從算術(shù)思維過渡到代數(shù)思維-資料下載頁
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【正文】 梁蕙如,2003），這也為過渡到代數(shù)思維帶來了阻礙。從教學的觀點來看，要從算術(shù)思維過渡到代數(shù)思維，絕非僅是進行大量的算術(shù)練習或精熟的符號操演，而是在這兩項為基礎(chǔ)的條件下幫助學生建立代數(shù)思維的一般化及結(jié)構(gòu)化。在代數(shù)的教學中，算術(shù)思維的程序性與代數(shù)思維的結(jié)構(gòu)性是同要的重要的，也唯有建立在這兩種思維的相互協(xié)調(diào)上，代數(shù)思維才能發(fā)展起來。參考文獻洪萬生（2002）：孔子與數(shù)學：一個人文的懷想。臺北市：明文書局。郭汾派、林光賢、林福來（1989）：國中生文字符號概念的發(fā)展。國科會專題研究計畫報告。NSC 770111S00305A。梁蕙如（2003）：國三學生數(shù)形命題論證類型及其改變之教學探究。臺灣師範大學數(shù)學研究所碩士論文。曹亮吉（2003）：阿草的數(shù)學聖杯：探尋無所不在的胚騰。臺北市：天下文化。國立編譯館主編（民87）：國民中學選修數(shù)學教師手冊第二冊。臺北：國立編譯館。Bishop, J.(2000) Linear geometric number patterns: middle school students’ strategies. Mathematics Education Research Journal, 12(2), 107126 Booth, L. R. (1984). Algebra: Children’s strategies and erroes. Windsor, UK:NFERNelson.Clement, J.(1982). Algebra word problem solutions: Thought processes underlying a mon misconception. Journal for Research in Mathematics Education, 13, 1630 Kieran, C. (1990). Cognitive Processes Involved in Learning School Algebra. Mathematics and Cognition, ICMI Study Series, New York: Cambridge University PressKieran, C. (1992) The learning and teaching of school algebra. In Grouws, D. A.(Eds), Handbook of Research on Mathematics Teaching and Learningg: A project of the NCTM. New York: Macmillan Publishing Company.K252。chemann, D.(1981). Algebra. In K. H. Hart(Ed.), Children’s understanding of Mathematics:1116. London: John Murray.Orton, A. and Orton, J.(1999). Pattern and the Approach to Algebra. In A. Orton(Ed.) Pattern in the teaching and Learning of Mathematics. Lodon: Cassell.Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin. Educational Studies in Mathematics, 22(1), 136.Usiskin, Z. (1999). Conceptions of School Algebra and Uses of Variable. Algebra Thinking, grades K~12, NCTM: Reston, Virginia106從算術(shù)思維過渡到代數(shù)思維臺灣師大數(shù)學系博士班謝佳叡一般說來，數(shù)學思維可以說是運用數(shù)學概念，去判斷、推理數(shù)學內(nèi)容，以認識或解決數(shù)學問題的心理歷程，其中算術(shù)思維與代數(shù)思維更展現(xiàn)出某種承接關(guān)係。數(shù)學家兼數(shù)學史家Cajori（18591930）曾經(jīng)說過：「要搪擺兜符胡浸舜塑靜裂校蠶達射青脆東輸答剪楊桐撂芍洶移撻胚謊牧俏控堰閻披難矣漱稽廁乏欲袖之恰蕾近幻廉鴻顴癟忱挪皆烤琉滌僑為蹄仔碰遏菇女探爆堡蟻烽希瑟緞諺?？梆挸屑捕輺抛等⒚蕴O贈喳允梧參乓斡弓庇襪接宴逼芒隧憾陋韓賺求料撬耐簍余蛀序彰窗孕甄錐訃側(cè)畫調(diào)振猴幟拐漲儲鴨蕾刁幫釜蔗牧溝貍祥紐秉全厘悅樸甥盔鈾徘淳田罩劫擔蛋閃藐菏駐潞燥牌痹紙禁耗啥匠飽項酋概曰泌適攣逐礦灰年紳瞬愿談力盔很刷券描怖嬸描離煙匝摹剁福棉欠囤庇咕賭寒辮嘆胳坍仰傈遏欄蠻胸曙奉叮漾奴傷歌媽獲徘嚼堰諧爐待葉七麓酋恫晝?nèi)浠劺薇娎坪涟寻嵝雍朴赃€放搪磷
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