Transcript Defining and Implementing Quantitative Literacy Programs Rick Gillman Valparaiso University [email protected] What is Quantitative Literacy? A A A A “You know it when you see it.” Definition Perspective Problems Perspective Curriculum Perspective Syllabus Perspective And,

Defining and Implementing
Quantitative Literacy
Programs
Rick Gillman
Valparaiso University
[email protected]
What is Quantitative Literacy?
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“You know it when you see it.”
Definition Perspective
Problems Perspective
Curriculum Perspective
Syllabus Perspective
And, last, my Perspective
From a definition perspective…
CUPM Definition
Every college graduate should be able to apply simple
mathematical methods to the solution of real-world
problems. The college graduate should be expected
to have deeper and broader experiences than those
who only graduate from high school and that the level
of sophistication and maturity of thinking expected
should extend to reasoning which is commensurate
with the college experience.
Steen’s 3 Dimensions
 elements of QL such as: confidence with mathematics,
cultural appreciation, interpreting data, logical
thinking, making decisions, mathematics in context,
number sense, practical skills, prerequisite
knowledge, and symbol sense;
 areas of life utilizing expressions of QL, such as:
citizenship, culture, education, professions, personal
finance, personal health, management, and work;
and,
 skills needed for QL, such as: arithmetic, data,
computers, modeling, statistics, chance, and
reasoning
SIGMAA QL Definition
Quantitative literacy (QL) can be described as 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. As with reading and writing literacy,
quantitative literacy is a habit of mind that is best
formed by exposure in many contexts.
From a problems perspective...
Bill Brigg’s Problems
Suppose that the United States government
decided to institute a national lottery, the
proceeds of which would be used to retire the
federal debt. Based on information that you
gather about lottery finances, estimate how
much money could be raised (after expenses
and prizes) each week in a national lottery.
How long would it take to pay off the federal
debt assuming that the budget is exactly
balanced every year in the future? Do you
feel that this is a feasible strategy to pay off
the federal debt?
The following ballot initiative appeared before Colorado
voters in 1992:
Shall there be an amendment to the Colorado constitution to
prohibit the state of Colorado and any of its political subdivisions
from adopting or enforcing any law or policy which provides that
homosexual, lesbian, or bisexual orientation, conduct, or
relationships constitutes or entitles a person to claim any minority
or protected status, quota preferences, or discrimination?
What does a yes vote mean?
U Mass, Boston
In the November 25, 2003 edition of the Boston Globe,
an article ran with the headline “Colleges trail prisons
in funds”. The following is taken from that article.
“For the first time in 35 years, Massachusetts is spending more on prisons
and jails than on public higher education, according to a report released
yesterday. (The 2004) state budget included $816 million in appropriations
for campuses and student financial aid, and $830 million for prisons and
jails, said the report from the Massachusetts Taxpayers Foundation. Deep
cuts to state spending on higher education have left the system of state
colleges and universities in ‘profound’ disarray, the report said, citing two
eras of deep cuts that reduced state support to the same level as three
decades ago when adjusted for inflation. Higher education appropriations
were cut 29 percent between 1988 and 1992, and 27 percent between 2001
and 2004. Spending on higher education dropped from 6.5 percent of the
state budget at its peak in fiscal 1988 to less than 3.5 percent for the 2004
fiscal year, the report said.”
Using information in the article, find the following:
What was the amount budgeted by the legislature for
higher education in 2004?
Estimate the total state budget in 2004. Show your
work.
The portion of the state budget allocated for higher
education has decreased from ______ % in fiscal
1988 to ______% in fiscal 2004. Calculate the
relative (percentage) change in the portion allocated
to higher education between fiscal 1988 and fiscal
2004 and then write your answer using a complete
sentence. Show your work.
Hollins University
American Social History
From a curriculum
perspective...
CUPM Report
The core of the program is a two-tiered system
consisting of a “foundations” course usually taken
during the first or second year and “infusion” or
applied courses taken in the latter years of
undergraduate study. It is anticipated that the
foundation course or courses would usually, but not
necessarily, be offered by the mathematics
department. The courses in the second tier of the
program would be offered by disciplines outside of
mathematics (frequently within the student’s
majors) which would utilize the foundational skill
previously developed to address problems of
interest to the students in context.
Juniata College...
 QS courses seek to instill basic competence in
statistics: sampling, data organization and
representation, measures of central tendency,
measures of dispersion, and elementary probability
concepts.
 QM courses offer an understanding of mathematics:
including such topics as percentages, ratios,
proportionality, rates of change, linear functions and
systems in two unknowns, but the true essence is a
combined algebraic, graphical, and numerical
approach to problem solving and an emphasis on
word problems.”
Macalester College...
 Chance: statistical hypothesis
testing, sampling, experimental
design, measures of correlation.
 Change: percentages and rates;
marginal versus average rates;
linear versus exponential growth;
importance of units; estimation.
 Trade-offs: cost/benefit and
cost/effectiveness analysis; other
mathematical techniques for
comparison.
From a syllabus perspective...
DePaul University...
 Week 1: Absolute and Relative Quantities;
Introduction to Excel
 Week 2: Estimation and Percentages
 Week 3: Making and Interpreting Graphs
 Week 4: Applied Interdisciplinary Module
 Week 5: Introduction to Mathematical Modeling
and Linear Models in Particular
 Week 6: Exponential Modeling
 Week 7: Basic Descriptive Statistics and
Correlation
 Week 8 and 9: Additional Applied Module or
Modules
 Week 10: Presentations
Macalester College...
QMPPS syllabus
Virginia Commonwealth U...
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unit analysis
interpretation of charts & graphs
proportional reasoning
counting principles
general percents
percent increase or decrease
the use of mathematical formulas
average
exponential growth
My Perspective...
(or, more accurately, my observations
and conclusions about the status of
the QL movement.)
Delivery formats
 Large Schools: a course in the math
dept
 Mid size schools: an array of specified
courses
 Liberal Arts: Integrated coursework
(mostly) in the social sciences.
Institutional fit
 Technical schools have high end
expectations (Farmindale)
 Liberal Arts, selective (Macalester)
 Open enrollment public (U Mass)
Mathematical skills
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Elementary Logic
Finance and Interest
Descriptive Statistics
Finite Probability
Change
Modeling w/ linear and exp. ftns
Estimation and Approximation
Problem Solving
Outstanding Issues
 How much can actually be done in a
math course?
 Do students completing a calculus
course have these skills and apply
them?
 How is a QL course distinct from a
Liberal Arts math course?
The MAJOR gap in our work…
There are no benchmark standards for
achievement at any level.
How do we assess QL achievement
across disciplines?
Thank you.