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Tenses Bahasa Inggris . Present Tense juga digunakan untuk menyatakan suatu Fakta, atau sesuatu yang tejadi berulang- ulang dimasa KINI. Ingat, PRESENT artinya adalah kini, sekarang. Rumusnya: Positif: S + V1 (s/es)Negatif: S + DO/DOES + NOT + V1. Tanya: DO/DOES + S + V1. Contoh Kalimat Positif: I drink coffee. She drinks coffe. We drink coffee. Ya, sengaja pelajaran Tense bahasa inggris ini dibuat simple saja agar cepat faham. Anda perlu mengembangkannya sendiri misalnya dengan membuat 1. Pasti Anda perlu kamus juga, karena belajar tenses lalu mentok dengan suatu kata kerja maka biasanya tidak jadi, hehe. Cara Membaca Rumus: S artinya Subject, V1 artinya Verb. Garis miring artinya ya Atau dong! Kapan pakai S atau ES dan kapan tidak? Kalau Subjectnya He, She, It, John, Mufli, Ellen atau Orang ketiga TUNGGAL maka kata kerjanya tambah S atau ES. Tidak sembarang tambah S atau ES juga nih, ada daftarnya. Daftarnya itu bayak sekali, mustahal saya tulis disini, cape dehh nulisnya, Anda musti beli buku Grammar juga. Belajar bahasa Inggris perlu modal, hehe. Di atas tadi ada istilah Orang Ketiga Tunggal, maksudnya gini: Orang ketiga adalah orang yang kita bicarakan, yang kita omongin. Sedangkan orang pertama ya yang bicara. Orang kedua lawan bicara. Jadi orang ketiga tunggal adalah orang yang kita bicarakan dan satu saja dia itu. Misalnya kita berdua ngomongin John Scoping. Yang ngomong saya, yang dengar Anda, yang dibicarakan John Scoping (orang ketiga tunggal). Faham ya? John Scoping belajar Tenses. John Scoping learn. S english. Tidak bisa Learn. ES, mengapa? Tetapi yang ini malah tambah ES: John Scoping go. ES to School (tambah ES). Kalimat Negatif Present Tense. Bentuk Negatif, artinya menyatakan TIDAK. Maka sesuai rumus Present Tense, setelah SUBJECT ditambah DO atau DOES, baru NOT, lalu tambah kata kerja bentuk pertama tanpa S atau ES lagi. Sudah di do. ES tadi. Untuk I, WE, YOU, THEY tambah DOUntuk SHE, HE, IT, Mufli, Ellen tambah DOESI do not drink coffee. She does not drink coffee. John Scoping does not learn english. Coba perhatikan She does not drink coffee. Drink nya tidak pake S lagi, pindah ke do. ES. Biasakan saja, Present Simple Tense ini sepertinya rumit tetapi kalau faham maka enak banget. ![]() ![]() Here what a person says appears within quotation marks.Ulangi saja baca dari atas 1. Bikin juga 1. 0 contoh Anda sendiri dengan kata kerja yang berbeda. Yes, belajar bahasa Inggris tak boleh manja, harus aktif, baru akan bisa. Kalimat Tanya Present Tense. Kalimat tanya untuk Present Tense sesuai rumus diatas, atau saya tulis lagi seperti ini: Tanya: DO/DOES + S + V1. Education.com Pro Members Get Unlimited Access to: Complete Curriculum of Guided Lessons Covering 800+ Skills in Math, Reading, and Writing for Grades Pre-K through 5th. Sama saja pasangannya. Untuk I, WE, YOU, THEY gunakan DO. Untuk SHE, HE, IT, Mufli, Ellen gunakan DOES. Contohnya begini: Kalimat positifnya: I drink coffee. Kalimat tanya menjadi: DO you drink cofee? Kalimat positif: She drinks coffe. Kalimat tanya: DOES She drink coffee? Kalimat tanya seperti diatas disebut juga YES/NO Question. Karena jawabannya memang Yes atau No. Atau bisa bisa dijawab dengan lengkap: “Yes, I do drink coffee”. Dihilangkan DO nya juga boleh, menjadi kalimat positif lagi: “Yes I drink coffee”. Ya, memang benar kalau Present Tense ini lebih rumit dibandingkan dengan Present Continuous Tense karena tiba- tiba kok pake DO, eh untuk orang ketiga tunggal pakai DOES segala, hehe. Kalau dalam Present Continuous Tense nanti tinggal dibalik doang. Ngapain sih belajar ginian? Rumus past continuous tense. Past continuous tense yang dikenal dengan past progressive tense merupakan salah satu tenses yang sering digunakan dalam percakapan. Study basic English grammar to help you become fluent in English. Understand the basic concepts of English grammar and learn English easily. Semoga penjelasan materi 16 tenses bahasa Inggris ini bermanfaat dan mohon maaf jika ada kekurangan. References: Simple Present Tense. Www.englishgrammarsecrets.com page 12 of 66 Present perfect (Please note that British and American English have different rules for the use of this. Materi dan contoh recount text terlengkap dan terbaru di tahun 2015 pilihan bapak & ibu guru. Practice with these Simple Past exercises: Click Here for Step-by-Step Rules, Stories and Exercises to Practice All English Tenses. Simple Past Exercise 01. This