quantitative reasoning dr. robert mayes science & math teaching center university of wyoming...
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Quantitative ReasoningQuantitative ReasoningDr. Robert MayesDr. Robert Mayes
Science & Math Teaching CenterScience & Math Teaching CenterUniversity of WyomingUniversity of Wyomingrmayes2@uwyo.edurmayes2@uwyo.edu
Why Quantitative Reasoning?Why Quantitative Reasoning?
STEM (Science, Technology, STEM (Science, Technology, Engineering, Math) Remediation CrisisEngineering, Math) Remediation Crisis Significant number of high school Significant number of high school
graduates need remediation at collegiate graduates need remediation at collegiate levellevel
STEM PipelineSTEM Pipeline STEM majors not meeting national needsSTEM majors not meeting national needs STEM course dropout rates excessiveSTEM course dropout rates excessive
Avoidance of quantitative disciplines Avoidance of quantitative disciplines due to lack of QR competencedue to lack of QR competence
Achieving QRAchieving QR
Cognitive development in QR appears to Cognitive development in QR appears to be an intractable problem for educationbe an intractable problem for education Transition from High School to College: Transition from High School to College:
courses are currency in which articulation is courses are currency in which articulation is measuredmeasured
QR is rarely explicit in courses across STEM QR is rarely explicit in courses across STEM and is often avoided to reduce student painand is often avoided to reduce student pain
Course by course articulation works against Course by course articulation works against QR since interdisciplinary topic (Steen, 2004)QR since interdisciplinary topic (Steen, 2004)
QR as LiteracyQR as Literacy QR is an interdisciplinary concern, so QR is an interdisciplinary concern, so
Departments across K-12 schools and Departments across K-12 schools and university need to share the burdenuniversity need to share the burden Qualitative Literacy: writing across the Qualitative Literacy: writing across the
curriculumcurriculum Quantitative Literacy – literacy, Quantitative Literacy – literacy,
interpretation, & reasoninginterpretation, & reasoning Collegiate leadership void impacts K-12, Collegiate leadership void impacts K-12,
not articulated as entry requirementnot articulated as entry requirement
Quantitative ReasoningQuantitative Reasoning
What is QR?What is QR? Includes quantitative literacy, Includes quantitative literacy,
numeracy, and mathematical literacynumeracy, and mathematical literacy Skills needed for citizens of a Skills needed for citizens of a
democratic societydemocratic society Reasoning and conceptual Reasoning and conceptual
understanding required in the STEM understanding required in the STEM disciplinesdisciplines
Quantitative ReasoningQuantitative Reasoning
Defining QRDefining QR Why Numbers Count: Quantitative Why Numbers Count: Quantitative
Literacy for Tomorrow’s AmericaLiteracy for Tomorrow’s America (College Board, 1997)(College Board, 1997)
Mathematics and Democracy: The Mathematics and Democracy: The Case for Quantitative LiteracyCase for Quantitative Literacy (National Council on Education and (National Council on Education and the Disciplines, 2001) the Disciplines, 2001)
Quantitative ReasoningQuantitative Reasoning
Components of QRComponents of QR Algebra for All: modest ability in reading and Algebra for All: modest ability in reading and
interpreting formulas, understanding graphs, interpreting formulas, understanding graphs, and solving simple equationsand solving simple equations
Civic Literacy: understanding need for data, Civic Literacy: understanding need for data, ability to sort through conflicting claims, ability to sort through conflicting claims, skepticism about the reliability or significance of skepticism about the reliability or significance of data, recognizing the limits of computer modelsdata, recognizing the limits of computer models
Computer Mathematics: solving quantitative Computer Mathematics: solving quantitative problems using standard computer packagesproblems using standard computer packages
Cultural Literacy: recognize the contributions of Cultural Literacy: recognize the contributions of mathematicians to societymathematicians to society
Quantitative ReasoningQuantitative Reasoning
Components of QRComponents of QR Functional Mathematics: skills needed by ordinary Functional Mathematics: skills needed by ordinary
people in life and workpeople in life and work Instrumental Mathematics: ability to interpret and Instrumental Mathematics: ability to interpret and
apply mathematics and to understand, predict, apply mathematics and to understand, predict, and control relevant factors in a variety of and control relevant factors in a variety of contextscontexts
Language of Science: support prospective Language of Science: support prospective scientists, engineers, life sciences, statisticsscientists, engineers, life sciences, statistics
Mathematical Modeling: process of hypothesis-Mathematical Modeling: process of hypothesis-building and testing as in science, mathematicizing building and testing as in science, mathematicizing the problem, analyzing the mathematics, the problem, analyzing the mathematics, collecting data to verify a prediction of the modelcollecting data to verify a prediction of the model
Quantitative ReasoningQuantitative Reasoning Components of QRComponents of QR
Problem Solving: the problem and possible Problem Solving: the problem and possible solutions are paramount, skills are secondarysolutions are paramount, skills are secondary
