...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
Paul HalmosRead
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
Interpretation
What this quote means
Teachers should focus on presenting students with problems to solve rather than just facts to memorize.
In this quote, Paul Halmos emphasizes the importance of engaging students with challenging problems in mathematics rather than solely delivering factual knowledge. This approach encourages critical thinking and deeper understanding, fostering a learning environment where students learn to apply concepts and develop problem-solving skills, which are vital for their growth and success in the subject and beyond.
Themes
EducationTeachingMathematicsProblem-SolvingStudent Engagement
In practice
Example use cases
In a seminar on innovative teaching methods, I would use this quote to explain the importance of problem-based learning.
More from Paul Halmos
All quotes β[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
Paul HalmosRead
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