建構取向教學是數學科今後主要的教學取向，但是許多家長與教師的疑慮仍然未消除。有人認為建構取向教學將使學生成績低落，數學能力變差；有人認為指導教學扼殺了學生思考能力及學習興趣。眾說紛紜的原因是缺乏實證研究的佐證，因此本研究以實證資料來探究這兩種教學取向與數學成續、學習適應的關係。 此外，針對Coleman(1996)提出的論點：「學生的學業成就與個人背景因素相關較高，而與教師因素相關較低」，本研究亦一併作探討。看看學生的背景因素以及教師的教學方法，對於學生的成續及影響力如何？並看看教師教學方法對於學生背景所造成的學習差異，是否有可以著力之處？ 本研究結果顯示：1.補習、有專用書桌、請家教及雙親家庭等個人背景因素，對於數學成續有顯著正影響力。這顯示家庭背景是影響學生成續的主因，教師教學方法對於成續的影響並不顯著。2.背景因素對於學生的學習適應具有影響力，不過教學方法對於學習適應的影響力更高。而且建構取向教學對於學生數學科的學習適應，呈現顯著有利的影響。這個結果支持了許多學者提倡數學科建構取向教學的論點。顯示了教育上重大的意義是：雖然教師教學方法在提昇學生數學成續上，並無強大影響力，以至於背景因素是主要顯著影響數學成續的因素。但是學校教師的建構取向教學，卻能讓學生學習適應更好。這或許是教師建構取向教學上更重要的意義。3.本研究結果也顯示，部份教師經過教學反省後，採建構/指導混合教學，修改後的建構/指導混合教學與建構取向教學相較之下，在學習適應、數學成續上並無顯著的差異。

Constructional approach teaching will become the mainstream for future mathematics teaching, but many parents and teachers have doubts about it. Some think that constructional approach teaching brings about a drop in grades of students a decrease in their mathematical ability. Others think that direct teaching will hinder thinking ability and learning interests of students. These various concerns are due to a lack of actual data. So this study uses data to explore the relationship between the two types of teaching and their influence on mathematics grades or learning adaptation. The study will also further explore Coleman’s theory developed in 1966 : Grades of students are much more related to background factors than teacher factors. The study also explores the two following questions : How are grades of students affected by background factors of students and teaching methods of teaching ? And what can we do with learning differences in background caused by teaching methods of teachers? The study shows : First, some elements which have a crucial influence on mathematics grades are cram school education, having one’s own desk, and having tutors and parents. This means the family background is the main factor that affects grades of students and has little connection with teaching methods of teachers. Second, the learning adaptation of students is influenced more by teaching methods than by background factors. Also, constructional approach teaching will have a positive effect on mathematics learning adaptation. The result supports the theory of constructional approach teaching produced by many scholars. It means a lot in education that teaching methods have little influence on promotion of mathematics grades, so background factors have become the prime factor in the influence of mathematics grades. But teaching methods of teachers will help students have getter learning adaptation. This may be the importance of constructional approach teaching. Third, the study also finds that some teachers after their teaching introspection use mixed constructional and direct teaching. Compared with constructional approach teaching, the mixed constructional and direct teaching makes no difference in learning adaptation or mathematical grades.