PowerPoint presentation will give your students additional practice of the difference between the present simple and present continuous tenses. Ya agar bahasa inggris Anda lebih terstruktur dan punya landasan kuat untuk belajar lebih lanjut nanti. Misalnya Anda perlu menulis untuk blog Anda dalam bahasa Inggris untuk menjalankan bisnis periklanan periklanan Adsense, malu dong kalau tensesnya kacau kan? Ok deh, itu tadi sedikit selingan. BTemplates,Responsive,Best Blogger Templates,Wordpress Themes,Premium Blogger Templates,4u,New Blogger Templates,Blogspot Themes,Latest,Blogger Themes,2011,2012,2013. Daftar Kursus/Les Pelajaran Bahasa Inggris untuk Anak Remaja SMA Frontrunner di EF English First menggunakan sistem aplikasi pendukung Materi Soal Latihan Belajar. Contoh: Aku bawakan buku untukmu. Definisi report text ini juga hampir mirip dengan apa yang sering disebutkan dalam berbagai buku bahasa Inggris di tingkat menengah, "Report is a text which present. First of all, the tops and branches of the trees are cut out and then the logs are taken out to the mill. At the mill, the bark of the logs is removed and the logs. Berikut ini adalah 50 contoh kalimat present perfect tense beserta dengan artinya: Dalam bentuk pernyataan: I have told you not to disturb my girl friend. Nah, kalau tadi kan Kalimat Tanya Present Tense yang jawabannya Yes atau No doang. Gimana kalau pertanyaan yang jawabannya panjang atau yang jawabannya kalimat? Contohnya begini: -When Do you drink coffee? Contoh jawaban: I drink coffee everyday.- What does she drink? She drinks coffee la yau! Gampang kan? Kalau Anda sering praktekkan dalam bahasa inggris sehari- hari maka tentu saja akan terasa mudah. Silahkan berkreasi dengan kalimat- kalimat Anda dalam Present Tense ya. Ok, begitu dulu pelajaran Present Tensenya. Kalau ada pertanyaan tentang Present Tense silahkan masukkan lewat komentar di bawah ini. Boleh juga kalau Anda ingin menambahkan, caranya silahkan masukkan di komentar juga. Kalau itu sangat keren dan merupakan tambahan pelajaran maka bisa jadi posting ini saya edit lalu tulisan anda dikomentar tersebut saya pindahkan ke bagian content. Anda yang membaca pertanyaan orang lain dan rasanya rela untuk menjawab, silahkan juga loh ya. Liat tu saya udah ngetik panjang untuk berbagi dengan Anda, cie. Oh ya by the way bus way lagi, jangan lupa jadi teman saya di facebook ya, alamat facebook saya disini: Facebook Mufli. Thank you banyak Anda telah setia mengikuti pelajaran saya tentang Present Tense kali ini. Silahkan pelajari juga Tenses yang lain dari menu di sebelah kanan ya. Best Regards. Mufli. Artikel Terbaru: Belajar Menterjemahkan. Bahasa Inggris Memang Harus Praktek (Sidoarjo)Mampu Bahasa Inggris Itu Enak. Report Text (Full Materi + Contoh)Secara umum, report text adalah salah satu jenis teks yang masuk kategori . Oleh karena itu, untuk mendalami apa itu report text, yuk kita simak bersama- sama keterangan di bawah ini: Pengertian Report Text. Istilah report text sering juga dikenal dengan sebutan informational report. Report, dalam Concise Oxford Dictionary Edisi 1. Jika disimpulkan, secara bahasa report text adalah teks yang berfungsi untuk memberikan informasi tentang suatu peristiwa atau situasi, setelah diadakannya investigasi dan melalui berbagai pertimbangan. Definisi report text ini juga hampir mirip dengan apa yang sering disebutkan dalam berbagai buku bahasa Inggris di tingkat menengah, . It is as a result of systematic observation and analyses. Teks ini adalah sebagai hasil dari observasi dan analisa secara sistematis. Generic Structure Report Text. Seperti halnya dengan descriptive text, Report text juga hanya memiliki dua struktur umum . Description: tells what the phenomenon under discussion ; in terms of parts, qualities, habits or behaviors; Pada bagian ini biasanya memberikan gambaran fenomena- fenomena yang terjadi; baik bagian- bagiannya, sifat- sifatnya, kebiasaannya, ataupun tingkah lakunya. Intinya adalah penjabaran dari klasifikasi yang disajikan dengan ilmiah. Ada juga beberapa keterangan mengenai generic structure report text, yang meliputi : General information. Bundles of Specific Information. General information adalah bagian yang menyebutkan informasi umum dari tema tulisan yang. Sedangkan Bundles of specific information, adalah penjabaran dari informasi umum tersebut. Saya sendiri lebih cenderung setuju dengan generic structure kedua; karena hal ini bisa membuat siswa lebih paham akan cara menulis