5 ms·

They should be taught in their historical context. Calculus was a very practical field, with axioms being discovered, and theories written based on engineering

They should be taught in their historical context. Calculus was a very practical field, with axioms being discovered, and theories written based on engineering need.

wolfgke 11y ago
A strange opinion: Do you also think that programming languages should be taught in the historical context? If not: How do you think mathematics should be taught this way. My opinion is clear: One should teach the material in the best modern understanding that is possible. If this is more complicated but worth it this is perfectly fine and even necessary.
- erichocean 11y ago
  > Do you also think that programming languages should be taught in the historical context? Not the OP, but: yes, absolutely.
  - wolfgke 11y ago
    So instead of teaching C in a semester one should teach you - Fortan - ALGOL 68 - B - BCPL - K&R C (with its historic syntax containing elements that are now disallowed) - C89/C90 - C95 - C99 - C11 and what reasons there were to introduce the changes/extensions? My opinion is clear: Teach the most modern version with its best practises and leave away all the historic baggage that is only of historic importance.
    - gshubert17 11y ago
      This might be good for a "History of Programming Languages" course. To teach programming languages in an historical context, is a different task. While teaching the most modern version with its best practices, one could mention that feature X was first used in language L, for example.
      - wolfgke 11y ago
        > To teach programming languages in an historical context, is a different task. To present the topic in a historical context the students first have to know what was context/standard at that time, under what circumstances the solutions of their time were developed, whether the restrictions still hold etc. In other words: You would have to include half of a "History of Programming Languages" course, since this is surely not common knowledge.
    - mjevans 11y ago
      Some of those can and should be skipped. You're also missing a native assembly language. Programming should be taught from the point of view of writing your own forth interpreter, up through BIOSes, based off of it, then in to higher level languages. Logical composition, however, should be taught inversely. Take a high level language (SQL comes to mind, yes that's high level in some respects!) and teach how to isolate and logically differentiate between elements. However I'm also for the more simple base test first. Show someone a few examples of how to play Mastermind (game), see if it clicks. Show someone basic register algebra, as one labeled context, and then show them VHDL style flow definition statements as another context. Keep the contexts labeled. Anyone that can apply those rules to 'play the games' is probably capable of being a programmer; and anyone that doesn't find it fun probably shouldn't /be/ a programmer.
      - wolfgke 11y ago
        Your approach might make sense: But this is clearly not teaching programming from the historical context.
- yomly 11y ago
  Completely agree with this. I used to marvel/sob quietly at how an entire PhD/lifetime's work could be summarized into a single sentence in a given textbook, but human's single greatest advantage is that we can absorb other people's knowledge and wisdom orders of magnitude faster than it took them to acquire it. A given human life is finite in length and that length is relatively narrow in distribution. We are able to progress as a race as we don't have to waste time relearning how to start fire or engineer a wheel from first principles, much less derive calculus in the absence of other knowledge. If only we could find ways to teach current maths at a younger age, we would faster raise the next generation of mathematicians!
  - wolfgke 11y ago
    In particular your last sentence could come from me. :-)

They should be taught in their historical context. Calculus was a very practical field, with axioms being discovered, and theories written based on engineering need.

wolfgke 11y ago

A strange opinion: Do you also think that programming languages should be taught in the historical context? If not: How do you think mathematics should be taught this way. My opinion is clear: One should teach the material in the best modern understanding that is possible. If this is more complicated but worth it this is perfectly fine and even necessary.

erichocean 11y ago
> Do you also think that programming languages should be taught in the historical context? Not the OP, but: yes, absolutely.
- wolfgke 11y ago
  So instead of teaching C in a semester one should teach you - Fortan - ALGOL 68 - B - BCPL - K&R C (with its historic syntax containing elements that are now disallowed) - C89/C90 - C95 - C99 - C11 and what reasons there were to introduce the changes/extensions? My opinion is clear: Teach the most modern version with its best practises and leave away all the historic baggage that is only of historic importance.
  - gshubert17 11y ago
    This might be good for a "History of Programming Languages" course. To teach programming languages in an historical context, is a different task. While teaching the most modern version with its best practices, one could mention that feature X was first used in language L, for example.
    - wolfgke 11y ago
      > To teach programming languages in an historical context, is a different task. To present the topic in a historical context the students first have to know what was context/standard at that time, under what circumstances the solutions of their time were developed, whether the restrictions still hold etc. In other words: You would have to include half of a "History of Programming Languages" course, since this is surely not common knowledge.
  - mjevans 11y ago
    Some of those can and should be skipped. You're also missing a native assembly language. Programming should be taught from the point of view of writing your own forth interpreter, up through BIOSes, based off of it, then in to higher level languages. Logical composition, however, should be taught inversely. Take a high level language (SQL comes to mind, yes that's high level in some respects!) and teach how to isolate and logically differentiate between elements. However I'm also for the more simple base test first. Show someone a few examples of how to play Mastermind (game), see if it clicks. Show someone basic register algebra, as one labeled context, and then show them VHDL style flow definition statements as another context. Keep the contexts labeled. Anyone that can apply those rules to 'play the games' is probably capable of being a programmer; and anyone that doesn't find it fun probably shouldn't /be/ a programmer.
    - wolfgke 11y ago
      Your approach might make sense: But this is clearly not teaching programming from the historical context.
yomly 11y ago
Completely agree with this. I used to marvel/sob quietly at how an entire PhD/lifetime's work could be summarized into a single sentence in a given textbook, but human's single greatest advantage is that we can absorb other people's knowledge and wisdom orders of magnitude faster than it took them to acquire it. A given human life is finite in length and that length is relatively narrow in distribution. We are able to progress as a race as we don't have to waste time relearning how to start fire or engineer a wheel from first principles, much less derive calculus in the absence of other knowledge. If only we could find ways to teach current maths at a younger age, we would faster raise the next generation of mathematicians!
- wolfgke 11y ago
  In particular your last sentence could come from me. :-)