ASA Strategic InitiativeASA Strategic InitiativeGAISEGAISE

Special thanks to Robin Lock

Jack and Sylvia Burry Professor of StatisticsSt. Lawrence University

Slides with yellow text are courtesy of Robin Lock

Guidelines for Assessment and Instruction in Statistics Education

College Report

Outline of This TalkOutline of This Talk• Overview of GAISE projectOverview of GAISE project

– Funded by American Statistical AssociationFunded by American Statistical Association– College ProjectCollege Project– K-12 Project (will not discuss this one)K-12 Project (will not discuss this one)

• GAISE recommendations on GAISE recommendations on howhow to teach to teach the introductory coursethe introductory course

• Recommendations on Recommendations on what what should be should be includedincluded

GAISE College GroupGAISE College Group

Joan Garfield Univ. of Minnesota (Chair)Martha Aliaga ASA George Cobb Mt. Holyoke CollegeCarolyn Cuff Westminster CollegeRob Gould UCLARobin Lock St. Lawrence UniversityTom Moore Grinnell CollegeAllan Rossman Cal Poly San Luis ObispoBob Stephenson Iowa StateJessica Utts UC DavisPaul Velleman Cornell UniversityJeff Witmer Oberlin College

The GoalThe Goal

Produce a set of recommendations and guidelines for instruction and

assessment in introductory statistics courses at the undergraduate level.

The Many Flavors of The Many Flavors of Introductory StatisticsIntroductory Statistics

Consumer Producer

GeneralDiscipline-specific

Large lecture Small class

Year BlockSemester Quarter

H.S. (AP)

UniversityTwo year college

Four year

college

Challenge in Writing Challenge in Writing GuidelinesGuidelines

Give sufficient structure to provide

real guidance to instructors.

Allow sufficient generality to include good practices in the

many flavors.

Four Part ReportFour Part Report• Introduction and HistoryIntroduction and History• Goals for Students in an Introductory Goals for Students in an Introductory

Course: Course: What it Means to be What it Means to be Statistically EducatedStatistically Educated

• Six Six RecommendationsRecommendations for helping for helping teachers achieve those goalsteachers achieve those goals

• Appendix of Appendix of Examples and SuggestionsExamples and Suggestions

ASA EndorsementASA Endorsement

The ASA Board of Directors appreciates The ASA Board of Directors appreciates and supports the efforts of and supports the efforts of the undergraduate statistics writing the undergraduate statistics writing group and endorses the six GAISE group and endorses the six GAISE recommendations for introductory recommendations for introductory college statistics courses as an aid to college statistics courses as an aid to enhancing statistics education at the enhancing statistics education at the undergraduate level. undergraduate level.

By Unanimous vote on May 17, 2005

Outline of This TalkOutline of This Talk• Overview of GAISE projectOverview of GAISE project

– Funded by American Statistical AssociationFunded by American Statistical Association– College ProjectCollege Project– K-12 Project (will not discuss this one)K-12 Project (will not discuss this one)

• GAISE recommendations on GAISE recommendations on howhow to teach the to teach the introductory courseintroductory course

• Recommendations on Recommendations on what what should be should be includedincluded

Six RecommendationsSix Recommendations1. Emphasize statistical literacy and develop

statistical thinking2. Use real data3. Stress conceptual understanding rather than

mere knowledge of procedures4. Foster active learning in the classroom5. Use technology for developing conceptual

understanding and analyzing data6. Integrate assessments that are aligned with

course goals to improve as well as evaluate student learning.

Recommendation #1Recommendation #1Emphasize statistical literacy and develop statistical thinking.

•Statistical literacy: understanding the language and ideas of statistics

•Statistical thinking: the thought process statisticians use to answer a scientific question with data

Suggestions for TeachersSuggestions for Teachers• Model statistical thinking for students, working Model statistical thinking for students, working

examples and explaining the questions and examples and explaining the questions and processes involved in solving statistical problems processes involved in solving statistical problems from conception to conclusion.from conception to conclusion.

