建構數學科層級式知識地圖-以高職課綱數學科為例

Abstract

因應十二年國民基本教育實施，以及面對後期中等教育在數學科目的學習上呈現越來越嚴重之雙峰傾向，如何在教學上兼顧「差異化」及「效率化」，又如何在資訊與通訊科技發達的助益下，善用資訊科技幫助學生有效學習，實為一線基層教師在教育場域中之一大挑戰。 據此，本研究以「99高職課綱」中的數學(C)為研究範圍，並以高職工業類群數學科教師及學生為研究對象，採課程之「節」為單元，輔以編序教學法之理念為架構，藉由強調「先備知識」（prior knowledge）及「後位知識」（posterior knowledge）之先後關係，重新建構出「層級式知識地圖」（hierarchical knowledge map），並為每個學習單元建立本研究所發展之「影響權重」（impact weighting）、「關鍵係數」（critical coefficient）、「複雜指數」（the complexity index）、「學習鷹架層數」（learning scaffolding layers）以及「學習負荷權數」（learning load weighting）等參數指標，且評估未來必然是資訊科技輔助學習，因此進一步設計出一套簡單易用之資訊系統，透過該系統之分析結果，協助教學端有效診斷學習者之差異與需求，即時調整教學方式，以執行適性化之教學策略。又為求審慎可信，本研究以專家訪談、焦點座談、專家一致性分析、波達計數法（Borda Count）等方法探討驗證後，確立以本研究所建構之相關參數指標，搭配所發展之輔助分析系統，確實能協助教學者有效的掌握教材內涵，幫助學習者釐清學習迷思，並建立個別化的學習單元順序，且相關之參數指標同時具有識別學生的學習定位，引導其透過知識地圖進行學習規劃，達成領航目標之效果。本研究結果希冀提供給教育相關單位參酌，裨益教與學之雙方皆能夠清楚學習導航知識地圖以及未來智慧化學習之延伸應用。To coping with “The National Twelve-Year Basic Education Implementation Project” and facing the appeared serious bimodal tendencies of mathematics learning of post-secondary high school students. Therefore, it was a huge challenge that teachers must to overcome either differentiation or efficient should be satisfied during teaching and learning activities, and assist students to learn efficiently via information and communication technology (ICT). Thus, the “Mathematic Version C” of “99 Vocational High School Curriculum Guideline” to be set as research field. Subjects retrieved from vocational high school. The selected “section” had been set as research unit and aligned with Programmed Instruction. It was emphasized that the order relationships among “prior knowledge” and “posterior knowledge” should be clear marked and defined. Hence, a reformed “hierarchical knowledge map” to be developed in this study. Further, “impact weighting”, “critical coefficient”, “the complexity index”, “learning scaffolding layers”, and “learning load weighting” has developed for each unit to match the characteristic of hierarchical knowledge map in this study. To imply ICT to assist mathematic learning and teaching, therefore, a designed and ease of used information system had developed to estimate learner’s mathematic concept by researcher. Learners and teachers could adjust their learning and teaching temple or satisfy their demand via the generated response or feedback from this information system. Thus, the adoptive teaching strategy could implied in the mathematic class by diagnosed discrepancy and demand among learners. The expert interview, focus group, expert consistence analysis, and Borda Count had employed for reliability and validity check of developed parameters and information system. The result shows that curriculum contents, clarify learner’s misconception, and establish individualized learning sequence in the mathematic course by the developed parameters and information system. In addition, the developed parameters could provide helpful function to position anchored learning for each learner. Then, this information system could guide them to put themselves in planed schedule of mathematic learning. Indeed, the goal of this information system could be reached to pilot learners and teacher in mathematic learning. The research findings and suggestions will provided for support educators’ decision-making. In summary, the provided hierarchical knowledge map and further intelligence learning by developed information system and parameters of this study could satisfy teaching and learning of “Mathematic Version C” of “99 Vocational High School Curriculum Guideline”