Quantitative Practice: apprenticeship Quantitative Practice: apprenticeship environments in which mathematics is used environments in which mathematics is used and learned by use but perhaps never and learned by use but perhaps never explicitly exhibited in words and symbolsexplicitly exhibited in words and symbols
Quantitative Reasoning: emphasizes broad Quantitative Reasoning: emphasizes broad synthesis of logical, visual, verbal, and synthesis of logical, visual, verbal, and computational thinking; manipulative algebra computational thinking; manipulative algebra is incidental to this goalis incidental to this goal
SCANS Skills: acquiring information, allocating SCANS Skills: acquiring information, allocating resources, working with others, improving resources, working with others, improving systems, and working with technologysystems, and working with technology
National Numeracy NetworkNational Numeracy Network
Extensive work in qualitative literacy done Extensive work in qualitative literacy done byby Dartmouth CollegeDartmouth College Babson CollegeBabson College DePaul UniversityDePaul University Hollins UniversityHollins University Macalester CollegeMacalester College Trinity CollegeTrinity College University of Neveda at RenoUniversity of Neveda at Reno Washington Center at Evergreen State College Washington Center at Evergreen State College
National Numeracy NetworkNational Numeracy Network Babson College: eight competencies in Babson College: eight competencies in
numeracy:numeracy: Active listeners and readers, able to acquire, Active listeners and readers, able to acquire,
organize, synthesize, evaluate, interrogate, organize, synthesize, evaluate, interrogate, and interpret information of all kinds including and interpret information of all kinds including information from verbal, numerical, and visual information from verbal, numerical, and visual sourcessources
Able to formulate problems, identify Able to formulate problems, identify opportunities, construct and test hypotheses, opportunities, construct and test hypotheses, and apply to extend theoryand apply to extend theory
Adept at establishing criteria, discovering and Adept at establishing criteria, discovering and weighing alternatives, and using appropriate weighing alternatives, and using appropriate data to arrive at rational decisionsdata to arrive at rational decisions
Comfortable with the creative process, can Comfortable with the creative process, can tolerate ambiguity, and are conscious of the tolerate ambiguity, and are conscious of the limits as well as the value of rational and limits as well as the value of rational and logical thoughtlogical thought
National Numeracy NetworkNational Numeracy Network
Babson College: eight competencies in Babson College: eight competencies in numeracy:numeracy: Able to communicate logically and persuasively Able to communicate logically and persuasively
in spoken, written, and visual form, including in spoken, written, and visual form, including graphs and tablesgraphs and tables
Intellectually confident and independent and Intellectually confident and independent and are able to make responsible and thoughtful are able to make responsible and thoughtful ethical decisionsethical decisions
Adept at doing company, industry, and Adept at doing company, industry, and competitive analyses; they are able to collect, competitive analyses; they are able to collect, interpret, and communicate information with interpret, and communicate information with insight and imagination in an increasingly insight and imagination in an increasingly global and fast-changing environmentglobal and fast-changing environment
Familiar with new technology and its impact on Familiar with new technology and its impact on business environment and social changebusiness environment and social change
Interdisciplinary CallInterdisciplinary Call
A Collective Vision: Voice of Partner A Collective Vision: Voice of Partner Disciplines (Ganter & Barker, 2004) Disciplines (Ganter & Barker, 2004) provides insight from other disciplines provides insight from other disciplines on appropriate outcomes for on appropriate outcomes for mathematics courses. mathematics courses. stress mathematical modeling, conceptual stress mathematical modeling, conceptual
understanding, and critical thinking understanding, and critical thinking strategiesstrategies
increased emphasis on problem solving, increased emphasis on problem solving, communication, and real world applications communication, and real world applications
QR ExamplesQR Examples
Critical ThinkingCritical Thinking Is overpopulation a real problem? Modern Is overpopulation a real problem? Modern
technology, especially in bioengineering, will enable technology, especially in bioengineering, will enable scientists to develop far more efficient agriculture. scientists to develop far more efficient agriculture. In addition advances in irrigation technology, along In addition advances in irrigation technology, along with the development of crops that can grow in salt with the development of crops that can grow in salt water, will enable the conversion of much of the water, will enable the conversion of much of the world’s desert wastelands into productive farms. As world’s desert wastelands into productive farms. As a result agribusiness will be able to produce enough a result agribusiness will be able to produce enough food for at least 50 billion people, about 8 times the food for at least 50 billion people, about 8 times the current world population. Provide a logical current world population. Provide a logical argument related to balancing agribusiness and argument related to balancing agribusiness and environmental issues.environmental issues.
