What is QR and why is it important? February 6, 2010 ITQ Dissemination Workshop

Why is QR important? In today’s “world awash in numbers,” strong quantitative reasoning skills are required: in virtually all academic fieldsin virtually all academic fields in most every professionin most every profession and in decision-making in everyday lifeand in decision-making in everyday life -in being an informed citizen -in making medical decisions -in making financial decisions (Lynn Steen’s main argument in “The Case for Quantitative Literacy” in Mathematics and Democracy. ) in Mathematics and Democracy. )

QR is defined as…. the ability to understand and use quantitative measures and inferences that allow one to function as a responsible citizen, productive worker, and discerning consumer. (Bernie Madison) (Bernie Madison) the ability to identify, understand and use quantitative arguments in everyday contexts. Quantitative literacy describes a habit of mind rather than a set of topics of a list of skills. (Deborah Hughes Hallett)

How does “QR” differ from “Math”? (Bernie Madison’s “two mathematics”) Math Math track moves vertically to higher levels of abstraction….beauty and eleganceMath track moves vertically to higher levels of abstraction….beauty and elegance Focus on content and components: algebra, geometry, statistics, calculusFocus on content and components: algebra, geometry, statistics, calculusQR QR reaches out horizontally, applying processes of reasoning, deduction, and analysis to a wide array of applications in many practical fieldsQR reaches out horizontally, applying processes of reasoning, deduction, and analysis to a wide array of applications in many practical fields Focus on the hands-on use of logic, statistics, and math to solve problems in context-rich settingsFocus on the hands-on use of logic, statistics, and math to solve problems in context-rich settings

Mathematics vs. QR Mathematics Power in abstraction Power in abstraction Power in generality Power in generality Some context dependency Some context dependency Society independent Society independent Apolitical Apolitical Methods & algorithms Methods & algorithms Well-defined problems Well-defined problems Approximation Approximation Heavily disciplinary Heavily disciplinary Problem solutions Problem solutions Few opportunities to practice Few opportunities to practice Predictable PredictableQR Real, authentic contexts Real, authentic contexts Specific, particular applications Specific, particular applications Heavy context dependency Heavy context dependency Society dependent Society dependent Political Political Ad hoc methods Ad hoc methods Ill-defined problems Ill-defined problems Estimation is critical Estimation is critical Interdisciplinary Interdisciplinary Problem descriptions Problem descriptions Many practice opportunities Many practice opportunities Unpredictable Unpredictable

QR Competencies (MAA’s Standards for College Students) Reading and understanding quantitative info in graphs, tables, etc.Reading and understanding quantitative info in graphs, tables, etc. Interpreting quantitative info and drawing appropriate inferencesInterpreting quantitative info and drawing appropriate inferences Solving problems using logic, math, statisticsSolving problems using logic, math, statistics Estimating answers and checking for reasonablenessEstimating answers and checking for reasonableness Communicating quantitative info – verbally, graphically, numericallyCommunicating quantitative info – verbally, graphically, numerically Recognizing the limitations of mathematical or statistical modelsRecognizing the limitations of mathematical or statistical models

QR in Academic Fields at College (beyond physics, chemistry, and economics) Visual Arts Geometry, scaling and computer algorithms (for use of computer graphics) Language Arts quantitative and logical methods (for linguistics, ascertaining authorship, computer translation) Medicine statistics (assessing clinical trials), chance (comparing risks), and calculus (understanding the body's electrical, biochemical, and cardiovascular systems)

QR’s Importance to Professionals Lawyers probability (to establish or refute "reasonable doubt") Journalists understanding of risks, rates, samples, surveys, and statistical evidence (to develop an informed and skeptical understanding of current events) Social Workers logic, arithmetic (to explain to clients complex state and federal regulations about income and expenses and verify their clients' personal budgets)

QR Skills to be an Informed Citizen Understand quantitative voter info as relates to school budgets or tax proposals Understand how small samples can accurately predict public opinion; how biases can influence results Understand student test results in percentages or percentiles and their meaning about school quality Understand behavior of weighted averages used in ranking colleges, cities, products, etc.

QR Skills for Personal Health Calibrate eating and exercise habits in relation to health Interpret medical statistics and formulate questions about different treatments and their risks Understand medical dosages in relation to body weight, timing of meds, drug interactions Weigh costs, benefits, and health risks of advertised drugs

QR in Personal Finance Understand effects of compound interest for deposits and loans Understand the relation of risk to return for investments Be able to calculate income taxes Understand interactions among factors affecting personal loans incl. mortgages

Wellesley College’s Two-Part QR Requirement 1.The “Basic Skills” Requirement is satisfied either by: Passing the QR Assessment during Orientation, or Passing the QR Assessment during Orientation, or Passing “Intro to QR” – course that builds logic, math, and statistics skills in real world contexts Passing “Intro to QR” – course that builds logic, math, and statistics skills in real world contexts 2.The “QR Overlay” Requirement is satisfied by taking an approved course that deals extensively w/ the analysis and interpretation of data, e.g., Statistics classes Statistics classes Science labs with data collection & analysis Science labs with data collection & analysis

The QR Assessment Study packet sent in summer Administered during Orientation Test is 90 minutes; 18 questions; 9.5 to pass Most questions are NOT multiple-guess No calculators allowed

Sample Assessment Question Summer sublets tend to be expensive in the Cambridge area. This table from a local housing office advertises the monthly rental costs for two-bedroom apartments. For example, the table indicates that there are six apartments available for $1200/month. Use the table to answer the following questions.

Assessment Question Continued 1. What percentage of the apartments sublet for more than $1,200 per month? 2. What is the mean (average) monthly rent for a two- bedroom apartment?

Intro to QR Course Lectures and computer labs (using Excel) Emphasis on practical uses of logic, math, stats often QR skills taught “just-in-time” Topics include: *Education data *US demographics *Astronomically large to microscopically small – a physical sense of space physical sense of space *Personal finance Using & Understanding Mathematics: A Quantitative Reasoning Approach, by Bennett & Briggs

QR Overlay Courses Types of courses: Statistics classes with computer labs Statistics classes with computer labs Science classes with hands-on laboratories involving statistical analysis Science classes with hands-on laboratories involving statistical analysis Others: PHIL 209: Scientific Reasoning Others: PHIL 209: Scientific Reasoning Topics covered: Framework for data analysis Framework for data analysis Methods of data collection & measurement Methods of data collection & measurement Representing & summarizing data Representing & summarizing data Confidence intervals; hypothesis testing Confidence intervals; hypothesis testing ANOVA; multiple regression ANOVA; multiple regression

Tips on Incorporating QR in the Curriculum Create problems in authentic contexts of interest to students Have students figure out what skills are needed to solve the problems and teach new math skills “just in time” Give multiple opportunities to work with important concepts – each in an authentic area, e.g., linear versus exponential growth in demographics and later in personal finance Require students to write about their quantitative analyses Discuss common mistakes in the media or in your fields of interest, e.g., percent change versus percentage point difference