{"id":516,"date":"2025-11-08T03:44:23","date_gmt":"2025-11-08T03:44:23","guid":{"rendered":"https:\/\/learndeeplytw.com\/?p=516"},"modified":"2026-10-13T08:22:38","modified_gmt":"2026-10-13T08:22:38","slug":"data-introduction-2","status":"publish","type":"post","link":"https:\/\/learndeeplytw.com\/en\/data-introduction-2\/","title":{"rendered":"Understanding How Computers Represent Information: A Constructivist Approach"},"content":{"rendered":"<h3 class=\"wp-block-heading\">Part 1: What Exactly is a Computer? (Redefining the Computer)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">\u2705 Constructivist Strategy: Start with the child's life experiences to challenge their preconceived notions of a \"computer.\"<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\" translation-block\">Inquiry:\n\"Do you think a 'calculator' counts as a computer? What about a 'smartphone'? How about the electronic watch on your wrist? Or the washing machine at home?\"<\/li>\n\n\n\n<li class=\" translation-block\">Exploration:\n\"Computers used to be as big as a room, but now they fit in your pocket. They look different, but they are all doing the same thing. What do you think that thing is?\"<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">The word \"Computer\" originally meant \"a person who calculates,\" but today's computers are far more than just giant math machines. They are like magician librarians\u2014organizing our photos, playing movies, and sending messages.\nInterestingly, no matter how smart a computer gets, the method it uses to record all this is surprisingly simple\u2014it only recognizes two symbols: 0 and 1.\nWhy does such a powerful machine use such a simple language? That is the secret we are going to unlock.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part 2: Why 0 and 1? (The Physical Basis of Binary)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">\u2705 Constructivist Strategy: Explain using the most intuitive physical action: \"Switches.\"<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\" translation-block\">Inquiry:\n\"If I gave you a flashlight to send a message to a friend in the building opposite, how would you communicate? If you could only use 'Light On' and 'Light Off,' how would we agree on the signals?\"<\/li>\n\n\n\n<li class=\"\"><strong>\u63a2\u7a76<\/strong>\uff1a\u300c\u96fb\u8166\u88e1\u9762\u5176\u5be6\u4f4f\u8457\u5e7e\u5341\u5104\u500b\u5c0f\u5c0f\u7684\u300e\u958b\u95dc\u300f\u3002\u6bd4\u8d77\u5206\u8fa8\u300e\u5f88\u4eae\u300f\u3001\u300e\u6709\u9ede\u4eae\u300f\u6216\u300e\u4e0d\u4eae\u300f\uff0c\u4f60\u89ba\u5f97\u53ea\u5206\u300e\u958b\u300f\u8ddf\u300e\u95dc\u300f\u662f\u4e0d\u662f\u6bd4\u8f03\u4e0d\u6703\u770b\u932f\uff1f\u300d<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u96fb\u8166\u5176\u5be6\u4e00\u9ede\u90fd\u4e0d\u8907\u96dc\uff0c\u5b83\u53ea\u662f\u7531\u5e7e\u5341\u5104\u500b\u5fae\u5c0f\u7684\u300c\u958b\u95dc\u300d\u7d44\u6210\u7684\u3002<br>\u60f3\u50cf\u4e00\u4e0b\uff0c\u5982\u679c\u8981\u96fb\u8def\u5206\u8fa8 10 \u7a2e\u4e0d\u540c\u5f37\u5ea6\u7684\u96fb\u58d3\uff0c\u53ea\u8981\u96fb\u58d3\u7a0d\u5fae\u4e0d\u7a69\uff0c\u96fb\u8166\u5c31\u6703\u641e\u6df7\u3002\u4f46\u5982\u679c\u53ea\u5206\u8fa8\u300c\u958b\uff081\uff09\u300d\u548c\u300c\u95dc\uff080\uff09\u300d\uff0c\u90a3\u5c31\u7c21\u55ae\u591a\u4e86\uff01<\/p>\n\n\n\n<div class=\"wp-block-media-text has-media-on-the-right is-stacked-on-mobile\" style=\"grid-template-columns:auto 41%\"><div class=\"wp-block-media-text__content\">\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-995f960e wp-block-group-is-layout-flex\">\n<ul class=\"wp-block-list\">\n<li style=\"font-size:14px\" class=\"\">In a Hard Drive: It\u2019s like the \"North Pole\" and \"South Pole\" of a magnet.