基隆市國中生的家庭社經地位對數學學習成就影響之潛在成長模式探究：以數學補習時間與學習動機軌跡為中介變項

Using a Latent Growth Model to Explore the Effect of Family Socioeconomic Status on Mathematics Learning Achievement of Junior High School Students in Keelung City: Taking Mathematics Tutoring Time and Learning Motivation Trajectory as Mediating Variables

儘管許多研究探討數學學習動機，但學習動機成長軌跡影響數學學習成就知之甚少。為了解國中生家庭社經地位、數學補習時間、學習動機成長軌跡對數學學習成就的影響，本研究以國中生學習狀況資料庫的1,251筆資料為樣本，以潛在成長模式分析獲得以下結論：一、七年級生的家庭社經地位對七年級的數學補習時間有正向影響，但對後來五學期的補習時間成長軌跡沒有明顯影響；二、七年級生的家庭社經地位對於數學學習動機、五學期成長軌跡及九年級的數學學習成就有正向顯著影響；三、七年級的數學補習時間對九年級的數學學習成就有正向顯著影響，然而五學期補習時間成長幅度對九年級數學學習成就沒有顯著影響。四、七年級的數學學習動機對九年級的數學學習成就有正向顯著影響，然而學習動機成長幅度對九年級的數學學習成就沒有顯著影響。五、七年級生的家庭SES透過數學補習時間與數學學習動機起始點對數學學習成就的影響具有部分中介效果，然而家庭SES透過數學補習時間與數學學習動機變化幅度對數學學習成就沒有顯著的中介效果。本研究成果在於發現，國中生家庭社經地位僅對短期的數學補習時間有明顯影響，無法對五學期數學補習時間成長有明顯影響，然而，家庭社經地位對五學期學習動機成長軌跡有正向影響。針對結論深入討論，並提出建議。

Although many studies have explored the role of learning motivation growth in studying mathematics, little is known about the role of that growth in predicting mathematics learning achievement. This study aims to understand the influence of students’ family socioeconomic status (SES), the time students spend being tutored in mathematics, and students’ learning motivation growth trajectories on their math learning achievement. It uses 1,251 samples taken from a database tracking junior high school students’ learning status. Data analysis using the latent growth model lead to the following conclusions: (1) The SES of seventh grade students had a positive effect on the time they spent receiving tutoring in mathematics while in the seventh grade, but had no significant effect on the growth rate of the time they spent receiving tutoring in mathematics in the subsequent five semesters; (2) The SES of grade seven students had a positive effect on their motivation toward learning mathematics, the growth rate of their learning motivation in the subsequent five semesters, and their learning achievement in mathematics in the ninth grade; (3) The mathematics tuition time of the seventh grade had a positive and significant effect on the mathematics learning achievement of the ninth grade, but the growth rate of the five-semester tuition time had no significant effect on the ninth grade mathematics learning achievement. (4) Mathematics learning motivation in the seventh grade had a positive and significant impact on the mathematics learning achievement in the ninth grade, but the growth rate of learning motivation had no significant impact on the mathematics learning achievement in the ninth grade. (5) The SES of the seventh grader had a partial mediated effect on the ninth grade mathematics learning achievement through the time of mathematics tutoring and the starting point of mathematics learning motivation, but the SES had no significant mediated effect on the mathematics learning achievement through the time of mathematics tutoring and the growth of mathematics learning motivation. The main contributions of this research include the finding that the family SES of seventh graders only had a positive and significant effect on the time they spent being tutored in mathematics while in seventh grade, and was not found to affect the time they spent being tutored in mathematics in the next three years. However, the family SES in the seventh grade had a significant effect. However, family SES had a positive impact on the growth of students’ learning motivation across five semesters. In addition to in-depth discussion of these conclusions and their implications, specific suggestions are offered for improving learning achievement in mathematics.