• Show students how to use technology effectively to Show students how to use technology effectively to manage data, explore data, perform inference, and manage data, explore data, perform inference, and check conditions that underlie inference procedures.check conditions that underlie inference procedures.

• Give students practice developing and using Give students practice developing and using statistical thinking. This should include open-ended statistical thinking. This should include open-ended problems and projects.problems and projects.

• Give students plenty of practice with choosing Give students plenty of practice with choosing appropriate questions and techniques, rather than appropriate questions and techniques, rather than telling them which technique to use and merely telling them which technique to use and merely having them implement it.having them implement it.

• Assess and give feedback on students’ statistical Assess and give feedback on students’ statistical thinking.thinking.

Recommendation #2Recommendation #2Use Real Data.Sources for real data include:•Textbooks•Websites such as

•“Dazzle” – data and storage library:lib.stat.cmu.edu/DASL/ •Journal of Statistics Education data archive:www.amstat.org/publications/jse/jse_data_archive.html•www.pollingreport.com (recent polls on numerous topics)

Suggestions for TeachersSuggestions for Teachers• Search for and use Search for and use summariessummaries based based

on real data on real data • Use data to Use data to answer questionsanswer questions relevant relevant

to the context, and to generate new to the context, and to generate new questions.questions.

• Make sure questions used with data Make sure questions used with data sets are sets are of interest to studentsof interest to students – if no – if no one cares about the questions, it’s not one cares about the questions, it’s not a good data set for the introductory a good data set for the introductory class.class.

More Suggestions for More Suggestions for TeachersTeachers

• Use class-generated data to formulate statistical Use class-generated data to formulate statistical questions and plan uses for the data before questions and plan uses for the data before developing the questionnaire and collecting the data. developing the questionnaire and collecting the data. (Example: ask questions likely to produce different (Example: ask questions likely to produce different shaped histograms, use interesting categorical shaped histograms, use interesting categorical variables to investigate relationships.) It is important variables to investigate relationships.) It is important that students’ privacy is maintained.that students’ privacy is maintained.

• Get students to practice entering raw data using a Get students to practice entering raw data using a small data set or a subset of data, rather than small data set or a subset of data, rather than spending time entering a large data set. Make larger spending time entering a large data set. Make larger data sets available electronically.data sets available electronically.

• Use subsets of variables in different parts of the Use subsets of variables in different parts of the course, but integrate the same data sets throughout. course, but integrate the same data sets throughout. (Example: do side-by-side boxplots to compare two (Example: do side-by-side boxplots to compare two groups, then later do two-sample groups, then later do two-sample tt-tests on the same -tests on the same data. Use histograms to investigate shape, then later data. Use histograms to investigate shape, then later to verify conditions for hypothesis tests.)to verify conditions for hypothesis tests.)

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

•Most introductory courses contain too much material.

•If students don’t understand the important concepts, there’s little value in knowing a set of procedures.

•If they do understand the concepts well, then particular procedures will be easy to learn

Suggestions for TeachersSuggestions for Teachers• View the primary goal as not to cover View the primary goal as not to cover

methods, but to discover concepts.methods, but to discover concepts. Focus on students’ understanding of key Focus on students’ understanding of key

concepts, illustrated by a few techniques, concepts, illustrated by a few techniques, rather than covering a multitude of rather than covering a multitude of techniques with minimal focus on underlying techniques with minimal focus on underlying ideas.ideas.

• Pare down content to focus on core ideas in Pare down content to focus on core ideas in more depth. more depth.

• Use technology for routine computations, use Use technology for routine computations, use formulas that enhance understanding.formulas that enhance understanding.

An Example of Using Formulas An Example of Using Formulas for Conceptual Understanding for Conceptual Understanding rather than for Computation:rather than for Computation:

1)( 2

n

yys 1)( 212

n

yys n

Recommendation #4Recommendation #4Foster active learning in the classroom.

Types of active learning include:• Group or individual problem solving,

activities and discussion.• Lab activities (physical and computer-based).• Demonstrations based on data generated on

the spot from the students.