report text. Tujuan Report Text. Setiap tulisan pasti memiliki tujuan mengapa tulisan itu ditulis. Begitu juga dengan report text. Beberapa pakar menyebutkan bahwa tujuan teks report adalah : Its social purpose is presenting information about something. They generally describe an entire class of things, whether natural or made: mammals, the planets, rocks, plants, countries of region, culture, transportation, and so on. Informasi yang dijelaskan dalam report text biasanya bersifat umum, baik itu alamiah ataupun buata seperti binatang mamalia, planet, bebatuan, tumbuh- tumbuhan, negara bagian, budaya, transportasi, dan lain sebagainya. Pola Tata Bahasa dalam Report Text. Setiap tulisan pasti memiliki ciri bahasa tersendiri; jika recount text dan narrative text cenderung memiliki ciri menggunakan simple past, lalu bagaimana dengan report text? Oke berikut adalah pola grammar yang umum digunakan dalam teks report, yang meliputi : Use of general nouns, eg hunting dogs, rather than particular nouns, eg our dog; Use of relating verbs to describe features, eg Molecules are tiny particles; Some use of action verbs when describing behaviour, eg Emus cannot fly; Use of timeless present tense to indicate usualness, eg Tropical cyclones always begin over the sea; Use of technical terms, eg Isobars are lines drawn on a weather map; Use of paragraphs with topic sentences to organise bundles of information; repeated naming of the topic as the beginning focus of the clause. Keterangan : General nouns, maksudnya adalah, suatu benda (baik itu hidup atau mati) yang bersifat umum. Coba bandingkan : Hunting dogs > < My dog. Hunting dogs bersifat umum; sedangkan my dog bersifat khusus. Relating verbs, dalam grammar disebut juga dengan linking verbs. Timeless present tense adalah salah satu penanda waktu dalam simple present seperti . Technical terms, maksudnya adalah istilah- istilah yang meliputi teks report tersebut. It is usually celebrated in late autumn. In the past, Thanksgiving was celebrated for their rich harvest in New England. In North America, however, it was originally held to thank God for their survival in the new land which was not easy for them. However, in Canada, it had been celebrated as in New England. Thanksgiving now is celebrated in United States of America and in Canada. Thanksgiving festivals are held every fourth Thursday of November in the U. S and on the second Monday of October in Canada. It is usually celebrated in four to five days in the North America and for three days in Canada. It is celebrated through families and friends gathering to eat and give good luck. Turkey is the main dish in the thanksgiving dinner. Thanksgiving parades are also usually held. In Thanksgiving homes are decorated with wreaths, fresh and dried flowers. Lamps are lighted to brighten the environment. 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Guard$ sudo apt- get install squid. Guard. 6. Now that Squid. Guard is installed, you will want to download a blacklist of websites and domains that you can block with Squid. Guard. You can find more information at http: //squidguard. Squid. Guard and where to find blacklists. A great resource is located at http: //dsi. The website http: //www. You will find links to other commercial blacklist sites as well. For this lab, I recommend downloading the shallalist. You can download it from the command line using wget or from the gui using a webbrowser. Download the blacklist file to your Downloads or home folder but before you install a full blacklist let’s create a testdomain file with test domains for Squid. Guard to practice blocking$ cd /var/lib/squidguard/db$ sudo nano testdomainstype in three lines of text to add some test- domains to block: yahoo. Now edit the squid. Guard. conf file to configure it to work with the testdomains file. You may want to back up the squid. Guard. conf file before making changes. Be careful in your edits, incorrect syntax will cause squid. Guard to fail. The beginning of the text file has been omitted.#dest adult . Now install the Apache. Blocked!< /title> < /head> < body> < h. You have been blocked by Raspberry Pi administrator!< /h. Save and exit. 9. Now you need to compile the Squid. Guard blacklists. Now give Squid. 3 ownership or access to some of the squidguard files and directories: $ sudo chown - R proxy: proxy /var/lib/squidguard/db$ sudo chown - R proxy: proxy /var/log/squidguard$ sudo chown - R proxy: proxy /usr/bin/squid. Guard. 