{"resolved":true,"match_type":"uuid","source_type":"original_book","book_id":"dde4e586-1def-4457-8ec5-0287b0b0511d","title":"认知 人行为背后的思维与智能","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787300273921","requested_by":"printed_page","book":{"source_type":"original_book","book_id":"dde4e586-1def-4457-8ec5-0287b0b0511d","id":"dde4e586-1def-4457-8ec5-0287b0b0511d","uuid":"dde4e586-1def-4457-8ec5-0287b0b0511d","title":"认知 人行为背后的思维与智能","normalized_title":"认知人行为背后的思维与智能","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787300273921","isbns":["9787300273921"],"parsed":true,"ai_readable":true,"document_type":"book","page_count":290,"navigation_url":"https://workshop.closeclaw.top/ai/book/dde4e586-1def-4457-8ec5-0287b0b0511d","title_url":"https://workshop.closeclaw.top/ai/title/%E8%AE%A4%E7%9F%A5%20%E4%BA%BA%E8%A1%8C%E4%B8%BA%E8%83%8C%E5%90%8E%E7%9A%84%E6%80%9D%E7%BB%B4%E4%B8%8E%E6%99%BA%E8%83%BD","fixed_page_url_template":"https://workshop.closeclaw.top/ai/book/dde4e586-1def-4457-8ec5-0287b0b0511d/page/{printed_page}","path_api_url_template":"https://workshop.closeclaw.top/api/ai/book/dde4e586-1def-4457-8ec5-0287b0b0511d/page/{printed_page}","read_url":"https://workshop.closeclaw.top/api/ai/read/dde4e586-1def-4457-8ec5-0287b0b0511d","page_url":"https://workshop.closeclaw.top/api/ai/books/dde4e586-1def-4457-8ec5-0287b0b0511d/page","search_url":"https://workshop.closeclaw.top/api/ai/books/dde4e586-1def-4457-8ec5-0287b0b0511d/search"},"page":{"printed_page":216,"pdf_page":227,"physical_index":227,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"c2cb44c27de7f79517b564335b1703d6ba491decb7f5594ff6c72035b2278615"},"chapter":"第六章","content":"认知\n\n例如老师出了两道题：\n\n$$\n( 3 + 2 ) ( 3 - 2 ) = ?\n$$\n\n$$\n\\left( 5 + 3 \\right) \\left( 5 - 3 \\right) = ?\n$$\n\n学生在演算这些题目的过程中可以找到一些规律：\n\n$$\n( 3 + 2 ) ( 3 - 2 ) = 9 + 6 - 6 - 4 = 9 - 4 = 5\n$$\n\n$$\n( 5 + 3 ) ( 5 - 3 ) = 2 5 + 1 5 - 1 5 - 9 = 2 5 - 9 = 1 6\n$$\n\n有的学生会发现中间两项可以消掉而省去一步计算；有的学生会进一步注意到数的平方关系，从解题中看出这无非是 $( a +$ $b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ 的形式。这种方法是从少数具体模式中概括出一般的规律性。\n\n2. 直接法教学。\n\n直接教学法就是直接给出 $\\left( a + b \\right) \\left( a - b \\right) = a ^ { 2 } - b ^ { 2 }$ 的公式，让学生去套用。现在的教科书一般采取的就是这种方法。\n\n这两种方法无论是从信息加工的观点看，还是从动机理论的观点看，似乎都很复杂，各有利弊。用发现法教学，学生可以在做中学，自己找到关键点，如 $a ^ { 2 } - b ^ { 2 }$ ，但他不可避免地也要做一系列与所要掌握的规律(公式）无关的机械活动。用直接法教学，虽然可以节约时间，但学生可能不懂公式的结构，在上例中就是不了解 $a ^ { 2 } - b ^ { 2 }$ 中的a、b与原式有什么关系。这样，学生只好死记硬背，容易厌烦。\n\n216","previous_page":215,"next_page":217}