<\/li>\n\n\n\n<li style=\"font-size:14px\" class=\"\">\u5728\u5149\u789f\u4e0a\uff0c\u9019\u5c31\u50cf\u662f\u8868\u9762\u300c\u6703\u53cd\u5149\u300d\u6216\u300c\u4e0d\u53cd\u5149\u300d\uff08\u5be6\u969b\u7684\u7de8\u78bc\u65b9\u5f0f\u66f4\u8907\u96dc\u4e00\u4e9b\uff09\u3002<\/li>\n\n\n\n<li style=\"font-size:14px\" class=\"\">In a Microchip: It\u2019s like a circuit being \"connected\" or \"disconnected.\"<\/li>\n<\/ul>\n<\/div>\n<\/div><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"292\" src=\"https:\/\/learndeeplytw.com\/wp-content\/uploads\/2025\/11\/image-8.webp\" alt=\"\" class=\"wp-image-437 size-full\" srcset=\"https:\/\/learndeeplytw.com\/wp-content\/uploads\/2025\/11\/image-8.webp 602w, https:\/\/learndeeplytw.com\/wp-content\/uploads\/2025\/11\/image-8-300x146.webp 300w, https:\/\/learndeeplytw.com\/wp-content\/uploads\/2025\/11\/image-8-18x9.webp 18w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Although we write them as 0 and 1, to the computer, these are actually two physical states. When we combine these states (like turning 8 switches into one Byte), the computer can start performing magic, creating numbers, text, and even colors.<\/p>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">Further Reading: <a href=\"https:\/\/learndeeplytw.com\/binary-digits\/\" data-type=\"post\" data-id=\"506\" target=\"_self\">Don't rush to teach arithmetic! Let children crack the \"Binary Digit\" code themselves.<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part 3: Painting with Numbers (Image Representation)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">\u2705 Constructivist Strategy: Approach via concepts of \"Mosaic Art\" or a \"Magnifying Glass.\"<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\" translation-block\">Observation:\n\"Have you ever seen Perler beads or mosaic tiles? If we stand far away, it looks like a picture; but if we take a magnifying glass and look closely, what do you see?\"<\/li>\n\n\n\n<li class=\" translation-block\">Inquiry:\n\"If I want to make this mosaic very colorful, like a real photo, do I need beads in more colors, or fewer?\"<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">Every photo you see on a screen is actually an illusion! If you put a magnifying glass up to the screen, you will discover that the beautiful photo is actually composed of countless little squares called Pixels.\nThe computer uses a string of 0s and 1s to decide what color to paint each square.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\" translation-block\">The Space-Saving Way: If each square only uses 1 bit (0 is black, 1 is white), we can only draw black-and-white images, but the file size is small.<\/li>\n\n\n\n<li class=\"\"><strong>\u7cbe\u7dfb\u7684\u756b\u6cd5<\/strong>\uff1a\u5982\u679c\u6bcf\u4e00\u683c\u7528 24 \u500b\u4f4d\u5143\u4f86\u8abf\u8272\uff0c\u6211\u5011\u53ef\u4ee5\u8abf\u51fa\u8d85\u904e 1,600 \u842c\u7a2e\u984f\u8272\uff0c\u756b\u51fa\u8d85\u903c\u771f\u7684\u7167\u7247\uff0c\u4f46\u4ee3\u50f9\u5c31\u662f\u6a94\u6848\u6703\u8b8a\u5f97\u8d85\u7d1a\u5927\uff01<br>\u9019\u4e5f\u662f\u70ba\u4ec0\u9ebc\u9ad8\u756b\u8cea\u7684\u7167\u7247\u548c\u5f71\u7247\u6a94\u6848\u9019\u9ebc\u5927\u2014\u2014\u6bcf\u4e00\u683c\u90fd\u8981\u8a18\u4e0b\u66f4\u591a\u4f4d\u5143\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">Further Reading: <a href=\"https:\/\/learndeeplytw.com\/image-representation\/\" data-type=\"post\" data-id=\"496\" target=\"_self\">Don't just tell kids \"0 is black, 1 is white\"\u2014Teaching Image Representation through puzzle games.