# Quantitative Reasoning

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Quantitative Reasoning. Dr. Robert Mayes Science & Math Teaching Center University of Wyoming rmayes2@uwyo.edu. Why Quantitative Reasoning?. STEM (Science, Technology, Engineering, Math) Remediation Crisis Significant number of high school graduates need remediation at collegiate level - PowerPoint PPT PresentationTRANSCRIPT

Quantitative Reasoning

Quantitative ReasoningDr. Robert MayesScience & Math Teaching CenterUniversity of Wyomingrmayes2@uwyo.edu

Why Quantitative Reasoning?STEM (Science, Technology, Engineering, Math) Remediation CrisisSignificant number of high school graduates need remediation at collegiate levelSTEM PipelineSTEM majors not meeting national needsSTEM course dropout rates excessiveAvoidance of quantitative disciplines due to lack of QR competence

Achieving QRCognitive development in QR appears to be an intractable problem for educationTransition from High School to College: courses are currency in which articulation is measuredQR is rarely explicit in courses across STEM and is often avoided to reduce student painCourse by course articulation works against QR since interdisciplinary topic (Steen, 2004)QR as LiteracyQR is an interdisciplinary concern, so Departments across K-12 schools and university need to share the burdenQualitative Literacy: writing across the curriculumQuantitative Literacy literacy, interpretation, & reasoningCollegiate leadership void impacts K-12, not articulated as entry requirement

Cooperative TaskPLC What is quantitative reasoning in STEM disciplines?Each person in the learning community is given a minute to identify and explain a characteristic of QROne clarifying question can be asked not a correction or challengeRepeat for each person in the PLCRecord four characteristics of QR on large note sheet and post on wallQuantitative ReasoningWhat is QR?Includes quantitative literacy, numeracy, and mathematical literacySkills needed for citizens of a democratic societyReasoning and conceptual understanding required in the STEM disciplines

Quantitative ReasoningDefining QRWhy Numbers Count: Quantitative Literacy for Tomorrows America (College Board, 1997)Mathematics and Democracy: The Case for Quantitative Literacy (National Council on Education and the Disciplines, 2001)

Quantitative ReasoningComponents of QRAlgebra for All: modest ability in reading and interpreting formulas, understanding graphs, and solving simple equationsCivic Literacy: understanding need for data, ability to sort through conflicting claims, skepticism about the reliability or significance of data, recognizing the limits of computer modelsComputer Mathematics: solving quantitative problems using standard computer packagesCultural Literacy: recognize the contributions of mathematicians to societyQuantitative ReasoningComponents of QRFunctional Mathematics: skills needed by ordinary people in life and workInstrumental Mathematics: ability to interpret and apply mathematics and to understand, predict, and control relevant factors in a variety of contextsLanguage of Science: support prospective scientists, engineers, life sciences, statisticsMathematical Modeling: process of hypothesis-building and testing as in science, mathematicizing the problem, analyzing the mathematics, collecting data to verify a prediction of the modelQuantitative ReasoningComponents of QRProblem Solving: the problem and possible solutions are paramount, skills are secondaryQuantitative Practice: apprenticeship environments in which mathematics is used and learned by use but perhaps never explicitly exhibited in words and symbolsQuantitative Reasoning: emphasizes broad synthesis of logical, visual, verbal, and computational thinking; manipulative algebra is incidental to this goalSCANS Skills: acquiring information, allocating resources, working with others, improving systems, and working with technologyNational Numeracy NetworkExtensive work in qualitative literacy done byDartmouth CollegeBabson CollegeDePaul UniversityHollins UniversityMacalester CollegeTrinity CollegeUniversity of Neveda at RenoWashington Center at Evergreen State College National Numeracy NetworkBabson 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 sourcesAble to formulate problems, identify opportunities, construct and test hypotheses, and apply to extend theoryAdept at establishing criteria, discovering and weighing alternatives, and using appropriate data to arrive at rational decisionsComfortable with the creative process, can tolerate ambiguity, and are conscious of the limits as well as the value of rational and logical thoughtNational Numeracy NetworkBabson College: eight competencies in numeracy:Able to communicate logically and persuasively in spoken, written, and visual form, including graphs and tablesIntellectually confident and independent and are able to make responsible and thoughtful ethical decisionsAdept 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 environmentFamiliar with new technology and its impact on business environment and social changeInterdisciplinary CallA 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 strategiesincreased emphasis on problem solving, communication, and real world applications QR ExamplesCritical ThinkingIs 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 worlds 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 ExamplesCritical Thinking visualizationAnalyze the Venn Diagram to determine what percentage of the population has AB+ bloodA- 8%A+ 34%B+ 8%ABOO+ 35%B- 2%AB- 1%O- 9%QR ExamplesProblem Solving Unit AnalysisMeasurements 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 Earths oceans is about 340 million square kilometers?QR ExamplesProblem Solving Strategies & HeuristicsIn 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 familys 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 ExamplesNumber Sense exponential growthAccording to the 2000 census, the population of Albany county is approximately 50,000. A power company predicts the countys 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 ExamplesNumber Sense percentagesThe 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 ExampleInterpreting Visual DataThe graph below shows the percentage change in the value of a companys 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 continuumChallenge 2: Need to understand how to assess student progress in development of quantitative reasoningCenter 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 continuumChallenge 4: Research articulation policies from high school to college that impact quantitative reasoning, such as the focus on preparation for calculusCenter 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 students quantitative reasoningChallenge 6: Research appropriate goals and benchmarks for quantitative reasoning at the high school, community college, and college levelChallenge 7: Can quantitative reasoning be successfully embedded across the disciplinesQR QuestionsWhat 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 LeadershipMath

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