國中小學生的數學詞彙知識與數學成就之相互影響

Reciprocal Effects of Mathematics Vocabulary Knowledge and Mathematics Achievement Among Elementary and Middle School Students

研究目的
探討數學詞彙知識與數學成就兩者的相互影響，並比較在國小與國中階段的現象異同，以提供數學能力間因果關係的理論觀點與知識網絡發展的啟示，同時提示數學教學的著力點。
研究設計／方法／取徑
本研究對200位國小高年級學生和231位國中生，間隔兩學年後重複測量數學詞彙知識與數學成就。在考量智力的情況下，運用預測路徑分析與延宕交互模式來探討兩變項之相互影響。
研究發現或結論
預測路徑分析與延宕交互模式的適配度佳，各模式對後期數學詞彙知識或數學成就之解釋力大約50%。研究發現，一、國小生與國中生前期數學詞彙知識對後期數學成就的預測類似，延宕預測的整體效果與其中的間接效果都顯著，但直接效果都不顯著；二、國小生與國中生前期數學成就對後期數學詞彙知識的延宕預測整體效果及其中的間接效果都顯著，但直接效果僅在國中生顯著；三、同時納入兩變項前期資料對後期另一變項之預測，國中小生的結果不同。國小生僅前期數學成就顯著預測後期數學詞彙知識，國中生的兩個前期變項都能交互地顯著預測另一個後期變項；四、綜合資料顯示，數學詞彙知識對數學成就的預測較弱，在國中小生都僅有間接效果而無直接效果，只在國中生的延宕交互模式下存在數學詞彙知識對數學成就的延宕影響；數學成就對數學詞彙知識的預測則較強，不但在國小生的延宕交互模式下存在影響，且國中生在兩種模式中都有顯著影響。
研究原創性／價值
國際上探討數學詞彙知識與其它數學能力之關係的研究方興未艾，多數為橫斷性研究，也未必有控制智力。本文蒐集橫跨兩學年的資料，考量智力因素，同時包含國小高年級與國中生的模式，是少見的能從知識網絡之長期發展來解釋國中小生在數學詞彙知識與數學成就相互影響的研究。
教育政策建議與應用
數學詞彙知識對長達兩學年之後的數學成就存在間接效果，且此預測在國中階段比國小高年級階段更強，建議應發展數學詞彙知識的教學方案，以及對低數學成就學生在掌握新數學詞彙時提供額外之舉例、說明、釐清的教學策略。

Research Purpose
This study aimed to analyze the reciprocal relationship between mathematics vocabulary knowledge and achievement, and identify their similarities and differences among elementary and middle school students through a theoretical perspective on the causal relationship between mathematics abilities and the development of knowledge networks. It also aimed to provide suggestions for enhancing mathematics instruction.
Research Design/Method/Approach
This study sampled 200 elementary and 231 middle school students, measuring their mathematical vocabulary knowledge and mathematical achievement twice over two school years. After controlling intelligence, predicted path analysis models and cross-lagged effect models were used to explore the reciprocal effects.
Research Findings or Conclusions
a good pattern fit, and indicating that each model had approximately 50% explanatory power for later mathematics vocabulary knowledge or achievement. The results showed that: (a) The prediction patterns of elementary and middle school students’prior mathematics vocabulary knowledge on their later mathematics achievement were similar. The total and indirect effects of delayed predictions were significant, but the direct effects were not. (b) The prediction patterns of elementary and middle school students’prior mathematics achievements regarding their later mathematics vocabulary knowledge were different. The total and indirect effects were significant for both groups; however the direct effects were significant only for middle school students. (c) The prediction patterns of the cross-lagged model differed between the groups. Only mathematics achievement significantly predicted later mathematics vocabulary knowledge among elementary school students, whereas both variables predicted their later counterparts among middle school students with significant cross-lagged effects. (d) In both groups, mathematics vocabulary knowledge was a weak predictor of mathematics achievement. Delayed effects in the cross-lagged effect model were observed only among middle school students. Mathematics achievement was a strong predictor of mathematics vocabulary knowledge. Besides influencing the cross-lagged effect model of elementary school students, it also had a significant influence on various models of middle school students.
Research Originality/Value
There is a growing body of international research exploring the relationship between mathematics vocabulary knowledge and other mathematical skills, most of which are cross-sectional and do not necessarily control for intelligence. Considering intelligence factors, this study explains the reciprocal relationship between mathematics vocabulary knowledge and achievement in elementary and middle school students using data collected across two school years from the perspective of developing a mathematics vocabulary knowledge network.
Educational Policy Recommendations and Applications
Mathematics vocabulary knowledge had an indirect effect on mathematics achievement after two years of school, and this prediction was stronger at the middle school level than at the elementary school level. We was recommended that mathematics vocabulary instruction programs be developed and provided to students with low mathematics achievement alongside extra instruction to provide examples, explanations, and clarifications when students acquire new mathematics vocabulary.