We present and discuss initiatives to develop source-centered teaching materials in history of ma... more We present and discuss initiatives to develop source-centered teaching materials in history of mathematics for upper secondary education, aiming at meeting the objective of the Danish curriculum to make history of mathematics relevant. To this end we present the design template for such multi-purpose materials we developed, which allows devising materials neither too superficial nor too specialized, and we address the constraints on and affordances of historical sources in adapting to teaching objectives. It includes differentiation and scalability for using historical sources, and provides opportunity for interdisciplinary teaching, another requirement for Danish upper secondary education. We also report on (i) the recent application of our design approach to develop such source-centered materials in collaboration with small groups of dedicated teachers, and (ii) students’ positive response to the inquiry-driven teaching based on this material.
Mathematicians appear to have quite high standards for when they will rely on testimony. Many mat... more Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the proof contains no substantial errors increases because different experts will validate the proof in different ways depending on their background knowledge and individual preferences. If this is correct, there is much to be gained for a mathematician from requiring that a number of experts have checked the proof of p before she will rely on p in her own proofs without checking the proof of p. In this way a mathematician can protect her own work and the work of others from errors. Our argument thus provides an explanation for mathematicians’ attitude towards relying on testimony.
Just like any other cultural group, mathematicians like to tell stories. We tell heroic stories a... more Just like any other cultural group, mathematicians like to tell stories. We tell heroic stories about famous mathematicians, to inspire or reinforce our cultural values, and we encase our results in narratives to explain how they are interesting and how they relate to other results. We also tell stories to convince others that our results are valid, and preferably also to explain why they are true. These stories are what you know as "proofs".
Med dette nummer er Stenomusen udkommet i 80 udgaver. I den anledning fortaeller en litteraturhis... more Med dette nummer er Stenomusen udkommet i 80 udgaver. I den anledning fortaeller en litteraturhistoriker og en matematikhistoriker om tallet 80, spejlsymmetri og matematiske finurligheder.
We present and discuss initiatives to develop source-centered teaching materials in history of ma... more We present and discuss initiatives to develop source-centered teaching materials in history of mathematics for upper secondary education, aiming at meeting the objective of the Danish curriculum to make history of mathematics relevant. To this end we present the design template for such multi-purpose materials we developed, which allows devising materials neither too superficial nor too specialized, and we address the constraints on and affordances of historical sources in adapting to teaching objectives. It includes differentiation and scalability for using historical sources, and provides opportunity for interdisciplinary teaching, another requirement for Danish upper secondary education. We also report on (i) the recent application of our design approach to develop such source-centered materials in collaboration with small groups of dedicated teachers, and (ii) students’ positive response to the inquiry-driven teaching based on this material.
Mathematicians appear to have quite high standards for when they will rely on testimony. Many mat... more Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the proof contains no substantial errors increases because different experts will validate the proof in different ways depending on their background knowledge and individual preferences. If this is correct, there is much to be gained for a mathematician from requiring that a number of experts have checked the proof of p before she will rely on p in her own proofs without checking the proof of p. In this way a mathematician can protect her own work and the work of others from errors. Our argument thus provides an explanation for mathematicians’ attitude towards relying on testimony.
Just like any other cultural group, mathematicians like to tell stories. We tell heroic stories a... more Just like any other cultural group, mathematicians like to tell stories. We tell heroic stories about famous mathematicians, to inspire or reinforce our cultural values, and we encase our results in narratives to explain how they are interesting and how they relate to other results. We also tell stories to convince others that our results are valid, and preferably also to explain why they are true. These stories are what you know as "proofs".
Med dette nummer er Stenomusen udkommet i 80 udgaver. I den anledning fortaeller en litteraturhis... more Med dette nummer er Stenomusen udkommet i 80 udgaver. I den anledning fortaeller en litteraturhistoriker og en matematikhistoriker om tallet 80, spejlsymmetri og matematiske finurligheder.
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Papers by Henrik Kragh Sørensen