11. Edit the squid. Squid$ sudo nano - c /etc/squid. Add the following line to the squid. Now open the Firefox browser from another computer and test to see if the domains listed in the testdomains file in step 6 are successfully blocked. Domains not listed in the testdomains file should be allowed. In other words, from another computer with the web browser configured with the proxy settings of the Raspberry Pi’s ip address and port number 3. If you were successful at blocking the testdomains then it’s time to extract and decompress the shallalist. Step 6. When you extract shallalist. BL. You will then copy BL to the squidguard db folder$ cd ~/Downloads$ tar - xzf shallalist. BL - R /var/lib/squidguard/db$ cd /var/lib/squidguard/db. Now recursively change permissions on the BL blacklists folder so you can list through the various blacklist categories that you may wish to activate. You will need to know the name paths of the categories, folders and files that you will want to compile to work with Squid. Guard$ sudo chmod - R 7. BL$ sudo chown - R proxy: proxy /var/lib/squidguard/db/BL$ ls /var/lib/squidguard/db/BL1. Now you can edit the squid. Guard. conf file to configure it to begin blocking undesirable content$ sudo nano - c /etc/squidguard/squid. Guard. conf. In the config file, change the following lines in red. Be careful in your edits, incorrect syntax will cause squid. Guard to fail. You will need to add a dest gamble block as well as changing the paths to the content you intend to block. Notice under dest gamble that I change the paths under domainlist and urllist to match the content and paths in the BL folder<. Now you need to recompile the Squid. Guard blacklists which will create new squid. Guard blacklist database files. Then change ownership of the files in the db folder to proxy$ sudo squid. Guard - C all$ sudo chown - R proxy: proxy /var/lib/squidguard/db. Reload Squid and then use Firefox from another computer to test to see if Squid and Squid. Guard are blocking websites with known adult content. You may want to execute this test privately or with the majority of the web browser dragged off screen ! Zero- configuration networking - Wikipedia. Zero- configuration networking (zeroconf) is a set of technologies that automatically creates a usable computer network based on the Internet Protocol Suite (TCP/IP) when computers or network peripherals are interconnected. It does not require manual operator intervention or special configuration servers. Zeroconf is built on three core technologies: automatic assignment of numeric network addresses for networked devices, automatic distribution and resolution of computer hostnames, and automatic location of network services, such as printing devices. Without zeroconf, a network administrator must set up network services, such as Dynamic Host Configuration Protocol (DHCP) and Domain Name System (DNS), or configure each computer's network settings manually. Background. This is similar to the telephone network, which assigns a string of digits to identify each telephone. In modern networking protocols, information to be transmitted is divided into a series of network packets. Every packet contains the source and destination addresses for the transmission. Network routers examine these addresses to determine the best network path in forwarding the data packet at each step toward its destination. Similarly to telephones being labeled with their telephone number, it was a common practice in early networks to attach an address label to networked devices. The dynamic nature of modern networks, especially residential networks in which devices are powered up only when needed, requires ad- hoc, dynamic address assignment mechanisms that do not require user involvement for initialization and management. These systems automatically give themselves common names chosen either by the equipment manufacturer, such as a brand and model number, or chosen by users for identifying their equipment. The names and addresses are then automatically entered into a directory service. The early history of computer networking built upon technologies of the telecommunications networks and thus, protocols tended to fall into two groups: those intended to connect local devices into a local area network (LAN), and those intended primarily for long- distance communications. Wide area network (WAN) systems tended to have centralized setup, where an authority would assign addresses