Suggestions for TeachersSuggestions for Teachers• Ground activities in the context of real problems.Ground activities in the context of real problems.• Intermix lectures with activities, discussions, labs. Intermix lectures with activities, discussions, labs. • Precede computer simulations with physical Precede computer simulations with physical

explorations.explorations.• Collect data from students.Collect data from students.• Encourage predictions from students about the results Encourage predictions from students about the results

of a study before analyzing data.of a study before analyzing data.• Do not use activities that lead students step by step Do not use activities that lead students step by step

through a list of procedures, but allow students to through a list of procedures, but allow students to discuss and think about the data and the problem. discuss and think about the data and the problem.

• Plan sufficient time to introduce, conduct and wrap up Plan sufficient time to introduce, conduct and wrap up the activity all in the same class.the activity all in the same class.

• Provide lots of feedback and assessment.Provide lots of feedback and assessment.

Recommendation #5Recommendation #5Use technology for developing

conceptual understanding and analyzing data.

Graphing calculators Statistical packages Educational software Applets Spreadsheets Web-based resources including data sources, on-

line texts, and data analysis routine Classroom response systems.

Suggestions for teachers on Suggestions for teachers on ways to use technology:ways to use technology:

•Access large real data sets•Automate calculations•Generate and modify appropriate

statistical graphics•Perform simulations to illustrate abstract

concepts•Explore “what happens if…”- type

questions•Create reports

Things for teachers to Things for teachers to consider when selecting consider when selecting

technology tools:technology tools:

•Ease of data entry, ability to import data in multiple formats

•Interactive capabilities•Dynamic linking between data, graphical,

and numerical analyses •Ease of use for particular audiences •Availability to students •Portability

Recommendation #6Recommendation #6Integrate assessments that are aligned

with course goals to improve as well as evaluate student learning.

• Students will value what you assess.• Assessments need to focus on understanding key

ideas and not just on skills, procedures, and computations.

• Useful and timely feedback is essential for assessments to lead to learning.

• Various types of assessment may be more or less practical in different types of courses. However, it is possible, even in large classes, to implement good assessments.

Types of AssessmentTypes of Assessment•Homework•Quizzes and exams•Projects•Activities•Oral Presentations•Written reports•Minute papers •Article critiques

Suggestions for TeachersSuggestions for Teachers• Integrate assessment as an essential (and current) Integrate assessment as an essential (and current)

component of the course.component of the course.• Use a variety of assessment methods. Use a variety of assessment methods. • Assess statistical literacy using assessments such Assess statistical literacy using assessments such

as interpreting or critiquing articles in the news as interpreting or critiquing articles in the news and graphs in media. and graphs in media.

• Assess statistical thinking using assessments such Assess statistical thinking using assessments such as student projects and open-ended investigative as student projects and open-ended investigative tasks.tasks.

• For large classesFor large classes – Use group projects instead of individual projectsUse group projects instead of individual projects– Use peer reviewUse peer review– Use multiple choice questions that focus on choosing Use multiple choice questions that focus on choosing

interpretations (e.g. of graphs and studies) or selecting interpretations (e.g. of graphs and studies) or selecting appropriate statistical procedures. appropriate statistical procedures.

Recommendations for Recommendations for Making It HappenMaking It Happen

Start with small steps, for example:•Add an activity to your course•Have your students do a small project•Integrate an applet into a lecture•Demonstrate the use of software to your students•Increase the use of real data sets•Add a case study (newspaper story <-> journal article)•Choose one topic to delete from the list you currently try to cover and using the time saved to focus more on understanding concepts.

Outline of This TalkOutline of This Talk• Overview of GAISE projectOverview of GAISE project

– Funded by American Statistical AssociationFunded by American Statistical Association– College ProjectCollege Project– K-12 Project (will not discuss this one)K-12 Project (will not discuss this one)

• GAISE recommendations on GAISE recommendations on howhow to teach the to teach the introductory courseintroductory course

• Recommendations on Recommendations on what what should be should be includedincluded

Recommendations on What Recommendations on What Should be TaughtShould be Taught

GAISE Section titled GAISE Section titled Goals for Students Goals for Students in an Introductory Course: What it in an Introductory Course: What it Means to be Statistically Educated Means to be Statistically Educated

Students should believe Students should believe and understand why:and understand why:• Data beat anecdotes.Data beat anecdotes.• Variability is natural and is also predictable and quantifiable.Variability is natural and is also predictable and quantifiable.• Random Random samplingsampling allows results of surveys and experiments allows results of surveys and experiments

to be extended to the population from which the sample to be extended to the population from which the sample was taken.was taken.

