Quantitative literacy?

We, as mathematicians, really appreciate definitions — concise and consistent definitions.

What is ‘quantitative literacy’?  How does it differ (if it does) from ‘mathematical reasoning’?

This post focuses on ‘quantitative literacy’ to clarify my own thinking.  Since mathematics is the set of sciences of quantities, using ‘quantitative’ instead of ‘mathematical’ does not necessarily change the meaning.  However, the use of the word ‘quantitative’ implies that we might emphasize more the application of mathematics, rather than the structure of the sciences of mathematics.

To many people, ‘quantitative’ will tend to suggest the science of arithmetic (known quantities) rather than other mathematics.   When I look at courses that include quantitative in the title, I generally see applications of arithmetic … with perhaps a little basic geometry.  Only occasionally do I see statistics in such a course, and I have yet to see calculus included.  Since the science of calculus involves quantities under change, this seems ironic.  Are the concepts of calculus so advanced or obscure that students in a general education math class can not understand them?

I am concluding that I would prefer ‘mathematical’ to the ‘quantitative’ — not that I want to have the theory of mathematics exclude the application of the mathematics.  Rather, I want us to focus on multiple mathematics, not just arithmetic and some geometry.

How about the word ‘literacy’?  This word is problematic, since the synonyms include ‘knowledge’, ‘learning’ and ‘education’.   However, we can overcome this problem by being precise and consistent in our definition.  Perhaps we can define ‘literacy’ to mean ‘understands and can apply basic concepts’, as a parallel to the language literacy definition (‘can read and write’).  With that definition, I rather like the word ‘literacy’ appended to mathematical.

Of course, we have much work to do before we KNOW what ‘mathematical literacy’ means.  Which mathematics? What are the basic concepts of the ones we include?  Our professional community needs to deal with these questions, as many of our colleges have shifted away from a pre-calculus/calculus type of general education course … and towards a reasoning/literacy type of course.  Much valuable and creative work is being done; however, we need to develop some shared conceptions of this type of curriculum.  A lack of shared curricular concepts creates problems for articulation and transfer, and causes us to develop this part of the profession in more isolation than would be ideal.

 
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2 Comments

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  By David Graser, October 26, 2011 @ 3:44 pm

  Jack

  I saw your posting to mathedcc. I appreciate your posts, but what is wrong with the descriptions of these terms and the characteristics of them in BC?
  See page 39 of http://beyondcrossroads.amatyc.org/doc/PDFs/BCCh6.pdf . I am pretty comfortable with what is there and I am guessing many others are too since it was ratified by the Delegate Assembly of AMATYC a few years ago.

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  By Jack Rotman, October 27, 2011 @ 1:07 pm

  David:
  Thanks for the comment … and the question. There are several reasons why the QL definition in “BC” are not adequate, starting with the fact that few of us make use of BC in any way. In the case of the QL definition, it suffers the same fate as many definitions written by committee — it ends up including so much that it is hard to see what is left out. I find the BC definition to be not practical in the context of designing curriculum. I would be surprised if there are many posts on the discussion that refer to BC.
  As you know, I am involved with two projects that deal with this QL stuff (New Life, and the Carnegie Pathways). When we looked at the resources on QL, there seemed to be no professional consensus on what QL is (or QR or Mathematical Reasoning); the BC wording is heavily influenced by the ‘MAD’ materials (Mathematics and Democracy), but I do not find that the community sees this as a good implementation of QL.
  Essentially, I wanted to start the discussion to see if we could move closer to having a shared and workable definition of an idea and about the language to use for it. Personally, I do not like ‘QL’ and prefer ‘ML’, with the hope that students will experience a scientific treatment, as opposed to a collection of interesting applications. However, the major thing is how we (as a community) see this. In spite of the BC definitions, and others like it in other documents, we do not have much consistency across colleges for this type of general education mathematics. I am hoping that there is enough discussion that we can get more consistency, and therefore more authority, in this trend for general mathematics at college.
  I’d encourage you to raise your question to mathedcc — it ‘s a good question, and people’s answers might be quite helpful.

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