At that level,
rigor should not mean proof-based (except with Geometry).
At that level in Algebra, I believe that rigor should mean that all techniques are based upon properties of the real numbers and involve a process which uses those properties. That is
NOT to say that diagrams (such as a rectangle in the case of multiplying polynomials) are not permitted. Diagrams are wonderful. Visual representations are wonderful as well, if they are consistent with the action and not just gimmicks. However, a 'technique' which involves special (based upon the specific case) manual adjustments to what is there and which have no grounding in mathematical principles, are not techniques which are going to bear fruit in future work with algebra. They are 'techniques' which will be forgotten and misapplied.
If the mathematical principles are always involved, then they will eventually become a part of the student; if the principles are typically avoided, then they will always be new and uncomfortable whenever encountered.
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Edward Thome
Chair and Associate Professor of Mathematics
Murray KY
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Original Message:
Sent: 04-12-2022 11:45
From: Tadanobu (Tad) Watanabe
Subject: What does "rigor" mean to you?
Many people have responded to my recent question about Algebra II as a HS graduation requirements, and thank you all who have responded so far. I would still like to hear from others.
But, as I read some of the responses, another question came to my mind - which is the subject of this discussion.
I hear a lot about the importance of "rigor" in a mathematics curriculum, but what does "rigor" mean? Sometimes I wonder if people are simply equating "rigor" with "difficult" or "challenging." I think mathematicians use the word "rigor" in a different sense - a rigorous course is very much a proof-based course.
So, I'm wondering what we mean by "rigor" when we say a math curriculum should be rigorous.
Thanks.
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Tadanobu (Tad) Watanabe
Professor of Mathematics Education
Kennesaw State Univ - Math Dept
Kennesaw GA
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