Quantitative Reasoning
Dr. Robert Mayes
Science & Math Teaching Center
University of Wyoming
rmayes2@uwyo.edu
Why Quantitative Reasoning?
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STEM (Science, Technology, Engineering,
Math) Remediation Crisis
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STEM Pipeline
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Significant number of high school graduates
need remediation at collegiate level
STEM majors not meeting national needs
STEM course dropout rates excessive
Avoidance of quantitative disciplines due
to lack of QR competence
Achieving QR
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Cognitive development in QR appears to
be an intractable problem for education
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Transition from High School to College:
courses are currency in which articulation is
measured
QR is rarely explicit in courses across STEM
and is often avoided to reduce student pain
Course by course articulation works against
QR since interdisciplinary topic (Steen, 2004)
QR as Literacy
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QR is an interdisciplinary concern, so
Departments across K-12 schools and
university need to share the burden
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Qualitative Literacy: writing across the
curriculum
Quantitative Literacy – literacy, interpretation,
& reasoning
Collegiate leadership void impacts K-12,
not articulated as entry requirement
Quantitative Reasoning
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What is QR?
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Includes quantitative literacy, numeracy, and
mathematical literacy
Skills needed for citizens of a democratic
society
Reasoning and conceptual understanding
required in the STEM disciplines
Quantitative Reasoning
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Defining QR
Why Numbers Count: Quantitative Literacy
for Tomorrow’s America (College Board,
1997)
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Mathematics and Democracy: The Case
for Quantitative Literacy (National Council
on Education and the Disciplines, 2001)
Quantitative Reasoning
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Components of QR
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Algebra for All: modest ability in reading and
interpreting formulas, understanding graphs, and
solving simple equations
Civic Literacy: understanding need for data, ability to
sort through conflicting claims, skepticism about the
reliability or significance of data, recognizing the
limits of computer models
Computer Mathematics: solving quantitative problems
using standard computer packages
Cultural Literacy: recognize the contributions of
mathematicians to society
Quantitative Reasoning
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Components of QR
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Functional Mathematics: skills needed by ordinary
people in life and work
Instrumental Mathematics: ability to interpret and
apply mathematics and to understand, predict, and
control relevant factors in a variety of contexts
Language of Science: support prospective scientists,
engineers, life sciences, statistics
Mathematical Modeling: process of hypothesisbuilding and testing as in science, mathematicizing
the problem, analyzing the mathematics, collecting
data to verify a prediction of the model
Quantitative Reasoning
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Components of QR
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Problem Solving: the problem and possible solutions
are paramount, skills are secondary
Quantitative Practice: apprenticeship environments in
which mathematics is used and learned by use but
perhaps never explicitly exhibited in words and
symbols
Quantitative Reasoning: emphasizes broad synthesis
of logical, visual, verbal, and computational thinking;
manipulative algebra is incidental to this goal
SCANS Skills: acquiring information, allocating
resources, working with others, improving systems,
and working with technology
National Numeracy Network
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Extensive work in qualitative literacy done by
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Dartmouth College
Babson College
DePaul University
Hollins University
Macalester College
Trinity College
University of Neveda at Reno
Washington Center at Evergreen State College
National Numeracy Network
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Babson College: eight competencies in
numeracy:
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Active listeners and readers, able to acquire,
organize, synthesize, evaluate, interrogate, and
interpret information of all kinds including information
from verbal, numerical, and visual sources
Able to formulate problems, identify opportunities,
construct and test hypotheses, and apply to extend
theory
Adept at establishing criteria, discovering and
weighing alternatives, and using appropriate data to
arrive at rational decisions
Comfortable with the creative process, can tolerate
ambiguity, and are conscious of the limits as well as
the value of rational and logical thought
National Numeracy Network
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Babson College: eight competencies in
numeracy:
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Able to communicate logically and persuasively in
spoken, written, and visual form, including graphs
and tables
Intellectually confident and independent and are able
to make responsible and thoughtful ethical decisions
Adept at doing company, industry, and competitive
analyses; they are able to collect, interpret, and
communicate information with insight and
imagination in an increasingly global and fastchanging environment
Familiar with new technology and its impact on
business environment and social change
Interdisciplinary Call
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A Collective Vision: Voice of Partner
Disciplines (Ganter & Barker, 2004)
provides insight from other disciplines on
appropriate outcomes for mathematics
courses.
