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
Some Key Distinctions
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
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"
"even though cover sheets are really
annoying and time consuming they are helpful in
explaining things.."
In fact, even students who don't like it
("writing assignments in a math class!?") often recognize item
2.--
"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.
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.
NAC (2') inclusion of QA: "intrinsic need" → "could
benefit from".
What's out there?
"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
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).
(Recent CNN/Money full article on 100pt changes in Dow boils down
to: percents)
-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.]
-Rock Oil, Rock Oil, everywhere Let's pause & accord to think..
[9pp.]
Assessment
.. Only ~40% of students described activity as 'fun' ("only"!?)
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.
"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.."
can be enormous (IMO)
Likewise, NAC has two analogous justifications:
(*Somewhere between "Pilot QL" and "Pilot NAC")
Three in-depth exploration activities created:
Note money.cnn.com "extra! extra! read all about it:
"100 pts is a smaller percent now than then!"
Pun: both percents and impact of prices as
function of socioeconomic class.
Yet despite that, students self-reported learning/gaining something:
"..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!).
"..Across the Curriculum"
...But payoff in terms of
student learning: