This study tested the mediating role of self‐directed learning skills (SDL) between students’ conceptions of mathematics and their achievement in mathematics using a structural equation model. Data were collected using the “Conceptions of Mathematics Questionnaire” and the “Self‐Rating Scale of Self‐Directed Learning”, together with students’ achievement in mathematics. A sample of 440 first year university students at King Saud University participated in the study. The findings confirm the moderating role of students’ self‐directed learning skills between their conceptions of mathematics and their achievement in mathematics. Students who have a highly fragmented conception of mathematics tended to have low SDL skills, and in turn low mathematics achievement (partial mediation), whereas students who have a highly cohesive conception of mathematics tended to have high self‐directed learning skills, and in turn high mathematics achievement (full mediation). Mathematics educators should be aware that students’ conceptions of mathematics may be influential, but not sufficient to predict achievement in mathematics. Equipping students with appropriate conceptions of mathematics and self‐directed learning skills is key to enhancing their performance in mathematics.

中文翻译：

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数学概念和自主学习技能对大学生数学成绩的影响

本研究使用结构方程模型测试了自我指导学习技能（SDL）在学生的数学观念与他们的数学成就之间的中介作用。使用“数学问卷调查的概念”和“自我学习的自我评价量表”收集数据，并结合学生的数学成绩。沙特国王大学440名第一年大学生的样本参加了该研究。研究结果证实了学生的自主学习技能在他们的数学观念和他们的数学成就之间的调节作用。数学概念高度分散的学生往往SDL技能较低，因而数学成绩也较低（部分调解），而具有高度凝聚力的数学概念的学生往往具有较高的自我导向的学习技能，进而具有较高的数学成就（充分调解）。数学教育者应意识到，学生的数学观念可能会产生影响，但不足以预测数学成绩。为学生配备适当的数学概念和自主学习技能是提高他们在数学中的表现的关键。