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fubarobfusco comments on [Link] Why the kids don’t know no algebra - Less Wrong Discussion

21 Post author: GLaDOS 04 July 2012 10:29AM

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Comment author: fubarobfusco 05 July 2012 11:33:43PM 3 points [-]

It seems like part of the problem is that people don't really know or agree what mathematical education is for. If we knew for what reasons or purposes we were teaching everyone math, that might help us figure out what math they should learn.

It seems to me like various purposes for math education include:

  • Teaching students how to work with numerical and geometric quantities — for "real-life" purposes such as making change, planning schedules, and measuring furniture to put in a house;
  • Teaching problem-solving techniques and mathematical intuition — to improve general problem-solving ability as an intellectual skill;
  • Teaching techniques of explicit reasoning and methods of logical proof — such as might be applied to analysis of arguments in everyday life; or in law, politics, or other subjects too;
  • Preparing some students for science, engineering, computing, and other subjects that require particular mathematical techniques (e.g. calculus for physics);
  • Preparing some students (very few!) to become mathematicians.
Comment author: Viliam_Bur 06 July 2012 09:36:17AM 7 points [-]

More generally, people don't even agree what education is for. It could be:

  • preparing people for their future jobs;
  • preserving the knowledge of humankind, maintaining culture;
  • improving people mentally, creating better neighbors and citizen.

Generally, all these goals are considered good, but sometimes they are in conflict, if you try to optimize for one of them too much. For example the first rule, in extreme, would require learning only details related to one's future job, nothing more; but students could learn more details, and have more practice when they finish the school. The second rule, in extreme, would require teaching everyone everything. The third rule requires a value judgement what makes a person good citizen, and in extreme, it would require focusing on those skills and ignoring everything else.

In many discussions about education, one of these ideas is assumed implicitly, and then there is a suggestion how to get closer to this goal... usually at the expense of the remaining goals, which is why other people protest against the suggestion.

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