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GAISE Robin Lock Jack and Sylvia Burry Professor of Statistics St. Lawrence University rlock@stlawu.edu Guidelines for Assessment and Instruction in Statistics Education COLLEGE REPORT

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GAISE College Group Joan Garfield Univ. of Minnesota (Chair) Martha AliagaASA George CobbMt. Holyoke College Carolyn CuffWestminster College Rob GouldUCLA Robin LockSt. Lawrence University Tom MooreGrinnell College Allan RossmanCal Poly San Luis Obispo Bob StephensonIowa State Jessica UttsUC Davis Paul VellemanCornell University Jeff WitmerOberlin College

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The Many Flavors of Introductory Statistics ConsumerProducer GeneralDiscipline-specific Large lectureSmall class YearBlockSemesterQuarter H.S. (AP) UniversityTwo year college Four year college

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Challenge in Writing Guidelines Give sufficient structure to provide real guidance to instructors. Allow sufficient generality to include good practices in the many flavors.

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Starting point: Cobb Report (1992) Report from discussions of the Focus Group on Statistics Education in Heeding the Call for Change Three Recommendations: Emphasize statistical thinking More data and concepts, less theory and fewer recipes Foster active learning

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Statistically Educated Students Should believe and understand why… Data beat anecdotes. Variability is natural and is also predictable and quantifiable. Random sampling allows results to be extended to the population. Random assignment in experiments allows cause and effect conclusions.

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Statistically Educated Students Should believe and understand why… Association is not causation. Statistical significance does not necessarily imply practical significance. Finding no statistical significance in a small sample does not necessarily mean there is no difference/relationship in the population.

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Statistically Educated Students Should recognize… Common sources of bias in surveys and experiments. How to determine the population (if any) to which inference results may be extended. How to determine when a cause and effect inference can be drawn. That words such as “normal”, “random” and “correlation” have specific statistical meanings.

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Statistically Educated Students Should understand the process through which statistics works to answer questions. How to… Obtain or generate data. Graph data as an initial step in analysis. Interpret numerical summaries and graphical displays (answer questions / check conditions). Make appropriate use of statistical inference. Communicate results of a statistical analysis.

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Statistically Educated Students Should understand the basic ideas of statistical inference, including the concepts of Sampling distribution and how it applies to making inferences from samples. Statistical significance, including significance level and p-values. Confidence interval, including the confidence level and margin of error.

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Statistically Educated Students Should know How to interpret statistical results in context. How to read and critique news stories and journal articles that include statistical information. When to call for help from an experienced statistician.

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Guideline #1 Emphasize statistical literacy and develop statistical thinking.

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Statistical literacy: understanding the basic language and fundamental ideas of statistics. Statistical thinking: the processes that statisticians use when approaching or solving practical problems. Statistical Literacy and Thinking

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Suggestions for Teachers Model statistical thinking for students. Have students practice statistical thinking (e.g. open-ended problems and projects). Let students practice with choosing appropriate questions and techniques.

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Guideline #2 Use real data.

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Levels of Reality Real: Data that were actually collected or generated to answer some question(s). Realistic: Hypothetical data with a context that illustrate a specific point. Naked: Numbers with no context (and thus no interest).

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Suggestions for Teachers Search for raw data from textbooks, software packages, web data repositories. Use summary data from textbooks, articles, and websites with poll/survey results. Get data from class activities and simulations. Make larger data sets available electronically. Practice data entry on small data sets. Return to a rich data set at various points in the course. Use data with students to answer interesting questions and generate new questions.

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Guideline #3 Stress conceptual understanding rather than mere knowledge of procedures.

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Concepts vs. Procedures Many (most?) introductory courses contain too much material. If students don’t understand concepts, there’s little value in knowing procedures. If students do understand concepts, specific new procedures are easy to learn.

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Suggestions for Teachers Primary goal is not to cover methods, but to discover concepts. Focus on understanding of key concepts, illustrated by a few techniques, rather than a multitude of techniques with minimal focus on underlying ideas. Pare down content to focus on core ideas in more depth. Use technology for routine computations, use formulas that enhance understanding.

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Guideline #4 Foster active learning in the classroom.

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Types of Active Learning Group or individual: problem solving, exploratory activities and discussion Lab activities: physical and computer-based Demonstrations: based on “live” results from students or software

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Suggestions for Teachers Ground activities in the context of real problems. Intermix lectures with activities and discussions. Precede computer simulations with physical explorations. Collect data from students. Encourage predictions from students anticipating statistical results. Plan sufficient time to do and wrap up the activity. Provide lots of feedback and assessment.

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Guideline #5 Use technology for developing concepts and analyzing data.

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Types of Technology Graphing calculators Traditional statistical packages Conceptual statistical software Educational support Applets Spreadsheets

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Suggestions for Teachers Access large real data sets. Automate calculations. Generate and modify appropriate statistical graphics. Perform simulations to illustrate abstract concepts. Explore “what happens if...” scenarios. Create reports Consider –Ease of data entry, ability to import data –Interactive capabilities –Dynamic linking between data, graphs, numerics –Ease of use and availability

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Guideline #6 Use assessments to improve and evaluate student learning.

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Types of Assessment Homework Quizzes and exams Projects Activities Presentations Lab reports Minute papers Article critiques Class discussion/participation

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Suggestions for Teachers Integrate assessment as an essential (and current) component of the course. Use a variety of assessment methods. Assess statistical literacy (e.g. by interpreting or critiquing articles and graphs in the media). Assess statistical thinking (e.g. by doing student projects or open-ended investigative tasks). For large classes –Use group projects instead of individual –Use peer review of projects –Use multiple choice items that focus on choosing interpretations or appropriate statistical approaches.

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Six Recommendations 1.Emphasize statistical literacy and develop statistical thinking 2.Use real data 3.Stress conceptual understanding rather than mere knowledge of procedures 4.Foster active learning 5.Use technology to develop conceptual understanding and analyze data 6.Use assessments to improve and evaluate learning

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Making It Happen Evolution through small steps: Find/develop a case study of statistical interest Find a new real data set Delete a topic from the list you currently cover Have students do a small project or new activity Integrate a neat applet into a lecture Try some new types of quiz/exam questions

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