mahimmin batu ta hanyar ɗaukar abin da aka samo da saita shi zuwa sifili: $\frac{dA}{dr} = 4\pi r - \frac{2000}{r^2} = 0$. Warware don $r$: $4\pi r^3 = 2000 \Rightarrow r = \sqrt[3]{\frac{500}{\pi}} \approx 5.42\, cm$. Sannan nemo $h \approx 10.84\, cm$. Lura: $h = 2r$, mafi kyawun rabo.
  4. Haɗawa ta Jiki (Wurin Ƙirƙira): ɗalibai suna amfani da software na CAD don ƙirƙira siliki tare da ma'auni da aka lissafa, sannan su ƙirƙira shi ta amfani da buga 3D ko haɗa shi daga yankakken acrylic na laser. Suna auna girmansa ta zahiri don tabbatar da cewa yana riƙe da ~ lita 1.
  5. Bincike & Tunani: ɗalibai suna kwatanta ƙirar su da aka inganta da wanda bai dace ba (misali, siliki mai tsayi, siriri). Suna lissafin kashi na kayan da aka adana kuma suna tattauna tasirin haƙiƙanin duniya ga dorewa da farashi. Samfurin zahiri yana ƙarfafa aikin lissafi na rabe-rabe.

Wannan lamari yana nuna yadda wurin ƙirƙira ke aiki a matsayin "tabbacin ra'ayi" na lissafi na rabe-rabe, yana rufe madaukin koyo.

8. Aikace-aikace na Gaba & Hanyoyin Ci Gaba

Samfurin Wurin Ƙirƙira na STEAM da aka ba da shawara yana da babban yuwuwar sikelin da juyin halitta:

  • Haɗa Kai a Tsaye: Ƙara tsarin samfurin zuwa wasu yankuna na lissafi (misali, ƙididdiga ta hanyar ayyukan ƙirƙira bayanai na zahiri, algebra ta hanyar shirye-shiryen motsi na mutum-mutumi).
  • Faɗaɗa Haɗin Kai: Ƙirƙiri ayyukan haɗin kai tare da Kimiyyar Lissafi (gina trebuchets don motsin harbi), Biology (ƙira ingantattun rufin rana masu kama da ganye), ko Fasaha (ƙirƙirar fasaha na algorithm da sassaka bisa ga jiyometry mai ɓarna).
  • Haɗuwar Fasaha: Haɗa Haɓakar Gaskiya (AR) don rufe dabarun jiyometry da ƙarfin vectors akan samfuran zahiri yayin gini, ko amfani da na'urori masu auna firikwensin da microcontrollers (misali, Arduino) don tattarawa da bincika bayanai daga hanyoyin da ɗalibai suka gina, haɗa lamba da kimiyyar bayanai.
  • Haɗin Kai na Al'umma & Masana'antu: Haɗa kai tare da masana'antu na gida don gabatar da ƙalubalen injiniyanci na zahiri. Shigar da al'umma ta hanyar baje kolin ayyukan ɗalibai, nuna ƙimar aiki na koyon lissafi.
  • Dandalin Bincike: Kamar yadda aka ba da shawara a cikin ra'ayi na mai bincike, sararin zai iya zama dakin gwaje-gwaje na rayuwa don binciken ilimi, yana ba da gudummawa ga fahimtar duniya game da fahimtar jiki da ilimin da fasaha ta haɓaka a cikin lissafi.

9. Nassoshi

  • Avila, A. (2016). Hangen nesa na tarihi akan ilimin lissafi a Mexico. [Nassi daga PDF].
  • Cibiyar Ƙasa don Tantance Ilimi (INEE) / SEP. (2015-2017). Sakamakon Tantancewar PLANEA. An samo daga http://planea.sep.gob.mx/
  • OECD. (2015). Sakamakon PISA 2015: Mexico. An samo daga https://www.oecd.org/pisa/
  • Senechal, M. (2004). Siffa. Koyarwar lissafi mai daɗi. Limusa. [An ambata a cikin PDF].
  • Kahneman, D. (2011). Tunani, Sauri da Sannu. Farrar, Straus da Giroux. [Tushen waje akan tsarin fahimi].
  • Mishra, P., & Koehler, M. J. (2006). Ilimin Fasaha na Ilimin Koyarwa da Abubuwan Ciki: Tsarin Ilimin Malami. Rikodin Kwalejin Malamai, 108(6), 1017-1054. [Tsarin waje don horar da malamai].
  • Hukumar Kimiyya ta Ƙasa. (b.t.). Kimiyyar Koyo: Tunani na Sarari. An samo daga nsf.gov [Misali na ingantaccen bincike na waje].
  • Uttal, D. H., et al. (2013). Iya canzawa na ƙwarewar sarari: Meta-bincike na nazarin horo. Bulletin na Psychological, 139(2), 352–402. [Meta-bincike na waje wanda ke goyan bayan horon sarari].