<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part 4: Broken Telephone (Error Detection and Correction)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">\u2705 Constructivist Strategy: Demonstrate how errors occur and how to spot them using the \"Telephone Game\" or magic tricks.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\" translation-block\">Game:\n\"Let's play the game 'Telephone' (or Broken Telephone). The first person whispers a sentence, and by the time it reaches the last person, what does it usually become? Why does it change?\"<\/li>\n\n\n\n<li class=\" translation-block\">Reflection:\n\"If we were transmitting a code to blow up a spaceship, getting one digit wrong would be a disaster. How can we know if the message was corrupted without asking the person to say it all over again?\"<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e16\u754c\u662f\u4e0d\u5b8c\u7f8e\u7684\u3002\u7db2\u8def\u8a0a\u865f\u6703\u4e2d\u65b7\uff0c\u786c\u789f\u6703\u58de\u8ecc\uff0c\u5c31\u50cf\u50b3\u8a71\u904a\u6232\u4e00\u6a23\uff0c\u8cc7\u6599\u5728\u50b3\u9001\u904e\u7a0b\u4e2d\u5f88\u5bb9\u6613\u300c\u807d\u932f\u300d\u3002\u5982\u679c\u90a3\u662f\u9280\u884c\u8f49\u5e33\u7684\u91d1\u984d\uff0c\u591a\u4e00\u500b 0 \u6216\u5c11\u4e00\u500b 0 \u53ef\u662f\u5927\u707d\u96e3\uff01<br>\u96fb\u8166\u79d1\u5b78\u5bb6\u60f3\u51fa\u4e86\u4e00\u500b\u8070\u660e\u7684\u8fa6\u6cd5\uff1a<strong>\u300c\u6aa2\u67e5\u78bc\u300d<\/strong>\u3002<br>\u9019\u5c31\u50cf\u6211\u5011\u5728\u50b3\u9001\u5361\u7247\u6642\uff0c\u6545\u610f\u591a\u52a0\u4e00\u5f35\u5361\u7247\u4f86\u6e4a\u6210\u5076\u6578\u3002\u5982\u679c\u4f60\u6536\u5230\u6642\u767c\u73fe\u8b8a\u6210\u5947\u6578\uff0c\u4f60\u5c31\u77e5\u9053\uff1a\u300c\u554a\uff01\u4e2d\u9593\u4e00\u5b9a\u6709\u6771\u897f\u51fa\u932f\u4e86\uff01\u300d<br>\u9019\u7a2e\u6280\u5de7\uff08\u540c\u4f4d\u6aa2\u67e5\uff09\u8b93\u6211\u5011\u80fd\u7acb\u523b\u767c\u73fe\u300c\u6709\u6771\u897f\u51fa\u932f\u4e86\u300d\uff0c\u8acb\u5c0d\u65b9\u91cd\u50b3\u4e00\u6b21\u3002\u5982\u679c\u518d\u591a\u52a0\u5e7e\u5c64\u6aa2\u67e5\u78bc\uff08\u66f4\u9032\u968e\u7684\u932f\u8aa4\u66f4\u6b63\u78bc\uff09\uff0c\u751a\u81f3\u80fd\u76f4\u63a5\u7b97\u51fa\u932f\u5728\u54ea\u3001\u81ea\u52d5\u4fee\u597d\u2014\u2014\u786c\u789f\u58de\u6389\u4e00\u90e8\u5206\u3001\u6216\u5f9e\u9059\u9060\u7684\u6728\u661f\u50b3\u56de\u7167\u7247\u6642\uff0c\u7528\u7684\u5c31\u662f\u9019\u985e\u6280\u8853\uff0c\u4e0d\u9700\u8981\u53eb\u5916\u661f\u4eba\u91cd\u50b3\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">Further Reading: <a href=\"https:\/\/learndeeplytw.com\/parity-error-correction-2\/\" data-type=\"post\" data-id=\"519\" target=\"_self\">Using \"Mind Reading\" tricks to learn how computers self-repair (Parity Error Correction).<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part 5: Surprise is Information (Information Theory)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">\u2705 Constructivist Strategy: Quantify information using the \"Guess the Number (20 Questions)\" game.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\" translation-block\">Game:\n\"I'm thinking of a number between 1 and 100. How many questions do you need to guess it? If you ask 'Is it 3?', 'Is it 5?', it will take forever. What kind of question can eliminate half the answers instantly?\"<\/li>\n\n\n\n<li class=\" translation-block\">Conclusion:\n\"Every question that helps you cut the possibilities in half represents 1 bit of information.