Previous research repeatedly found basic numerical abilities (e.g., magnitude understanding, arithmetic fact knowledge, etc.) to predict young students' current and later arithmetic achievement as assessed by achievement tests – even when controlling for the influence of domain-general abilities (e.g., intelligence, working memory). However, to the best of our knowledge, previous studies hardly addressed this issue in secondary school students. Additionally, they primarily assessed basic numerical abilities in a between-task approach (i.e., using different tasks for different abilities). Finally, their relevance for real-life academic outcomes such as mathematics grades has only rarely been investigated. The present study therefore pursued an approach using one and the same task (i.e., a within-task approach) to reduce confounding effects driven by between-task differences. In particular, we evaluated the relevance of i) number magnitude understanding, ii) arithmetic fact knowledge, and iii) conceptual and procedural knowledge for the mathematics grades of 81 students aged between ten and thirteen (i.e., in Grades 5 and 6) employing the number bisection task. Results indicated that number magnitude understanding, arithmetic fact knowledge, and conceptual and procedural knowledge contributed to explaining mathematics grades even when controlling for domain-general cognitive abilities. Methodological and practical implications of the results are discussed.

先前的研究反复发现基本的数字能力（例如，理解力，算术事实知识等）可以预测学生通过成绩测试评估的当前和以后的算术成绩-即使在控制领域通用能力的影响时（例如，智力，工作记忆）。然而，据我们所知，以前的研究几乎没有针对中学生解决这个问题。此外，他们主要通过任务间方法（即对不同能力使用不同任务）评估基本数字能力。最后，很少研究它们与现实生活中的学术成果（例如数学成绩）的相关性。因此，本研究采用了一种使用相同任务的方法（即，任务内方法），以减少任务间差异导致的混淆影响。特别是，我们评估了i）数量级理解，ii）算术事实知识和iii）概念知识和过程知识与81位年龄在10到13岁（即5和6年级）的学生在数学上的相关性，数字二等分任务。结果表明，即使控制领域通用的认知能力，数量级的理解，算术事实知识以及概念和程序知识也有助于解释数学成绩。结果的方法和实际意义进行了讨论。iii）运用数字二等分任务为81位年龄在10到13岁（即5和6年级）的学生的数学年级提供了概念和程序知识。结果表明，即使控制领域通用的认知能力，数量级的理解，算术事实知识以及概念和程序知识也有助于解释数学成绩。结果的方法和实际意义进行了讨论。iii）运用数字二等分任务为81位年龄在10到13岁（即5和6年级）的学生的数学年级提供了概念和程序知识。结果表明，即使控制领域通用的认知能力，数量级的理解，算术事实知识以及概念和程序知识也有助于解释数学成绩。结果的方法和实际意义进行了讨论。