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This study investigated student mathematics teachers' ability to recognise and explain their understanding of school level functions. We challenged the assumption that studying advanced mathematics automatically develops an understanding of school mathematics that is sufficient to explain concepts and justify reasoning. This case study tested this assumption by exploring the depth of pre-service mathematics student teachers' understanding of school function concepts at the University of Zambia. The test items required calculation, as well as justification of the answers, and an explanation of the concepts. Of the 22 participants, all final year mathematics education students, 18 student teachers scored below the 50% pass mark. The average mark was 8 out of a possible 28 (27%). The majority of the participants found it difficult to explain and justify their reasoning. This study resulted in the development of a new school mathematics module for prospective mathematics teachers at the University of Zambia. 2019 by the authors.