Style of teaching/learning mathematics: by proofs of theorems only?

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Discussion Overview

The discussion revolves around different methods of teaching and learning mathematics, particularly focusing on the Moore method, which emphasizes students proving theorems themselves. Participants explore the effectiveness and challenges of this approach compared to more traditional methods, including "chalk and talk" and problem-solving strategies.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants identify the method of forcing students to prove theorems as the Moore method, noting its focus on student-led discovery.
  • Concerns are raised about the Moore method's effectiveness, with one participant recalling that it may lead to students learning incorrect answers through experimentation.
  • Another participant argues that mathematics is inherently deductive and that inductive methods, like those used in the Moore method, are flawed.
  • Some participants advocate for a combination of direct instruction ("chalk and talk") and active problem-solving, suggesting that this approach may better support deeper understanding.
  • There are mentions of the educational community's shift in perspective regarding teaching methods, with some expressing skepticism about modern competence-oriented approaches.
  • Participants share personal experiences with different teaching styles, highlighting the importance of mathematical maturity for methods like the Moore method.
  • One participant emphasizes that learning to solve tough problems requires independent effort, suggesting that guidance from teachers is valuable but not a substitute for student initiative.

Areas of Agreement / Disagreement

Participants express a range of opinions on the effectiveness of various teaching methods, with no clear consensus on the superiority of one approach over another. Disagreements persist regarding the appropriateness of the Moore method and the balance between direct instruction and student-led learning.

Contextual Notes

Some participants note that the Moore method may not be suitable for all educational levels, particularly for students lacking sufficient mathematical maturity. Additionally, there are concerns about the potential for students to internalize incorrect concepts when learning through experimentation.

  • #31
martinbn said:
The very idea of the method. Moor (sic) puts a statement on the board and waits for the students to prove it. He does not move on until it is done, and he only shows what is wrong with their attempts but doesn't give hints.
Seems to me that showing that some work is wrong is a pretty powerful hint.
 
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  • #32
martinbn said:
The very idea of the method. Moor puts a statement on the board and waits for the students to prove it. He does not move on until it is done, and he only shows what is wrong with their attempts but doesn't give hints.
As I experienced the Moore method (as used by one of Moore's students), the class is asked to prove or disprove statements. They don't know in advance whether a statement should be proven or disproven. They get experience in giving counterexamples.

In my opinion, the Moore method places a great demand on the instructor's ability to organize the subject matter so the class proceeds at an appropriate pace. It doesn't suit instructors who may have an encyclopedic knowledge of their field but don't have a vision of it as a sequence of inquiries and deductions. Perhaps there are fields of study where nobody has such a vision. And there may be mathematical results created by some genius that nobody else can understand as a step-by-step sequence of inquiries performed by mere mortals.

In addition to the general objections that have been raised against the method in this thread, there are some mundane ones. I think Moore (R. L. Moore) applied the method to teaching point set topology ,which is not everyone's favorite mathematics and did not use terminology completely matching that used by modern texts. Also (the web says) that R. L. Moore supported segregation and refused to admit black students to his classes. So a method associated with his name is tarnished by that.
 
  • #33
Yes, " Moore Spaces" , in Topology, are named after him :

Screenshot_20230917_141445_Samsung Internet.jpg

And , as per Stephen Tashi's post, we have the issue of whether we separate the artist's/author's work from their personal lives.
 
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