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  • 1.  What does "rigor" mean to you?

    Posted 04-12-2022 11:45

    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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  • 2.  RE: What does "rigor" mean to you?

    Posted 04-13-2022 10:17
    I think too many adults, and too many math programs, think of "rigor" in terms of adult understanding and vocabulary. Then they create problems that are rigorous to a college student, but near impossible for a middle or high school student who is encountering the topic for the first time. I also find that too many programs think of rigor in terms of mixing topics or question types (i.e., every homework problem has a slightly new step or a different look). This doesn't give kids time to master any of the problems, and they push through with a lack of confidence.

    I think true rigor comes from moving a student from Point A to Point E, with Point A defined by the student, not by the topic.

    Thanks for asking!

    Nora

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    Honora Wall
    Osage IA
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    Original Message


  • 3.  RE: What does "rigor" mean to you?

    Posted 04-14-2022 00:42
    Rigor is taking those difficult concepts and challenges and make sense of it. I could go on but that is rigor. The students must have opportunities to define the  problem (world issues in their community), find logical solutions that make sense, and try to make a difference in their community, home life, or even the city.

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    Lorna Randle
    Houson TX
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    Original Message


  • 4.  RE: What does "rigor" mean to you?

    Posted 04-14-2022 09:31
    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


  • 5.  RE: What does "rigor" mean to you?

    Posted 04-14-2022 10:30
    The first time I saw the term "rigor" in education was in the front matter of State Standards for Mathematics.  "Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades."  The source goes on to explain that educators will need to "pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skills and fluency, and application."  I picture rigor as a three-legged stool with each leg representing one of the aspects of rigor mentioned.  .  

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    Denise Porch
    Union Grove AL
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    Original Message


  • 6.  RE: What does "rigor" mean to you?

    Posted 04-14-2022 14:11
    Rigor means 'comprehensive.'  In this respect, mathematics in an elementary grade
    can be rigorous.  In a sense, it is 'all things considered' especially the underpinnings
    of the primary objective or standard and not just the 'how to' portion of the topic.

    And in being comprehensive, it helps the learners to develop "Productive Persistence"
    to keep their focus even if there are 'bumps in the road.'

    Students may see 'proof-based' rigorous courses as being pedantic.  And this can
    create two groups, 'those who do' and 'those who don't' take more mathematics.

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    Frank Gardella
    Associate Professor
    Hunter College
    New York, NY
    fgardell@hunter.cuny.edu
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    Original Message


  • 7.  RE: What does "rigor" mean to you?

    Posted 04-14-2022 16:49
    As a group of math consultants working with their state math consultant, we have had many discussions on the word "rigor" and what it looks and sounds like.  In an effort to define rigor as concisely as possible, this is what we have so far:  
    "Mathematical Rigor is achieved when students are able to select and use appropriate processes  , then communicate their ideas and reasoning with clarity and precision by using the appropriate mathematical symbols and language."
    This is a draft and the truth is that it may be impossible to confine rigor to a one sentence statement.


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    Linda Null
    Mathematics Consultant
    Southeast Missouri State Univ
    Cape Girardeau MO
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    Original Message


  • 8.  RE: What does "rigor" mean to you?

    Posted 04-21-2022 11:20
    This question, for me, is like that very old tale of asking a group of blind men to describe an elephant when all of them are positioned at different places around the elephant. I do know when an problem or task isn't rigorous; and for me that would be when most students can reach the answer or completion without much mental effort and/or work on paper. On the other side of that statement is the issue of too much "rigor" which has already been described in another response, where many students can't even find ways to start the problem.

    I think a rigorous problem or task is one for which students should already have an adequate toolbox of math skills and concepts to not only begin but also complete the problem or task, in ways that are possibly, but not necessarily, different from the previous routines of their classroom assignments. That may mean such things as solving an equivalent equation to 2 + x > 4, by moving the placement of the variable 4 < 2 + x, to see how students use their knowledge of math in its solution.

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    Penelope Tolle
    teacher, retired
    Pleasureville, KY
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    Original Message