and names, often by a network administrator using manual means. LAN systems tended to provide more automation of these tasks, so that new equipment could be added to a LAN with a minimum of operator and administrator intervention. An early example of a zero- configuration LAN system is Apple. Talk, a protocol introduced by Apple Inc. Macs, as well as other devices supporting the protocol like the Apple IIGS and a variety of printers and file servers, could be added to the network by plugging them in, all further configuration was automated. Network addresses were automatically selected by each device using a protocol known as AARP, while each machine built its own local directory service using a protocol known as NBP. NBP included not only a name, but the type of device and any additional user- provided information like its physical location or device status. Users could look up any device on the network with the application Chooser, which filtered names based on the device type. On Internet Protocol networks, the Domain Name System was initially maintained manually by a network administrator. This led to the introduction of a number of new protocols providing automated services, such as the Dynamic Host Configuration Protocol (DHCP). Address selection. These addresses operate in a fashion similar to telephone numbers, allowing devices to connect to each other by identifying the remote device by its address in the same way that a telephone call is connected by dialling in a telephone number. Unlike the phone system, an IP network does not necessarily include some sort of central authority that assigns these addresses as new devices are added. Mechanisms were introduced to handle this task, and both IPv. IPv. 6 now include systems for address autoconfiguration, which allows a device to determine a safe address to use through simple mechanisms. For link- local addressing, IPv. RFC 3. 92. 7 while IPv. More commonly, in modern networks addresses are assigned by a DHCP server, often built into common networking hardware like computer hosts or routers. Most IPv. 4 hosts use link- local addressing only as a last resort when a DHCP server is unavailable. An IPv. 4 host otherwise uses its DHCP- assigned address for all communications, global or link- local. One reason is that IPv. Another is that not every IPv. DNS), so discovering the autoconfigured link- local address of another host on the network can be difficult. However, discovering the DHCP- assigned address of another host also requires either distributed name resolution or a unicast DNS server with this information, and some networks feature DNS servers that are automatically updated with DHCP- assigned host and address information. IPv. 6 hosts are required to support multiple addresses per interface; moreover, every IPv. IPv. 6 hosts may additionally self- configure additional addresses on receipt of router advertisement messages, thus eliminating the need for a DHCP server. IPv. 6 hosts generally combine a prefix of up to 6. EUI- 6. 4 derived from the factory- assigned 4. IEEEMAC address. The MAC address has the advantage of being globally unique, a property inherited by the EUI- 6. The IPV6 protocol stack includes duplicate address detection to avoid conflicts with other hosts. In IPv. 4, the method is called link- local address autoconfiguration. To address this issue, the internet has long used the Domain Name System (DNS), which allows human- readable names to be associated with IP addresses, and includes code for looking up these names from a hierarchical database system. Users type in common names, like wikipedia. DNS software looks up in the remote DNS databases, translates to the proper IP address, and then hands off that address to the networking software for further communications. This has normally been accomplished by typing in the address of a known server into a field in one of the devices on the network. In early systems this was normally required on every device, but this has been pushed up one layer in the hierarchy to the DHCP servers or wide- area network devices like cable modems that receive this information from their IP provider. This has reduced the user- side administration load and provides a key element of zero- configuration access. Assigning an address to a local device, e. DNS server and is often accomplished manually. Additionally, traditional DNS servers are not expected to automatically correct for changes in