Evolution of my interest
in QL & NAC.

What is QL/QR/Numeracy
(QA = Quantitative Analysis) Some definitions:

"The heart of quantitative literacy is real world problem solving--the use of mathematics in everyday life, on the job, and as an intelligent citizen. Problem solving must be both mathematically defensible and useful in the real world" -Henry Pollak, applied mathematician

"..an aggregate of skills, knowledge, beliefs, dispositions, habits of mind, communication capabilities, and problem solving skills that people need in order to engage effectively in quantitative situations arising in life and work" -Policy Research Initiative, Statistics Canada, 2000

"[Elements include] confidence in mathematics, cultural appreciation, interpreting data, logical thinking, making decisions, mathematics in context, number sense, practical skills, prerequisite knowledge, symbol sense" -Lynn A. Steen, The Case for Quantitative Literacy (Mathematics and Democracy: The Case for Quantitative Literacy)

"an individual's capacity to identify and understand the role that mathematics plays in the world, to make well-founded mathematical judgments and to engage in mathematics in ways that meet the needs of that individual's current and future life as a constructive, concerned and reflective citizen" -Programme for International Assessment (Organization for Economic Cooperation and Development, 2000)

Above From: http://www-math.cudenver.edu/~wbriggs/qr/whatisit.html

Some Topics central to QL

QL is "not merely a set of skills" (see below) yet some topics are "generally accepted":  ratios, percentages, probabilities, interpretation of information presented in graphical form, the language of statistics" (Charlotte Chell, review of "Achieving Quantitative Literacy", MAA online)

Also: logical inference ( (A⇒B) and (¬ A) does not imply ¬B etc), estimation skills comfort with back-of-envelope calculations, comfort and facility working with large numbers, modeling, interpretation of graphs of functions (population growth, stock price increases, etc, plus bar graphs etc "graphical form" above)

"Quantitative literacy can be defined as the level of mathematical knowledge and skills required of all citizens. It includes the ability to apply aspects of mathematics (including measurement, data representation, number sense, variables geometric shapes, spatial visualization, and chance) to understand, predict, and control routine events in people's [own] lives. -John Dossey, mathematics educator


Varieties of QL (one paragraph about each):
  • Yet another def: http://www.msmc.la.edu/pages/2480.asp
  • (More defs (and K-12 focus) in UK, Australia,...)



    Re "Civic Literacy" Above-- Recent news story:

  • Improving scientific literacy would raise public understanding of environmental issues, and: "An innumerate population is less likely to devise good solutions to climate change and a host of other environmental problems than one at home with mathematical and scientific concepts," -Frances Cairncross, President of the British Association for the Advancement of Science (BA), at the BA annual festival. (Monday, 4 September 2006, BBC) http://news.bbc.co.uk/2/hi/science/nature/5312072.stm

    Some Key Distinctions

    1. Numeracy ≠ Mathematics (see above definitions)
      Inter-disciplinary versus a discipline

      QL includes "the ability to apply quantitative ideas in unfamiliar contexts;" and it requires "flexible thinking that adapts readily to new circumstances [p. 24]." Quantitative Literacy involves "sophisticated thinking with elementary mathematics more often than elementary thinking with sophisticated mathematics [p. 9]." QL is not a discipline but a way of thinking, a habit of mind.

      QL "is not simply a set of "basic skills" that can be taught in a single academic course: it is a cumulative knowledge responsive to the dynamics of real life problems and experiential data, requiring the ability to develop appropriate analytic strategies and apply quantitative tools in context" (yet "some topics are generally accepted" -- see above) -Charlotte Chell, review of "Achieving Quantitative Literacy" http://www.maa.org/reviews/achievingQL.html

    2. QL course(s) vs. (e.g. universal) QL requirement


    3. QL-enhancing courses ≠ QL across the curriculum (aka NAC)

    Two key reasons for WAC:

    1. Citizens need exposure to writing in a diverse array of contexts to improve writing skills worth having as engaged citizens, and

    2. Writing can advance deeper learning in those disciplines -- better learning of College Algebra, e.g.

    "I find coversheets most valuable b/c they allow me to go back over my notes and review them. They also clear up any questions I had that week"


    In fact, even students who don't like it ("writing assignments in a math class!?") often recognize item 2.--

    "even though cover sheets are really annoying and time consuming they are helpful in explaining things.."

    Even though its a pain at times, making coversheets each week is a good format to review when studying for a test.


    "The coversheets seem tedious when I am doing them but are helpful for studying for tests so they are working for me



    → "Writing to Learn" can be very effective pedagogy in mathematics.

    Two key reasons for WAC (cont)

    1. Citizens need exposure to writing in a diverse array of contexts to improve writing skills worth having as engaged citizens, and

    2. Writing can advance deeper learning in those disciplines -- better learning of College Algebra, e.g.

    Likewise, NAC has two analogous justifications:

    1'. Citizens need exposure and practice engaging in QA in a diverse array of contexts to improve QL abilities important for engaged citizens and

    2' Secondly, QA (or QR, or the application of QL/Numeracy) can promote and advance deeper learning in non-mathematical academic disciplines -- and help advance the goals of their courses.

  • "Every college graduate should be able to apply simple mathematical methods to the solution of real-world problems" (CUPM Definition) focuses on (1').

