The goal of this study is to show a novel way of using large-scale data ( N = 6203) to identify pupils’ strategies when solving missing value number equations. It is based on the assumption that wrong numerical results appearing more frequently than would be the case if they were consequences of random guessing can be expected to be underlain by a pupil’s rational, theoretically justifiable, solving procedure. We determined all of the numerical results suggested by the pupils in the study for three problems with the same format and classified them based on their occurrence. Possible solving procedures leading to them were inferred using a priori analysis. Next, we identified pupils’ strategies based on the anticipated solving procedures in two problems of the same format and validated them by comparing them to the pupils’ results in the third problem and to the pupils’ whole test result. We identified six strategies, some of them underlain by clearly identified procedures. Our analysis showed a high predictive power of the identified pupils’ strategies for their achievement in the mathematics test written 3 years later and in a more difficult problem of the same format. Our study has implications for test makers and teacher practice.

中文翻译：

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使用大规模数据确定学生在缺失值数字方程中的策略和错误

本研究的目标是展示一种使用大规模数据 (N = 6203) 的新方法来确定学生在求解缺失值数字方程时的策略。它基于这样一个假设，即错误的数值结果比随机猜测的结果出现的频率更高，可以预期学生的理性、理论上合理的求解程序会掩盖这些结果。我们确定了学生在研究中针对三个具有相同格式的问题建议的所有数值结果，并根据它们的出现对它们进行分类。使用先验分析推断出导致它们的可能解决程序。下一个，我们根据相同格式的两个问题的预期解决程序确定学生的策略，并通过将它们与学生在第三个问题中的结果和学生的整体测试结果进行比较来验证它们。我们确定了六种策略，其中一些策略由明确确定的程序构成。我们的分析表明，在 3 年后编写的数学测试和相同格式的更困难的问题中，所识别学生的策略具有很高的预测能力。我们的研究对考试制作者和教师实践有影响。我们的分析表明，在 3 年后编写的数学测试和相同格式的更困难的问题中，所识别学生的策略具有很高的预测能力。我们的研究对考试制作者和教师实践有影响。我们的分析表明，在 3 年后编写的数学测试和相同格式的更困难的问题中，所识别学生的策略具有很高的预测能力。我们的研究对考试制定者和教师实践有影响。