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The use of history in mathematics teaching depends, either implicitly or explicitly, on some view of the rationale of mathematical development. We suppose that changes in mathematics are made for good reasons, which are simultaneously clarified and tested in the process. Therefore, philosophically comprehended accounts of historical developments are relevant means of conveying to learners the rationale of mathematical concepts and precepts. As a case in point, it will be shown how the genesis and development of complex numbers can be explained on - hence supports - a fallibilist model of ‘trials and tests’. The educational implications of this ‘quasi-experimental’ approach are briefly discussed.