4 ms·

Appreciating Mathematical Structure for All (2009) [pdf]

15 points by poindontcare 12y ago

marktangotango 12y ago
I typically read math or computer science papers, so reading a paper like this is very odd. The paper is about mathematics education and the authors talk about the importance of encouraging 'structural thinking' in students. It's all very hand wavy, there is no introductory section outlining what the paper is about, no definitions, and no summary. There is a conclusion which is just as hand wavy as the rest. Very odd to get a glimpse into other fields this way.
- keithpeter 12y ago
  "We first consider some recent research that supports this view and then go on to argue that unless students are encouraged to attend to structure and to engage in structural thinking they will be blocked from thinking productively and deeply about mathematics. We provide several illustrative cases in which structural thinking helps to bridge the mythical chasm between conceptual and procedural approaches to teaching and learning mathematics. Finally we place our proposals in the context of how several writers in the past have attempted to explore the importance of structure in mathematics teaching and learning." This is about mathematical education rather than programming or mathematics. A different subject, therefore different 'rules of engagement'. As a practical example of the problem that the authors are trying to confront, find half a dozen early teenagers and ask them to explain to you why 7 - - 3 = 10. Disclaimer: I have not read this 22 page paper in detail yet but the quote from the abstract above suggests that I will and that I will find it useful.
- gohrt 12y ago
  > no definitions, "We take mathematical structure to mean the identification of general properties which are instantiated in particular situations as relationships between elements or subsets of elements of a set." In case you missed it (it's the first sentence of the abstract), it's also repeated as the first sentence of the paper. Compare to, say, a paper published by a well-respected famous mathematician: https://www.renyi.hu/~p_erdos/1989-39.pdf https://www.renyi.hu/~p_erdos/1989-39.pdf
  - marktangotango 12y ago
    I qualify that as 'hand wavy' because none of properties, instantions, or situations are defined, and/or are not well known mathematical concepts as elements and sets are.

15 points by poindontcare 12y ago

I typically read math or computer science papers, so reading a paper like this is very odd. The paper is about mathematics education and the authors talk about the importance of encouraging 'structural thinking' in students. It's all very hand wavy, there is no introductory section outlining what the paper is about, no definitions, and no summary. There is a conclusion which is just as hand wavy as the rest. Very odd to get a glimpse into other fields this way.

keithpeter 12y ago
"We first consider some recent research that supports this view and then go on to argue that unless students are encouraged to attend to structure and to engage in structural thinking they will be blocked from thinking productively and deeply about mathematics. We provide several illustrative cases in which structural thinking helps to bridge the mythical chasm between conceptual and procedural approaches to teaching and learning mathematics. Finally we place our proposals in the context of how several writers in the past have attempted to explore the importance of structure in mathematics teaching and learning." This is about mathematical education rather than programming or mathematics. A different subject, therefore different 'rules of engagement'. As a practical example of the problem that the authors are trying to confront, find half a dozen early teenagers and ask them to explain to you why 7 - - 3 = 10. Disclaimer: I have not read this 22 page paper in detail yet but the quote from the abstract above suggests that I will and that I will find it useful.
gohrt 12y ago
> no definitions, "We take mathematical structure to mean the identification of general properties which are instantiated in particular situations as relationships between elements or subsets of elements of a set." In case you missed it (it's the first sentence of the abstract), it's also repeated as the first sentence of the paper. Compare to, say, a paper published by a well-respected famous mathematician: https://www.renyi.hu/~p_erdos/1989-39.pdf https://www.renyi.hu/~p_erdos/1989-39.pdf
- marktangotango 12y ago
  I qualify that as 'hand wavy' because none of properties, instantions, or situations are defined, and/or are not well known mathematical concepts as elements and sets are.