configuration. For instance, if a printer is moved from one floor to another it might be assigned a new IP address by the local DHCP server. Net. BIOS Name Service is zero- configuration on networks with a single subnet and may be used in conjunction with a WINS server or a (Microsoft) DNS server that supports (secure) automatic registration of addresses to have a management overhead that is small but not zero even on very large (enterprise) networks. The protocols Net. BIOS can use are part of the SMB suite of open protocols. For example, Computer Browser Services running on server operating systems or later versions of Windows will be elected as so called Master Browser over those that are not running a server operating system or run older versions of Windows. Both implementations are very similar. Apple's Multicast DNS (m. DNS) is published as a standards track proposal (RFC 6. Microsoft's Link- local Multicast Name Resolution (LLMNR) is published as informational RFC 4. LLMNR is included in every Windows version from Windows Vista onwards. Apple's implementation is available as the Bonjour Service, previously Rendezvous, since 2. Mac OS X v. 10. 2. The Bonjour implementation (m. DNSResponder) is available under the Apache 2 Open Source license. DNS suffixes in effect) and (in corporate networks) the policies in effect (whether LLMNR or Net. BIOS are disabled), although developers may opt into bypassing these services for individual address lookups. The m. DNS and LLMNR protocols have minor differences in their approach to name resolution. This introduces special semantics for the domain local. A user looking for a nearby printer, for instance, might be stymied if the printer was given the name . Service discovery provides additional information about devices. Service discovery is sometimes combined with a name service, as in Apple's name binding protocol and Microsoft's Net. BIOS (including SMB as supported on non- Microsoft operating systems). Net. BIOS Service Discovery. It also supports for example a network printer to advertise itself as a host sharing a printer device and any related services it supports. Depending on how a device is attached (to the network directly, or to the host which shares it) and which protocols are supported however, Windows clients connecting to it may prefer to use SSDP or WSD over using Net. BIOS. Net. BIOS is one of the providers on Windows implementing the more general discovery process dubbed 'Function Discovery' which includes built- in providers for Pn. P, Registry, Net. BIOS, SSDP and WSD. None of these need any configuration for use on the local subnet. Net. BIOS has traditionally been supported only in expensive printers for use in companies and the cheapest devices of some brands today still don't have support for it, but home and SOHO users would connect printers to a computer over say a parallel port or USB and share it from the computer. However, today even entry- level printers with Wi- Fi or Ethernet support of some brands support it natively, allowing the printer to be used without configuration even on very old operating systems (combined with a generic Post. Script driver, for example). WS- Discovery. It operates over TCP and UDP port 3. IP multicast address 2. Italia ed Europa a confronto. Pristem/Storia. Note di matematica, storia, cultura, vol. Sharp IMG Viewer 2008 è un esploratore di risorse che consente. Una storia dallo svolgimento lineare ma che richiede alcune. PDF, foto, pagine web e appunti. Esiste una data combinazione lineare delle velocità di tutte le particelle. Non garantisco che i. Il nuovo requisito impone una profondità di 100 mm. La profondità di base deve. Nei locali o a casa propria senza dover studiare centinaia di pagine di. Tra visualizzazioni di pagine e bozze. Operatori e funzioni di algebra lineare . Mathcad Prime 3.0 (viewer). Rogora), dicembre 2. La condizione della matematica nell’insegnamento contemporaneo – non soltanto in Italia – manifesta un singolare paradosso: mai la materia . Harry Potter, con il suo straordinario “realismo magico”, . La matematica, infatti, . Merlo, “Ma siamo un popolo di grandi calcolatori”, La Repubblica, 3 agosto 2. Merlo ha preso una posizione talmente polemica da definire la letteratura e persino il brutto voto a scuola come la risorsa per sfuggire dall’ossessione della matematica. Sarebbe facile, e in parte giustificato, liquidare tutto ci. Ma gli anatemi non servono a nulla e non . A ben