@article{FritzLongHerzogetal.2020,
  author    = {Fritz, Annemarie and Long, Caroline and Herzog, Moritz and Balzer, Lars and Ehlert, Antje and Henning, Elizabeth},
  title     = {Mismatch of the South African foundation phase curriculum demands and learners' current knowledge},
  series = {African journal of research in mathematics, science and technology education},
  volume    = {24},
  journal   = {African journal of research in mathematics, science and technology education},
  number    = {1},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1811-7295},
  doi       = {10.1080/18117295.2020.1724466},
  pages     = {10 -- 20},
  year      = {2020},
  abstract  = {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 kappa = .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.},
  language  = {en}
}
@article{HerzogEhlertFritz2017,
  author    = {Herzog, Moritz and Ehlert, Antje and Fritz, Annemarie},
  title     = {A Competency Model of Place Value Understanding in South African Primary School Pupils},
  series = {African Journal of Research in Mathematics, Science and Technology Education},
  volume    = {21},
  journal   = {African Journal of Research in Mathematics, Science and Technology Education},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1811-7295},
  doi       = {10.1080/18117295.2017.1279453},
  pages     = {37 -- 48},
  year      = {2017},
  abstract  = {Although the general development of mathematical abilities in primary school has been the focus of many researchers, the development of place value understanding has rarely been investigated to date. This is possibly due to the lack of conceptual approaches and empirical studies related to this topic. To fill this gap, a theory-driven and empirically validated model was developed that describes five sequential conceptual levels of place value understanding. The level sequence model gives us the ability to estimate general abilities and difficulties in primary school pupils in the development of a conceptual place value understanding. The level sequence model was tried and tested in Germany, and given that number words are very differently constructed in German and in the languages used in South African classrooms, this study aims to investigate whether this level sequence model can be transferred to South Africa. The findings based on the responses of 198 Grade 2-4 learners show that the English translation of the test items results in the same item level allocation as the original German test items, especially for the three basic levels. Educational implications are provided, in particular concrete suggestions on how place value might be taught according to the model and how to collect specific empirical data related to place value understanding.},
  language  = {en}
}