學習機會的分布及其對數學成就的效果：以美國為例

The Distribution and the Effects of Opportunity to Learn on Mathematics Achievement：An American Perspective

本文旨在拓展吾人對學習機會（opportunity to learn）之分佈及其對學生數學成就之效果等二方面的認識。文中除了對學習機會的分佈情形作描述性的分析外，更進一歩運用一組二個層次的階層線性模式（hierarchical linear models），分析從美國「1988年全國教育縱貫研究」（National Education Longitudinal Study of 1988）限制版資料庫中所抽取的樣本資料。其分析結果顯示：各項數學學習機會對學生的數學成就有不同程度的關連，而且不幸的，學習機會在不同類別的學校的分佈情形並不均等。根據研究的發現，本文對教育政策制訂提出四項建議：聘用、再訓練、和保留具有充足數學知識的教師；鼓勵高內容和教學程度（包括高程度的教學、高程度的涵蓋教學內容、和適量的家庭作業）。

The focus of this study is to further our understanding of the distribution and the effects of an expanded conception of opportunity to learn on student mathematics achievement. In addition to descriptive statistics， a set of two─level hierarchical linear models was employed to analyze a subset of the restricted use National Education Longitudinal Study of 1988 data base. The results revealed that， at different scale， various kinds of opportunity to learn mathematics do associate with student mathematics achievement and， unfortunately， opportunities are unequally distributed among different categories of schools. Four recommendations for educational policymaking are provided. They are：The need to recruit， retain and retain teachers with adequate mathematical knowledge， to encourage high content and level of instruction（including high level of instruction， coverage， and appropriate amount of homework）， to provide more advanced mathematics courses， and to increase opportunity in disadvantaged areas.