vedere, Cartesio non si era espresso in termini molto diversi qualche secolo fa: «. Ma quando, in seguito, mi chiesi da che cosa dipendeva il fatto che i primi filosofi non volessero ammettere allo studio del sapere coloro che ignoravano la matematica, quasi che questa disciplina fosse per loro la pi. Le Roy), Paris, Boivin, 1. Difatti, la matematica intesa come un occuparsi di “figure immaginarie” o di “numeri vuoti” si presenta come uno sterile gioco dell’intelletto. A che pro’ spendersi per qualcosa che gira a vuoto su questioni vuote – tanto vale darsi all’enigmistica – o, tutt’al pi. Come allora, anche oggi non . Oggi, mentre la matematica . Di certo, gli ultimi decenni – dominati dall’ansia di rinnovare l’insegnamento della matematica, sia per adeguarlo alle nuove forme che essa aveva assunto sia per adeguarlo a una scuola di massa – hanno visto emergere l’idea paradossale che soltanto ora si inizi a capire come vada insegnata. Generazioni e generazioni di uomini hanno appreso la matematica, l’hanno applicata con grande maestria, l’hanno fatta progredire e ne hanno trasmesso efficacemente contenuti e metodi. Eppure, da tempo ragioniamo come se nessuno abbia mai pensato a come insegnarla efficacemente, come se tutto quanto . Se fossimo obbiettivi, a giudicare dai risultati, e a giudicare dallo scarso interesse, per non dire dall’antipatia, che circonda la matematica, dovremmo dire esattamente il contrario! A ben vedere, le difficolt. Negli anni settanta vi . Rileggere oggi un libro come Algebra lineare e geometria elementare di Jean Dieudonn. Eppure sono passati soltanto quarant’anni. L’autore intimava di cancellare ogni figura dai manuali di geometria, proponeva di spazzare via persino dal linguaggio riferimenti a materie “desuete” come, la “geometria analitica”, la “geometria proiettiva”, la “trigonometria”, le “geometrie non euclidee”, e via dicendo. Proponeva un approccio assolutamente astratto e rigorosamente insiemistico. E il libro veniva presentato allora come l’avvenire dell’insegnamento della matematica. Oggi tutto questo sembra archeologia, spazzato via dal fallimento clamoroso della “nuova matematica”; anche se il fallimento ha lasciato sul terreno molti detriti, almeno sul suolo italiano. Difatti, abbiamo conservato la pessima eredit. Inoltre, da quel fallimento abbiamo tratto una conclusione completamente sbagliata: e cio. La “matematica del cittadino” dovrebbe destare l’interesse per la materia, in quanto pi. A giudicare dagli esiti, la risposta . I concetti e le astrazioni sarebbero difficili e repulsivi? Si risponde con un approccio pratico, concreto. La matematica appare difficile? Si abbassa il livello, si indora la pillola, si avanza sempre pi. Le tecniche matematiche risultano di difficile assimilazione? Si spezzettano in una miriade di definizioni, sempre nuove, sempre pi. Diceva il grande matematico Hermann Weyl che la matematica . Di certo, la matematica ha sfidato come nessuna disciplina il tema dell’infinito ed . Ma la tematica dell’infinito non si lega soltanto a quella della tecnologia, bens. Eppure Leonardo ammoniva: «Quelli che s’innamoran di pratica sanza scienzia son come . Studia prima la scienzia, e poi seguita la pratica nata da essa scienzia». Questo occorre insegnare agli allievi e non il contrario, sottolineando che la matematica . Nessuno potrebbe seriamente dissentire. Magari le nostre scuole fossero tutte dotate di laboratori moderni ed efficaci! Ma nel laboratorio si deve entrare con una base teorica, con delle idee su cosa si vuole andare a cercare, a verificare o smentire. Non si entra in laboratorio per fare bricolage, per cercare a casaccio quel che non si sa neppure cosa sia: questo sarebbe soltanto gioco vanesio (perch. Come ha detto il famoso Nobel per Medicina Albert Szent- Gyorgyi (il padre della vitamina C), con un fulminante aforisma, «lo scoprire consiste nel vedere ci. Di certo, se si vuole apprendere a risolvere un’equazione di secondo grado, occorre esercitarsi a farlo in un numero ragionevole di casi, ma non . Occorre assimilare le tecniche con un apprendistato ragionevole e non soffocante e concentrare l’attenzione sui problemi. Del resto, che esista un’enorme confusione in merito, spesso provocata da persone che hanno una conoscenza indiretta e superficiale della materia, . Come altrimenti potrebbe essere definita se non frutto di ignoranza e confusione la definizione della matematica come scienza procedurale che viene proposta da alcuni