When the National Benchmark Tests (NBTs) were first considered, it was suggested that the results would assess entry-level students’ academic and quantitative literacy, and mathematical competence, assess the relationships between higher education entry-level requirements and school-level exit outcomes, provide a service to higher education institutions with regard to selection and placement, and assist with curriculum development, particularly in relation to foundation and augmented courses. We recognise there is a need for better communication of the findings arising from analysis of test data, in order to inform teaching and learning and thus attempt to narrow the gap between basic education outcomes and higher education requirements. Specifically, we focus on identification of mathematical errors made by those who have performed in the upper third of the cohort of test candidates. This information may help practitioners in basic and higher education. The NBTs became operational in 2009. Data have been systematically accumulated and analysed. Here, we provide some background to the data, discuss some of the issues relevant to mathematics, present some of the common errors and problems in conceptual understanding identified from data collected from Mathematics (MAT) tests in 2012 and 2013, and suggest how this could be used to inform mathematics teaching and learning. While teachers may anticipate some of these issues, it is important to note that the identified problems are exhibited by the top third of those who wrote the Mathematics NBTs. This group will constitute a large proportion of first-year students in mathematically demanding programmes. Our aim here is to raise awareness in higher education and at school level of the extent of the common errors and problems in conceptual understanding of mathematics. We cannot analyse all possible interventions that could be put in place to remediate the identified mathematical problems, but we do provide information that can inform choices when planning such interventions.

中文翻译：

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由表现出色的应聘者撰写的国家基准测试所犯的数学错误

首次考虑国家基准测试（NBT）时，建议该结果将评估入门级学生的学术和定量素养，数学能力，评估高等教育入门级要求与学校退出成绩之间的关系。 ，为高等教育机构提供选拔和安置方面的服务，并协助课程开发，尤其是与基础课程和增补课程有关的课程。我们认识到有必要更好地交流由测试数据分析得出的结果，以便为教与学提供信息，从而努力缩小基础教育成果与高等教育要求之间的差距。特别，我们专注于识别那些在应试者队列中上三分之一中表现出色的人所犯的数学错误。这些信息可以帮助基础教育和高等教育的从业者。NBTs于2009年开始运作。已经系统地收集和分析了数据。在这里，我们为数据提供了一些背景知识，讨论了与数学有关的一些问题，并提出了一些常见的错误和概念理解上的问题，这些错误和问题是从2012年和2013年从数学（MAT）测试收集的数据中识别出来的，并提出了建议可用于数学教学。尽管教师可能会预料到其中一些问题，但重要的是要注意，发现的问题在撰写数学NBT的人中占三分之一。在数学要求很高的课程中，这一组将构成很大的一年级学生。我们的目的是在高等教育和学校级别上提高人们对数学概念理解中常见错误和问题程度的认识。我们无法分析可以采取的所有可能的干预措施来补救已确定的数学问题，但是我们确实提供了可以在规划此类干预措施时提供选择信息的信息。