• Random Random assignmentassignment in comparative experiments allows in comparative experiments allows cause and effect conclusions to be drawn. cause and effect conclusions to be drawn.

• Association is not causation.Association is not causation.• Statistical significance does not necessarily imply practical Statistical significance does not necessarily imply practical

importance, especially for studies with large sample sizes.importance, especially for studies with large sample sizes.• Finding no statistically significant difference or relationship Finding no statistically significant difference or relationship

does not necessarily mean there is no difference or no does not necessarily mean there is no difference or no relationship in the population, especially for studies with relationship in the population, especially for studies with small sample sizes.small sample sizes.

Students should Students should recognize:recognize:• Common sources of bias in surveys and Common sources of bias in surveys and

experiments.experiments.• How to determine the population to which the How to determine the population to which the

results of statistical inference can be extended, if results of statistical inference can be extended, if any, based on how the data were collected.any, based on how the data were collected.

• How to determine when a cause and effect How to determine when a cause and effect inference can be drawn from an association, based inference can be drawn from an association, based on how the data were collected (e.g., the design of on how the data were collected (e.g., the design of the study)the study)

• That words such as “normal”, “random” and That words such as “normal”, “random” and “correlation” have specific meanings in statistics “correlation” have specific meanings in statistics that may differ from common usage. that may differ from common usage.

Students should understand Students should understand the parts of the process the parts of the process through which statistics works through which statistics works to answer questions, namely:to answer questions, namely:• How to obtain or generate data.How to obtain or generate data.• How to graph the data as a first step in analyzing How to graph the data as a first step in analyzing

data, and how to know when that’s enough to data, and how to know when that’s enough to answer the question of interest.answer the question of interest.

• How to interpret numerical summaries and graphical How to interpret numerical summaries and graphical displays of data - both to answer questions and to displays of data - both to answer questions and to check conditions (in order to use statistical check conditions (in order to use statistical procedures correctly).procedures correctly).

• How to make appropriate use of statistical inference.How to make appropriate use of statistical inference.• How to communicate the results of a statistical How to communicate the results of a statistical

analysis. analysis.

Students should understand Students should understand the basic ideas of statistical the basic ideas of statistical inference:inference:• The concept of a sampling distribution and The concept of a sampling distribution and

how it applies to making statistical how it applies to making statistical inferences based on samples of data inferences based on samples of data (including the idea of standard error)(including the idea of standard error)

• The concept of statistical significance The concept of statistical significance including significance levels and including significance levels and pp-values.-values.

• The concept of confidence interval, The concept of confidence interval, including the interpretation of confidence including the interpretation of confidence level and margin of error.level and margin of error.

Finally, students should Finally, students should know:know:• How to interpret statistical results in How to interpret statistical results in

context.context.• How to critique news stories and journal How to critique news stories and journal

articles that include statistical information, articles that include statistical information, including identifying what's missing in the including identifying what's missing in the presentation and the flaws in the studies presentation and the flaws in the studies or methods used to generate the or methods used to generate the information.information.

• When to call for help from a statistician.When to call for help from a statistician.

Some ResourcesSome ResourcesGAISE Reports:GAISE Reports:http://www.amstat.org/education/gaisehttp://www.amstat.org/education/gaise

American Statistician paper on concepts:American Statistician paper on concepts:http://anson.ucdavis.edu/~utts/AmerStat2003.pdfhttp://anson.ucdavis.edu/~utts/AmerStat2003.pdf

Good Resources for Statistics Teachers:Good Resources for Statistics Teachers:http://anson.ucdavis.edu/~utts/statlinks.htmlhttp://anson.ucdavis.edu/~utts/statlinks.html