\"<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">How do we measure how much \"information\" there is? By the weight of a book? By word count?\n<br>Computer scientists have a cool definition:<strong> \"Information is the degree of surprise.\"<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"\">If your friend says, \"I walked to school today,\" that\u2019s not surprising because he walks every day. The amount of information is low.<\/li>\n\n\n\n<li class=\"\">If he says, \"I took a helicopter to school today!\" that makes your jaw drop. The amount of information is super high!<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph translation-block\">We can play \"Ultimate Code\" to measure information. To guess a number between 1 and 100, the smartest method is to cut it in half every time: \"Is it bigger than 50?\" (This way, you delete 50 wrong answers in one breath).\n<br>This logic of \"Binary Search\" is the foundation of how computers measure information. A seemingly simple number-guessing game actually hides the wisdom computers use to process massive data!<\/p>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"720\" style=\"aspect-ratio: 1280 \/ 720;\" width=\"1280\" controls src=\"https:\/\/learndeeplytw.com\/wp-content\/uploads\/2025\/11\/How_Computers_REALLY_Work.mp4\"><\/video><\/figure>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-995f960e wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u5ef6\u4f38\u95b1\u8b80<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"\"><a href=\"https:\/\/learndeeplytw.com\/zh_tw\/binary-digits\/\">Don't Rush to Teach Arithmetic! Let Children Crack the \"Binary Digits\" Code Themselves<\/a><\/li>\n\n\n\n<li class=\"\"><a href=\"https:\/\/learndeeplytw.com\/zh_tw\/image-representation\/\">Don't Just Say \"0 is Black, 1 is White\": Teaching Image Representation via Puzzle Games<\/a><\/li>\n\n\n\n<li class=\"\"><a href=\"https:\/\/learndeeplytw.com\/zh_tw\/parity-error-correction-2\/\">Mastering Computer Self-Repair with \"Mind Reading\" (Parity Error Correction)<\/a><\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>\u96fb\u8166\u5982\u4f55\u8868\u9054\u8cc7\u8a0a\uff1f\u5f9e\u5efa\u69cb\u5f0f\u6559\u5b78\u51fa\u767c\uff0c\u7528\u751f\u6d3b\u4f8b\u5b50\u5e36\u5b69\u5b50\u7406\u89e3 0 \u8207 1\u3001\u4f4d\u5143\u3001\u50cf\u7d20\u8207\u540c\u4f4d\u6aa2\u67e5\u3002\u672c\u6587\u662f\u4e0d\u63d2\u96fb\u300c\u8cc7\u6599\u8868\u793a\u300d\u55ae\u5143\u7684\u7e3d\u8ad6\uff0c\u542b\u5404\u6d3b\u52d5\u7684\u6559\u5b78\u8108\u7d61\u8207\u63d0\u554f\u8a2d\u8a08\u3002<\/p>","protected":false},"author":2,"featured_media":469,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[9,17],"tags":[26,24],"class_list":["post-516","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cs-unplugged","category-representing-information","tag-26","tag-24"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":8}},"_links":{"self":[{"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/posts\/516","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/comments?post=516"}],"version-history":[{"count":8,"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/posts\/516\/revisions"}],"predecessor-version":[{"id":984,"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/posts\/516\/revisions\/984"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/media\/469"}],"wp:attachment":[{"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/media?parent=516"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/categories?post=516"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learndeeplytw.com\/en\/wp-json\/wp\/v2\/tags?post=516"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}