QR ExamplesQR Examples
Critical Thinking – visualizationCritical Thinking – visualization Analyze the Venn Diagram to determine Analyze the Venn Diagram to determine
what percentage of the population has what percentage of the population has AB+ bloodAB+ blood
A- 8%
A+ 34%
B+ 8%
A B
OO+ 35%
B- 2%AB- 1%
O- 9%
QR ExamplesQR Examples
Problem Solving – Unit AnalysisProblem Solving – Unit Analysis Measurements of polar ice show that if Measurements of polar ice show that if
all the ice melts, about 25 million cubic all the ice melts, about 25 million cubic kilometers of water will be added to the kilometers of water will be added to the oceans, most of it coming from oceans, most of it coming from Antarctica. How much will sea level rise Antarctica. How much will sea level rise as a result, given that the total surface as a result, given that the total surface area of the Earth’s oceans is about 340 area of the Earth’s oceans is about 340 million square kilometers?million square kilometers?
QR ExamplesQR Examples
Problem Solving – Strategies & Problem Solving – Strategies & HeuristicsHeuristics In an effort to reduce population growth, in 1978 In an effort to reduce population growth, in 1978
China instituted a policy that allows only one child China instituted a policy that allows only one child per family. One unintended consequence has been per family. One unintended consequence has been that, because of a cultural bias toward sons, China that, because of a cultural bias toward sons, China now has many more boys than girls. To solve this now has many more boys than girls. To solve this problem some people have suggested replacing problem some people have suggested replacing the one-child policy with a one-son policy – if a the one-child policy with a one-son policy – if a family’s first child is a boy, the family has reached family’s first child is a boy, the family has reached its limit, but if it is a girl the family can have its limit, but if it is a girl the family can have additional children until one is a boy. How would additional children until one is a boy. How would this affect the overall birth rate and the number of this affect the overall birth rate and the number of boys versus girls?boys versus girls?
QR ExamplesQR Examples
Number Sense – exponential growthNumber Sense – exponential growth According to the 2000 census, the According to the 2000 census, the
population of Albany county is population of Albany county is approximately 50,000. A power approximately 50,000. A power company predicts the county’s company predicts the county’s population will increase 7% per year population will increase 7% per year while the county supervisors predict that while the county supervisors predict that the population will increase by 7,500 the population will increase by 7,500 each year. Which group predicts the each year. Which group predicts the largest population in 10 years?largest population in 10 years?
QR ExamplesQR Examples
Number Sense – percentagesNumber Sense – percentages The percentage of students in a school The percentage of students in a school
passing the PAWS test decreased by passing the PAWS test decreased by 15% from 2005 to 2006. After worried 15% from 2005 to 2006. After worried teachers redoubled their efforts, the teachers redoubled their efforts, the percentage who passed increased by percentage who passed increased by 15% from 2006 to 2007. In which of the 15% from 2006 to 2007. In which of the years was the percentage of students years was the percentage of students who passed PAWS the highest, 2005, who passed PAWS the highest, 2005, 2006 or 2007?2006 or 2007?