psicologi dell’apprendimento? L’idea di alleggerire l’insegnamento della matematica mediante nuove definizioni che frammentano e spezzettano i concetti . Stiamo assistendo al sorgere di una casistica degna della peggiore scolastica medioevale. Si trasformano i diversi approcci didattici in nuove definizioni, fino a parlare (come in un syllabus ministeriale) della “divisione per ripartizione” e della “divisione per contenenza” come due forme di divisione diverse di cui occorrerebbe addirittura dimostrare l’equivalenza. Potremmo anche qui dire che si tratta di una forma di tardo- scolastica. Quel che non capiscono i teorici delle “misconcezioni” . Se seguissimo la via delle “misconcezioni” per valutare la storia della matematica del passato dovremmo catalogare due secoli di storia della fondazione del calcolo infinitesimale come una sequenza di “misconcezioni”. Eulero, uno dei massimi matematici di tutti i tempi, ha prodotto una mole sterminata di risultati di enorme rilevanza basandosi sull’idea bizzarra (una vera “misconcezione”!) che il calcolo non sia altro che la determinazione del valore dei rapporti 0/0. Basta rileggere un brano di Federigo Enriques per recuperare una visione equilibrata, di buon senso e sorprendentemente adeguata ai problemi della modernit. Egli parlava dell’«interesse della societ. Se coll’insegnamento informativo si intende di porgere all’allievo una serie di nozioni da accogliere passivamente come un dono, questo non ha ragion d’essere in alcun ordine di scuole, perch. Due pedagogisti soprattutto hanno lavorato a portare le conoscenze matematiche nell’educazione del fanciullo, come elemento del suo sviluppo intellettuale: Pestalozzi e Fr. Il primo ammaestra “come Geltrude insegna ai suoi bambini”, indicando lor di buon’ora la consapevolezza dei rapporti di numero e misura, che essi debbono apprendere presto e con chiarezza. Per le scuole infantili come per le popolari, . Enriques, Le matematiche nella storia e nella cultura, Bologna, Zanichelli, 1. Se si parte dall’acquisizione del fatto che conoscenza e utilit. Anche le tecniche, di per s. Si tratta di due “porte d’ingresso” alla matematica che seguono percorsi diversi, che la matematica moderna ha parzialmente conciliato ma che conservano un’autonomia di fondo. Questo fu compreso in modo profondo dai Greci antichi che scoprirono le difficolt. Naturalmente il prezzo che veniva cos. La sintesi tra numero e geometria, realizzata attraverso la creazione della geometria analitica, ha aperto la strada alle applicazioni della matematica e al suo ruolo centrale nella fisica. Resta il fatto che, dal punto di vista concettuale, il continuo geometrico e il continuo numerico sono due cose diverse e, in fin dei conti irriducibili. Trattasi di una questione sottile e delicata che deve essere progressivamente affrontata nell’insegnamento della matematica, conservando una certa autonomia tra i due punti di vista e preservando un ruolo all’approccio geometrico sintetico, che si lega in modo profondo alla visione intuitiva dello spazio. Pertanto, . Ne discende che l’approccio geometrico- sintetico deve conservare un ruolo importante nell’insegnamento. Va sottolineato, al riguardo, che la disciplina matematica che offre la gamma di problemi pi. Qui risiede un altro errore di certi approcci didattici contemporanei quando – sempre nell’ansia della concretezza – si confonde lo spazio rappresentativo con lo spazio geometrico. Esso ha un carattere strettamente antropocentrico. Peggio ancora per il “destra/sinistra” che indica un privilegio di un lato rispetto all’altro e fa riferimento a una dissimmetria. In geometria, si definisce un orientamento sulla retta o si definisce un verso di rotazione, ma si tratta di distinzioni convenzionali, che non hanno carattere sostanziale come lo hanno nel “mondo della vita”. Definire un’orientazione sulla retta . Non esiste il “sopra” e il “sotto” di una figura geometrica, non esiste il “davanti” e il “dietro” di una piramide, se non in relazione a un modo di vedere gli oggetti di una persona: proprio qui si vede la differenza tra lo sguardo di una persona nel “mondo della vita” e lo sguardo geometrico. Le concezioni geometriche hanno un punto di appoggio fondamentale nell’esperienza, ma l’apprendimento della geometria se ne allontana. Ma allora bisognerebbe avere la coerenza di rigettare in toto l’insegnamento scientifico. However, it looks like you listened to. |
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