Quantitative ReasoningDr. Robert Mayes

Science & Math Teaching CenterUniversity of Wyomingrmayes2@uwyo.edu

Why Quantitative Reasoning? STEM (Science, Technology,

Engineering, Math) Remediation Crisis Significant number of high school

graduates need remediation at collegiate level

STEM Pipeline STEM majors not meeting national

needs STEM course dropout rates excessive

Avoidance of quantitative disciplines due to lack of QR competence

Achieving QR Cognitive development in QR

appears to be an intractable problem for education 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 QR is an interdisciplinary concern, so

Departments across K-12 schools and university need to share the burden Qualitative Literacy: writing across the

curriculum Quantitative Literacy – literacy,

interpretation, & reasoning Collegiate leadership void impacts K-

12, not articulated as entry requirement

Cooperative Task PLC – What is quantitative reasoning

in STEM disciplines? Each person in the learning community

is given a minute to identify and explain a characteristic of QR

One clarifying question can be asked – not a correction or challenge

Repeat for each person in the PLC Record four characteristics of QR on

large note sheet and post on wall

Quantitative Reasoning What is QR?

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 Defining QR Why Numbers Count: Quantitative

Literacy for Tomorrow’s America (College Board, 1997)

Mathematics and Democracy: The Case for Quantitative Literacy (National Council on Education and the Disciplines, 2001)

Quantitative Reasoning Components of QR

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 Components of QR

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 hypothesis-building and testing as in science, mathematicizing the problem, analyzing the mathematics, collecting data to verify a prediction of the model

Quantitative Reasoning Components of QR

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 Extensive work in qualitative literacy done

by 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 Babson College: eight competencies in

numeracy: 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 Babson College: eight competencies in

numeracy: 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 fast-changing environment

Familiar with new technology and its impact on business environment and social change

Interdisciplinary Call A Collective Vision: Voice of Partner

Disciplines (Ganter & Barker, 2004) provides insight from other disciplines on appropriate outcomes for mathematics courses. stress mathematical modeling,

conceptual understanding, and critical thinking strategies

increased emphasis on problem solving, communication, and real world applications

QR Examples Critical Thinking

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 Critical Thinking – visualization

Analyze the Venn Diagram to determine what percentage of the population has AB+ blood

A- 8%

A+ 34%

B+ 8%

A B

OO+ 35%

B- 2%AB- 1%

O- 9%

QR Examples Problem Solving – Unit Analysis

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 Problem Solving – Strategies &

Heuristics 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 Number Sense – exponential growth

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 Number Sense – percentages

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 Interpreting Visual Data

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) CRQRSD will extend and complement

the work of the National Numeracy Network by addressing several challenges for implementing quantitative reasoning: 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) 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) 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 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 Math Departments are natural

candidate 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 Willing to focus on data analysis and

modeling

Articulation K-12, Community College, and

University articulation discussions concerning QR 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 MayesUniversity of

WyomingScience and Mathematics

Teaching Centerrmayes2@uwyo.edu