第四章 分析與討論
第二節 建議
依據本研究分析結果，提出下列建議。
一、國家政策與教育啟示方面
(一)本研究中將全部的數學學習個人變項一起加入分析時，發現數學課外學習時
數越少，學生數學能力越好，而芬蘭數學課外學習時數最少，但其數學能力 卻僅次於香港，與國人一般見解不同，此一現象在教育理念上可做進一步省 思。
(二) GDP、GCI、NRI 越高，平均數學能力越好，此一研究結果顯示國家經濟力、
競爭力與資訊科技整備程度越高的國家，該國學生數學能力越好，因此可對 照數學能力相近的國家，其國家政策有何異同，以做為借鏡。
(三)在本研究中，EI 是以 15 歲以上人口識字率與各級學校在學率計算而得，EI 越高，平均數學能力越好，顯示教育的普及有其重要性存在，因此國家政策 擬定時，應該著重提升教育普及化。
(四)本研究結果顯示班級規模越小，數學能力越好，因此建議降低班級規模，進 行小班教學，班級學生數少，有助於促進教育品質的提升。
二、未來研究方面
(一)PISA 2003 參與國家可依其國家背景特質分組，如：OECD 會員國與非 OECD 會員國，東方國家與西方國家，分析比較不同國家背景特質分組下，其數學 能力的差異情形。
(二)本研究僅以數學課外學習時數、數學課自我效能與數學課上課情形，以及 GDP、GCI、NRI、EI 與班級規模進行分析，未來可探討其他有關學習的個 人變項與國家變項對學生數學能力之影響。
(三)在隨機效果單因子共變數分析模式、隨機效果迴歸模式、帶有非隨機變化之 斜率的模式和完整模式等四個模式中，分別將數學課外學習時數、數學課自 我感覺和數學課上課情形三個變項，觀察其對數學能力的影響，以及在將全 部的數學學習個人變項一起加入分析，觀察其對數學能力的影響，兩種情況 得到不盡相同的結果，這意味著可能存在多元共線性(multicollonearity)或壓抑 變項(suppressor variable)導致分析結果不一(余民寧，1994，1995)，未來可進
一步探討其影響。
(四)本研究結果可提供學生數學學習與提升數學能力，大型國際性評量資料庫的 資料分析方向，與國家教育政策的建議之參考。
(五)PISA 實施的一系列評量，目前已完成 PISA 2000、PISA 2003、PISA 2006，
可以將資料庫進行縱貫研究，以期得到不同角度的資料結構訊息。
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附錄一 PISA 2003 學生問卷 Q33
The following question asks about the time you spend studying and doing Mathematics homework outside of your regular Mathematics classes.
On average, how much time do you spend each week on the following?
When answering include time at the weekend too.
a) Homework or other study set by your Mathematics teacher. .... ___ hours per week b) <Remedial classes> in Mathematics at school. …... ___ hours per week c) <Enrichment classes> in Mathematics at school. ... ___ hours per week d) Work with a <Mathematics tutor>. ………... ___ hours per week e) Attending <out-of-school> Mathematics classes. ………... ___ hours per week Q33
f) Other Mathematics activities (e.g. <Mathematics
competitions, Mathematics Club>). ...…... ___ hours per week
附錄二 PISA 2003 學生問卷 Q37
Q37 Thinking about your <Mathematics> classes: To what extent do you agree with the following statements?
(Please <tick> only one box in each row.)
Strongly
agree Agree Disagree
Strongly disagree a) I would like to be the best in my class
in Mathematics. ... □1 □2 □3 □4
b) In Mathematics I enjoy working with
other students in groups. ... □1 □2 □3 □4
c) I try very hard in Mathematics because I want to do better in the exams than
the others. ... □1 □2 □3 □4
d) When we work on a project in
Mathematics, I think that it is a good idea to combine the ideas of all the
students in a group. ... □1 □2 □3 □4
e) I make a real effort in Mathematics
because I want to be one of the best. .... □1 □2 □3 □4
f) I do my best work in Mathematics
when I work with other students. ... □1 □2 □3 □4
g) In Mathematics I always try to do better than the other students in my
class. ………. □1 □2 □3 □4
h) In Mathematics, I enjoy helping others
to work well in a group. ... □1 □2 □3 □4
i) In Mathematics I learn most when I
work with other students in my class. .. □1 □2 □3 □4
j) I do my best work in Mathematics
when I try to do better than others. ... □1 □2 □3 □4
附錄三 PISA 2003 學生問卷 Q38
Q38 How often do these things happen in your <Mathematics> lessons?
(Please <tick> only one box in each row.)
Every lesson
Most lessons
Some lessons
Never or hardly
ever a) The teacher shows an interest in every
student’s learning. ... □1 □2 □3 □4
b) Students don’t listen to what the teacher
says. ………... □1 □2 □3 □4
c) The teacher gives extra help when
students need it. ……..…... □1 □2 □3 □4
d) Students work from books and other printed material. ...
□1 □2 □3 □4
e) The teacher helps students with their
learning. ………..…... □1 □2 □3 □4
f) There is noise and disorder. ... □1 □2 □3 □4
g) The teacher continues teaching until the
students understand. ………... □1 □2 □3 □4
h) The teacher has to wait a long time for
students to <quieten down>. ... □1 □2 □3 □4
i) Students cannot work well. …... □1 □2 □3 □4
j) The teacher gives students an
opportunity to express opinions. …….... □1 □2 □3 □4
k) Students don’t start working for a long
time after the lesson begins. …...……… □1 □2 □3 □4