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stress mathematical modeling, conceptual
understanding, and critical thinking strategies
increased emphasis on problem solving,
communication, and real world applications
QR Examples
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Critical Thinking
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Is overpopulation a real problem? Modern
technology, especially in bioengineering, will enable
scientists to develop far more efficient agriculture. In
addition advances in irrigation technology, along with
the development of crops that can grow in salt water,
will enable the conversion of much of the world’s
desert wastelands into productive farms. As a result
agribusiness will be able to produce enough food for
at least 50 billion people, about 8 times the current
world population. Provide a logical argument related
to balancing agribusiness and environmental issues.
QR Examples
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Critical Thinking – visualization
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Analyze the Venn Diagram to determine what
percentage of the population has AB+ blood
A
B
A- 8%
A+
34%
O- 9%
AB1%
B- 2%
B+ 8%
O+ 35%
O
QR Examples
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Problem Solving – Unit Analysis
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Measurements of polar ice show that if all the
ice melts, about 25 million cubic kilometers of
water will be added to the oceans, most of it
coming from Antarctica. How much will sea
level rise as a result, given that the total
surface area of the Earth’s oceans is about
340 million square kilometers?
QR Examples
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Problem Solving – Strategies & Heuristics
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In an effort to reduce population growth, in 1978
China instituted a policy that allows only one child per
family. One unintended consequence has been that,
because of a cultural bias toward sons, China now
has many more boys than girls. To solve this
problem some people have suggested replacing the
one-child policy with a one-son policy – if a family’s
first child is a boy, the family has reached its limit,
but if it is a girl the family can have additional
children until one is a boy. How would this affect the
overall birth rate and the number of boys versus
girls?
QR Examples
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Number Sense – exponential growth
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According to the 2000 census, the population
of Albany county is approximately 50,000. A
power company predicts the county’s
population will increase 7% per year while the
county supervisors predict that the population
will increase by 7,500 each year. Which
group predicts the largest population in 10
years?
QR Examples
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Number Sense – percentages
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The percentage of students in a school
passing the PAWS test decreased by 15%
from 2005 to 2006. After worried teachers
redoubled their efforts, the percentage who
passed increased by 15% from 2006 to 2007.
In which of the years was the percentage of
students who passed PAWS the highest,
2005, 2006 or 2007?
QR Example
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Interpreting Visual Data
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The graph below shows the percentage
change in the value of a company’s stock. In
2000 did the stock reach its highest value or
was the stock still increasing in value but
declining after 2000?
Center for Research on Quantitative
Reasoning across the STEM
Disciplines (CRQRSD)
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CRQRSD will extend and complement the
work of the National Numeracy Network
by addressing several challenges for
implementing quantitative reasoning:
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Challenge 1: Need to understand student
development of quantitative reasoning across
the high school and college continuum
Challenge 2: Need to understand how to
assess student progress in development of
quantitative reasoning
Center for Research on Quantitative
Reasoning across the STEM
Disciplines (CRQRSD)
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Challenge 3: Development, implementation,
and analysis of effective measures of
quantitative reasoning across the high school
and college continuum
Challenge 4: Research articulation policies
from high school to college that impact
quantitative reasoning, such as the focus on
preparation for calculus
Center for Research on Quantitative
Reasoning across the STEM
Disciplines (CRQRSD)
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Challenge 5: Research the current status of
quantitative reasoning at the high school,
community college, and college level – what is
the current profile of student’s quantitative
reasoning
Challenge 6: Research appropriate goals and
benchmarks for quantitative reasoning at the
high school, community college, and college
level
Challenge 7: Can quantitative reasoning be
successfully embedded across the disciplines
QR Questions
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What are the enduring QR understandings,
concepts, and processes in STEM disciplines that
students should carry from high school to
college?
What is the appropriate development of
expertise in QR over the high school and college
continuum?
How should college science and mathematics
courses change to build on and extend high
school QR?
How can we improve QR?
What is the impact of QR on increasing students’
engagement in science and mathematics so they
are motivated to study and remain in STEM
disciplines?
Lack of QR Leadership
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Math Departments are natural candidate
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Look on QR as only Quantitative Literacy,
which is considered an inferior lower track
Traditional College Algebra and Calculus for
all versus QR
Statistics Departments could serve
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Willing to focus on data analysis and modeling
Articulation
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K-12, Community College, and University
articulation discussions concerning QR
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Biology Articulation as model (University
Partnership – Audrey Kleinsasser and Director
of Biology Mark Lyford)
Evaluation of student work with QR focus
Determining what QR looks like in STEM
disciplines across the K-16 continuum
Development of QR in STEM Performance
Tasks
Dr. Robert Mayes
University of Wyoming
Science and
Mathematics
Teaching Center
rmayes2@uwyo.edu