• Pre-service mathematics teachers’ (PMTs) subject competency continues to engage scholars and researchers.
    Understanding level of knowledge of concepts that PMTs bring to their learning in university is crucial to
    developing their teacher knowledge. This article examines genetic decomposition of schemas PMTs in one
    university in South Africa build (to know about rules) for solving logarithmic equations. A mixed methods
    approach, and the action-process-object-schema (APOS) theory were employed to examine mental construction
    the 19 purposively selected PMTs that responded to a 90-minute simple logarithm research task (LRT) made while
    solving problems. Analysis of task scripts using percentage score forms the basis of the qualitative phase of the
    research. Individual interview was useful to elicit PMTs’ views and perceptions of their encountered difficulties in
    solving LRT problems. One common difficulty was proving the logarithmic equation. This highlights gaps in PMTs’
    prior knowledge of logarithmic concepts and basic rules. Implications of the findings for PMT subject competency
    were discussed.