QR ExampleQR Example
Interpreting Visual DataInterpreting Visual Data The graph below shows the percentage The graph below shows the percentage
change in the value of a company’s change in the value of a company’s stock. In 2000 did the stock reach its stock. In 2000 did the stock reach its highest value or was the stock still highest value or was the stock still increasing in value but declining after increasing in value but declining after 2000?2000?
Center for Research on Quantitative Center for Research on Quantitative Reasoning across the STEM Reasoning across the STEM
Disciplines (CRQRSD)Disciplines (CRQRSD) CRQRSD will extend and complement the CRQRSD will extend and complement the
work of the National Numeracy Network work of the National Numeracy Network by addressing several challenges for by addressing several challenges for implementing quantitative reasoning:implementing quantitative reasoning: Challenge 1: Need to understand student Challenge 1: Need to understand student
development of quantitative reasoning across development of quantitative reasoning across the high school and college continuumthe high school and college continuum
Challenge 2: Need to understand how to Challenge 2: Need to understand how to assess student progress in development of assess student progress in development of quantitative reasoningquantitative reasoning
Center for Research on Quantitative Center for Research on Quantitative Reasoning across the STEM Reasoning across the STEM
Disciplines (CRQRSD)Disciplines (CRQRSD) Challenge 3: Development, Challenge 3: Development,
implementation, and analysis of implementation, and analysis of effective measures of quantitative effective measures of quantitative reasoning across the high school and reasoning across the high school and college continuumcollege continuum
Challenge 4: Research articulation Challenge 4: Research articulation policies from high school to college that policies from high school to college that impact quantitative reasoning, such as impact quantitative reasoning, such as the focus on preparation for calculusthe focus on preparation for calculus
Center for Research on Quantitative Center for Research on Quantitative Reasoning across the STEM Reasoning across the STEM
Disciplines (CRQRSD)Disciplines (CRQRSD) Challenge 5: Research the current Challenge 5: Research the current
status of quantitative reasoning at the status of quantitative reasoning at the high school, community college, and high school, community college, and college level – what is the current profile college level – what is the current profile of student’s quantitative reasoningof student’s quantitative reasoning
Challenge 6: Research appropriate goals Challenge 6: Research appropriate goals and benchmarks for quantitative and benchmarks for quantitative reasoning at the high school, community reasoning at the high school, community college, and college levelcollege, and college level
Challenge 7: Can quantitative reasoning Challenge 7: Can quantitative reasoning be successfully embedded across the be successfully embedded across the disciplinesdisciplines
QR QuestionsQR Questions What are the enduring QR understandings, What are the enduring QR understandings,
concepts, and processes in STEM concepts, and processes in STEM disciplines that students should carry from disciplines that students should carry from high school to college? high school to college?
What is the appropriate development of What is the appropriate development of expertise in QR over the high school and expertise in QR over the high school and college continuum? college continuum?
How should college science and How should college science and mathematics courses change to build on mathematics courses change to build on and extend high school QR?and extend high school QR?
How can we improve QR?How can we improve QR? What is the impact of QR on increasing What is the impact of QR on increasing
students’ engagement in science and students’ engagement in science and mathematics so they are motivated to mathematics so they are motivated to study and remain in STEM disciplines? study and remain in STEM disciplines?
Lack of QR LeadershipLack of QR Leadership
Math Departments are natural Math Departments are natural candidatecandidate Look on QR as only Quantitative Literacy, Look on QR as only Quantitative Literacy,
which is considered an inferior lower trackwhich is considered an inferior lower track Traditional College Algebra and Calculus Traditional College Algebra and Calculus
for all versus QRfor all versus QR Statistics Departments could serveStatistics Departments could serve
Willing to focus on data analysis and Willing to focus on data analysis and modelingmodeling
ArticulationArticulation
K-12, Community College, and K-12, Community College, and University articulation discussions University articulation discussions concerning QRconcerning QR Biology Articulation as model (University Biology Articulation as model (University
Partnership – Audrey Kleinsasser and Partnership – Audrey Kleinsasser and Director of Biology Mark Lyford)Director of Biology Mark Lyford)
Evaluation of student work with QR focusEvaluation of student work with QR focus Determining what QR looks like in STEM Determining what QR looks like in STEM
disciplines across the K-16 continuumdisciplines across the K-16 continuum Development of QR in STEM Performance Development of QR in STEM Performance
TasksTasks
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