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In this study, we focus on describing the understanding of pre-service mathematics teachers with low and high math anxiety levels of derivative function based on the APOS theory. All 26 pre-service mathematics teachers who had taken calculus courses were given a math anxiety questionnaire then 1 student with low math anxiety level and 1 student with high math anxiety level were selected and given derivative functions tasks and interviewed based on the results of their work. The results showed that the subject with high math anxiety levels were in Action determined derivative function in the form of two-function multiplication by multiplying it distributively first and then derived it using the derivative rule, while the subject with low math anxiety directly used the derivative rule for multiplying two functions. In the Process, all subjects can explain the steps to determine the derivative function. The subject with high math anxiety has not yet reached the object and schema stage but subject with low math anxiety level at Object identified a composition function using the chain rule to determine the derivative of the composition function. In Schema, the subject determined a certain equation of a curve at a point and used several rules

Teacher’s understanding; APOS; Derivative Function; Math Anxiety