Against the background of the low mathematical performance of South African learners in international panel studies, there is an urgent need to improve mathematical education. In particular, the curriculum and its structure raise questions. It is logical that the prescribed curricula should align with learners’ developmental trajectories. Given the hierarchical structure of mathematics, the curricular requirements should pay attention to learners’ current knowledge of mathematical concepts. The aim of this study was to compare the curricular requirements as defined by the CAPS with the conceptual current knowledge of South African learners. South African Grade 1 learners (N = 602) were assessed on a test of numeracy concepts, based on a theoretically informed and empirically validated model of developing mathematical proficiency. The content of the CAPS for Grade 1 was aligned to the model levels by two experts (Cohen’s κ = .753, p < 0.001). Results show that the curricular requirements go far beyond the current knowledge required to engage with these new concepts of the vast majority of South African Grade 1 learners. The mismatch may to some extent be responsible for the unsatisfactory results in international comparison studies. These results show that the intended curriculum is beyond the grasp of most South African Grade 1 learners. These children are unlikely to develop new arithmetic concepts based on their lack of required foundation knowledge. We therefore argue that the intended curriculum for Grade 1 should focus more on counting skills, ordinal relations between numbers and—most importantly—set-based number representations and part–part–whole relations.

中文翻译：

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南非基础阶段课程要求与学习者当前知识不匹配

在南非学习者在国际小组研究中数学表现不佳的背景下，迫切需要改善数学教育。特别是，课程及其结构提出了问题。规定的课程应与学习者的发展轨迹保持一致是合乎逻辑的。给定数学的层次结构，课程要求应注意学习者当前的数学概念知识。这项研究的目的是将CAPS定义的课程要求与南非学习者当前的概念知识进行比较。南非1年级学习者（N = 602）在一项对数学概念的测验中得到了评估，该测验是基于理论知识和经验验证的数学能力发展模型进行的。两名专家将1级CAPS的内容与模型水平进行了匹配（Cohenκ= .753，p <0.001）。结果表明，课程要求远远超出了与绝大多数南非1年级学习者的这些新概念相适应的当前知识。失配在某种程度上可能是国际比较研究中结果不令人满意的原因。这些结果表明，预期的课程是大多数南非1年级学习者无法掌握的。这些孩子由于缺乏所需的基础知识而不太可能开发新的算术概念。因此，我们认为，一年级的预期课程应更多地侧重于计算技能，数字之间的序数关系，最重要的是基于集合的数字表示法以及部分-部分-整体关系。