Title: Aspects of the Nature and State of Research in Mathematics Education

This paper offers an outline and a characterisation of the didactics of mathematics, alias the science of mathematics education, as a scientific and scholarly discipline. It further presents a number of major, rather aggregate findings in the discipline, including \textsl{the astonishing complexity of mathematical learning}, \textsl{the key role of domain specificity}, \textsl{obstacles produced by the process-object duality}, \textsl{students' alienation from proof and proving}, and \textsl{the marvels and pitfalls of information technology in mathematics education}.

1991 Mathematics Subject Classification: 00A35, 00--02

Keywords and Phrases: the didactics of mathematics, mathematics education research

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