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Interesting read. Though Socratic method much? The writer uses leading questions[1] as a primary expository method, directing the kid towards conclusions that "

Interesting read. Though Socratic method much? The writer uses leading questions[1] as a primary expository method, directing the kid towards conclusions that "should" be made within the proposed system, rather than merely exposing a small set of rules and letting the child freely explore their consequences. All the talk about the different infinities felt that way. This leading style may be good for teaching the history of mathematics, i.e. introducing concepts that have been relevant to solve problems in the past. But for teaching math skills I prefer methods where a problem is stated, and the student is left to build their own abstractions about it; the IOUs and thermometer examples were more in this line. This competence will prove more useful when solving new problems than merely following the trodden path of already invented mathematics. [1] https://en.wikipedia.org/wiki/Leading_question https://en.wikipedia.org/wiki/Leading_question

jmilloy 10y ago
I think it's noteworthy that the article you point to pertains to common law and testimony, rather than to philosophy, pedagogy, or education. When a student freely explores a concept, that clearly demonstrates a higher ability or skill in mathematics. But "leading questions" are scaffold to show the student how to explore and build abstractions, and most will have to learn how to do that from example.
- TuringTest 10y ago
  The Wikipedia article may be primarily written about legal cases, but leading questions appear in many other contexts. In psychology and interviews they're often advised against, as they induce a precise answer and thus make it hard to learn about the subject of study, instead reinforcing the interviewer preconceptions; in user interface design they can produce the wrong conclusions about how easy an interface is to use. Leading questions have their use in education, but as the other commentator below points out, the child might be giving the answer that the questioner wants to hear, rather than showing a true understanding of the topic. Having a stated problem to solve may prevent that, as the child can instead answer the question in a way that solves the problem.

jmilloy 10y ago

I think it's noteworthy that the article you point to pertains to common law and testimony, rather than to philosophy, pedagogy, or education. When a student freely explores a concept, that clearly demonstrates a higher ability or skill in mathematics. But "leading questions" are scaffold to show the student how to explore and build abstractions, and most will have to learn how to do that from example.

TuringTest 10y ago
The Wikipedia article may be primarily written about legal cases, but leading questions appear in many other contexts. In psychology and interviews they're often advised against, as they induce a precise answer and thus make it hard to learn about the subject of study, instead reinforcing the interviewer preconceptions; in user interface design they can produce the wrong conclusions about how easy an interface is to use. Leading questions have their use in education, but as the other commentator below points out, the child might be giving the answer that the questioner wants to hear, rather than showing a true understanding of the topic. Having a stated problem to solve may prevent that, as the child can instead answer the question in a way that solves the problem.