  • "the ability to adequately use elementary mathematical tools to interpret and manipulate quantitative data and ideas that arise in individuals' private, civic, and work lives." (1') "It is the obligation of collegiate level mathematics community to take leadership in..assisting colleagues in other disciplines to infuse appropriate QL experiences into their courses... (2') -Rick Gillman, SIGMAA on QL website.
  • Implicitly, (1') includes private & civic life; Course goals advanced in (2') are meant to advance future workplace success as well.
  • "Writing to Learn" → "Engaging-in-QA to Learn"

    NAC (2') inclusion of QA: "intrinsic need" vs. "could benefit from".

    NAC (2') Re: inclusion of QA: "intrinsic need" vs. "could benefit from".

    Proposed Criterion (NAC definition, as rough analogue of WAC) of:

    "Wherever/whenever educationally appropriate" (WEA)

  • Include quantitative thinking in all courses, any time, for any topic where QL/QA, properly used, can advance the course's learning goals.

    What's out there?

  • Incomplete survey (online searches + communication with most prominent mathematicians involved in QL)...still few if any "full" NAC models exist. Among the closest:

  • Quantitative Reasoning Across the Curriculum (Hollins University, 2000-2001 NSF grant; implemented 2001)
    • "QR Basic Skills" pass QR Assessment or Math 100 (Intro to QR) (algebra, graphing, geometry, data analysis and linearity).

    • The QR Applied Skills Requirement-- pass a course designated as a QR applied course (intended: course in student's major or minor)
  • 1994 report by MAA Committee on Undergraduate Mathematics Programs (CUPM), Achieving Quantitative Literacy suggested two-tier program; "foundations" course and an infusion/applied course.

    "In the decade since the report*, a modest number of colleges (are known to) have implemented a variety of QL programs" (http://www.maa.org/reviews/achievingQL.html)

    -Achieving Quantitative Literacy: An Urgent Challenge for Higher Education (Lynn Arthur Steen, MAA notes 2004)

    Pilot Program* at Salisbury University
    (*Somewhere between "Pilot QL" and "Pilot NAC")

  • Worked with two social science faculty members
    • US. Environmental History (in History Dept)
    • Sociology 101 (Sociology Dept)
      (only first half, for Gender class in Sociology, pers. family reasons)
  • Worked with faculty to learn about:
    • Key themes and topics in their discipline & their course(s).
    • What QL skills would help their course? (fairly long list)
    • What content (for which QA would help) did they most want their students to understand more deeply?

    With faculty collaborator's input and review of draft materials, chose to focus on: percents, comfort with large numbers, estimation, some visual/geometric representations, and percents "revisited" (QA areas). Content focus on consumption of fossil fuels (with peek at peak oil), and effects of prices and price increases on cost of living depending on income level (content areas). Three in-depth exploration activities created:

    -Mastering Percents: A Quantitative Literacy Exploration [9 pp.]

    A la "Writing to learn", created "QA to learn" explorations:

    -Budgeting and Percents: It's all Relative [ 7 pp.]
    Pun: both percents and impact of prices as function of socioeconomic class.

    -Rock Oil, Rock Oil, everywhere Let's pause & accord to think.. [9pp.]

    Assessment

    • (Disruption of SOC pilot due to personal family reasons)
    • Student surveys indicate, generally:
    • Activities needed (much!) more time than just 1 class!

    .. Only ~40% of students described activity as "fun" ("only"!?)
    Yet despite that, students self-reported learning/gaining something:

    Percents: 57% of Soc and 73% of Env Hist students: would likely be useful to them in the future as they continue in their discipline (U)

    Budgeting: 73% learned (significant amount of) new mathematics or successfully refreshed (L/R) via the activity; 69% were more comfortable (C) w/that math after the activity ; 60% (U).

    "Rock Oil" (more upper-class students), 53% (L/R), 53% (C) yet a higher figure of 67% (U). in future in their discipline.

    "..my wife instructed me to tell you that she loved the percent package you put together. She happened to see a copy on the desk at home, started reading it, and couldn't put it down (she has a MS in biology, and has taken loads of statistics and a bit of calculus, so she comes to this with quite a bit more background than do I!). In any event, she thought that it was a masterful piece of instructional writing, and that it should be widely published and used She hasn't seen the oil [student activity] yet (though she asked me to bring it home), and I'm sure that she'll like it even more. Thanks for letting me be part of this.." -Prof. Mike Lewis, Dept of History

    Some Environment related Examples

  • Peak Oil groups -- sometimes sloppy with definition
    • Peak supply vs. "when supply won't meet demand"

    • Date of peak oil versus 'peak amount' amount...peak versus "when supply does not meet demand" and other sloppy work (one of speakers re 1billion to 6 billion people..."600% increase"



  • Population increased from 1 billion to 6 billion an increase of ____%"
    [any guesses which common error was made?]


  • "Looking back before humans were around, we note that Earth has had periods of warming (x1) or has had higher CO2 (x2) without any [human fossil fuel burning (y)] 'therefore' [human fossil fuel burning does not cause (x1 or x2)]"

  • x can happen without y (so "x=>y" is false) 'therefore' "y=>x" is false

    Challenges posed by "..Across the Curriculum"

    • Enough interest by faculty in "non-" or less-quantitative" disciplines?

    • Ability of such faculty to teach QA thoroughly and accurately?

    • Will mathematics departments "lose courses"?

    • Time/energy/effort required by interdisciplinary collaboration

    • Challenges of QL interdisciplinary collaboration

      ...including challenges inherent in any educational collaboration e.g. differences in pedagogical goals/philosophy. And add "different department/discipline culture" to that mix...